diff options
Diffstat (limited to 'src')
-rw-r--r-- | src/share/algebra/browse.daase | 1280 | ||||
-rw-r--r-- | src/share/algebra/category.daase | 1400 | ||||
-rw-r--r-- | src/share/algebra/compress.daase | 1325 | ||||
-rw-r--r-- | src/share/algebra/interp.daase | 9040 | ||||
-rw-r--r-- | src/share/algebra/operation.daase | 27138 |
5 files changed, 20093 insertions, 20090 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 5b5d10f2..8c11e2ea 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2267553 . 3477887507) +(2267652 . 3479296388) (-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."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . 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}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4440 . T) (-4438 . T) (-4437 . T) ((-4445 "*") . T) (-4436 . T) (-4441 . T) (-4435 . T)) +((-4441 . T) (-4439 . T) (-4438 . T) ((-4446 "*") . T) (-4437 . T) (-4442 . T) (-4436 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -1649) +(-32 R -1666) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (-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 -4443))) +((|HasAttribute| |#1| (QUOTE -4444))) (-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}."))) -((-4443 . T) (-4444 . T)) +((-4444 . T) (-4445 . 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"))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . 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 -1649 UP UPUP -1864) +(-40 -1666 UP UPUP -3283) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4436 |has| (-412 |#2|) (-367)) (-4441 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-353))) (-2718 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-2718 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (-2718 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-353))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-569)))) (-2718 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) -(-41 R -1649) +((-4437 |has| (-412 |#2|) (-367)) (-4442 |has| (-412 |#2|) (-367)) (-4436 |has| (-412 |#2|) (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-353))) (-2774 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-2774 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (-2774 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-353))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-569)))) (-2774 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) +(-41 R -1666) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -435) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-310)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4440 |has| |#1| (-561)) (-4438 . T) (-4437 . T)) +((-4441 |has| |#1| (-561)) (-4439 . T) (-4438 . T)) ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-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."))) -((-4443 . T) (-4444 . T)) -((-2718 (-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|))))))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|))))))) +((-4444 . T) (-4445 . T)) +((-2774 (-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|))))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-569))))) (-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}."))) -((-4440 . T)) +((-4441 . 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 -1649) +(-54 |Base| R -1666) ((|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"))) -((-4443 . T) (-4444 . T)) +((-4444 . T) (-4445 . 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}"))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|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}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-61 -3458) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-61 -3570) ((|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 -3458) +(-62 -3570) ((|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 -3458) +(-63 -3570) ((|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 -3458) +(-64 -3570) ((|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 -3458) +(-65 -3570) ((|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 -3458) +(-66 -3570) ((|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 -3458) +(-67 -3570) ((|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 -3458) +(-68 -3570) ((|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 -3458) +(-69 -3570) ((|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 -3458) +(-70 -3570) ((|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 -3458) +(-71 -3570) ((|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 -3458) +(-72 -3570) ((|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 -3458) +(-73 -3570) ((|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 -3458) +(-74 -3570) ((|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 -3458) +(-77 -3570) ((|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 -3458) +(-78 -3570) ((|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 -3458) +(-79 -3570) ((|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 -3458) +(-80 -3570) ((|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 -3458) +(-81 -3570) ((|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 -3458) +(-82 -3570) ((|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 -3458) +(-83 -3570) ((|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 -3458) +(-84 -3570) ((|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 -3458) +(-85 -3570) ((|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 -3458) +(-86 -3570) ((|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 -3458) +(-87 -3570) ((|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 -3458) +(-88 -3570) ((|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 -3458) +(-89 -3570) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-367)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-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\"."))) -((-4443 . T)) +((-4444 . 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."))) -((-4443 . T) ((-4445 "*") . T) (-4444 . T) (-4440 . T) (-4438 . T) (-4437 . T) (-4436 . T) (-4441 . T) (-4435 . T) (-4434 . T) (-4433 . T) (-4432 . T) (-4431 . T) (-4439 . T) (-4442 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4430 . T)) +((-4444 . T) ((-4446 "*") . T) (-4445 . T) (-4441 . T) (-4439 . T) (-4438 . T) (-4437 . T) (-4442 . T) (-4436 . T) (-4435 . T) (-4434 . T) (-4433 . T) (-4432 . T) (-4440 . T) (-4443 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4431 . 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}."))) -((-4440 . T)) +((-4441 . 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}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-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 (-4445 "*")))) +((|HasAttribute| |#1| (QUOTE (-4446 "*")))) (-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"))) -((-4443 . T)) +((-4444 . 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."))) -((-4444 . T)) +((-4445 . 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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2718 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2774 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1106))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1106))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-867))))) (-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}"))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -388,22 +388,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-115 -1649 UP) +(-115 -1666 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL (-116 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-915))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-116 |#1|) (QUOTE (-1028))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-2718 (|HasCategory| (-116 |#1|) (QUOTE (-825))) (|HasCategory| (-116 |#1|) (QUOTE (-855)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (QUOTE (-1158))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (QUOTE (-234))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-310))) (|HasCategory| (-116 |#1|) (QUOTE (-550))) (|HasCategory| (-116 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-915)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-915))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-116 |#1|) (QUOTE (-1028))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-2774 (|HasCategory| (-116 |#1|) (QUOTE (-825))) (|HasCategory| (-116 |#1|) (QUOTE (-855)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (QUOTE (-1158))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (QUOTE (-234))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-310))) (|HasCategory| (-116 |#1|) (QUOTE (-550))) (|HasCategory| (-116 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-915)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4444))) +((|HasAttribute| |#1| (QUOTE -4445))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -414,15 +414,15 @@ NIL NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,20 +430,20 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4443 . T) (-4444 . T)) +((-4444 . T) (-4445 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|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."))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129)))))) (-2718 (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-129) (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-129) (QUOTE (-1106)))) (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129)))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129)))))) (-2774 (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-129) (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-129) (QUOTE (-1106)))) (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129)))))) (-129) ((|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 @@ -466,13 +466,13 @@ NIL NIL (-134) ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4445 "*") . T)) +(((-4446 "*") . T)) NIL -(-135 |minix| -2358 S T$) +(-135 |minix| -2406 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2358 R) +(-136 |minix| -2406 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -494,8 +494,8 @@ NIL NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4443 . T) (-4433 . T) (-4444 . T)) -((-2718 (-12 (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4444 . T) (-4434 . T) (-4445 . T)) +((-2774 (-12 (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -510,7 +510,7 @@ NIL NIL (-145) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4440 . T)) +((-4441 . T)) NIL (-146 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -518,9 +518,9 @@ NIL NIL (-147) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4440 . T)) +((-4441 . T)) NIL -(-148 -1649 UP UPUP) +(-148 -1666 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -531,14 +531,14 @@ NIL (-150 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasAttribute| |#1| (QUOTE -4443))) +((|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasAttribute| |#1| (QUOTE -4444))) (-151 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-152 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4438 . T) (-4437 . T) (-4440 . T)) +((-4439 . T) (-4438 . T) (-4441 . T)) NIL (-153) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -560,7 +560,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-158 R -1649) +(-158 R -1666) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -591,10 +591,10 @@ NIL (-165 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4439)) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-561)))) +((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4440)) (|HasAttribute| |#2| (QUOTE -4443)) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-561)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4436 -2718 (|has| |#1| (-561)) (-12 (|has| |#1| (-310)) (|has| |#1| (-915)))) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4439 |has| |#1| (-6 -4439)) (-4442 |has| |#1| (-6 -4442)) (-3016 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 -2774 (|has| |#1| (-561)) (-12 (|has| |#1| (-310)) (|has| |#1| (-915)))) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4440 |has| |#1| (-6 -4440)) (-4443 |has| |#1| (-6 -4443)) (-3098 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -610,8 +610,8 @@ NIL NIL (-170 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}."))) -((-4436 -2718 (|has| |#1| (-561)) (-12 (|has| |#1| (-310)) (|has| |#1| (-915)))) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4439 |has| |#1| (-6 -4439)) (-4442 |has| |#1| (-6 -4442)) (-3016 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . 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T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-353))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-234))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-915)))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-915))))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-915))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-367)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-234))) (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasAttribute| |#1| (QUOTE -4440)) (|HasAttribute| |#1| (QUOTE -4443)) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-353))))) (-171 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 @@ -622,7 +622,7 @@ NIL NIL (-173) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-174) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -630,7 +630,7 @@ NIL NIL (-175 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4445 "*") . T) (-4436 . T) (-4441 . T) (-4435 . T) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") . T) (-4437 . T) (-4442 . T) (-4436 . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-176) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -684,7 +684,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-189 R -1649) +(-189 R -1666) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -792,23 +792,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-216 -1649 UP UPUP R) +(-216 -1666 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-217 -1649 FP) +(-217 -1666 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-218) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2718 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2774 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) (-219) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-220 R -1649) +(-220 R -1666) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -822,19 +822,19 @@ NIL NIL (-223 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-224 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4440 . T)) +((-4441 . T)) NIL -(-225 R -1649) +(-225 R -1666) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-226) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3006 . T) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3088 . T) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-227) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -842,15 +842,15 @@ NIL NIL (-228 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4445 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4446 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-229 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-230 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4444 . T)) +((-4445 . T)) NIL (-231 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -858,7 +858,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (-232 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4440 . T)) +((-4441 . T)) NIL (-233 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -866,36 +866,36 @@ NIL NIL (-234) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4440 . T)) +((-4441 . T)) NIL (-235 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4443))) +((|HasAttribute| |#1| (QUOTE -4444))) (-236 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4444 . T)) +((-4445 . T)) NIL (-237) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-238 S -2358 R) +(-238 S -2406 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (QUOTE (-853))) (|HasAttribute| |#3| (QUOTE -4440)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (QUOTE (-1106)))) -(-239 -2358 R) +((|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (QUOTE (-853))) (|HasAttribute| |#3| (QUOTE -4441)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (QUOTE (-1106)))) +(-239 -2406 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4437 |has| |#2| (-1055)) (-4438 |has| |#2| (-1055)) (-4440 |has| |#2| (-6 -4440)) ((-4445 "*") |has| |#2| (-173)) (-4443 . T)) +((-4438 |has| |#2| (-1055)) (-4439 |has| |#2| (-1055)) (-4441 |has| |#2| (-6 -4441)) ((-4446 "*") |has| |#2| (-173)) (-4444 . T)) NIL -(-240 -2358 A B) +(-240 -2406 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 -(-241 -2358 R) +(-241 -2406 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. 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(LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-853))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))))) (|HasCategory| (-569) (QUOTE (-855))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-2774 (|HasCategory| |#2| (QUOTE (-1055))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-1106)))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))))) (-242) ((|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 @@ -906,7 +906,7 @@ NIL NIL (-244) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4436 . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-245 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -914,16 +914,16 @@ NIL NIL (-246 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-247 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-248 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4445 "*") |has| |#2| (-173)) (-4436 |has| |#2| (-561)) (-4441 |has| |#2| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#2| (QUOTE (-915))) (-2718 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2718 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4446 "*") |has| |#2| (-173)) (-4437 |has| |#2| (-561)) (-4442 |has| |#2| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#2| (QUOTE (-915))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) (-249) ((|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 @@ -938,23 +938,23 @@ NIL NIL (-252 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4440 -2718 (-1739 (|has| |#4| (-1055)) (|has| |#4| (-234))) (-1739 (|has| |#4| (-1055)) (|has| |#4| (-906 (-1183)))) (|has| |#4| (-6 -4440)) (-1739 (|has| |#4| (-1055)) (|has| |#4| (-644 (-569))))) (-4437 |has| |#4| (-1055)) (-4438 |has| |#4| (-1055)) ((-4445 "*") |has| |#4| (-173)) (-4443 . 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(QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (-254 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 (-234)))) (-255 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) NIL (-256 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4443 . T) (-4444 . T)) +((-4444 . T) (-4445 . T)) NIL (-257) ((|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."))) @@ -994,8 +994,8 @@ NIL NIL (-266 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-267 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1040,11 +1040,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-278 R -1649) +(-278 R -1666) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-279 R -1649) +(-279 R -1666) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1070,7 +1070,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106)))) (-285 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4444 . T)) +((-4445 . T)) NIL (-286 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1091,18 +1091,18 @@ NIL (-290 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4444))) +((|HasAttribute| |#1| (QUOTE -4445))) (-291 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-292 S R |Mod| -3594 -3719 |exactQuo|) +(-292 S R |Mod| -3440 -2126 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-293) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4436 . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-294) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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"))) @@ -1118,21 +1118,21 @@ NIL NIL (-297 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."))) -((-4440 -2718 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4437 |has| |#1| (-1055)) (-4438 |has| |#1| (-1055))) -((|HasCategory| |#1| (QUOTE (-367))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2718 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731)))) (|HasCategory| |#1| (QUOTE (-478))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2718 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1118)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-305))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478)))) (-2718 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731)))) (-2718 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-731)))) +((-4441 -2774 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4438 |has| |#1| (-1055)) (-4439 |has| |#1| (-1055))) +((|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2774 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731)))) (|HasCategory| |#1| (QUOTE (-478))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2774 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1118)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-305))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478)))) (-2774 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731)))) (-2774 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-731)))) (-298 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|)))))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-299) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-300 -1649 S) +(-300 -1666 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 -(-301 E -1649) +(-301 E -1666) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1170,7 +1170,7 @@ NIL NIL (-310) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-311 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1180,7 +1180,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-313 -1649) +(-313 -1666) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1194,8 +1194,8 @@ NIL NIL (-316 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-1028))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (-2718 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-855)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-1158))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-234))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -312) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -289) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-310))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-550))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-855))) (-12 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| $ (QUOTE (-145)))) (-2718 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| $ (QUOTE (-145)))))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-1028))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (-2774 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-855)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-1158))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-234))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -312) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -289) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-310))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-550))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-855))) (-12 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| $ (QUOTE (-145)))) (-2774 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| $ (QUOTE (-145)))))) (-317 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 @@ -1206,9 +1206,9 @@ NIL NIL (-319 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."))) -((-4440 -2718 (-1739 (|has| |#1| (-1055)) (|has| |#1| (-644 (-569)))) (-12 (|has| |#1| (-561)) (-2718 (-1739 (|has| |#1| (-1055)) (|has| |#1| (-644 (-569)))) (|has| |#1| (-1055)) (|has| |#1| (-478)))) (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) ((-4445 "*") |has| |#1| (-561)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-561)) (-4435 |has| |#1| (-561))) -((-2718 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))))) (|HasCategory| |#1| (QUOTE (-561))) (-2718 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (QUOTE (-21))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-2718 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1118)))) (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055)))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561)))) (-2718 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1118)))) (-2718 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))))) (-2718 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1118)))) (-2718 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))))) (-2718 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2718 (-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-569))))) -(-320 R -1649) +((-4441 -2774 (-1756 (|has| |#1| (-1055)) (|has| |#1| (-644 (-569)))) (-12 (|has| |#1| (-561)) (-2774 (-1756 (|has| |#1| (-1055)) (|has| |#1| (-644 (-569)))) (|has| |#1| (-1055)) (|has| |#1| (-478)))) (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) ((-4446 "*") |has| |#1| (-561)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-561)) (-4436 |has| |#1| (-561))) +((-2774 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (QUOTE (-21))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1118)))) (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055)))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1118)))) (-2774 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))))) (-2774 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1118)))) (-2774 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))))) (-2774 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-569))))) +(-320 R -1666) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1218,8 +1218,8 @@ NIL NIL (-322 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -2388) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2718 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3865) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-323 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1230,7 +1230,7 @@ NIL NIL (-325 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) ((|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-797)))) (-326 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1246,19 +1246,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173)))) (-329 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-330 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) -(-331 S -1649) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +(-331 S -1666) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-372)))) -(-332 -1649) +(-332 -1666) ((|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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-333) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1280,15 +1280,15 @@ 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 -(-338 S -1649 UP UPUP R) +(-338 S -1666 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 -(-339 -1649 UP UPUP R) +(-339 -1666 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 -(-340 -1649 UP UPUP R) +(-340 -1666 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 @@ -1302,32 +1302,32 @@ NIL NIL (-343 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-383)))) (|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-569))))) (-344 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 -(-345 S -1649 UP UPUP) +(-345 S -1666 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-367)))) -(-346 -1649 UP UPUP) +(-346 -1666 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."))) -((-4436 |has| (-412 |#2|) (-367)) (-4441 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 |has| (-412 |#2|) (-367)) (-4442 |has| (-412 |#2|) (-367)) (-4436 |has| (-412 |#2|) (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-347 |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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) (-348 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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-349 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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-350 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 @@ -1342,33 +1342,33 @@ NIL NIL (-353) ((|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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL -(-354 R UP -1649) +(-354 R UP -1666) ((|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 (-355 |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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) (-356 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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-357 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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-358 |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}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) (-359 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) -(-360 -1649 GF) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +(-360 -1666 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 @@ -1376,21 +1376,21 @@ 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 -(-362 -1649 FP FPP) +(-362 -1666 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-363 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-364 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-365 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4440 . T)) +((-4441 . T)) NIL (-366 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1398,7 +1398,7 @@ NIL NIL (-367) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-368 |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."))) @@ -1414,7 +1414,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-561)))) (-371 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4440 |has| |#1| (-561)) (-4438 . T) (-4437 . T)) +((-4441 |has| |#1| (-561)) (-4439 . T) (-4438 . T)) NIL (-372) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1426,7 +1426,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-367)))) (-374 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) NIL (-375 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1435,14 +1435,14 @@ NIL (-376 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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106)))) +((|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106)))) (-377 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4443 . T)) +((-4444 . T)) NIL (-378 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4438 . T) (-4437 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4439 . T) (-4438 . T)) NIL (-379 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1454,7 +1454,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-381 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4440 . T)) +((-4441 . T)) NIL (-382 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1462,7 +1462,7 @@ NIL NIL (-383) ((|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}."))) -((-4426 . T) (-4434 . T) (-3006 . T) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4427 . T) (-4435 . T) (-3088 . T) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-384 |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}."))) @@ -1470,11 +1470,11 @@ NIL NIL (-385 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}"))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) ((|HasCategory| |#1| (QUOTE (-173)))) (-386 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}."))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) NIL (-387) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) @@ -1486,7 +1486,7 @@ NIL NIL (-389 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."))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) ((|HasCategory| |#1| (QUOTE (-173)))) (-390 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1498,7 +1498,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-855)))) (-392) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-393) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1510,13 +1510,13 @@ NIL NIL (-395 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) NIL (-396) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-397 -1649 UP UPUP R) +(-397 -1666 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1540,11 +1540,11 @@ NIL ((|constructor| (NIL "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 -(-403 -3458 |returnType| -3856 |symbols|) +(-403 -3570 |returnType| -3936 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-404 -1649 UP) +(-404 -1666 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1558,15 +1558,15 @@ NIL NIL (-407) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-408 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4426)) (|HasAttribute| |#1| (QUOTE -4434))) +((|HasAttribute| |#1| (QUOTE -4427)) (|HasAttribute| |#1| (QUOTE -4435))) (-409) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3006 . T) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3088 . T) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-410 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."))) @@ -1578,15 +1578,15 @@ NIL NIL (-412 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4430 -12 (|has| |#1| (-6 -4441)) (|has| |#1| (-457)) (|has| |#1| (-6 -4430))) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-825))) (-2718 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-855)))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833))))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasAttribute| |#1| (QUOTE -4441)) (|HasAttribute| |#1| (QUOTE -4430)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4431 -12 (|has| |#1| (-6 -4442)) (|has| |#1| (-457)) (|has| |#1| (-6 -4431))) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-825))) (-2774 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-855)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833))))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasAttribute| |#1| (QUOTE -4442)) (|HasAttribute| |#1| (QUOTE -4431)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-413 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 (-414 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) NIL (-415 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1600,11 +1600,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-418 R -1649 UP A) +(-418 R -1666 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4440 . T)) +((-4441 . T)) NIL -(-419 R -1649 UP A |ibasis|) +(-419 R -1666 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1044) (|devaluate| |#2|)))) @@ -1618,12 +1618,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-422 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4440 |has| |#1| (-561)) (-4438 . T) (-4437 . T)) +((-4441 |has| |#1| (-561)) (-4439 . T) (-4438 . T)) NIL (-423 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."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -312) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -289) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1227))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-457)))) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -312) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -289) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1227))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-457)))) (-424 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1650,17 +1650,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) (-430 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4443 . T) (-4433 . T) (-4444 . T)) +((-4444 . T) (-4434 . T) (-4445 . T)) NIL -(-431 R -1649) +(-431 R -1666) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-432 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4430 -12 (|has| |#1| (-6 -4430)) (|has| |#2| (-6 -4430))) (-4437 . T) (-4438 . T) (-4440 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4430)) (|HasAttribute| |#2| (QUOTE -4430)))) -(-433 R -1649) +((-4431 -12 (|has| |#1| (-6 -4431)) (|has| |#2| (-6 -4431))) (-4438 . T) (-4439 . T) (-4441 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4431)) (|HasAttribute| |#2| (QUOTE -4431)))) +(-433 R -1666) ((|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 @@ -1670,17 +1670,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-1118))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (-435 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}."))) -((-4440 -2718 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) ((-4445 "*") |has| |#1| (-561)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-561)) (-4435 |has| |#1| (-561))) +((-4441 -2774 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) ((-4446 "*") |has| |#1| (-561)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-561)) (-4436 |has| |#1| (-561))) NIL -(-436 R -1649) +(-436 R -1666) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-437 R -1649) +(-437 R -1666) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-438 R -1649) +(-438 R -1666) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1688,7 +1688,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-440 R -1649 UP) +(-440 R -1666 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-48))))) @@ -1720,7 +1720,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-448 R UP -1649) +(-448 R UP -1666) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1758,16 +1758,16 @@ NIL NIL (-457) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-458 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4440 |has| (-412 (-958 |#1|)) (-561)) (-4438 . T) (-4437 . T)) +((-4441 |has| (-412 (-958 |#1|)) (-561)) (-4439 . T) (-4438 . T)) ((|HasCategory| (-412 (-958 |#1|)) (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| (-412 (-958 |#1|)) (QUOTE (-561)))) (-459 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4445 "*") |has| |#2| (-173)) (-4436 |has| |#2| (-561)) (-4441 |has| |#2| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#2| (QUOTE (-915))) (-2718 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2718 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4446 "*") |has| |#2| (-173)) (-4437 |has| |#2| (-561)) (-4442 |has| |#2| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#2| (QUOTE (-915))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) (-460 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 @@ -1794,7 +1794,7 @@ NIL NIL (-466 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) NIL (-467 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1802,7 +1802,7 @@ NIL NIL (-468 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) (-469 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1832,7 +1832,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-476 |lv| -1649 R) +(-476 |lv| -1666 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1842,23 +1842,23 @@ NIL NIL (-478) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4440 . T)) +((-4441 . T)) NIL (-479 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -2388) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2718 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3865) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-480 |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."))) -((-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|)))))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106)))) +((-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106)))) (-481 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) (-482) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-483) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1866,29 +1866,29 @@ NIL NIL (-484 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|)))))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-485) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-486 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4445 "*") |has| |#2| (-173)) (-4436 |has| |#2| (-561)) (-4441 |has| |#2| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . 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(|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-2774 (|HasCategory| |#2| (QUOTE (-1055))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-1106)))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))))) (-488) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-489 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-490 -1649 UP UPUP R) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-490 -1666 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1898,12 +1898,12 @@ NIL NIL (-492) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2718 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2774 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) (-493 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4443)) (|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) +((|HasAttribute| |#1| (QUOTE -4444)) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (-494 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1924,33 +1924,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-499 -1649 UP |AlExt| |AlPol|) +(-499 -1666 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-500) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-569))))) (-501 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-502 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-503 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-504 R UP -1649) +(-504 R UP -1666) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-505 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1106))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1106))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-867))))) (-506 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) @@ -1964,7 +1964,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-509 -1649 |Expon| |VarSet| |DPoly|) +(-509 -1666 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-1183))))) @@ -2014,36 +2014,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-797)))) (-521 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-522) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-523 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((-2718 (|HasCategory| (-586 |#1|) (QUOTE (-145))) (|HasCategory| (-586 |#1|) (QUOTE (-372)))) (|HasCategory| (-586 |#1|) (QUOTE (-147))) (|HasCategory| (-586 |#1|) (QUOTE (-372))) (|HasCategory| (-586 |#1|) (QUOTE (-145)))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-2774 (|HasCategory| (-586 |#1|) (QUOTE (-145))) (|HasCategory| (-586 |#1|) (QUOTE (-372)))) (|HasCategory| (-586 |#1|) (QUOTE (-147))) (|HasCategory| (-586 |#1|) (QUOTE (-372))) (|HasCategory| (-586 |#1|) (QUOTE (-145)))) (-524 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-525 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-526 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4444))) +((|HasAttribute| |#3| (QUOTE -4445))) (-527 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4444))) +((|HasAttribute| |#7| (QUOTE -4445))) (-528 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4445 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4446 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-529) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2076,7 +2076,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-537 K -1649 |Par|) +(-537 K -1666 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2100,7 +2100,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-543 K -1649 |Par|) +(-543 K -1666 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2130,7 +2130,7 @@ NIL NIL (-550) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4441 . T) (-4442 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4442 . T) (-4443 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-551) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2150,13 +2150,13 @@ NIL NIL (-555 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|)))))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) -(-556 R -1649) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +(-556 R -1666) ((|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 -(-557 R0 -1649 UP UPUP R) +(-557 R0 -1666 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 @@ -2166,7 +2166,7 @@ NIL NIL (-559 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."))) -((-3006 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3088 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-560 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."))) @@ -2174,9 +2174,9 @@ NIL NIL (-561) ((|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."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL -(-562 R -1649) +(-562 R -1666) ((|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 @@ -2188,7 +2188,7 @@ 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 -(-565 R -1649 L) +(-565 R -1666 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 -661) (|devaluate| |#2|)))) @@ -2196,31 +2196,31 @@ 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 -(-567 -1649 UP UPUP R) +(-567 -1666 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 -(-568 -1649 UP) +(-568 -1666 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 (-569) ((|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."))) -((-4425 . T) (-4431 . T) (-4435 . T) (-4430 . T) (-4441 . T) (-4442 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4426 . T) (-4432 . T) (-4436 . T) (-4431 . T) (-4442 . T) (-4443 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-570) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-571 R -1649 L) +(-571 R -1666 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 -661) (|devaluate| |#2|)))) -(-572 R -1649) +(-572 R -1666) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1145)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-634))))) -(-573 -1649 UP) +(-573 -1666 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2228,27 +2228,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-575 -1649) +(-575 -1666) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-576 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-3006 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3088 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-577) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-578 R -1649) +(-578 R -1666) ((|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 -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-287))) (|HasCategory| |#2| (QUOTE (-634))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-287)))) (|HasCategory| |#1| (QUOTE (-561)))) -(-579 -1649 UP) +(-579 -1666 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 -(-580 R -1649) +(-580 R -1666) ((|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 @@ -2261,7 +2261,7 @@ NIL NIL NIL (-583) -((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|bothWays| (($) "`bothWays' indicates that an IO conduit is for both input and output.")) (|output| (($) "`output' indicates that an IO conduit is for output")) (|input| (($) "`input' indicates that an IO conduit is for input."))) +((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input."))) NIL NIL (-584) @@ -2270,21 +2270,21 @@ NIL NIL (-585 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-586 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-372)))) (-587) ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-588 R -1649) +(-588 R -1666) ((|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 -(-589 E -1649) +(-589 E -1666) ((|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 @@ -2292,9 +2292,9 @@ 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 -(-591 -1649) +(-591 -1666) ((|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}."))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) ((|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183))))) (-592 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"))) @@ -2322,19 +2322,19 @@ NIL NIL (-598 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-2718 (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-2774 (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-599 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-600 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-569)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-569)) (|devaluate| |#1|)))) (|HasCategory| (-569) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2388) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-569)))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-569)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-569)) (|devaluate| |#1|)))) (|HasCategory| (-569) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-569)))))) (-601 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4445 "*") |has| |#1| (-561)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-561)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-561)))) (-602) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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"))) @@ -2348,7 +2348,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-605 R -1649 FG) +(-605 R -1666 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2358,12 +2358,12 @@ NIL NIL (-607 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-608 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#2| (QUOTE (-855))) (|HasAttribute| |#1| (QUOTE -4443)) (|HasCategory| |#3| (QUOTE (-1106)))) +((|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#2| (QUOTE (-855))) (|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#3| (QUOTE (-1106)))) (-609 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2378,19 +2378,19 @@ NIL NIL (-612 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4440 -2718 (-1739 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4438 . T) (-4437 . T)) -((-2718 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) +((-4441 -2774 (-1756 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4439 . T) (-4438 . T)) +((-2774 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-613 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-614 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL (-615 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4444 . T)) +((-4445 . T)) NIL (-616 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"))) @@ -2408,7 +2408,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-620 -1649 UP) +(-620 -1666 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2430,19 +2430,19 @@ NIL NIL (-625 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."))) -((-4440 . T)) +((-4441 . T)) NIL (-626 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}."))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-853)))) -(-627 R -1649) +(-627 R -1666) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL (-628 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-4438 . T) (-4437 . T) ((-4445 "*") . T) (-4436 . T) (-4440 . T)) +((-4439 . T) (-4438 . T) ((-4446 "*") . T) (-4437 . T) (-4441 . T)) ((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (-629 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) @@ -2458,7 +2458,7 @@ NIL NIL (-632 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4440 . T)) +((-4441 . T)) NIL (-633 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2468,30 +2468,30 @@ 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 -(-635 R -1649) +(-635 R -1666) ((|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 -(-636 |lv| -1649) +(-636 |lv| -1666) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-637) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2179) (QUOTE (-52))))))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-1165) (QUOTE (-855))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 (-52))) (QUOTE (-1106)))) +((-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2214) (QUOTE (-52))))))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-1165) (QUOTE (-855))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (QUOTE (-1106)))) (-638 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-639 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4438 . T) (-4437 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4439 . T) (-4438 . T)) NIL (-640 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4440 -2718 (-1739 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4438 . T) (-4437 . T)) -((-2718 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) +((-4441 -2774 (-1756 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4439 . T) (-4438 . T)) +((-2774 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-641 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "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 @@ -2503,10 +2503,10 @@ NIL (-643 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1728 (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-367)))) +((-1745 (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-367)))) (-644 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4440 . T)) +((-4441 . T)) NIL (-645 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2526,8 +2526,8 @@ NIL NIL (-649 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-650 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2538,8 +2538,8 @@ NIL NIL (-652 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-653 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2551,22 +2551,22 @@ NIL (-655 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4444))) +((|HasAttribute| |#1| (QUOTE -4445))) (-656 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-657 R -1649 L) +(-657 R -1666 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 (-658 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}}"))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-659 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-660 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2574,15 +2574,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-661 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}."))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) NIL -(-662 -1649 UP) +(-662 -1666 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)))) -(-663 A -3731) +(-663 A -2222) ((|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}}"))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-664 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."))) @@ -2598,7 +2598,7 @@ NIL NIL (-667 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}."))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) ((|HasCategory| |#1| (QUOTE (-796)))) (-668 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."))) @@ -2606,7 +2606,7 @@ NIL NIL (-669 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4438 . T) (-4437 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4439 . T) (-4438 . T)) ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-173)))) (-670 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) @@ -2614,13 +2614,13 @@ NIL NIL (-671 S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL -(-672 -1649) +(-672 -1666) ((|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 -(-673 -1649 |Row| |Col| M) +(-673 -1666 |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 @@ -2630,8 +2630,8 @@ NIL NIL (-675 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) -((-4440 . T) (-4443 . T) (-4437 . T) (-4438 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4445 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561))) (-2718 (|HasAttribute| |#2| (QUOTE (-4445 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) +((-4441 . T) (-4444 . T) (-4438 . T) (-4439 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561))) (-2774 (|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) (-676) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2651,7 +2651,7 @@ NIL (-680 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-681) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2695,10 +2695,10 @@ NIL (-691 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4445 "*"))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561)))) +((|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561)))) (-692 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4443 . T) (-4444 . T)) +((-4444 . T) (-4445 . T)) NIL (-693 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."))) @@ -2706,8 +2706,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561)))) (-694 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) -((-4443 . T) (-4444 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4445 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4445 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4446 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-695 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2716,7 +2716,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-697 S -1649 FLAF FLAS) +(-697 S -1666 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2726,11 +2726,11 @@ NIL NIL (-699) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4436 . T) (-4441 |has| (-704) (-367)) (-4435 |has| (-704) (-367)) (-3016 . T) (-4442 |has| (-704) (-6 -4442)) (-4439 |has| (-704) (-6 -4439)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-704) (QUOTE (-147))) (|HasCategory| (-704) (QUOTE (-145))) (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-704) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-704) (QUOTE (-372))) (|HasCategory| (-704) (QUOTE (-367))) (-2718 (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-704) (QUOTE (-234))) (-2718 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-353)))) (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (LIST (QUOTE -289) (QUOTE (-704)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -312) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (-2718 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-353)))) (|HasCategory| (-704) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-704) (QUOTE (-1028))) (|HasCategory| (-704) (QUOTE (-1208))) (-12 (|HasCategory| (-704) (QUOTE (-1008))) (|HasCategory| (-704) (QUOTE (-1208)))) (-2718 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-367))) (-12 (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (QUOTE (-915))))) (-2718 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (-12 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-915)))) (-12 (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (QUOTE (-915))))) (|HasCategory| (-704) (QUOTE (-550))) (-12 (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-1208)))) (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915))) (-2718 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-367)))) (-2718 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-561)))) (-12 (|HasCategory| (-704) (QUOTE (-234))) (|HasCategory| (-704) (QUOTE (-367)))) (-12 (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-704) (QUOTE (-561))) (|HasAttribute| (-704) (QUOTE -4442)) (|HasAttribute| (-704) (QUOTE -4439)) (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-145)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-353))))) +((-4437 . T) (-4442 |has| (-704) (-367)) (-4436 |has| (-704) (-367)) (-3098 . T) (-4443 |has| (-704) (-6 -4443)) (-4440 |has| (-704) (-6 -4440)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-704) (QUOTE (-147))) (|HasCategory| (-704) (QUOTE (-145))) (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-704) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-704) (QUOTE (-372))) (|HasCategory| (-704) (QUOTE (-367))) (-2774 (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-704) (QUOTE (-234))) (-2774 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-353)))) (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (LIST (QUOTE -289) (QUOTE (-704)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -312) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (-2774 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-353)))) (|HasCategory| (-704) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-704) (QUOTE (-1028))) (|HasCategory| (-704) (QUOTE (-1208))) (-12 (|HasCategory| (-704) (QUOTE (-1008))) (|HasCategory| (-704) (QUOTE (-1208)))) (-2774 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-367))) (-12 (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (QUOTE (-915))))) (-2774 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (-12 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-915)))) (-12 (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (QUOTE (-915))))) (|HasCategory| (-704) (QUOTE (-550))) (-12 (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-1208)))) (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915))) (-2774 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-367)))) (-2774 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-561)))) (-12 (|HasCategory| (-704) (QUOTE (-234))) (|HasCategory| (-704) (QUOTE (-367)))) (-12 (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-704) (QUOTE (-561))) (|HasAttribute| (-704) (QUOTE -4443)) (|HasAttribute| (-704) (QUOTE -4440)) (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-145)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-353))))) (-700 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}."))) -((-4444 . T)) +((-4445 . T)) NIL (-701 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2740,13 +2740,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "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 -(-703 OV E -1649 PG) +(-703 OV E -1666 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-704) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3006 . T) (-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-3088 . T) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-705 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2754,7 +2754,7 @@ NIL NIL (-706) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4442 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4443 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-707 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-711 S -2749 I) +(-711 S -2830 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2782,7 +2782,7 @@ NIL NIL (-713 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) NIL (-714 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2792,25 +2792,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-716 R |Mod| -3594 -3719 |exactQuo|) +(-716 R |Mod| -3440 -2126 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-717 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4439 |has| |#1| (-367)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4440 |has| |#1| (-367)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-718 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-719 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) +((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-720 R |Mod| -3594 -3719 |exactQuo|) +(-720 R |Mod| -3440 -2126 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4440 . T)) +((-4441 . T)) NIL (-721 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2818,11 +2818,11 @@ NIL NIL (-722 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) NIL -(-723 -1649) +(-723 -1666) ((|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]]}."))) -((-4440 . T)) +((-4441 . T)) NIL (-724 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2846,7 +2846,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-353))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-372)))) (-729 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4436 |has| |#1| (-367)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 |has| |#1| (-367)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-730 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) @@ -2856,7 +2856,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-732 -1649 UP) +(-732 -1666 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2874,8 +2874,8 @@ NIL NIL (-736 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) -(((-4445 "*") |has| |#2| (-173)) (-4436 |has| |#2| (-561)) (-4441 |has| |#2| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#2| (QUOTE (-915))) (-2718 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2718 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4446 "*") |has| |#2| (-173)) (-4437 |has| |#2| (-561)) (-4442 |has| |#2| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#2| (QUOTE (-915))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) (-737 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2890,15 +2890,15 @@ NIL NIL (-740 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) +((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-855)))) (-741 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4433 . T) (-4444 . T)) +((-4434 . T) (-4445 . T)) NIL (-742 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}."))) -((-4443 . T) (-4433 . T) (-4444 . T)) +((-4444 . T) (-4434 . T) (-4445 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-743) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) @@ -2910,7 +2910,7 @@ NIL NIL (-745 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4438 . T) (-4437 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4439 . T) (-4438 . T) (-4441 . T)) NIL (-746 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2926,7 +2926,7 @@ NIL NIL (-749 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) NIL (-750) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -3008,11 +3008,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-770 -1649) +(-770 -1666) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-771 P -1649) +(-771 P -1666) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3020,7 +3020,7 @@ NIL NIL NIL NIL -(-773 UP -1649) +(-773 UP -1666) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3034,9 +3034,9 @@ NIL NIL (-776) ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) -(((-4445 "*") . T)) +(((-4446 "*") . T)) NIL -(-777 R -1649) +(-777 R -1666) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3056,7 +3056,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-782 -1649 |ExtF| |SUEx| |ExtP| |n|) +(-782 -1666 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3070,23 +3070,23 @@ NIL NIL (-785 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL (-787 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-789 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-790 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) @@ -3138,25 +3138,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) (-802 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) NIL -(-803 -2718 R OS S) +(-803 -2774 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-804 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-2718 (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2718 (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) +((-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-2774 (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (-805) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-806 R -1649 L) +(-806 R -1666 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-807 R -1649) +(-807 R -1666) ((|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 @@ -3164,7 +3164,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-809 R -1649) +(-809 R -1666) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3172,11 +3172,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-811 -1649 UP UPUP R) +(-811 -1666 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-812 -1649 UP L LQ) +(-812 -1666 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3184,41 +3184,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-814 -1649 UP L LQ) +(-814 -1666 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-815 -1649 UP) +(-815 -1666 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 -(-816 -1649 L UP A LO) +(-816 -1666 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-817 -1649 UP) +(-817 -1666 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-818 -1649 LO) +(-818 -1666 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-819 -1649 LODO) +(-819 -1666 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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T) (-4438 . T) (-4437 . T)) +(((-4446 "*") |has| |#2| (-367)) (-4437 |has| |#2| (-367)) (-4442 |has| |#2| (-367)) (-4436 |has| |#2| (-367)) (-4441 . T) (-4439 . T) (-4438 . T)) ((|HasCategory| |#2| (QUOTE (-367)))) (-823 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -3230,7 +3230,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-855)))) (-825) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-826) ((|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}"))) @@ -3258,7 +3258,7 @@ NIL NIL (-832 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}."))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-234)))) (-833) ((|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."))) @@ -3270,7 +3270,7 @@ NIL NIL (-835 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4443 . T) (-4433 . T) (-4444 . T)) +((-4444 . T) (-4434 . T) (-4445 . T)) NIL (-836) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3282,8 +3282,8 @@ NIL NIL (-838 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."))) -((-4440 |has| |#1| (-853))) -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-2718 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2718 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4441 |has| |#1| (-853))) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-2774 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2774 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-550)))) (-839 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 @@ -3294,7 +3294,7 @@ NIL NIL (-841 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) +((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-842) ((|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)."))) @@ -3322,13 +3322,13 @@ NIL NIL (-848 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4440 |has| |#1| (-853))) -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-2718 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2718 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4441 |has| |#1| (-853))) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-2774 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2774 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-550)))) (-849) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-850 -2358 S) +(-850 -2406 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3342,7 +3342,7 @@ NIL NIL (-853) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4440 . T)) +((-4441 . T)) NIL (-854 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3358,19 +3358,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173)))) (-857 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) NIL (-858 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) -(-859 R |sigma| -3011) +(-859 R |sigma| -3111) ((|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."))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) -(-860 |x| R |sigma| -3011) +(-860 |x| R |sigma| -3111) ((|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}."))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-367)))) (-861 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) @@ -3414,7 +3414,7 @@ NIL NIL (-871 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) +((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (-872 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3426,24 +3426,24 @@ NIL NIL (-874 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-875 |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)."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-876 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-875 |#1|) (QUOTE (-915))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-875 |#1|) (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-147))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-875 |#1|) (QUOTE (-1028))) (|HasCategory| (-875 |#1|) (QUOTE (-825))) (-2718 (|HasCategory| (-875 |#1|) (QUOTE (-825))) (|HasCategory| (-875 |#1|) (QUOTE (-855)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (QUOTE (-1158))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (QUOTE (-234))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -875) (|devaluate| |#1|)) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (QUOTE (-310))) (|HasCategory| (-875 |#1|) (QUOTE (-550))) (|HasCategory| (-875 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-915)))) (|HasCategory| (-875 |#1|) (QUOTE (-145))))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-875 |#1|) (QUOTE (-915))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-875 |#1|) (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-147))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-875 |#1|) (QUOTE (-1028))) (|HasCategory| (-875 |#1|) (QUOTE (-825))) (-2774 (|HasCategory| (-875 |#1|) (QUOTE (-825))) (|HasCategory| (-875 |#1|) (QUOTE (-855)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (QUOTE (-1158))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (QUOTE (-234))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -875) (|devaluate| |#1|)) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (QUOTE (-310))) (|HasCategory| (-875 |#1|) (QUOTE (-550))) (|HasCategory| (-875 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-915)))) (|HasCategory| (-875 |#1|) (QUOTE (-145))))) (-877 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-825))) (-2718 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1158))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-825))) (-2774 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1158))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) (-878 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))))) (-879) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3503,7 +3503,7 @@ NIL (-893 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-1728 (|HasCategory| |#2| (QUOTE (-1055)))) (-1728 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (-1728 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) +((-12 (-1745 (|HasCategory| |#2| (QUOTE (-1055)))) (-1745 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (-1745 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) (-894 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 @@ -3512,7 +3512,7 @@ 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 -(-896 R -2749) +(-896 R -2830) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3536,7 +3536,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-902 UP -1649) +(-902 UP -1666) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3554,19 +3554,19 @@ NIL NIL (-906 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1, n1)..., sn, nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{D(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4440 . T)) +((-4441 . T)) NIL (-907 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-908 |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 (-909 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4440 . T)) +((-4441 . T)) NIL (-910 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3574,8 +3574,8 @@ NIL NIL (-911 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4440 . T)) -((-2718 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) +((-4441 . T)) +((-2774 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (-912 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 @@ -3590,13 +3590,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-145)))) (-915) ((|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}."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-916 |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."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-372)))) -(-917 R0 -1649 UP UPUP R) +(-917 R0 -1666 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3610,7 +3610,7 @@ NIL NIL (-920 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-921 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) @@ -3624,7 +3624,7 @@ 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 -(-924 -1649) +(-924 -1666) ((|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 @@ -3634,17 +3634,17 @@ NIL NIL (-926) ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-927) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4445 "*") . T)) +(((-4446 "*") . T)) NIL -(-928 -1649 P) +(-928 -1666 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-929 |xx| -1649) +(-929 |xx| -1666) ((|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 @@ -3668,7 +3668,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-935 R -1649) +(-935 R -1666) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3680,7 +3680,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-938 S R -1649) +(-938 S R -1666) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3700,11 +3700,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -892) (|devaluate| |#1|)))) -(-943 R -1649 -2749) +(-943 R -1666 -2830) ((|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 -(-944 -2749) +(-944 -2830) ((|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 @@ -3726,8 +3726,8 @@ NIL NIL (-949 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-950 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3747,12 +3747,12 @@ NIL (-954 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 (-915))) (|HasAttribute| |#2| (QUOTE -4441)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) +((|HasCategory| |#2| (QUOTE (-915))) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (-955 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}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) NIL -(-956 E V R P -1649) +(-956 E V R P -1666) ((|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 @@ -3762,9 +3762,9 @@ NIL NIL (-958 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}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-959 E V R P -1649) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-959 E V R P -1666) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-457)))) @@ -3786,13 +3786,13 @@ NIL NIL (-964 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-965) ((|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 -(-966 -1649) +(-966 -1666) ((|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 @@ -3806,12 +3806,12 @@ NIL NIL (-969 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}"))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4441))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4442))) (-970 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) 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(-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) +((-4441 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-971) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3826,7 +3826,7 @@ NIL NIL (-974 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4443 . T) (-4444 . T)) +((-4444 . T) (-4445 . T)) NIL (-975 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3846,7 +3846,7 @@ NIL NIL (-979 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-980) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3858,7 +3858,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-561)))) (-982 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4443 . T)) +((-4444 . T)) NIL (-983 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3874,7 +3874,7 @@ NIL NIL (-986 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-987 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3892,7 +3892,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-991 K R UP -1649) +(-991 K R UP -1666) ((|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 @@ -3922,7 +3922,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1158)))) (-998 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}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-999 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3934,7 +3934,7 @@ NIL NIL (-1001 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4443 . T) (-4444 . T)) +((-4444 . T) (-4445 . T)) NIL (-1002 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}."))) @@ -3942,7 +3942,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-293)))) (-1003 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}."))) -((-4436 |has| |#1| (-293)) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 |has| |#1| (-293)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1004 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}."))) @@ -3950,12 +3950,12 @@ NIL NIL (-1005 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.}"))) -((-4436 |has| |#1| (-293)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-367))) (-2718 (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4437 |has| |#1| (-293)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550)))) (-1006 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-1007 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3964,14 +3964,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1009 -1649 UP UPUP |radicnd| |n|) +(-1009 -1666 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4436 |has| (-412 |#2|) (-367)) (-4441 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-353))) (-2718 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-2718 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (-2718 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-353))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-569)))) (-2718 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) +((-4437 |has| (-412 |#2|) (-367)) (-4442 |has| (-412 |#2|) (-367)) (-4436 |has| (-412 |#2|) (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-353))) (-2774 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-2774 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (-2774 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-353))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-569)))) (-2774 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) (-1010 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2718 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2774 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) (-1011) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3991,7 +3991,7 @@ NIL (-1015 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#2| (QUOTE (-1106)))) +((|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#2| (QUOTE (-1106)))) (-1016 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -4002,21 +4002,21 @@ NIL NIL (-1018) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4436 . T) (-4441 . T) (-4435 . T) (-4438 . T) (-4437 . T) ((-4445 "*") . T) (-4440 . T)) +((-4437 . T) (-4442 . T) (-4436 . T) (-4439 . T) (-4438 . T) ((-4446 "*") . T) (-4441 . T)) NIL -(-1019 R -1649) +(-1019 R -1666) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1020 R -1649) +(-1020 R -1666) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1021 -1649 UP) +(-1021 -1666 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1022 -1649 UP) +(-1022 -1666 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4050,9 +4050,9 @@ NIL NIL (-1030 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) -((-4436 . T) (-4441 . T) (-4435 . T) (-4438 . T) (-4437 . T) ((-4445 "*") . T) (-4440 . T)) -((-2718 (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (QUOTE (-569))))) -(-1031 -1649 L) +((-4437 . T) (-4442 . T) (-4436 . T) (-4439 . T) (-4438 . T) ((-4446 "*") . T) (-4441 . T)) +((-2774 (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (QUOTE (-569))))) +(-1031 -1666 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4062,12 +4062,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1106)))) (-1033 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) (-1034 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 (-4445 "*")))) +((|HasAttribute| |#1| (QUOTE (-4446 "*")))) (-1035 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -4088,14 +4088,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1040 -1649 |Expon| |VarSet| |FPol| |LFPol|) +(-1040 -1666 |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"))) -(((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1041) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2179) (QUOTE (-52))))))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-52) (QUOTE (-1106))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2214) (QUOTE (-52))))))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-52) (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867))))) (-1042) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4138,7 +4138,7 @@ NIL NIL (-1052 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) ((-12 (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1106))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -785) (|devaluate| |#1|) (LIST (QUOTE -869) (|devaluate| |#2|)))))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| (-869 |#2|) (QUOTE (-372))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-1053) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) @@ -4150,9 +4150,9 @@ NIL NIL (-1055) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4440 . T)) +((-4441 . T)) NIL -(-1056 |xx| -1649) +(-1056 |xx| -1666) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4166,12 +4166,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-310))) (|HasCategory| |#4| (QUOTE (-367))) (|HasCategory| |#4| (QUOTE (-561))) (|HasCategory| |#4| (QUOTE (-173)))) (-1059 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4443 . T) (-4438 . T) (-4437 . T)) +((-4444 . T) (-4439 . T) (-4438 . T)) NIL (-1060 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4443 . T) (-4438 . T) (-4437 . T)) -((|HasCategory| |#3| (QUOTE (-173))) (-2718 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (QUOTE (-310))) (|HasCategory| |#3| (QUOTE (-561))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4439 . T) (-4438 . T)) +((|HasCategory| |#3| (QUOTE (-173))) (-2774 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (QUOTE (-310))) (|HasCategory| |#3| (QUOTE (-561))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-867))))) (-1061 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4194,7 +4194,7 @@ NIL NIL (-1066) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1067 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4202,19 +4202,19 @@ NIL NIL (-1068) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4431 . T) (-4435 . T) (-4430 . T) (-4441 . T) (-4442 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4432 . T) (-4436 . T) (-4431 . T) (-4442 . T) (-4443 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1069) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2179) (QUOTE (-52))))))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (QUOTE (-1106))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-52) (QUOTE (-1106))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2214) (QUOTE (-52))))))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-52) (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867))))) (-1070 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -998) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-1183))))) (-1071 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) NIL (-1072) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -4238,7 +4238,7 @@ NIL NIL (-1077 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-1078 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -4256,11 +4256,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1082 |Base| R -1649) +(-1082 |Base| R -1666) ((|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 -(-1083 |Base| R -1649) +(-1083 |Base| R -1666) ((|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 @@ -4274,8 +4274,8 @@ NIL NIL (-1086 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."))) -((-4436 |has| |#1| (-367)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-353))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-353)))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))))) +((-4437 |has| |#1| (-367)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-353))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-353)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))))) (-1087 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 @@ -4302,8 +4302,8 @@ NIL NIL (-1093 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1094 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4346,7 +4346,7 @@ NIL NIL (-1104 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}."))) -((-4433 . T)) +((-4434 . T)) NIL (-1105 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4362,8 +4362,8 @@ NIL NIL (-1108 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)}}"))) -((-4443 . T) (-4433 . T) (-4444 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4444 . T) (-4434 . T) (-4445 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-1109 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,...,an), [i1,...,im])} returns \\spad{(a_i1,...,a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,...,an), i)} returns \\spad{ai}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4390,7 +4390,7 @@ NIL NIL (-1115 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-1116) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4406,8 +4406,8 @@ NIL NIL (-1119 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4437 |has| |#3| (-1055)) (-4438 |has| |#3| (-1055)) (-4440 |has| |#3| (-6 -4440)) ((-4445 "*") |has| |#3| (-173)) (-4443 . 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(LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-853))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569)))))) (|HasCategory| (-569) (QUOTE (-855))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-234))) (|HasCategory| |#3| (QUOTE (-1055)))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183))))) (-2774 (|HasCategory| |#3| (QUOTE (-1055))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569)))))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#3| (QUOTE (-1106)))) (|HasAttribute| |#3| (QUOTE -4441)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (-1120 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4416,7 +4416,7 @@ 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 -(-1122 R -1649) +(-1122 R -1666) ((|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 @@ -4434,19 +4434,19 @@ NIL NIL (-1126) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4431 . T) (-4435 . T) (-4430 . T) (-4441 . T) (-4442 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4432 . T) (-4436 . T) (-4431 . T) (-4442 . T) (-4443 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1127 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4443 . T) (-4444 . T)) +((-4444 . T) (-4445 . T)) NIL (-1128 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-367))) (|HasAttribute| |#3| (QUOTE (-4445 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) +((|HasCategory| |#3| (QUOTE (-367))) (|HasAttribute| |#3| (QUOTE (-4446 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) (-1129 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-4443 . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4444 . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1130 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4454,17 +4454,17 @@ NIL NIL (-1131 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2718 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1132 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367)))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367)))) (-1133 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL -(-1134 UP -1649) +(-1134 UP -1666) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4518,19 +4518,19 @@ NIL NIL (-1147 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106))) (-2718 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106))))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106))) (-2774 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106))))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-867))))) (-1148 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) -((-4440 . T) (-4432 |has| |#2| (-6 (-4445 "*"))) (-4443 . T) (-4437 . T) (-4438 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4445 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2718 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-367))) (-2718 (|HasAttribute| |#2| (QUOTE (-4445 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) +((-4441 . T) (-4433 |has| |#2| (-6 (-4446 "*"))) (-4444 . T) (-4438 . T) (-4439 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-367))) (-2774 (|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) (-1149 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1150) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-1151 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4538,12 +4538,12 @@ NIL NIL (-1152 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) (-1153 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-1154 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4554,8 +4554,8 @@ NIL NIL (-1156 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|)))))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106)))) +((-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106)))) (-1157) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4582,20 +4582,20 @@ NIL NIL (-1163 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) -((-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4445 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-1164) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-1165) NIL -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-1166 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#1|)))))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (QUOTE (-1106))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#1|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-1167 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4626,9 +4626,9 @@ NIL NIL (-1174 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4445 "*") -2718 (-1739 (|has| |#1| (-367)) (|has| (-1181 |#1| |#2| |#3|) (-825))) (|has| |#1| (-173)) (-1739 (|has| |#1| (-367)) (|has| (-1181 |#1| |#2| |#3|) (-915)))) (-4436 -2718 (-1739 (|has| |#1| (-367)) (|has| (-1181 |#1| |#2| |#3|) (-825))) (|has| |#1| (-561)) (-1739 (|has| |#1| (-367)) (|has| (-1181 |#1| |#2| |#3|) (-915)))) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -2388) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2718 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3865) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -2388) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-2718 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3865) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1182) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4670,8 +4670,8 @@ NIL NIL (-1185 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-6 -4441)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2718 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| (-977) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasAttribute| |#1| (QUOTE -4441))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| (-977) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasAttribute| |#1| (QUOTE -4442))) (-1186) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4714,8 +4714,8 @@ NIL NIL (-1196 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4443 . T) (-4444 . T)) -((-12 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1963) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2179) (|devaluate| |#2|)))))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2718 (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4444 . T) (-4445 . T)) +((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-1197 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL @@ -4726,7 +4726,7 @@ NIL NIL (-1199 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4444 . T)) +((-4445 . T)) NIL (-1200 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4766,8 +4766,8 @@ NIL NIL (-1209 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4444 . T) (-4443 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4445 . T) (-4444 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-1210 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4776,7 +4776,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1212 R -1649) +(-1212 R -1666) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4784,7 +4784,7 @@ 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 -(-1214 R -1649) +(-1214 R -1666) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -892) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -892) (|devaluate| |#1|))))) @@ -4794,12 +4794,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-372)))) (-1216 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-1217 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367)))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367)))) (-1218 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4812,7 +4812,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1221 -1649) +(-1221 -1666) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4838,7 +4838,7 @@ NIL NIL (-1227) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1228) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4862,7 +4862,7 @@ NIL NIL (-1233 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1234 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)}."))) @@ -4870,16 +4870,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-1235 |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)}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1236 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . 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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 @@ -4914,8 +4914,8 @@ NIL NIL (-1246 |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| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4445 "*") |has| |#2| (-173)) (-4436 |has| |#2| (-561)) (-4439 |has| |#2| (-367)) (-4441 |has| |#2| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4926,15 +4926,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-1158)))) (-1249 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\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}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4439 |has| |#1| (-367)) (-4441 |has| |#1| (-6 -4441)) (-4438 . T) (-4437 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4440 |has| |#1| (-367)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) NIL (-1250 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1118))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2388) (LIST (|devaluate| |#2|) (QUOTE (-1183)))))) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1118))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3793) (LIST (|devaluate| |#2|) (QUOTE (-1183)))))) (-1251 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1252 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4946,7 +4946,7 @@ NIL NIL (-1254 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1255 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)}."))) @@ -4954,24 +4954,24 @@ NIL NIL (-1256 |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)}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1257 |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)}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -2388) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2718 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3865) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-1258 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4441 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2718 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -2388) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2718 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3865) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1259 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) -(((-4445 "*") |has| (-1258 |#2| |#3| |#4|) (-173)) (-4436 |has| (-1258 |#2| |#3| |#4|) (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-173))) (-2718 (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-457))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-561)))) +(((-4446 "*") |has| (-1258 |#2| |#3| |#4|) (-173)) (-4437 |has| (-1258 |#2| |#3| |#4|) (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-173))) (-2774 (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-457))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-561)))) (-1260 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4444))) +((|HasAttribute| |#1| (QUOTE -4445))) (-1261 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4983,20 +4983,20 @@ NIL (-1263 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-569)))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasSignature| |#2| (LIST (QUOTE -3865) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3313) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasSignature| |#2| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2488) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367)))) (-1264 |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."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1265 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4445 "*") |has| |#1| (-173)) (-4436 |has| |#1| (-561)) (-4437 . T) (-4438 . T) (-4440 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2718 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -2388) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-2718 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3313) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3865) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1266 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1267 -1649 UP L UTS) +(-1267 -1666 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 (-561)))) @@ -5014,7 +5014,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1271 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) NIL (-1272 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -5022,8 +5022,8 @@ NIL NIL (-1273 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4444 . T) (-4443 . T)) -((-2718 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2718 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2718 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4445 . T) (-4444 . T)) +((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-1274) ((|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|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5050,13 +5050,13 @@ NIL NIL (-1280 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4438 . T) (-4437 . T)) +((-4439 . T) (-4438 . T)) NIL (-1281 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1282 K R UP -1649) +(-1282 K R UP -1666) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5070,56 +5070,56 @@ NIL NIL (-1285 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4438 |has| |#1| (-173)) (-4437 |has| |#1| (-173)) (-4440 . T)) +((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (-1286 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4444 . T) (-4443 . T)) +((-4445 . T) (-4444 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) (-1287 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})"))) -((-4437 . T) (-4438 . T) (-4440 . T)) +((-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1288 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4440 . T) (-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4436))) +((-4441 . T) (-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4437))) (-1289 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL (-1290 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) +((-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) NIL -(-1291 S -1649) +(-1291 S -1666) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1292 -1649) +(-1292 -1666) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4435 . T) (-4441 . T) (-4436 . T) ((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL (-1293 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -722) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasAttribute| |#2| (QUOTE -4436))) +((-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -722) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasAttribute| |#2| (QUOTE -4437))) (-1294 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) +((-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) NIL (-1295 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4436 |has| |#1| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4436))) +((-4437 |has| |#1| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4437))) (-1296 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4440 . T) (-4441 |has| |#1| (-6 -4441)) (-4436 |has| |#1| (-6 -4436)) (-4438 . T) (-4437 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4440)) (|HasAttribute| |#1| (QUOTE -4441)) (|HasAttribute| |#1| (QUOTE -4436))) +((-4441 . T) (-4442 |has| |#1| (-6 -4442)) (-4437 |has| |#1| (-6 -4437)) (-4439 . T) (-4438 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasAttribute| |#1| (QUOTE -4442)) (|HasAttribute| |#1| (QUOTE -4437))) (-1297 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4436 |has| |#2| (-6 -4436)) (-4438 . T) (-4437 . T) (-4440 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4436))) +((-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4437))) (-1298 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL @@ -5134,7 +5134,7 @@ NIL NIL (-1301 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4445 "*") . T) (-4437 . T) (-4438 . T) (-4440 . T)) +(((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) NIL NIL NIL @@ -5152,4 +5152,4 @@ NIL NIL NIL NIL -((-3 NIL 2267533 2267538 2267543 2267548) (-2 NIL 2267513 2267518 2267523 2267528) (-1 NIL 2267493 2267498 2267503 2267508) (0 NIL 2267473 2267478 2267483 2267488) (-1301 "ZMOD.spad" 2267282 2267295 2267411 2267468) (-1300 "ZLINDEP.spad" 2266348 2266359 2267272 2267277) (-1299 "ZDSOLVE.spad" 2256293 2256315 2266338 2266343) (-1298 "YSTREAM.spad" 2255788 2255799 2256283 2256288) (-1297 "XRPOLY.spad" 2255008 2255028 2255644 2255713) (-1296 "XPR.spad" 2252803 2252816 2254726 2254825) (-1295 "XPOLY.spad" 2252358 2252369 2252659 2252728) (-1294 "XPOLYC.spad" 2251677 2251693 2252284 2252353) (-1293 "XPBWPOLY.spad" 2250114 2250134 2251457 2251526) (-1292 "XF.spad" 2248577 2248592 2250016 2250109) (-1291 "XF.spad" 2247020 2247037 2248461 2248466) (-1290 "XFALG.spad" 2244068 2244084 2246946 2247015) (-1289 "XEXPPKG.spad" 2243319 2243345 2244058 2244063) (-1288 "XDPOLY.spad" 2242933 2242949 2243175 2243244) (-1287 "XALG.spad" 2242593 2242604 2242889 2242928) (-1286 "WUTSET.spad" 2238432 2238449 2242239 2242266) (-1285 "WP.spad" 2237631 2237675 2238290 2238357) (-1284 "WHILEAST.spad" 2237429 2237438 2237621 2237626) (-1283 "WHEREAST.spad" 2237100 2237109 2237419 2237424) (-1282 "WFFINTBS.spad" 2234763 2234785 2237090 2237095) (-1281 "WEIER.spad" 2232985 2232996 2234753 2234758) (-1280 "VSPACE.spad" 2232658 2232669 2232953 2232980) (-1279 "VSPACE.spad" 2232351 2232364 2232648 2232653) (-1278 "VOID.spad" 2232028 2232037 2232341 2232346) (-1277 "VIEW.spad" 2229708 2229717 2232018 2232023) (-1276 "VIEWDEF.spad" 2224909 2224918 2229698 2229703) (-1275 "VIEW3D.spad" 2208870 2208879 2224899 2224904) (-1274 "VIEW2D.spad" 2196761 2196770 2208860 2208865) (-1273 "VECTOR.spad" 2195435 2195446 2195686 2195713) (-1272 "VECTOR2.spad" 2194074 2194087 2195425 2195430) (-1271 "VECTCAT.spad" 2191978 2191989 2194042 2194069) (-1270 "VECTCAT.spad" 2189689 2189702 2191755 2191760) (-1269 "VARIABLE.spad" 2189469 2189484 2189679 2189684) (-1268 "UTYPE.spad" 2189113 2189122 2189459 2189464) (-1267 "UTSODETL.spad" 2188408 2188432 2189069 2189074) (-1266 "UTSODE.spad" 2186624 2186644 2188398 2188403) (-1265 "UTS.spad" 2181428 2181456 2185091 2185188) (-1264 "UTSCAT.spad" 2178907 2178923 2181326 2181423) (-1263 "UTSCAT.spad" 2176030 2176048 2178451 2178456) (-1262 "UTS2.spad" 2175625 2175660 2176020 2176025) (-1261 "URAGG.spad" 2170298 2170309 2175615 2175620) (-1260 "URAGG.spad" 2164935 2164948 2170254 2170259) (-1259 "UPXSSING.spad" 2162580 2162606 2164016 2164149) (-1258 "UPXS.spad" 2159734 2159762 2160712 2160861) (-1257 "UPXSCONS.spad" 2157493 2157513 2157866 2158015) (-1256 "UPXSCCA.spad" 2156064 2156084 2157339 2157488) (-1255 "UPXSCCA.spad" 2154777 2154799 2156054 2156059) (-1254 "UPXSCAT.spad" 2153366 2153382 2154623 2154772) (-1253 "UPXS2.spad" 2152909 2152962 2153356 2153361) (-1252 "UPSQFREE.spad" 2151323 2151337 2152899 2152904) (-1251 "UPSCAT.spad" 2148934 2148958 2151221 2151318) (-1250 "UPSCAT.spad" 2146251 2146277 2148540 2148545) (-1249 "UPOLYC.spad" 2141291 2141302 2146093 2146246) (-1248 "UPOLYC.spad" 2136223 2136236 2141027 2141032) (-1247 "UPOLYC2.spad" 2135694 2135713 2136213 2136218) (-1246 "UP.spad" 2132893 2132908 2133280 2133433) (-1245 "UPMP.spad" 2131793 2131806 2132883 2132888) (-1244 "UPDIVP.spad" 2131358 2131372 2131783 2131788) (-1243 "UPDECOMP.spad" 2129603 2129617 2131348 2131353) (-1242 "UPCDEN.spad" 2128812 2128828 2129593 2129598) (-1241 "UP2.spad" 2128176 2128197 2128802 2128807) (-1240 "UNISEG.spad" 2127529 2127540 2128095 2128100) (-1239 "UNISEG2.spad" 2127026 2127039 2127485 2127490) (-1238 "UNIFACT.spad" 2126129 2126141 2127016 2127021) (-1237 "ULS.spad" 2116687 2116715 2117774 2118203) (-1236 "ULSCONS.spad" 2109083 2109103 2109453 2109602) (-1235 "ULSCCAT.spad" 2106820 2106840 2108929 2109078) (-1234 "ULSCCAT.spad" 2104665 2104687 2106776 2106781) (-1233 "ULSCAT.spad" 2102897 2102913 2104511 2104660) (-1232 "ULS2.spad" 2102411 2102464 2102887 2102892) (-1231 "UINT8.spad" 2102288 2102297 2102401 2102406) (-1230 "UINT64.spad" 2102164 2102173 2102278 2102283) (-1229 "UINT32.spad" 2102040 2102049 2102154 2102159) (-1228 "UINT16.spad" 2101916 2101925 2102030 2102035) (-1227 "UFD.spad" 2100981 2100990 2101842 2101911) (-1226 "UFD.spad" 2100108 2100119 2100971 2100976) (-1225 "UDVO.spad" 2098989 2098998 2100098 2100103) (-1224 "UDPO.spad" 2096482 2096493 2098945 2098950) (-1223 "TYPE.spad" 2096414 2096423 2096472 2096477) (-1222 "TYPEAST.spad" 2096333 2096342 2096404 2096409) (-1221 "TWOFACT.spad" 2094985 2095000 2096323 2096328) (-1220 "TUPLE.spad" 2094471 2094482 2094884 2094889) (-1219 "TUBETOOL.spad" 2091338 2091347 2094461 2094466) (-1218 "TUBE.spad" 2089985 2090002 2091328 2091333) (-1217 "TS.spad" 2088584 2088600 2089550 2089647) (-1216 "TSETCAT.spad" 2075711 2075728 2088552 2088579) (-1215 "TSETCAT.spad" 2062824 2062843 2075667 2075672) (-1214 "TRMANIP.spad" 2057190 2057207 2062530 2062535) (-1213 "TRIMAT.spad" 2056153 2056178 2057180 2057185) (-1212 "TRIGMNIP.spad" 2054680 2054697 2056143 2056148) (-1211 "TRIGCAT.spad" 2054192 2054201 2054670 2054675) (-1210 "TRIGCAT.spad" 2053702 2053713 2054182 2054187) (-1209 "TREE.spad" 2052277 2052288 2053309 2053336) (-1208 "TRANFUN.spad" 2052116 2052125 2052267 2052272) (-1207 "TRANFUN.spad" 2051953 2051964 2052106 2052111) (-1206 "TOPSP.spad" 2051627 2051636 2051943 2051948) (-1205 "TOOLSIGN.spad" 2051290 2051301 2051617 2051622) (-1204 "TEXTFILE.spad" 2049851 2049860 2051280 2051285) (-1203 "TEX.spad" 2046997 2047006 2049841 2049846) (-1202 "TEX1.spad" 2046553 2046564 2046987 2046992) (-1201 "TEMUTL.spad" 2046108 2046117 2046543 2046548) (-1200 "TBCMPPK.spad" 2044201 2044224 2046098 2046103) (-1199 "TBAGG.spad" 2043251 2043274 2044181 2044196) (-1198 "TBAGG.spad" 2042309 2042334 2043241 2043246) (-1197 "TANEXP.spad" 2041717 2041728 2042299 2042304) (-1196 "TABLE.spad" 2040128 2040151 2040398 2040425) (-1195 "TABLEAU.spad" 2039609 2039620 2040118 2040123) (-1194 "TABLBUMP.spad" 2036412 2036423 2039599 2039604) (-1193 "SYSTEM.spad" 2035640 2035649 2036402 2036407) (-1192 "SYSSOLP.spad" 2033123 2033134 2035630 2035635) (-1191 "SYSPTR.spad" 2033022 2033031 2033113 2033118) (-1190 "SYSNNI.spad" 2032204 2032215 2033012 2033017) (-1189 "SYSINT.spad" 2031608 2031619 2032194 2032199) (-1188 "SYNTAX.spad" 2027814 2027823 2031598 2031603) (-1187 "SYMTAB.spad" 2025882 2025891 2027804 2027809) (-1186 "SYMS.spad" 2021905 2021914 2025872 2025877) (-1185 "SYMPOLY.spad" 2020912 2020923 2020994 2021121) (-1184 "SYMFUNC.spad" 2020413 2020424 2020902 2020907) (-1183 "SYMBOL.spad" 2017916 2017925 2020403 2020408) (-1182 "SWITCH.spad" 2014687 2014696 2017906 2017911) (-1181 "SUTS.spad" 2011592 2011620 2013154 2013251) (-1180 "SUPXS.spad" 2008733 2008761 2009724 2009873) (-1179 "SUP.spad" 2005546 2005557 2006319 2006472) (-1178 "SUPFRACF.spad" 2004651 2004669 2005536 2005541) (-1177 "SUP2.spad" 2004043 2004056 2004641 2004646) (-1176 "SUMRF.spad" 2003017 2003028 2004033 2004038) (-1175 "SUMFS.spad" 2002654 2002671 2003007 2003012) (-1174 "SULS.spad" 1993199 1993227 1994299 1994728) (-1173 "SUCHTAST.spad" 1992968 1992977 1993189 1993194) (-1172 "SUCH.spad" 1992650 1992665 1992958 1992963) (-1171 "SUBSPACE.spad" 1984765 1984780 1992640 1992645) (-1170 "SUBRESP.spad" 1983935 1983949 1984721 1984726) (-1169 "STTF.spad" 1980034 1980050 1983925 1983930) (-1168 "STTFNC.spad" 1976502 1976518 1980024 1980029) (-1167 "STTAYLOR.spad" 1969137 1969148 1976383 1976388) (-1166 "STRTBL.spad" 1967642 1967659 1967791 1967818) (-1165 "STRING.spad" 1967051 1967060 1967065 1967092) (-1164 "STRICAT.spad" 1966839 1966848 1967019 1967046) (-1163 "STREAM.spad" 1963757 1963768 1966364 1966379) (-1162 "STREAM3.spad" 1963330 1963345 1963747 1963752) (-1161 "STREAM2.spad" 1962458 1962471 1963320 1963325) (-1160 "STREAM1.spad" 1962164 1962175 1962448 1962453) (-1159 "STINPROD.spad" 1961100 1961116 1962154 1962159) (-1158 "STEP.spad" 1960301 1960310 1961090 1961095) (-1157 "STEPAST.spad" 1959535 1959544 1960291 1960296) (-1156 "STBL.spad" 1958061 1958089 1958228 1958243) (-1155 "STAGG.spad" 1957136 1957147 1958051 1958056) (-1154 "STAGG.spad" 1956209 1956222 1957126 1957131) (-1153 "STACK.spad" 1955566 1955577 1955816 1955843) (-1152 "SREGSET.spad" 1953270 1953287 1955212 1955239) (-1151 "SRDCMPK.spad" 1951831 1951851 1953260 1953265) (-1150 "SRAGG.spad" 1946974 1946983 1951799 1951826) (-1149 "SRAGG.spad" 1942137 1942148 1946964 1946969) (-1148 "SQMATRIX.spad" 1939753 1939771 1940669 1940756) (-1147 "SPLTREE.spad" 1934305 1934318 1939189 1939216) (-1146 "SPLNODE.spad" 1930893 1930906 1934295 1934300) (-1145 "SPFCAT.spad" 1929702 1929711 1930883 1930888) (-1144 "SPECOUT.spad" 1928254 1928263 1929692 1929697) (-1143 "SPADXPT.spad" 1919849 1919858 1928244 1928249) (-1142 "spad-parser.spad" 1919314 1919323 1919839 1919844) (-1141 "SPADAST.spad" 1919015 1919024 1919304 1919309) (-1140 "SPACEC.spad" 1903214 1903225 1919005 1919010) (-1139 "SPACE3.spad" 1902990 1903001 1903204 1903209) (-1138 "SORTPAK.spad" 1902539 1902552 1902946 1902951) (-1137 "SOLVETRA.spad" 1900302 1900313 1902529 1902534) (-1136 "SOLVESER.spad" 1898830 1898841 1900292 1900297) (-1135 "SOLVERAD.spad" 1894856 1894867 1898820 1898825) (-1134 "SOLVEFOR.spad" 1893318 1893336 1894846 1894851) (-1133 "SNTSCAT.spad" 1892918 1892935 1893286 1893313) (-1132 "SMTS.spad" 1891190 1891216 1892483 1892580) (-1131 "SMP.spad" 1888665 1888685 1889055 1889182) (-1130 "SMITH.spad" 1887510 1887535 1888655 1888660) (-1129 "SMATCAT.spad" 1885620 1885650 1887454 1887505) (-1128 "SMATCAT.spad" 1883662 1883694 1885498 1885503) (-1127 "SKAGG.spad" 1882625 1882636 1883630 1883657) (-1126 "SINT.spad" 1881457 1881466 1882491 1882620) (-1125 "SIMPAN.spad" 1881185 1881194 1881447 1881452) (-1124 "SIG.spad" 1880515 1880524 1881175 1881180) (-1123 "SIGNRF.spad" 1879633 1879644 1880505 1880510) (-1122 "SIGNEF.spad" 1878912 1878929 1879623 1879628) (-1121 "SIGAST.spad" 1878297 1878306 1878902 1878907) (-1120 "SHP.spad" 1876225 1876240 1878253 1878258) (-1119 "SHDP.spad" 1865936 1865963 1866445 1866576) (-1118 "SGROUP.spad" 1865544 1865553 1865926 1865931) (-1117 "SGROUP.spad" 1865150 1865161 1865534 1865539) (-1116 "SGCF.spad" 1858313 1858322 1865140 1865145) (-1115 "SFRTCAT.spad" 1857243 1857260 1858281 1858308) (-1114 "SFRGCD.spad" 1856306 1856326 1857233 1857238) (-1113 "SFQCMPK.spad" 1850943 1850963 1856296 1856301) (-1112 "SFORT.spad" 1850382 1850396 1850933 1850938) (-1111 "SEXOF.spad" 1850225 1850265 1850372 1850377) (-1110 "SEX.spad" 1850117 1850126 1850215 1850220) (-1109 "SEXCAT.spad" 1847718 1847758 1850107 1850112) (-1108 "SET.spad" 1846042 1846053 1847139 1847178) (-1107 "SETMN.spad" 1844492 1844509 1846032 1846037) (-1106 "SETCAT.spad" 1843814 1843823 1844482 1844487) (-1105 "SETCAT.spad" 1843134 1843145 1843804 1843809) (-1104 "SETAGG.spad" 1839683 1839694 1843114 1843129) (-1103 "SETAGG.spad" 1836240 1836253 1839673 1839678) (-1102 "SEQAST.spad" 1835943 1835952 1836230 1836235) (-1101 "SEGXCAT.spad" 1835099 1835112 1835933 1835938) (-1100 "SEG.spad" 1834912 1834923 1835018 1835023) (-1099 "SEGCAT.spad" 1833837 1833848 1834902 1834907) (-1098 "SEGBIND.spad" 1833595 1833606 1833784 1833789) (-1097 "SEGBIND2.spad" 1833293 1833306 1833585 1833590) (-1096 "SEGAST.spad" 1833007 1833016 1833283 1833288) (-1095 "SEG2.spad" 1832442 1832455 1832963 1832968) (-1094 "SDVAR.spad" 1831718 1831729 1832432 1832437) (-1093 "SDPOL.spad" 1829144 1829155 1829435 1829562) (-1092 "SCPKG.spad" 1827233 1827244 1829134 1829139) (-1091 "SCOPE.spad" 1826386 1826395 1827223 1827228) (-1090 "SCACHE.spad" 1825082 1825093 1826376 1826381) (-1089 "SASTCAT.spad" 1824991 1825000 1825072 1825077) (-1088 "SAOS.spad" 1824863 1824872 1824981 1824986) (-1087 "SAERFFC.spad" 1824576 1824596 1824853 1824858) (-1086 "SAE.spad" 1822751 1822767 1823362 1823497) (-1085 "SAEFACT.spad" 1822452 1822472 1822741 1822746) (-1084 "RURPK.spad" 1820111 1820127 1822442 1822447) (-1083 "RULESET.spad" 1819564 1819588 1820101 1820106) (-1082 "RULE.spad" 1817804 1817828 1819554 1819559) (-1081 "RULECOLD.spad" 1817656 1817669 1817794 1817799) (-1080 "RTVALUE.spad" 1817391 1817400 1817646 1817651) (-1079 "RSTRCAST.spad" 1817108 1817117 1817381 1817386) (-1078 "RSETGCD.spad" 1813486 1813506 1817098 1817103) (-1077 "RSETCAT.spad" 1803422 1803439 1813454 1813481) (-1076 "RSETCAT.spad" 1793378 1793397 1803412 1803417) (-1075 "RSDCMPK.spad" 1791830 1791850 1793368 1793373) (-1074 "RRCC.spad" 1790214 1790244 1791820 1791825) (-1073 "RRCC.spad" 1788596 1788628 1790204 1790209) (-1072 "RPTAST.spad" 1788298 1788307 1788586 1788591) (-1071 "RPOLCAT.spad" 1767658 1767673 1788166 1788293) (-1070 "RPOLCAT.spad" 1746732 1746749 1767242 1767247) (-1069 "ROUTINE.spad" 1742615 1742624 1745379 1745406) (-1068 "ROMAN.spad" 1741943 1741952 1742481 1742610) (-1067 "ROIRC.spad" 1741023 1741055 1741933 1741938) (-1066 "RNS.spad" 1739926 1739935 1740925 1741018) (-1065 "RNS.spad" 1738915 1738926 1739916 1739921) (-1064 "RNG.spad" 1738650 1738659 1738905 1738910) (-1063 "RNGBIND.spad" 1737810 1737824 1738605 1738610) (-1062 "RMODULE.spad" 1737575 1737586 1737800 1737805) (-1061 "RMCAT2.spad" 1736995 1737052 1737565 1737570) (-1060 "RMATRIX.spad" 1735819 1735838 1736162 1736201) (-1059 "RMATCAT.spad" 1731398 1731429 1735775 1735814) (-1058 "RMATCAT.spad" 1726867 1726900 1731246 1731251) (-1057 "RLINSET.spad" 1726261 1726272 1726857 1726862) (-1056 "RINTERP.spad" 1726149 1726169 1726251 1726256) (-1055 "RING.spad" 1725619 1725628 1726129 1726144) (-1054 "RING.spad" 1725097 1725108 1725609 1725614) (-1053 "RIDIST.spad" 1724489 1724498 1725087 1725092) (-1052 "RGCHAIN.spad" 1723072 1723088 1723974 1724001) (-1051 "RGBCSPC.spad" 1722853 1722865 1723062 1723067) (-1050 "RGBCMDL.spad" 1722383 1722395 1722843 1722848) (-1049 "RF.spad" 1720025 1720036 1722373 1722378) (-1048 "RFFACTOR.spad" 1719487 1719498 1720015 1720020) (-1047 "RFFACT.spad" 1719222 1719234 1719477 1719482) (-1046 "RFDIST.spad" 1718218 1718227 1719212 1719217) (-1045 "RETSOL.spad" 1717637 1717650 1718208 1718213) (-1044 "RETRACT.spad" 1717065 1717076 1717627 1717632) (-1043 "RETRACT.spad" 1716491 1716504 1717055 1717060) (-1042 "RETAST.spad" 1716303 1716312 1716481 1716486) (-1041 "RESULT.spad" 1714363 1714372 1714950 1714977) (-1040 "RESRING.spad" 1713710 1713757 1714301 1714358) (-1039 "RESLATC.spad" 1713034 1713045 1713700 1713705) (-1038 "REPSQ.spad" 1712765 1712776 1713024 1713029) (-1037 "REP.spad" 1710319 1710328 1712755 1712760) (-1036 "REPDB.spad" 1710026 1710037 1710309 1710314) (-1035 "REP2.spad" 1699684 1699695 1709868 1709873) (-1034 "REP1.spad" 1693880 1693891 1699634 1699639) (-1033 "REGSET.spad" 1691677 1691694 1693526 1693553) (-1032 "REF.spad" 1691012 1691023 1691632 1691637) (-1031 "REDORDER.spad" 1690218 1690235 1691002 1691007) (-1030 "RECLOS.spad" 1689001 1689021 1689705 1689798) (-1029 "REALSOLV.spad" 1688141 1688150 1688991 1688996) (-1028 "REAL.spad" 1688013 1688022 1688131 1688136) (-1027 "REAL0Q.spad" 1685311 1685326 1688003 1688008) (-1026 "REAL0.spad" 1682155 1682170 1685301 1685306) (-1025 "RDUCEAST.spad" 1681876 1681885 1682145 1682150) (-1024 "RDIV.spad" 1681531 1681556 1681866 1681871) (-1023 "RDIST.spad" 1681098 1681109 1681521 1681526) (-1022 "RDETRS.spad" 1679962 1679980 1681088 1681093) (-1021 "RDETR.spad" 1678101 1678119 1679952 1679957) (-1020 "RDEEFS.spad" 1677200 1677217 1678091 1678096) (-1019 "RDEEF.spad" 1676210 1676227 1677190 1677195) (-1018 "RCFIELD.spad" 1673396 1673405 1676112 1676205) (-1017 "RCFIELD.spad" 1670668 1670679 1673386 1673391) (-1016 "RCAGG.spad" 1668596 1668607 1670658 1670663) (-1015 "RCAGG.spad" 1666451 1666464 1668515 1668520) (-1014 "RATRET.spad" 1665811 1665822 1666441 1666446) (-1013 "RATFACT.spad" 1665503 1665515 1665801 1665806) (-1012 "RANDSRC.spad" 1664822 1664831 1665493 1665498) (-1011 "RADUTIL.spad" 1664578 1664587 1664812 1664817) (-1010 "RADIX.spad" 1661499 1661513 1663045 1663138) (-1009 "RADFF.spad" 1659912 1659949 1660031 1660187) (-1008 "RADCAT.spad" 1659507 1659516 1659902 1659907) (-1007 "RADCAT.spad" 1659100 1659111 1659497 1659502) (-1006 "QUEUE.spad" 1658448 1658459 1658707 1658734) (-1005 "QUAT.spad" 1657029 1657040 1657372 1657437) (-1004 "QUATCT2.spad" 1656649 1656668 1657019 1657024) (-1003 "QUATCAT.spad" 1654819 1654830 1656579 1656644) (-1002 "QUATCAT.spad" 1652740 1652753 1654502 1654507) (-1001 "QUAGG.spad" 1651567 1651578 1652708 1652735) (-1000 "QQUTAST.spad" 1651335 1651344 1651557 1651562) (-999 "QFORM.spad" 1650800 1650814 1651325 1651330) (-998 "QFCAT.spad" 1649503 1649513 1650702 1650795) (-997 "QFCAT.spad" 1647797 1647809 1648998 1649003) (-996 "QFCAT2.spad" 1647490 1647506 1647787 1647792) (-995 "QEQUAT.spad" 1647049 1647057 1647480 1647485) (-994 "QCMPACK.spad" 1641796 1641815 1647039 1647044) (-993 "QALGSET.spad" 1637875 1637907 1641710 1641715) (-992 "QALGSET2.spad" 1635871 1635889 1637865 1637870) (-991 "PWFFINTB.spad" 1633287 1633308 1635861 1635866) (-990 "PUSHVAR.spad" 1632626 1632645 1633277 1633282) (-989 "PTRANFN.spad" 1628754 1628764 1632616 1632621) (-988 "PTPACK.spad" 1625842 1625852 1628744 1628749) (-987 "PTFUNC2.spad" 1625665 1625679 1625832 1625837) (-986 "PTCAT.spad" 1624920 1624930 1625633 1625660) (-985 "PSQFR.spad" 1624227 1624251 1624910 1624915) (-984 "PSEUDLIN.spad" 1623113 1623123 1624217 1624222) (-983 "PSETPK.spad" 1608546 1608562 1622991 1622996) (-982 "PSETCAT.spad" 1602466 1602489 1608526 1608541) (-981 "PSETCAT.spad" 1596360 1596385 1602422 1602427) (-980 "PSCURVE.spad" 1595343 1595351 1596350 1596355) (-979 "PSCAT.spad" 1594126 1594155 1595241 1595338) (-978 "PSCAT.spad" 1592999 1593030 1594116 1594121) (-977 "PRTITION.spad" 1591960 1591968 1592989 1592994) (-976 "PRTDAST.spad" 1591679 1591687 1591950 1591955) (-975 "PRS.spad" 1581241 1581258 1591635 1591640) (-974 "PRQAGG.spad" 1580676 1580686 1581209 1581236) (-973 "PROPLOG.spad" 1579975 1579983 1580666 1580671) (-972 "PROPFRML.spad" 1578543 1578554 1579965 1579970) (-971 "PROPERTY.spad" 1578031 1578039 1578533 1578538) (-970 "PRODUCT.spad" 1575713 1575725 1575997 1576052) (-969 "PR.spad" 1574105 1574117 1574804 1574931) (-968 "PRINT.spad" 1573857 1573865 1574095 1574100) (-967 "PRIMES.spad" 1572110 1572120 1573847 1573852) (-966 "PRIMELT.spad" 1570191 1570205 1572100 1572105) (-965 "PRIMCAT.spad" 1569818 1569826 1570181 1570186) (-964 "PRIMARR.spad" 1568823 1568833 1569001 1569028) (-963 "PRIMARR2.spad" 1567590 1567602 1568813 1568818) (-962 "PREASSOC.spad" 1566972 1566984 1567580 1567585) (-961 "PPCURVE.spad" 1566109 1566117 1566962 1566967) (-960 "PORTNUM.spad" 1565884 1565892 1566099 1566104) (-959 "POLYROOT.spad" 1564733 1564755 1565840 1565845) (-958 "POLY.spad" 1562068 1562078 1562583 1562710) (-957 "POLYLIFT.spad" 1561333 1561356 1562058 1562063) (-956 "POLYCATQ.spad" 1559451 1559473 1561323 1561328) (-955 "POLYCAT.spad" 1552921 1552942 1559319 1559446) (-954 "POLYCAT.spad" 1545729 1545752 1552129 1552134) (-953 "POLY2UP.spad" 1545181 1545195 1545719 1545724) (-952 "POLY2.spad" 1544778 1544790 1545171 1545176) (-951 "POLUTIL.spad" 1543719 1543748 1544734 1544739) (-950 "POLTOPOL.spad" 1542467 1542482 1543709 1543714) (-949 "POINT.spad" 1541305 1541315 1541392 1541419) (-948 "PNTHEORY.spad" 1538007 1538015 1541295 1541300) (-947 "PMTOOLS.spad" 1536782 1536796 1537997 1538002) (-946 "PMSYM.spad" 1536331 1536341 1536772 1536777) (-945 "PMQFCAT.spad" 1535922 1535936 1536321 1536326) (-944 "PMPRED.spad" 1535401 1535415 1535912 1535917) (-943 "PMPREDFS.spad" 1534855 1534877 1535391 1535396) (-942 "PMPLCAT.spad" 1533935 1533953 1534787 1534792) (-941 "PMLSAGG.spad" 1533520 1533534 1533925 1533930) (-940 "PMKERNEL.spad" 1533099 1533111 1533510 1533515) (-939 "PMINS.spad" 1532679 1532689 1533089 1533094) (-938 "PMFS.spad" 1532256 1532274 1532669 1532674) (-937 "PMDOWN.spad" 1531546 1531560 1532246 1532251) (-936 "PMASS.spad" 1530556 1530564 1531536 1531541) (-935 "PMASSFS.spad" 1529523 1529539 1530546 1530551) (-934 "PLOTTOOL.spad" 1529303 1529311 1529513 1529518) (-933 "PLOT.spad" 1524226 1524234 1529293 1529298) (-932 "PLOT3D.spad" 1520690 1520698 1524216 1524221) (-931 "PLOT1.spad" 1519847 1519857 1520680 1520685) (-930 "PLEQN.spad" 1507137 1507164 1519837 1519842) (-929 "PINTERP.spad" 1506759 1506778 1507127 1507132) (-928 "PINTERPA.spad" 1506543 1506559 1506749 1506754) (-927 "PI.spad" 1506152 1506160 1506517 1506538) (-926 "PID.spad" 1505122 1505130 1506078 1506147) (-925 "PICOERCE.spad" 1504779 1504789 1505112 1505117) (-924 "PGROEB.spad" 1503380 1503394 1504769 1504774) (-923 "PGE.spad" 1494997 1495005 1503370 1503375) (-922 "PGCD.spad" 1493887 1493904 1494987 1494992) (-921 "PFRPAC.spad" 1493036 1493046 1493877 1493882) (-920 "PFR.spad" 1489699 1489709 1492938 1493031) (-919 "PFOTOOLS.spad" 1488957 1488973 1489689 1489694) (-918 "PFOQ.spad" 1488327 1488345 1488947 1488952) (-917 "PFO.spad" 1487746 1487773 1488317 1488322) (-916 "PF.spad" 1487320 1487332 1487551 1487644) (-915 "PFECAT.spad" 1485002 1485010 1487246 1487315) (-914 "PFECAT.spad" 1482712 1482722 1484958 1484963) (-913 "PFBRU.spad" 1480600 1480612 1482702 1482707) (-912 "PFBR.spad" 1478160 1478183 1480590 1480595) (-911 "PERM.spad" 1473845 1473855 1477990 1478005) (-910 "PERMGRP.spad" 1468607 1468617 1473835 1473840) (-909 "PERMCAT.spad" 1467165 1467175 1468587 1468602) (-908 "PERMAN.spad" 1465697 1465711 1467155 1467160) (-907 "PENDTREE.spad" 1465038 1465048 1465326 1465331) (-906 "PDRING.spad" 1463589 1463599 1465018 1465033) (-905 "PDRING.spad" 1462148 1462160 1463579 1463584) (-904 "PDEPROB.spad" 1461163 1461171 1462138 1462143) (-903 "PDEPACK.spad" 1455203 1455211 1461153 1461158) (-902 "PDECOMP.spad" 1454673 1454690 1455193 1455198) (-901 "PDECAT.spad" 1453029 1453037 1454663 1454668) (-900 "PCOMP.spad" 1452882 1452895 1453019 1453024) (-899 "PBWLB.spad" 1451470 1451487 1452872 1452877) (-898 "PATTERN.spad" 1446009 1446019 1451460 1451465) (-897 "PATTERN2.spad" 1445747 1445759 1445999 1446004) (-896 "PATTERN1.spad" 1444083 1444099 1445737 1445742) (-895 "PATRES.spad" 1441658 1441670 1444073 1444078) (-894 "PATRES2.spad" 1441330 1441344 1441648 1441653) (-893 "PATMATCH.spad" 1439527 1439558 1441038 1441043) (-892 "PATMAB.spad" 1438956 1438966 1439517 1439522) (-891 "PATLRES.spad" 1438042 1438056 1438946 1438951) (-890 "PATAB.spad" 1437806 1437816 1438032 1438037) (-889 "PARTPERM.spad" 1435206 1435214 1437796 1437801) (-888 "PARSURF.spad" 1434640 1434668 1435196 1435201) (-887 "PARSU2.spad" 1434437 1434453 1434630 1434635) (-886 "script-parser.spad" 1433957 1433965 1434427 1434432) (-885 "PARSCURV.spad" 1433391 1433419 1433947 1433952) (-884 "PARSC2.spad" 1433182 1433198 1433381 1433386) (-883 "PARPCURV.spad" 1432644 1432672 1433172 1433177) (-882 "PARPC2.spad" 1432435 1432451 1432634 1432639) (-881 "PARAMAST.spad" 1431563 1431571 1432425 1432430) (-880 "PAN2EXPR.spad" 1430975 1430983 1431553 1431558) (-879 "PALETTE.spad" 1429945 1429953 1430965 1430970) (-878 "PAIR.spad" 1428932 1428945 1429533 1429538) (-877 "PADICRC.spad" 1426266 1426284 1427437 1427530) (-876 "PADICRAT.spad" 1424281 1424293 1424502 1424595) (-875 "PADIC.spad" 1423976 1423988 1424207 1424276) (-874 "PADICCT.spad" 1422525 1422537 1423902 1423971) (-873 "PADEPAC.spad" 1421214 1421233 1422515 1422520) (-872 "PADE.spad" 1419966 1419982 1421204 1421209) (-871 "OWP.spad" 1419206 1419236 1419824 1419891) (-870 "OVERSET.spad" 1418779 1418787 1419196 1419201) (-869 "OVAR.spad" 1418560 1418583 1418769 1418774) (-868 "OUT.spad" 1417646 1417654 1418550 1418555) (-867 "OUTFORM.spad" 1407038 1407046 1417636 1417641) (-866 "OUTBFILE.spad" 1406456 1406464 1407028 1407033) (-865 "OUTBCON.spad" 1405462 1405470 1406446 1406451) (-864 "OUTBCON.spad" 1404466 1404476 1405452 1405457) (-863 "OSI.spad" 1403941 1403949 1404456 1404461) (-862 "OSGROUP.spad" 1403859 1403867 1403931 1403936) (-861 "ORTHPOL.spad" 1402344 1402354 1403776 1403781) (-860 "OREUP.spad" 1401797 1401825 1402024 1402063) (-859 "ORESUP.spad" 1401098 1401122 1401477 1401516) (-858 "OREPCTO.spad" 1398955 1398967 1401018 1401023) (-857 "OREPCAT.spad" 1393102 1393112 1398911 1398950) (-856 "OREPCAT.spad" 1387139 1387151 1392950 1392955) (-855 "ORDSET.spad" 1386311 1386319 1387129 1387134) (-854 "ORDSET.spad" 1385481 1385491 1386301 1386306) (-853 "ORDRING.spad" 1384871 1384879 1385461 1385476) (-852 "ORDRING.spad" 1384269 1384279 1384861 1384866) (-851 "ORDMON.spad" 1384124 1384132 1384259 1384264) (-850 "ORDFUNS.spad" 1383256 1383272 1384114 1384119) (-849 "ORDFIN.spad" 1383076 1383084 1383246 1383251) (-848 "ORDCOMP.spad" 1381541 1381551 1382623 1382652) (-847 "ORDCOMP2.spad" 1380834 1380846 1381531 1381536) (-846 "OPTPROB.spad" 1379472 1379480 1380824 1380829) (-845 "OPTPACK.spad" 1371881 1371889 1379462 1379467) (-844 "OPTCAT.spad" 1369560 1369568 1371871 1371876) (-843 "OPSIG.spad" 1369214 1369222 1369550 1369555) (-842 "OPQUERY.spad" 1368763 1368771 1369204 1369209) (-841 "OP.spad" 1368505 1368515 1368585 1368652) (-840 "OPERCAT.spad" 1367971 1367981 1368495 1368500) (-839 "OPERCAT.spad" 1367435 1367447 1367961 1367966) (-838 "ONECOMP.spad" 1366180 1366190 1366982 1367011) (-837 "ONECOMP2.spad" 1365604 1365616 1366170 1366175) (-836 "OMSERVER.spad" 1364610 1364618 1365594 1365599) (-835 "OMSAGG.spad" 1364398 1364408 1364566 1364605) (-834 "OMPKG.spad" 1363014 1363022 1364388 1364393) (-833 "OM.spad" 1361987 1361995 1363004 1363009) (-832 "OMLO.spad" 1361412 1361424 1361873 1361912) (-831 "OMEXPR.spad" 1361246 1361256 1361402 1361407) (-830 "OMERR.spad" 1360791 1360799 1361236 1361241) (-829 "OMERRK.spad" 1359825 1359833 1360781 1360786) (-828 "OMENC.spad" 1359169 1359177 1359815 1359820) (-827 "OMDEV.spad" 1353478 1353486 1359159 1359164) (-826 "OMCONN.spad" 1352887 1352895 1353468 1353473) (-825 "OINTDOM.spad" 1352650 1352658 1352813 1352882) (-824 "OFMONOID.spad" 1350773 1350783 1352606 1352611) (-823 "ODVAR.spad" 1350034 1350044 1350763 1350768) (-822 "ODR.spad" 1349678 1349704 1349846 1349995) (-821 "ODPOL.spad" 1347060 1347070 1347400 1347527) (-820 "ODP.spad" 1336907 1336927 1337280 1337411) (-819 "ODETOOLS.spad" 1335556 1335575 1336897 1336902) (-818 "ODESYS.spad" 1333250 1333267 1335546 1335551) (-817 "ODERTRIC.spad" 1329259 1329276 1333207 1333212) (-816 "ODERED.spad" 1328658 1328682 1329249 1329254) (-815 "ODERAT.spad" 1326273 1326290 1328648 1328653) (-814 "ODEPRRIC.spad" 1323310 1323332 1326263 1326268) (-813 "ODEPROB.spad" 1322567 1322575 1323300 1323305) (-812 "ODEPRIM.spad" 1319901 1319923 1322557 1322562) (-811 "ODEPAL.spad" 1319287 1319311 1319891 1319896) (-810 "ODEPACK.spad" 1305953 1305961 1319277 1319282) (-809 "ODEINT.spad" 1305388 1305404 1305943 1305948) (-808 "ODEIFTBL.spad" 1302783 1302791 1305378 1305383) (-807 "ODEEF.spad" 1298274 1298290 1302773 1302778) (-806 "ODECONST.spad" 1297811 1297829 1298264 1298269) (-805 "ODECAT.spad" 1296409 1296417 1297801 1297806) (-804 "OCT.spad" 1294545 1294555 1295259 1295298) (-803 "OCTCT2.spad" 1294191 1294212 1294535 1294540) (-802 "OC.spad" 1291987 1291997 1294147 1294186) (-801 "OC.spad" 1289508 1289520 1291670 1291675) (-800 "OCAMON.spad" 1289356 1289364 1289498 1289503) (-799 "OASGP.spad" 1289171 1289179 1289346 1289351) (-798 "OAMONS.spad" 1288693 1288701 1289161 1289166) (-797 "OAMON.spad" 1288554 1288562 1288683 1288688) (-796 "OAGROUP.spad" 1288416 1288424 1288544 1288549) (-795 "NUMTUBE.spad" 1288007 1288023 1288406 1288411) (-794 "NUMQUAD.spad" 1275983 1275991 1287997 1288002) (-793 "NUMODE.spad" 1267337 1267345 1275973 1275978) (-792 "NUMINT.spad" 1264903 1264911 1267327 1267332) (-791 "NUMFMT.spad" 1263743 1263751 1264893 1264898) (-790 "NUMERIC.spad" 1255857 1255867 1263548 1263553) (-789 "NTSCAT.spad" 1254365 1254381 1255825 1255852) (-788 "NTPOLFN.spad" 1253916 1253926 1254282 1254287) (-787 "NSUP.spad" 1246962 1246972 1251502 1251655) (-786 "NSUP2.spad" 1246354 1246366 1246952 1246957) (-785 "NSMP.spad" 1242585 1242604 1242893 1243020) (-784 "NREP.spad" 1240963 1240977 1242575 1242580) (-783 "NPCOEF.spad" 1240209 1240229 1240953 1240958) (-782 "NORMRETR.spad" 1239807 1239846 1240199 1240204) (-781 "NORMPK.spad" 1237709 1237728 1239797 1239802) (-780 "NORMMA.spad" 1237397 1237423 1237699 1237704) (-779 "NONE.spad" 1237138 1237146 1237387 1237392) (-778 "NONE1.spad" 1236814 1236824 1237128 1237133) (-777 "NODE1.spad" 1236301 1236317 1236804 1236809) (-776 "NNI.spad" 1235196 1235204 1236275 1236296) (-775 "NLINSOL.spad" 1233822 1233832 1235186 1235191) (-774 "NIPROB.spad" 1232363 1232371 1233812 1233817) (-773 "NFINTBAS.spad" 1229923 1229940 1232353 1232358) (-772 "NETCLT.spad" 1229897 1229908 1229913 1229918) (-771 "NCODIV.spad" 1228113 1228129 1229887 1229892) (-770 "NCNTFRAC.spad" 1227755 1227769 1228103 1228108) (-769 "NCEP.spad" 1225921 1225935 1227745 1227750) (-768 "NASRING.spad" 1225517 1225525 1225911 1225916) (-767 "NASRING.spad" 1225111 1225121 1225507 1225512) (-766 "NARNG.spad" 1224463 1224471 1225101 1225106) (-765 "NARNG.spad" 1223813 1223823 1224453 1224458) (-764 "NAGSP.spad" 1222890 1222898 1223803 1223808) (-763 "NAGS.spad" 1212551 1212559 1222880 1222885) (-762 "NAGF07.spad" 1210982 1210990 1212541 1212546) (-761 "NAGF04.spad" 1205384 1205392 1210972 1210977) (-760 "NAGF02.spad" 1199453 1199461 1205374 1205379) (-759 "NAGF01.spad" 1195214 1195222 1199443 1199448) (-758 "NAGE04.spad" 1188914 1188922 1195204 1195209) (-757 "NAGE02.spad" 1179574 1179582 1188904 1188909) (-756 "NAGE01.spad" 1175576 1175584 1179564 1179569) (-755 "NAGD03.spad" 1173580 1173588 1175566 1175571) (-754 "NAGD02.spad" 1166327 1166335 1173570 1173575) (-753 "NAGD01.spad" 1160620 1160628 1166317 1166322) (-752 "NAGC06.spad" 1156495 1156503 1160610 1160615) (-751 "NAGC05.spad" 1154996 1155004 1156485 1156490) (-750 "NAGC02.spad" 1154263 1154271 1154986 1154991) (-749 "NAALG.spad" 1153804 1153814 1154231 1154258) (-748 "NAALG.spad" 1153365 1153377 1153794 1153799) (-747 "MULTSQFR.spad" 1150323 1150340 1153355 1153360) (-746 "MULTFACT.spad" 1149706 1149723 1150313 1150318) (-745 "MTSCAT.spad" 1147800 1147821 1149604 1149701) (-744 "MTHING.spad" 1147459 1147469 1147790 1147795) (-743 "MSYSCMD.spad" 1146893 1146901 1147449 1147454) (-742 "MSET.spad" 1144851 1144861 1146599 1146638) (-741 "MSETAGG.spad" 1144696 1144706 1144819 1144846) (-740 "MRING.spad" 1141673 1141685 1144404 1144471) (-739 "MRF2.spad" 1141243 1141257 1141663 1141668) (-738 "MRATFAC.spad" 1140789 1140806 1141233 1141238) (-737 "MPRFF.spad" 1138829 1138848 1140779 1140784) (-736 "MPOLY.spad" 1136300 1136315 1136659 1136786) (-735 "MPCPF.spad" 1135564 1135583 1136290 1136295) (-734 "MPC3.spad" 1135381 1135421 1135554 1135559) (-733 "MPC2.spad" 1135027 1135060 1135371 1135376) (-732 "MONOTOOL.spad" 1133378 1133395 1135017 1135022) (-731 "MONOID.spad" 1132697 1132705 1133368 1133373) (-730 "MONOID.spad" 1132014 1132024 1132687 1132692) (-729 "MONOGEN.spad" 1130762 1130775 1131874 1132009) (-728 "MONOGEN.spad" 1129532 1129547 1130646 1130651) (-727 "MONADWU.spad" 1127562 1127570 1129522 1129527) (-726 "MONADWU.spad" 1125590 1125600 1127552 1127557) (-725 "MONAD.spad" 1124750 1124758 1125580 1125585) (-724 "MONAD.spad" 1123908 1123918 1124740 1124745) (-723 "MOEBIUS.spad" 1122644 1122658 1123888 1123903) (-722 "MODULE.spad" 1122514 1122524 1122612 1122639) (-721 "MODULE.spad" 1122404 1122416 1122504 1122509) (-720 "MODRING.spad" 1121739 1121778 1122384 1122399) (-719 "MODOP.spad" 1120404 1120416 1121561 1121628) (-718 "MODMONOM.spad" 1120135 1120153 1120394 1120399) (-717 "MODMON.spad" 1116930 1116946 1117649 1117802) (-716 "MODFIELD.spad" 1116292 1116331 1116832 1116925) (-715 "MMLFORM.spad" 1115152 1115160 1116282 1116287) (-714 "MMAP.spad" 1114894 1114928 1115142 1115147) (-713 "MLO.spad" 1113353 1113363 1114850 1114889) (-712 "MLIFT.spad" 1111965 1111982 1113343 1113348) (-711 "MKUCFUNC.spad" 1111500 1111518 1111955 1111960) (-710 "MKRECORD.spad" 1111104 1111117 1111490 1111495) (-709 "MKFUNC.spad" 1110511 1110521 1111094 1111099) (-708 "MKFLCFN.spad" 1109479 1109489 1110501 1110506) (-707 "MKBCFUNC.spad" 1108974 1108992 1109469 1109474) (-706 "MINT.spad" 1108413 1108421 1108876 1108969) (-705 "MHROWRED.spad" 1106924 1106934 1108403 1108408) (-704 "MFLOAT.spad" 1105444 1105452 1106814 1106919) (-703 "MFINFACT.spad" 1104844 1104866 1105434 1105439) (-702 "MESH.spad" 1102626 1102634 1104834 1104839) (-701 "MDDFACT.spad" 1100837 1100847 1102616 1102621) (-700 "MDAGG.spad" 1100128 1100138 1100817 1100832) (-699 "MCMPLX.spad" 1096139 1096147 1096753 1096954) (-698 "MCDEN.spad" 1095349 1095361 1096129 1096134) (-697 "MCALCFN.spad" 1092471 1092497 1095339 1095344) (-696 "MAYBE.spad" 1091755 1091766 1092461 1092466) (-695 "MATSTOR.spad" 1089063 1089073 1091745 1091750) (-694 "MATRIX.spad" 1087767 1087777 1088251 1088278) (-693 "MATLIN.spad" 1085111 1085135 1087651 1087656) (-692 "MATCAT.spad" 1076840 1076862 1085079 1085106) (-691 "MATCAT.spad" 1068441 1068465 1076682 1076687) (-690 "MATCAT2.spad" 1067723 1067771 1068431 1068436) (-689 "MAPPKG3.spad" 1066638 1066652 1067713 1067718) (-688 "MAPPKG2.spad" 1065976 1065988 1066628 1066633) (-687 "MAPPKG1.spad" 1064804 1064814 1065966 1065971) (-686 "MAPPAST.spad" 1064119 1064127 1064794 1064799) (-685 "MAPHACK3.spad" 1063931 1063945 1064109 1064114) (-684 "MAPHACK2.spad" 1063700 1063712 1063921 1063926) (-683 "MAPHACK1.spad" 1063344 1063354 1063690 1063695) (-682 "MAGMA.spad" 1061134 1061151 1063334 1063339) (-681 "MACROAST.spad" 1060713 1060721 1061124 1061129) (-680 "M3D.spad" 1058433 1058443 1060091 1060096) (-679 "LZSTAGG.spad" 1055671 1055681 1058423 1058428) (-678 "LZSTAGG.spad" 1052907 1052919 1055661 1055666) (-677 "LWORD.spad" 1049612 1049629 1052897 1052902) (-676 "LSTAST.spad" 1049396 1049404 1049602 1049607) (-675 "LSQM.spad" 1047626 1047640 1048020 1048071) (-674 "LSPP.spad" 1047161 1047178 1047616 1047621) (-673 "LSMP.spad" 1046011 1046039 1047151 1047156) (-672 "LSMP1.spad" 1043829 1043843 1046001 1046006) (-671 "LSAGG.spad" 1043498 1043508 1043797 1043824) (-670 "LSAGG.spad" 1043187 1043199 1043488 1043493) (-669 "LPOLY.spad" 1042141 1042160 1043043 1043112) (-668 "LPEFRAC.spad" 1041412 1041422 1042131 1042136) (-667 "LO.spad" 1040813 1040827 1041346 1041373) (-666 "LOGIC.spad" 1040415 1040423 1040803 1040808) (-665 "LOGIC.spad" 1040015 1040025 1040405 1040410) (-664 "LODOOPS.spad" 1038945 1038957 1040005 1040010) (-663 "LODO.spad" 1038329 1038345 1038625 1038664) (-662 "LODOF.spad" 1037375 1037392 1038286 1038291) (-661 "LODOCAT.spad" 1036041 1036051 1037331 1037370) (-660 "LODOCAT.spad" 1034705 1034717 1035997 1036002) (-659 "LODO2.spad" 1033978 1033990 1034385 1034424) (-658 "LODO1.spad" 1033378 1033388 1033658 1033697) (-657 "LODEEF.spad" 1032180 1032198 1033368 1033373) (-656 "LNAGG.spad" 1028012 1028022 1032170 1032175) (-655 "LNAGG.spad" 1023808 1023820 1027968 1027973) (-654 "LMOPS.spad" 1020576 1020593 1023798 1023803) (-653 "LMODULE.spad" 1020344 1020354 1020566 1020571) (-652 "LMDICT.spad" 1019631 1019641 1019895 1019922) (-651 "LLINSET.spad" 1019028 1019038 1019621 1019626) (-650 "LITERAL.spad" 1018934 1018945 1019018 1019023) (-649 "LIST.spad" 1016669 1016679 1018081 1018108) (-648 "LIST3.spad" 1015980 1015994 1016659 1016664) (-647 "LIST2.spad" 1014682 1014694 1015970 1015975) (-646 "LIST2MAP.spad" 1011585 1011597 1014672 1014677) (-645 "LINSET.spad" 1011207 1011217 1011575 1011580) (-644 "LINEXP.spad" 1010641 1010651 1011187 1011202) (-643 "LINDEP.spad" 1009450 1009462 1010553 1010558) (-642 "LIMITRF.spad" 1007378 1007388 1009440 1009445) (-641 "LIMITPS.spad" 1006281 1006294 1007368 1007373) (-640 "LIE.spad" 1004297 1004309 1005571 1005716) (-639 "LIECAT.spad" 1003773 1003783 1004223 1004292) (-638 "LIECAT.spad" 1003277 1003289 1003729 1003734) (-637 "LIB.spad" 1001327 1001335 1001936 1001951) (-636 "LGROBP.spad" 998680 998699 1001317 1001322) (-635 "LF.spad" 997635 997651 998670 998675) (-634 "LFCAT.spad" 996694 996702 997625 997630) (-633 "LEXTRIPK.spad" 992197 992212 996684 996689) (-632 "LEXP.spad" 990200 990227 992177 992192) (-631 "LETAST.spad" 989899 989907 990190 990195) (-630 "LEADCDET.spad" 988297 988314 989889 989894) (-629 "LAZM3PK.spad" 987001 987023 988287 988292) (-628 "LAUPOL.spad" 985694 985707 986594 986663) (-627 "LAPLACE.spad" 985277 985293 985684 985689) (-626 "LA.spad" 984717 984731 985199 985238) (-625 "LALG.spad" 984493 984503 984697 984712) (-624 "LALG.spad" 984277 984289 984483 984488) (-623 "KVTFROM.spad" 984012 984022 984267 984272) (-622 "KTVLOGIC.spad" 983524 983532 984002 984007) (-621 "KRCFROM.spad" 983262 983272 983514 983519) (-620 "KOVACIC.spad" 981985 982002 983252 983257) (-619 "KONVERT.spad" 981707 981717 981975 981980) (-618 "KOERCE.spad" 981444 981454 981697 981702) (-617 "KERNEL.spad" 980099 980109 981228 981233) (-616 "KERNEL2.spad" 979802 979814 980089 980094) (-615 "KDAGG.spad" 978911 978933 979782 979797) (-614 "KDAGG.spad" 978028 978052 978901 978906) (-613 "KAFILE.spad" 976991 977007 977226 977253) (-612 "JORDAN.spad" 974820 974832 976281 976426) (-611 "JOINAST.spad" 974514 974522 974810 974815) (-610 "JAVACODE.spad" 974380 974388 974504 974509) (-609 "IXAGG.spad" 972513 972537 974370 974375) (-608 "IXAGG.spad" 970501 970527 972360 972365) (-607 "IVECTOR.spad" 969271 969286 969426 969453) (-606 "ITUPLE.spad" 968432 968442 969261 969266) (-605 "ITRIGMNP.spad" 967271 967290 968422 968427) (-604 "ITFUN3.spad" 966777 966791 967261 967266) (-603 "ITFUN2.spad" 966521 966533 966767 966772) (-602 "ITFORM.spad" 965876 965884 966511 966516) (-601 "ITAYLOR.spad" 963870 963885 965740 965837) (-600 "ISUPS.spad" 956307 956322 962844 962941) (-599 "ISUMP.spad" 955808 955824 956297 956302) (-598 "ISTRING.spad" 954896 954909 954977 955004) (-597 "ISAST.spad" 954615 954623 954886 954891) (-596 "IRURPK.spad" 953332 953351 954605 954610) (-595 "IRSN.spad" 951336 951344 953322 953327) (-594 "IRRF2F.spad" 949821 949831 951292 951297) (-593 "IRREDFFX.spad" 949422 949433 949811 949816) (-592 "IROOT.spad" 947761 947771 949412 949417) (-591 "IR.spad" 945562 945576 947616 947643) (-590 "IRFORM.spad" 944886 944894 945552 945557) (-589 "IR2.spad" 943914 943930 944876 944881) (-588 "IR2F.spad" 943120 943136 943904 943909) (-587 "IPRNTPK.spad" 942880 942888 943110 943115) (-586 "IPF.spad" 942445 942457 942685 942778) (-585 "IPADIC.spad" 942206 942232 942371 942440) (-584 "IP4ADDR.spad" 941763 941771 942196 942201) (-583 "IOMODE.spad" 941384 941392 941753 941758) (-582 "IOBFILE.spad" 940745 940753 941374 941379) (-581 "IOBCON.spad" 940610 940618 940735 940740) (-580 "INVLAPLA.spad" 940259 940275 940600 940605) (-579 "INTTR.spad" 933641 933658 940249 940254) (-578 "INTTOOLS.spad" 931396 931412 933215 933220) (-577 "INTSLPE.spad" 930716 930724 931386 931391) (-576 "INTRVL.spad" 930282 930292 930630 930711) (-575 "INTRF.spad" 928706 928720 930272 930277) (-574 "INTRET.spad" 928138 928148 928696 928701) (-573 "INTRAT.spad" 926865 926882 928128 928133) (-572 "INTPM.spad" 925250 925266 926508 926513) (-571 "INTPAF.spad" 923114 923132 925182 925187) (-570 "INTPACK.spad" 913488 913496 923104 923109) (-569 "INT.spad" 912936 912944 913342 913483) (-568 "INTHERTR.spad" 912210 912227 912926 912931) (-567 "INTHERAL.spad" 911880 911904 912200 912205) (-566 "INTHEORY.spad" 908319 908327 911870 911875) (-565 "INTG0.spad" 902052 902070 908251 908256) (-564 "INTFTBL.spad" 896081 896089 902042 902047) (-563 "INTFACT.spad" 895140 895150 896071 896076) (-562 "INTEF.spad" 893525 893541 895130 895135) (-561 "INTDOM.spad" 892148 892156 893451 893520) (-560 "INTDOM.spad" 890833 890843 892138 892143) (-559 "INTCAT.spad" 889092 889102 890747 890828) (-558 "INTBIT.spad" 888599 888607 889082 889087) (-557 "INTALG.spad" 887787 887814 888589 888594) (-556 "INTAF.spad" 887287 887303 887777 887782) (-555 "INTABL.spad" 885805 885836 885968 885995) (-554 "INT8.spad" 885685 885693 885795 885800) (-553 "INT64.spad" 885564 885572 885675 885680) (-552 "INT32.spad" 885443 885451 885554 885559) (-551 "INT16.spad" 885322 885330 885433 885438) (-550 "INS.spad" 882825 882833 885224 885317) (-549 "INS.spad" 880414 880424 882815 882820) (-548 "INPSIGN.spad" 879862 879875 880404 880409) (-547 "INPRODPF.spad" 878958 878977 879852 879857) (-546 "INPRODFF.spad" 878046 878070 878948 878953) (-545 "INNMFACT.spad" 877021 877038 878036 878041) (-544 "INMODGCD.spad" 876509 876539 877011 877016) (-543 "INFSP.spad" 874806 874828 876499 876504) (-542 "INFPROD0.spad" 873886 873905 874796 874801) (-541 "INFORM.spad" 871085 871093 873876 873881) (-540 "INFORM1.spad" 870710 870720 871075 871080) (-539 "INFINITY.spad" 870262 870270 870700 870705) (-538 "INETCLTS.spad" 870239 870247 870252 870257) (-537 "INEP.spad" 868777 868799 870229 870234) (-536 "INDE.spad" 868506 868523 868767 868772) (-535 "INCRMAPS.spad" 867927 867937 868496 868501) (-534 "INBFILE.spad" 866999 867007 867917 867922) (-533 "INBFF.spad" 862793 862804 866989 866994) (-532 "INBCON.spad" 861083 861091 862783 862788) (-531 "INBCON.spad" 859371 859381 861073 861078) (-530 "INAST.spad" 859032 859040 859361 859366) (-529 "IMPTAST.spad" 858740 858748 859022 859027) (-528 "IMATRIX.spad" 857685 857711 858197 858224) (-527 "IMATQF.spad" 856779 856823 857641 857646) (-526 "IMATLIN.spad" 855384 855408 856735 856740) (-525 "ILIST.spad" 854042 854057 854567 854594) (-524 "IIARRAY2.spad" 853430 853468 853649 853676) (-523 "IFF.spad" 852840 852856 853111 853204) (-522 "IFAST.spad" 852454 852462 852830 852835) (-521 "IFARRAY.spad" 849947 849962 851637 851664) (-520 "IFAMON.spad" 849809 849826 849903 849908) (-519 "IEVALAB.spad" 849214 849226 849799 849804) (-518 "IEVALAB.spad" 848617 848631 849204 849209) (-517 "IDPO.spad" 848415 848427 848607 848612) (-516 "IDPOAMS.spad" 848171 848183 848405 848410) (-515 "IDPOAM.spad" 847891 847903 848161 848166) (-514 "IDPC.spad" 846829 846841 847881 847886) (-513 "IDPAM.spad" 846574 846586 846819 846824) (-512 "IDPAG.spad" 846321 846333 846564 846569) (-511 "IDENT.spad" 845971 845979 846311 846316) (-510 "IDECOMP.spad" 843210 843228 845961 845966) (-509 "IDEAL.spad" 838159 838198 843145 843150) (-508 "ICDEN.spad" 837348 837364 838149 838154) (-507 "ICARD.spad" 836539 836547 837338 837343) (-506 "IBPTOOLS.spad" 835146 835163 836529 836534) (-505 "IBITS.spad" 834349 834362 834782 834809) (-504 "IBATOOL.spad" 831326 831345 834339 834344) (-503 "IBACHIN.spad" 829833 829848 831316 831321) (-502 "IARRAY2.spad" 828821 828847 829440 829467) (-501 "IARRAY1.spad" 827866 827881 828004 828031) (-500 "IAN.spad" 826089 826097 827682 827775) (-499 "IALGFACT.spad" 825692 825725 826079 826084) (-498 "HYPCAT.spad" 825116 825124 825682 825687) (-497 "HYPCAT.spad" 824538 824548 825106 825111) (-496 "HOSTNAME.spad" 824346 824354 824528 824533) (-495 "HOMOTOP.spad" 824089 824099 824336 824341) (-494 "HOAGG.spad" 821371 821381 824079 824084) (-493 "HOAGG.spad" 818428 818440 821138 821143) (-492 "HEXADEC.spad" 816530 816538 816895 816988) (-491 "HEUGCD.spad" 815565 815576 816520 816525) (-490 "HELLFDIV.spad" 815155 815179 815555 815560) (-489 "HEAP.spad" 814547 814557 814762 814789) (-488 "HEADAST.spad" 814080 814088 814537 814542) (-487 "HDP.spad" 803923 803939 804300 804431) (-486 "HDMP.spad" 801137 801152 801753 801880) (-485 "HB.spad" 799388 799396 801127 801132) (-484 "HASHTBL.spad" 797858 797889 798069 798096) (-483 "HASAST.spad" 797574 797582 797848 797853) (-482 "HACKPI.spad" 797065 797073 797476 797569) (-481 "GTSET.spad" 796004 796020 796711 796738) (-480 "GSTBL.spad" 794523 794558 794697 794712) (-479 "GSERIES.spad" 791694 791721 792655 792804) (-478 "GROUP.spad" 790967 790975 791674 791689) (-477 "GROUP.spad" 790248 790258 790957 790962) (-476 "GROEBSOL.spad" 788742 788763 790238 790243) (-475 "GRMOD.spad" 787313 787325 788732 788737) (-474 "GRMOD.spad" 785882 785896 787303 787308) (-473 "GRIMAGE.spad" 778771 778779 785872 785877) (-472 "GRDEF.spad" 777150 777158 778761 778766) (-471 "GRAY.spad" 775613 775621 777140 777145) (-470 "GRALG.spad" 774690 774702 775603 775608) (-469 "GRALG.spad" 773765 773779 774680 774685) (-468 "GPOLSET.spad" 773219 773242 773447 773474) (-467 "GOSPER.spad" 772488 772506 773209 773214) (-466 "GMODPOL.spad" 771636 771663 772456 772483) (-465 "GHENSEL.spad" 770719 770733 771626 771631) (-464 "GENUPS.spad" 767012 767025 770709 770714) (-463 "GENUFACT.spad" 766589 766599 767002 767007) (-462 "GENPGCD.spad" 766175 766192 766579 766584) (-461 "GENMFACT.spad" 765627 765646 766165 766170) (-460 "GENEEZ.spad" 763578 763591 765617 765622) (-459 "GDMP.spad" 760634 760651 761408 761535) (-458 "GCNAALG.spad" 754557 754584 760428 760495) (-457 "GCDDOM.spad" 753733 753741 754483 754552) (-456 "GCDDOM.spad" 752971 752981 753723 753728) (-455 "GB.spad" 750497 750535 752927 752932) (-454 "GBINTERN.spad" 746517 746555 750487 750492) (-453 "GBF.spad" 742284 742322 746507 746512) (-452 "GBEUCLID.spad" 740166 740204 742274 742279) (-451 "GAUSSFAC.spad" 739479 739487 740156 740161) (-450 "GALUTIL.spad" 737805 737815 739435 739440) (-449 "GALPOLYU.spad" 736259 736272 737795 737800) (-448 "GALFACTU.spad" 734432 734451 736249 736254) (-447 "GALFACT.spad" 724621 724632 734422 734427) (-446 "FVFUN.spad" 721644 721652 724611 724616) (-445 "FVC.spad" 720696 720704 721634 721639) (-444 "FUNDESC.spad" 720374 720382 720686 720691) (-443 "FUNCTION.spad" 720223 720235 720364 720369) (-442 "FT.spad" 718520 718528 720213 720218) (-441 "FTEM.spad" 717685 717693 718510 718515) (-440 "FSUPFACT.spad" 716585 716604 717621 717626) (-439 "FST.spad" 714671 714679 716575 716580) (-438 "FSRED.spad" 714151 714167 714661 714666) (-437 "FSPRMELT.spad" 713033 713049 714108 714113) (-436 "FSPECF.spad" 711124 711140 713023 713028) (-435 "FS.spad" 705392 705402 710899 711119) (-434 "FS.spad" 699438 699450 704947 704952) (-433 "FSINT.spad" 699098 699114 699428 699433) (-432 "FSERIES.spad" 698289 698301 698918 699017) (-431 "FSCINT.spad" 697606 697622 698279 698284) (-430 "FSAGG.spad" 696723 696733 697562 697601) (-429 "FSAGG.spad" 695802 695814 696643 696648) (-428 "FSAGG2.spad" 694545 694561 695792 695797) (-427 "FS2UPS.spad" 689036 689070 694535 694540) (-426 "FS2.spad" 688683 688699 689026 689031) (-425 "FS2EXPXP.spad" 687808 687831 688673 688678) (-424 "FRUTIL.spad" 686762 686772 687798 687803) (-423 "FR.spad" 680478 680488 685786 685855) (-422 "FRNAALG.spad" 675597 675607 680420 680473) (-421 "FRNAALG.spad" 670728 670740 675553 675558) (-420 "FRNAAF2.spad" 670184 670202 670718 670723) (-419 "FRMOD.spad" 669594 669624 670115 670120) (-418 "FRIDEAL.spad" 668819 668840 669574 669589) (-417 "FRIDEAL2.spad" 668423 668455 668809 668814) (-416 "FRETRCT.spad" 667934 667944 668413 668418) (-415 "FRETRCT.spad" 667311 667323 667792 667797) (-414 "FRAMALG.spad" 665659 665672 667267 667306) (-413 "FRAMALG.spad" 664039 664054 665649 665654) (-412 "FRAC.spad" 661138 661148 661541 661714) (-411 "FRAC2.spad" 660743 660755 661128 661133) (-410 "FR2.spad" 660079 660091 660733 660738) (-409 "FPS.spad" 656894 656902 659969 660074) (-408 "FPS.spad" 653737 653747 656814 656819) (-407 "FPC.spad" 652783 652791 653639 653732) (-406 "FPC.spad" 651915 651925 652773 652778) (-405 "FPATMAB.spad" 651677 651687 651905 651910) (-404 "FPARFRAC.spad" 650164 650181 651667 651672) (-403 "FORTRAN.spad" 648670 648713 650154 650159) (-402 "FORT.spad" 647619 647627 648660 648665) (-401 "FORTFN.spad" 644789 644797 647609 647614) (-400 "FORTCAT.spad" 644473 644481 644779 644784) (-399 "FORMULA.spad" 641947 641955 644463 644468) (-398 "FORMULA1.spad" 641426 641436 641937 641942) (-397 "FORDER.spad" 641117 641141 641416 641421) (-396 "FOP.spad" 640318 640326 641107 641112) (-395 "FNLA.spad" 639742 639764 640286 640313) (-394 "FNCAT.spad" 638337 638345 639732 639737) (-393 "FNAME.spad" 638229 638237 638327 638332) (-392 "FMTC.spad" 638027 638035 638155 638224) (-391 "FMONOID.spad" 637692 637702 637983 637988) (-390 "FMONCAT.spad" 634845 634855 637682 637687) (-389 "FM.spad" 634540 634552 634779 634806) (-388 "FMFUN.spad" 631570 631578 634530 634535) (-387 "FMC.spad" 630622 630630 631560 631565) (-386 "FMCAT.spad" 628290 628308 630590 630617) (-385 "FM1.spad" 627647 627659 628224 628251) (-384 "FLOATRP.spad" 625382 625396 627637 627642) (-383 "FLOAT.spad" 618696 618704 625248 625377) (-382 "FLOATCP.spad" 616127 616141 618686 618691) (-381 "FLINEXP.spad" 615839 615849 616107 616122) (-380 "FLINEXP.spad" 615505 615517 615775 615780) (-379 "FLASORT.spad" 614831 614843 615495 615500) (-378 "FLALG.spad" 612477 612496 614757 614826) (-377 "FLAGG.spad" 609519 609529 612457 612472) (-376 "FLAGG.spad" 606462 606474 609402 609407) (-375 "FLAGG2.spad" 605187 605203 606452 606457) (-374 "FINRALG.spad" 603248 603261 605143 605182) (-373 "FINRALG.spad" 601235 601250 603132 603137) (-372 "FINITE.spad" 600387 600395 601225 601230) (-371 "FINAALG.spad" 589508 589518 600329 600382) (-370 "FINAALG.spad" 578641 578653 589464 589469) (-369 "FILE.spad" 578224 578234 578631 578636) (-368 "FILECAT.spad" 576750 576767 578214 578219) (-367 "FIELD.spad" 576156 576164 576652 576745) (-366 "FIELD.spad" 575648 575658 576146 576151) (-365 "FGROUP.spad" 574295 574305 575628 575643) (-364 "FGLMICPK.spad" 573082 573097 574285 574290) (-363 "FFX.spad" 572457 572472 572798 572891) (-362 "FFSLPE.spad" 571960 571981 572447 572452) (-361 "FFPOLY.spad" 563222 563233 571950 571955) (-360 "FFPOLY2.spad" 562282 562299 563212 563217) (-359 "FFP.spad" 561679 561699 561998 562091) (-358 "FF.spad" 561127 561143 561360 561453) (-357 "FFNBX.spad" 559639 559659 560843 560936) (-356 "FFNBP.spad" 558152 558169 559355 559448) (-355 "FFNB.spad" 556617 556638 557833 557926) (-354 "FFINTBAS.spad" 554131 554150 556607 556612) (-353 "FFIELDC.spad" 551708 551716 554033 554126) (-352 "FFIELDC.spad" 549371 549381 551698 551703) (-351 "FFHOM.spad" 548119 548136 549361 549366) (-350 "FFF.spad" 545554 545565 548109 548114) (-349 "FFCGX.spad" 544401 544421 545270 545363) (-348 "FFCGP.spad" 543290 543310 544117 544210) (-347 "FFCG.spad" 542082 542103 542971 543064) (-346 "FFCAT.spad" 535255 535277 541921 542077) (-345 "FFCAT.spad" 528507 528531 535175 535180) (-344 "FFCAT2.spad" 528254 528294 528497 528502) (-343 "FEXPR.spad" 519971 520017 528010 528049) (-342 "FEVALAB.spad" 519679 519689 519961 519966) (-341 "FEVALAB.spad" 519172 519184 519456 519461) (-340 "FDIV.spad" 518614 518638 519162 519167) (-339 "FDIVCAT.spad" 516678 516702 518604 518609) (-338 "FDIVCAT.spad" 514740 514766 516668 516673) (-337 "FDIV2.spad" 514396 514436 514730 514735) (-336 "FCTRDATA.spad" 513404 513412 514386 514391) (-335 "FCPAK1.spad" 511971 511979 513394 513399) (-334 "FCOMP.spad" 511350 511360 511961 511966) (-333 "FC.spad" 501357 501365 511340 511345) (-332 "FAXF.spad" 494328 494342 501259 501352) (-331 "FAXF.spad" 487351 487367 494284 494289) (-330 "FARRAY.spad" 485501 485511 486534 486561) (-329 "FAMR.spad" 483637 483649 485399 485496) (-328 "FAMR.spad" 481757 481771 483521 483526) (-327 "FAMONOID.spad" 481425 481435 481711 481716) (-326 "FAMONC.spad" 479721 479733 481415 481420) (-325 "FAGROUP.spad" 479345 479355 479617 479644) (-324 "FACUTIL.spad" 477549 477566 479335 479340) (-323 "FACTFUNC.spad" 476743 476753 477539 477544) (-322 "EXPUPXS.spad" 473576 473599 474875 475024) (-321 "EXPRTUBE.spad" 470864 470872 473566 473571) (-320 "EXPRODE.spad" 468024 468040 470854 470859) (-319 "EXPR.spad" 463299 463309 464013 464420) (-318 "EXPR2UPS.spad" 459421 459434 463289 463294) (-317 "EXPR2.spad" 459126 459138 459411 459416) (-316 "EXPEXPAN.spad" 456066 456091 456698 456791) (-315 "EXIT.spad" 455737 455745 456056 456061) (-314 "EXITAST.spad" 455473 455481 455727 455732) (-313 "EVALCYC.spad" 454933 454947 455463 455468) (-312 "EVALAB.spad" 454505 454515 454923 454928) (-311 "EVALAB.spad" 454075 454087 454495 454500) (-310 "EUCDOM.spad" 451649 451657 454001 454070) (-309 "EUCDOM.spad" 449285 449295 451639 451644) (-308 "ESTOOLS.spad" 441131 441139 449275 449280) (-307 "ESTOOLS2.spad" 440734 440748 441121 441126) (-306 "ESTOOLS1.spad" 440419 440430 440724 440729) (-305 "ES.spad" 433234 433242 440409 440414) (-304 "ES.spad" 425955 425965 433132 433137) (-303 "ESCONT.spad" 422748 422756 425945 425950) (-302 "ESCONT1.spad" 422497 422509 422738 422743) (-301 "ES2.spad" 422002 422018 422487 422492) (-300 "ES1.spad" 421572 421588 421992 421997) (-299 "ERROR.spad" 418899 418907 421562 421567) (-298 "EQTBL.spad" 417371 417393 417580 417607) (-297 "EQ.spad" 412176 412186 414963 415075) (-296 "EQ2.spad" 411894 411906 412166 412171) (-295 "EP.spad" 408220 408230 411884 411889) (-294 "ENV.spad" 406898 406906 408210 408215) (-293 "ENTIRER.spad" 406566 406574 406842 406893) (-292 "EMR.spad" 405773 405814 406492 406561) (-291 "ELTAGG.spad" 404027 404046 405763 405768) (-290 "ELTAGG.spad" 402245 402266 403983 403988) (-289 "ELTAB.spad" 401694 401712 402235 402240) (-288 "ELFUTS.spad" 401081 401100 401684 401689) (-287 "ELEMFUN.spad" 400770 400778 401071 401076) (-286 "ELEMFUN.spad" 400457 400467 400760 400765) (-285 "ELAGG.spad" 398428 398438 400437 400452) (-284 "ELAGG.spad" 396336 396348 398347 398352) (-283 "ELABOR.spad" 395682 395690 396326 396331) (-282 "ELABEXPR.spad" 394614 394622 395672 395677) (-281 "EFUPXS.spad" 391390 391420 394570 394575) (-280 "EFULS.spad" 388226 388249 391346 391351) (-279 "EFSTRUC.spad" 386241 386257 388216 388221) (-278 "EF.spad" 381017 381033 386231 386236) (-277 "EAB.spad" 379293 379301 381007 381012) (-276 "E04UCFA.spad" 378829 378837 379283 379288) (-275 "E04NAFA.spad" 378406 378414 378819 378824) (-274 "E04MBFA.spad" 377986 377994 378396 378401) (-273 "E04JAFA.spad" 377522 377530 377976 377981) (-272 "E04GCFA.spad" 377058 377066 377512 377517) (-271 "E04FDFA.spad" 376594 376602 377048 377053) (-270 "E04DGFA.spad" 376130 376138 376584 376589) (-269 "E04AGNT.spad" 371980 371988 376120 376125) (-268 "DVARCAT.spad" 368669 368679 371970 371975) (-267 "DVARCAT.spad" 365356 365368 368659 368664) (-266 "DSMP.spad" 362823 362837 363128 363255) (-265 "DROPT.spad" 356782 356790 362813 362818) (-264 "DROPT1.spad" 356447 356457 356772 356777) (-263 "DROPT0.spad" 351304 351312 356437 356442) (-262 "DRAWPT.spad" 349477 349485 351294 351299) (-261 "DRAW.spad" 342353 342366 349467 349472) (-260 "DRAWHACK.spad" 341661 341671 342343 342348) (-259 "DRAWCX.spad" 339131 339139 341651 341656) (-258 "DRAWCURV.spad" 338678 338693 339121 339126) (-257 "DRAWCFUN.spad" 328210 328218 338668 338673) (-256 "DQAGG.spad" 326388 326398 328178 328205) (-255 "DPOLCAT.spad" 321737 321753 326256 326383) (-254 "DPOLCAT.spad" 317172 317190 321693 321698) (-253 "DPMO.spad" 309398 309414 309536 309837) (-252 "DPMM.spad" 301637 301655 301762 302063) (-251 "DOMTMPLT.spad" 301297 301305 301627 301632) (-250 "DOMCTOR.spad" 301052 301060 301287 301292) (-249 "DOMAIN.spad" 300139 300147 301042 301047) (-248 "DMP.spad" 297399 297414 297969 298096) (-247 "DLP.spad" 296751 296761 297389 297394) (-246 "DLIST.spad" 295330 295340 295934 295961) (-245 "DLAGG.spad" 293747 293757 295320 295325) (-244 "DIVRING.spad" 293289 293297 293691 293742) (-243 "DIVRING.spad" 292875 292885 293279 293284) (-242 "DISPLAY.spad" 291065 291073 292865 292870) (-241 "DIRPROD.spad" 280645 280661 281285 281416) (-240 "DIRPROD2.spad" 279463 279481 280635 280640) (-239 "DIRPCAT.spad" 278407 278423 279327 279458) (-238 "DIRPCAT.spad" 277080 277098 278002 278007) (-237 "DIOSP.spad" 275905 275913 277070 277075) (-236 "DIOPS.spad" 274901 274911 275885 275900) (-235 "DIOPS.spad" 273871 273883 274857 274862) (-234 "DIFRING.spad" 273167 273175 273851 273866) (-233 "DIFRING.spad" 272471 272481 273157 273162) (-232 "DIFEXT.spad" 271642 271652 272451 272466) (-231 "DIFEXT.spad" 270730 270742 271541 271546) (-230 "DIAGG.spad" 270360 270370 270710 270725) (-229 "DIAGG.spad" 269998 270010 270350 270355) (-228 "DHMATRIX.spad" 268310 268320 269455 269482) (-227 "DFSFUN.spad" 261950 261958 268300 268305) (-226 "DFLOAT.spad" 258681 258689 261840 261945) (-225 "DFINTTLS.spad" 256912 256928 258671 258676) (-224 "DERHAM.spad" 254826 254858 256892 256907) (-223 "DEQUEUE.spad" 254150 254160 254433 254460) (-222 "DEGRED.spad" 253767 253781 254140 254145) (-221 "DEFINTRF.spad" 251304 251314 253757 253762) (-220 "DEFINTEF.spad" 249814 249830 251294 251299) (-219 "DEFAST.spad" 249182 249190 249804 249809) (-218 "DECIMAL.spad" 247288 247296 247649 247742) (-217 "DDFACT.spad" 245101 245118 247278 247283) (-216 "DBLRESP.spad" 244701 244725 245091 245096) (-215 "DBASE.spad" 243365 243375 244691 244696) (-214 "DATAARY.spad" 242827 242840 243355 243360) (-213 "D03FAFA.spad" 242655 242663 242817 242822) (-212 "D03EEFA.spad" 242475 242483 242645 242650) (-211 "D03AGNT.spad" 241561 241569 242465 242470) (-210 "D02EJFA.spad" 241023 241031 241551 241556) (-209 "D02CJFA.spad" 240501 240509 241013 241018) (-208 "D02BHFA.spad" 239991 239999 240491 240496) (-207 "D02BBFA.spad" 239481 239489 239981 239986) (-206 "D02AGNT.spad" 234295 234303 239471 239476) (-205 "D01WGTS.spad" 232614 232622 234285 234290) (-204 "D01TRNS.spad" 232591 232599 232604 232609) (-203 "D01GBFA.spad" 232113 232121 232581 232586) (-202 "D01FCFA.spad" 231635 231643 232103 232108) (-201 "D01ASFA.spad" 231103 231111 231625 231630) (-200 "D01AQFA.spad" 230549 230557 231093 231098) (-199 "D01APFA.spad" 229973 229981 230539 230544) (-198 "D01ANFA.spad" 229467 229475 229963 229968) (-197 "D01AMFA.spad" 228977 228985 229457 229462) (-196 "D01ALFA.spad" 228517 228525 228967 228972) (-195 "D01AKFA.spad" 228043 228051 228507 228512) (-194 "D01AJFA.spad" 227566 227574 228033 228038) (-193 "D01AGNT.spad" 223633 223641 227556 227561) (-192 "CYCLOTOM.spad" 223139 223147 223623 223628) (-191 "CYCLES.spad" 219995 220003 223129 223134) (-190 "CVMP.spad" 219412 219422 219985 219990) (-189 "CTRIGMNP.spad" 217912 217928 219402 219407) (-188 "CTOR.spad" 217603 217611 217902 217907) (-187 "CTORKIND.spad" 217206 217214 217593 217598) (-186 "CTORCAT.spad" 216455 216463 217196 217201) (-185 "CTORCAT.spad" 215702 215712 216445 216450) (-184 "CTORCALL.spad" 215291 215301 215692 215697) (-183 "CSTTOOLS.spad" 214536 214549 215281 215286) (-182 "CRFP.spad" 208260 208273 214526 214531) (-181 "CRCEAST.spad" 207980 207988 208250 208255) (-180 "CRAPACK.spad" 207031 207041 207970 207975) (-179 "CPMATCH.spad" 206535 206550 206956 206961) (-178 "CPIMA.spad" 206240 206259 206525 206530) (-177 "COORDSYS.spad" 201249 201259 206230 206235) (-176 "CONTOUR.spad" 200660 200668 201239 201244) (-175 "CONTFRAC.spad" 196410 196420 200562 200655) (-174 "CONDUIT.spad" 196168 196176 196400 196405) (-173 "COMRING.spad" 195842 195850 196106 196163) (-172 "COMPPROP.spad" 195360 195368 195832 195837) (-171 "COMPLPAT.spad" 195127 195142 195350 195355) (-170 "COMPLEX.spad" 189264 189274 189508 189769) (-169 "COMPLEX2.spad" 188979 188991 189254 189259) (-168 "COMPILER.spad" 188528 188536 188969 188974) (-167 "COMPFACT.spad" 188130 188144 188518 188523) (-166 "COMPCAT.spad" 186202 186212 187864 188125) (-165 "COMPCAT.spad" 184002 184014 185666 185671) (-164 "COMMUPC.spad" 183750 183768 183992 183997) (-163 "COMMONOP.spad" 183283 183291 183740 183745) (-162 "COMM.spad" 183094 183102 183273 183278) (-161 "COMMAAST.spad" 182857 182865 183084 183089) (-160 "COMBOPC.spad" 181772 181780 182847 182852) (-159 "COMBINAT.spad" 180539 180549 181762 181767) (-158 "COMBF.spad" 177921 177937 180529 180534) (-157 "COLOR.spad" 176758 176766 177911 177916) (-156 "COLONAST.spad" 176424 176432 176748 176753) (-155 "CMPLXRT.spad" 176135 176152 176414 176419) (-154 "CLLCTAST.spad" 175797 175805 176125 176130) (-153 "CLIP.spad" 171905 171913 175787 175792) (-152 "CLIF.spad" 170560 170576 171861 171900) (-151 "CLAGG.spad" 167065 167075 170550 170555) (-150 "CLAGG.spad" 163441 163453 166928 166933) (-149 "CINTSLPE.spad" 162772 162785 163431 163436) (-148 "CHVAR.spad" 160910 160932 162762 162767) (-147 "CHARZ.spad" 160825 160833 160890 160905) (-146 "CHARPOL.spad" 160335 160345 160815 160820) (-145 "CHARNZ.spad" 160088 160096 160315 160330) (-144 "CHAR.spad" 157962 157970 160078 160083) (-143 "CFCAT.spad" 157290 157298 157952 157957) (-142 "CDEN.spad" 156486 156500 157280 157285) (-141 "CCLASS.spad" 154635 154643 155897 155936) (-140 "CATEGORY.spad" 153677 153685 154625 154630) (-139 "CATCTOR.spad" 153568 153576 153667 153672) (-138 "CATAST.spad" 153186 153194 153558 153563) (-137 "CASEAST.spad" 152900 152908 153176 153181) (-136 "CARTEN.spad" 148187 148211 152890 152895) (-135 "CARTEN2.spad" 147577 147604 148177 148182) (-134 "CARD.spad" 144872 144880 147551 147572) (-133 "CAPSLAST.spad" 144646 144654 144862 144867) (-132 "CACHSET.spad" 144270 144278 144636 144641) (-131 "CABMON.spad" 143825 143833 144260 144265) (-130 "BYTEORD.spad" 143500 143508 143815 143820) (-129 "BYTE.spad" 142927 142935 143490 143495) (-128 "BYTEBUF.spad" 140786 140794 142096 142123) (-127 "BTREE.spad" 139859 139869 140393 140420) (-126 "BTOURN.spad" 138864 138874 139466 139493) (-125 "BTCAT.spad" 138256 138266 138832 138859) (-124 "BTCAT.spad" 137668 137680 138246 138251) (-123 "BTAGG.spad" 136796 136804 137636 137663) (-122 "BTAGG.spad" 135944 135954 136786 136791) (-121 "BSTREE.spad" 134685 134695 135551 135578) (-120 "BRILL.spad" 132882 132893 134675 134680) (-119 "BRAGG.spad" 131822 131832 132872 132877) (-118 "BRAGG.spad" 130726 130738 131778 131783) (-117 "BPADICRT.spad" 128707 128719 128962 129055) (-116 "BPADIC.spad" 128371 128383 128633 128702) (-115 "BOUNDZRO.spad" 128027 128044 128361 128366) (-114 "BOP.spad" 123209 123217 128017 128022) (-113 "BOP1.spad" 120675 120685 123199 123204) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2267632 2267637 2267642 2267647) (-2 NIL 2267612 2267617 2267622 2267627) (-1 NIL 2267592 2267597 2267602 2267607) (0 NIL 2267572 2267577 2267582 2267587) (-1301 "ZMOD.spad" 2267381 2267394 2267510 2267567) (-1300 "ZLINDEP.spad" 2266447 2266458 2267371 2267376) (-1299 "ZDSOLVE.spad" 2256392 2256414 2266437 2266442) (-1298 "YSTREAM.spad" 2255887 2255898 2256382 2256387) (-1297 "XRPOLY.spad" 2255107 2255127 2255743 2255812) (-1296 "XPR.spad" 2252902 2252915 2254825 2254924) (-1295 "XPOLY.spad" 2252457 2252468 2252758 2252827) (-1294 "XPOLYC.spad" 2251776 2251792 2252383 2252452) (-1293 "XPBWPOLY.spad" 2250213 2250233 2251556 2251625) (-1292 "XF.spad" 2248676 2248691 2250115 2250208) (-1291 "XF.spad" 2247119 2247136 2248560 2248565) (-1290 "XFALG.spad" 2244167 2244183 2247045 2247114) (-1289 "XEXPPKG.spad" 2243418 2243444 2244157 2244162) (-1288 "XDPOLY.spad" 2243032 2243048 2243274 2243343) (-1287 "XALG.spad" 2242692 2242703 2242988 2243027) (-1286 "WUTSET.spad" 2238531 2238548 2242338 2242365) (-1285 "WP.spad" 2237730 2237774 2238389 2238456) (-1284 "WHILEAST.spad" 2237528 2237537 2237720 2237725) (-1283 "WHEREAST.spad" 2237199 2237208 2237518 2237523) (-1282 "WFFINTBS.spad" 2234862 2234884 2237189 2237194) (-1281 "WEIER.spad" 2233084 2233095 2234852 2234857) (-1280 "VSPACE.spad" 2232757 2232768 2233052 2233079) (-1279 "VSPACE.spad" 2232450 2232463 2232747 2232752) (-1278 "VOID.spad" 2232127 2232136 2232440 2232445) (-1277 "VIEW.spad" 2229807 2229816 2232117 2232122) (-1276 "VIEWDEF.spad" 2225008 2225017 2229797 2229802) (-1275 "VIEW3D.spad" 2208969 2208978 2224998 2225003) (-1274 "VIEW2D.spad" 2196860 2196869 2208959 2208964) (-1273 "VECTOR.spad" 2195534 2195545 2195785 2195812) (-1272 "VECTOR2.spad" 2194173 2194186 2195524 2195529) (-1271 "VECTCAT.spad" 2192077 2192088 2194141 2194168) (-1270 "VECTCAT.spad" 2189788 2189801 2191854 2191859) (-1269 "VARIABLE.spad" 2189568 2189583 2189778 2189783) (-1268 "UTYPE.spad" 2189212 2189221 2189558 2189563) (-1267 "UTSODETL.spad" 2188507 2188531 2189168 2189173) (-1266 "UTSODE.spad" 2186723 2186743 2188497 2188502) (-1265 "UTS.spad" 2181527 2181555 2185190 2185287) (-1264 "UTSCAT.spad" 2179006 2179022 2181425 2181522) (-1263 "UTSCAT.spad" 2176129 2176147 2178550 2178555) (-1262 "UTS2.spad" 2175724 2175759 2176119 2176124) (-1261 "URAGG.spad" 2170397 2170408 2175714 2175719) (-1260 "URAGG.spad" 2165034 2165047 2170353 2170358) (-1259 "UPXSSING.spad" 2162679 2162705 2164115 2164248) (-1258 "UPXS.spad" 2159833 2159861 2160811 2160960) (-1257 "UPXSCONS.spad" 2157592 2157612 2157965 2158114) (-1256 "UPXSCCA.spad" 2156163 2156183 2157438 2157587) (-1255 "UPXSCCA.spad" 2154876 2154898 2156153 2156158) (-1254 "UPXSCAT.spad" 2153465 2153481 2154722 2154871) (-1253 "UPXS2.spad" 2153008 2153061 2153455 2153460) (-1252 "UPSQFREE.spad" 2151422 2151436 2152998 2153003) (-1251 "UPSCAT.spad" 2149033 2149057 2151320 2151417) (-1250 "UPSCAT.spad" 2146350 2146376 2148639 2148644) (-1249 "UPOLYC.spad" 2141390 2141401 2146192 2146345) (-1248 "UPOLYC.spad" 2136322 2136335 2141126 2141131) (-1247 "UPOLYC2.spad" 2135793 2135812 2136312 2136317) (-1246 "UP.spad" 2132992 2133007 2133379 2133532) (-1245 "UPMP.spad" 2131892 2131905 2132982 2132987) (-1244 "UPDIVP.spad" 2131457 2131471 2131882 2131887) (-1243 "UPDECOMP.spad" 2129702 2129716 2131447 2131452) (-1242 "UPCDEN.spad" 2128911 2128927 2129692 2129697) (-1241 "UP2.spad" 2128275 2128296 2128901 2128906) (-1240 "UNISEG.spad" 2127628 2127639 2128194 2128199) (-1239 "UNISEG2.spad" 2127125 2127138 2127584 2127589) (-1238 "UNIFACT.spad" 2126228 2126240 2127115 2127120) (-1237 "ULS.spad" 2116786 2116814 2117873 2118302) (-1236 "ULSCONS.spad" 2109182 2109202 2109552 2109701) (-1235 "ULSCCAT.spad" 2106919 2106939 2109028 2109177) (-1234 "ULSCCAT.spad" 2104764 2104786 2106875 2106880) (-1233 "ULSCAT.spad" 2102996 2103012 2104610 2104759) (-1232 "ULS2.spad" 2102510 2102563 2102986 2102991) (-1231 "UINT8.spad" 2102387 2102396 2102500 2102505) (-1230 "UINT64.spad" 2102263 2102272 2102377 2102382) (-1229 "UINT32.spad" 2102139 2102148 2102253 2102258) (-1228 "UINT16.spad" 2102015 2102024 2102129 2102134) (-1227 "UFD.spad" 2101080 2101089 2101941 2102010) (-1226 "UFD.spad" 2100207 2100218 2101070 2101075) (-1225 "UDVO.spad" 2099088 2099097 2100197 2100202) (-1224 "UDPO.spad" 2096581 2096592 2099044 2099049) (-1223 "TYPE.spad" 2096513 2096522 2096571 2096576) (-1222 "TYPEAST.spad" 2096432 2096441 2096503 2096508) (-1221 "TWOFACT.spad" 2095084 2095099 2096422 2096427) (-1220 "TUPLE.spad" 2094570 2094581 2094983 2094988) (-1219 "TUBETOOL.spad" 2091437 2091446 2094560 2094565) (-1218 "TUBE.spad" 2090084 2090101 2091427 2091432) (-1217 "TS.spad" 2088683 2088699 2089649 2089746) (-1216 "TSETCAT.spad" 2075810 2075827 2088651 2088678) (-1215 "TSETCAT.spad" 2062923 2062942 2075766 2075771) (-1214 "TRMANIP.spad" 2057289 2057306 2062629 2062634) (-1213 "TRIMAT.spad" 2056252 2056277 2057279 2057284) (-1212 "TRIGMNIP.spad" 2054779 2054796 2056242 2056247) (-1211 "TRIGCAT.spad" 2054291 2054300 2054769 2054774) (-1210 "TRIGCAT.spad" 2053801 2053812 2054281 2054286) (-1209 "TREE.spad" 2052376 2052387 2053408 2053435) (-1208 "TRANFUN.spad" 2052215 2052224 2052366 2052371) (-1207 "TRANFUN.spad" 2052052 2052063 2052205 2052210) (-1206 "TOPSP.spad" 2051726 2051735 2052042 2052047) (-1205 "TOOLSIGN.spad" 2051389 2051400 2051716 2051721) (-1204 "TEXTFILE.spad" 2049950 2049959 2051379 2051384) (-1203 "TEX.spad" 2047096 2047105 2049940 2049945) (-1202 "TEX1.spad" 2046652 2046663 2047086 2047091) (-1201 "TEMUTL.spad" 2046207 2046216 2046642 2046647) (-1200 "TBCMPPK.spad" 2044300 2044323 2046197 2046202) (-1199 "TBAGG.spad" 2043350 2043373 2044280 2044295) (-1198 "TBAGG.spad" 2042408 2042433 2043340 2043345) (-1197 "TANEXP.spad" 2041816 2041827 2042398 2042403) (-1196 "TABLE.spad" 2040227 2040250 2040497 2040524) (-1195 "TABLEAU.spad" 2039708 2039719 2040217 2040222) (-1194 "TABLBUMP.spad" 2036511 2036522 2039698 2039703) (-1193 "SYSTEM.spad" 2035739 2035748 2036501 2036506) (-1192 "SYSSOLP.spad" 2033222 2033233 2035729 2035734) (-1191 "SYSPTR.spad" 2033121 2033130 2033212 2033217) (-1190 "SYSNNI.spad" 2032303 2032314 2033111 2033116) (-1189 "SYSINT.spad" 2031707 2031718 2032293 2032298) (-1188 "SYNTAX.spad" 2027913 2027922 2031697 2031702) (-1187 "SYMTAB.spad" 2025981 2025990 2027903 2027908) (-1186 "SYMS.spad" 2022004 2022013 2025971 2025976) (-1185 "SYMPOLY.spad" 2021011 2021022 2021093 2021220) (-1184 "SYMFUNC.spad" 2020512 2020523 2021001 2021006) (-1183 "SYMBOL.spad" 2018015 2018024 2020502 2020507) (-1182 "SWITCH.spad" 2014786 2014795 2018005 2018010) (-1181 "SUTS.spad" 2011691 2011719 2013253 2013350) (-1180 "SUPXS.spad" 2008832 2008860 2009823 2009972) (-1179 "SUP.spad" 2005645 2005656 2006418 2006571) (-1178 "SUPFRACF.spad" 2004750 2004768 2005635 2005640) (-1177 "SUP2.spad" 2004142 2004155 2004740 2004745) (-1176 "SUMRF.spad" 2003116 2003127 2004132 2004137) (-1175 "SUMFS.spad" 2002753 2002770 2003106 2003111) (-1174 "SULS.spad" 1993298 1993326 1994398 1994827) (-1173 "SUCHTAST.spad" 1993067 1993076 1993288 1993293) (-1172 "SUCH.spad" 1992749 1992764 1993057 1993062) (-1171 "SUBSPACE.spad" 1984864 1984879 1992739 1992744) (-1170 "SUBRESP.spad" 1984034 1984048 1984820 1984825) (-1169 "STTF.spad" 1980133 1980149 1984024 1984029) (-1168 "STTFNC.spad" 1976601 1976617 1980123 1980128) (-1167 "STTAYLOR.spad" 1969236 1969247 1976482 1976487) (-1166 "STRTBL.spad" 1967741 1967758 1967890 1967917) (-1165 "STRING.spad" 1967150 1967159 1967164 1967191) (-1164 "STRICAT.spad" 1966938 1966947 1967118 1967145) (-1163 "STREAM.spad" 1963856 1963867 1966463 1966478) (-1162 "STREAM3.spad" 1963429 1963444 1963846 1963851) (-1161 "STREAM2.spad" 1962557 1962570 1963419 1963424) (-1160 "STREAM1.spad" 1962263 1962274 1962547 1962552) (-1159 "STINPROD.spad" 1961199 1961215 1962253 1962258) (-1158 "STEP.spad" 1960400 1960409 1961189 1961194) (-1157 "STEPAST.spad" 1959634 1959643 1960390 1960395) (-1156 "STBL.spad" 1958160 1958188 1958327 1958342) (-1155 "STAGG.spad" 1957235 1957246 1958150 1958155) (-1154 "STAGG.spad" 1956308 1956321 1957225 1957230) (-1153 "STACK.spad" 1955665 1955676 1955915 1955942) (-1152 "SREGSET.spad" 1953369 1953386 1955311 1955338) (-1151 "SRDCMPK.spad" 1951930 1951950 1953359 1953364) (-1150 "SRAGG.spad" 1947073 1947082 1951898 1951925) (-1149 "SRAGG.spad" 1942236 1942247 1947063 1947068) (-1148 "SQMATRIX.spad" 1939852 1939870 1940768 1940855) (-1147 "SPLTREE.spad" 1934404 1934417 1939288 1939315) (-1146 "SPLNODE.spad" 1930992 1931005 1934394 1934399) (-1145 "SPFCAT.spad" 1929801 1929810 1930982 1930987) (-1144 "SPECOUT.spad" 1928353 1928362 1929791 1929796) (-1143 "SPADXPT.spad" 1919948 1919957 1928343 1928348) (-1142 "spad-parser.spad" 1919413 1919422 1919938 1919943) (-1141 "SPADAST.spad" 1919114 1919123 1919403 1919408) (-1140 "SPACEC.spad" 1903313 1903324 1919104 1919109) (-1139 "SPACE3.spad" 1903089 1903100 1903303 1903308) (-1138 "SORTPAK.spad" 1902638 1902651 1903045 1903050) (-1137 "SOLVETRA.spad" 1900401 1900412 1902628 1902633) (-1136 "SOLVESER.spad" 1898929 1898940 1900391 1900396) (-1135 "SOLVERAD.spad" 1894955 1894966 1898919 1898924) (-1134 "SOLVEFOR.spad" 1893417 1893435 1894945 1894950) (-1133 "SNTSCAT.spad" 1893017 1893034 1893385 1893412) (-1132 "SMTS.spad" 1891289 1891315 1892582 1892679) (-1131 "SMP.spad" 1888764 1888784 1889154 1889281) (-1130 "SMITH.spad" 1887609 1887634 1888754 1888759) (-1129 "SMATCAT.spad" 1885719 1885749 1887553 1887604) (-1128 "SMATCAT.spad" 1883761 1883793 1885597 1885602) (-1127 "SKAGG.spad" 1882724 1882735 1883729 1883756) (-1126 "SINT.spad" 1881556 1881565 1882590 1882719) (-1125 "SIMPAN.spad" 1881284 1881293 1881546 1881551) (-1124 "SIG.spad" 1880614 1880623 1881274 1881279) (-1123 "SIGNRF.spad" 1879732 1879743 1880604 1880609) (-1122 "SIGNEF.spad" 1879011 1879028 1879722 1879727) (-1121 "SIGAST.spad" 1878396 1878405 1879001 1879006) (-1120 "SHP.spad" 1876324 1876339 1878352 1878357) (-1119 "SHDP.spad" 1866035 1866062 1866544 1866675) (-1118 "SGROUP.spad" 1865643 1865652 1866025 1866030) (-1117 "SGROUP.spad" 1865249 1865260 1865633 1865638) (-1116 "SGCF.spad" 1858412 1858421 1865239 1865244) (-1115 "SFRTCAT.spad" 1857342 1857359 1858380 1858407) (-1114 "SFRGCD.spad" 1856405 1856425 1857332 1857337) (-1113 "SFQCMPK.spad" 1851042 1851062 1856395 1856400) (-1112 "SFORT.spad" 1850481 1850495 1851032 1851037) (-1111 "SEXOF.spad" 1850324 1850364 1850471 1850476) (-1110 "SEX.spad" 1850216 1850225 1850314 1850319) (-1109 "SEXCAT.spad" 1847817 1847857 1850206 1850211) (-1108 "SET.spad" 1846141 1846152 1847238 1847277) (-1107 "SETMN.spad" 1844591 1844608 1846131 1846136) (-1106 "SETCAT.spad" 1843913 1843922 1844581 1844586) (-1105 "SETCAT.spad" 1843233 1843244 1843903 1843908) (-1104 "SETAGG.spad" 1839782 1839793 1843213 1843228) (-1103 "SETAGG.spad" 1836339 1836352 1839772 1839777) (-1102 "SEQAST.spad" 1836042 1836051 1836329 1836334) (-1101 "SEGXCAT.spad" 1835198 1835211 1836032 1836037) (-1100 "SEG.spad" 1835011 1835022 1835117 1835122) (-1099 "SEGCAT.spad" 1833936 1833947 1835001 1835006) (-1098 "SEGBIND.spad" 1833694 1833705 1833883 1833888) (-1097 "SEGBIND2.spad" 1833392 1833405 1833684 1833689) (-1096 "SEGAST.spad" 1833106 1833115 1833382 1833387) (-1095 "SEG2.spad" 1832541 1832554 1833062 1833067) (-1094 "SDVAR.spad" 1831817 1831828 1832531 1832536) (-1093 "SDPOL.spad" 1829243 1829254 1829534 1829661) (-1092 "SCPKG.spad" 1827332 1827343 1829233 1829238) (-1091 "SCOPE.spad" 1826485 1826494 1827322 1827327) (-1090 "SCACHE.spad" 1825181 1825192 1826475 1826480) (-1089 "SASTCAT.spad" 1825090 1825099 1825171 1825176) (-1088 "SAOS.spad" 1824962 1824971 1825080 1825085) (-1087 "SAERFFC.spad" 1824675 1824695 1824952 1824957) (-1086 "SAE.spad" 1822850 1822866 1823461 1823596) (-1085 "SAEFACT.spad" 1822551 1822571 1822840 1822845) (-1084 "RURPK.spad" 1820210 1820226 1822541 1822546) (-1083 "RULESET.spad" 1819663 1819687 1820200 1820205) (-1082 "RULE.spad" 1817903 1817927 1819653 1819658) (-1081 "RULECOLD.spad" 1817755 1817768 1817893 1817898) (-1080 "RTVALUE.spad" 1817490 1817499 1817745 1817750) (-1079 "RSTRCAST.spad" 1817207 1817216 1817480 1817485) (-1078 "RSETGCD.spad" 1813585 1813605 1817197 1817202) (-1077 "RSETCAT.spad" 1803521 1803538 1813553 1813580) (-1076 "RSETCAT.spad" 1793477 1793496 1803511 1803516) (-1075 "RSDCMPK.spad" 1791929 1791949 1793467 1793472) (-1074 "RRCC.spad" 1790313 1790343 1791919 1791924) (-1073 "RRCC.spad" 1788695 1788727 1790303 1790308) (-1072 "RPTAST.spad" 1788397 1788406 1788685 1788690) (-1071 "RPOLCAT.spad" 1767757 1767772 1788265 1788392) (-1070 "RPOLCAT.spad" 1746831 1746848 1767341 1767346) (-1069 "ROUTINE.spad" 1742714 1742723 1745478 1745505) (-1068 "ROMAN.spad" 1742042 1742051 1742580 1742709) (-1067 "ROIRC.spad" 1741122 1741154 1742032 1742037) (-1066 "RNS.spad" 1740025 1740034 1741024 1741117) (-1065 "RNS.spad" 1739014 1739025 1740015 1740020) (-1064 "RNG.spad" 1738749 1738758 1739004 1739009) (-1063 "RNGBIND.spad" 1737909 1737923 1738704 1738709) (-1062 "RMODULE.spad" 1737674 1737685 1737899 1737904) (-1061 "RMCAT2.spad" 1737094 1737151 1737664 1737669) (-1060 "RMATRIX.spad" 1735918 1735937 1736261 1736300) (-1059 "RMATCAT.spad" 1731497 1731528 1735874 1735913) (-1058 "RMATCAT.spad" 1726966 1726999 1731345 1731350) (-1057 "RLINSET.spad" 1726360 1726371 1726956 1726961) (-1056 "RINTERP.spad" 1726248 1726268 1726350 1726355) (-1055 "RING.spad" 1725718 1725727 1726228 1726243) (-1054 "RING.spad" 1725196 1725207 1725708 1725713) (-1053 "RIDIST.spad" 1724588 1724597 1725186 1725191) (-1052 "RGCHAIN.spad" 1723171 1723187 1724073 1724100) (-1051 "RGBCSPC.spad" 1722952 1722964 1723161 1723166) (-1050 "RGBCMDL.spad" 1722482 1722494 1722942 1722947) (-1049 "RF.spad" 1720124 1720135 1722472 1722477) (-1048 "RFFACTOR.spad" 1719586 1719597 1720114 1720119) (-1047 "RFFACT.spad" 1719321 1719333 1719576 1719581) (-1046 "RFDIST.spad" 1718317 1718326 1719311 1719316) (-1045 "RETSOL.spad" 1717736 1717749 1718307 1718312) (-1044 "RETRACT.spad" 1717164 1717175 1717726 1717731) (-1043 "RETRACT.spad" 1716590 1716603 1717154 1717159) (-1042 "RETAST.spad" 1716402 1716411 1716580 1716585) (-1041 "RESULT.spad" 1714462 1714471 1715049 1715076) (-1040 "RESRING.spad" 1713809 1713856 1714400 1714457) (-1039 "RESLATC.spad" 1713133 1713144 1713799 1713804) (-1038 "REPSQ.spad" 1712864 1712875 1713123 1713128) (-1037 "REP.spad" 1710418 1710427 1712854 1712859) (-1036 "REPDB.spad" 1710125 1710136 1710408 1710413) (-1035 "REP2.spad" 1699783 1699794 1709967 1709972) (-1034 "REP1.spad" 1693979 1693990 1699733 1699738) (-1033 "REGSET.spad" 1691776 1691793 1693625 1693652) (-1032 "REF.spad" 1691111 1691122 1691731 1691736) (-1031 "REDORDER.spad" 1690317 1690334 1691101 1691106) (-1030 "RECLOS.spad" 1689100 1689120 1689804 1689897) (-1029 "REALSOLV.spad" 1688240 1688249 1689090 1689095) (-1028 "REAL.spad" 1688112 1688121 1688230 1688235) (-1027 "REAL0Q.spad" 1685410 1685425 1688102 1688107) (-1026 "REAL0.spad" 1682254 1682269 1685400 1685405) (-1025 "RDUCEAST.spad" 1681975 1681984 1682244 1682249) (-1024 "RDIV.spad" 1681630 1681655 1681965 1681970) (-1023 "RDIST.spad" 1681197 1681208 1681620 1681625) (-1022 "RDETRS.spad" 1680061 1680079 1681187 1681192) (-1021 "RDETR.spad" 1678200 1678218 1680051 1680056) (-1020 "RDEEFS.spad" 1677299 1677316 1678190 1678195) (-1019 "RDEEF.spad" 1676309 1676326 1677289 1677294) (-1018 "RCFIELD.spad" 1673495 1673504 1676211 1676304) (-1017 "RCFIELD.spad" 1670767 1670778 1673485 1673490) (-1016 "RCAGG.spad" 1668695 1668706 1670757 1670762) (-1015 "RCAGG.spad" 1666550 1666563 1668614 1668619) (-1014 "RATRET.spad" 1665910 1665921 1666540 1666545) (-1013 "RATFACT.spad" 1665602 1665614 1665900 1665905) (-1012 "RANDSRC.spad" 1664921 1664930 1665592 1665597) (-1011 "RADUTIL.spad" 1664677 1664686 1664911 1664916) (-1010 "RADIX.spad" 1661598 1661612 1663144 1663237) (-1009 "RADFF.spad" 1660011 1660048 1660130 1660286) (-1008 "RADCAT.spad" 1659606 1659615 1660001 1660006) (-1007 "RADCAT.spad" 1659199 1659210 1659596 1659601) (-1006 "QUEUE.spad" 1658547 1658558 1658806 1658833) (-1005 "QUAT.spad" 1657128 1657139 1657471 1657536) (-1004 "QUATCT2.spad" 1656748 1656767 1657118 1657123) (-1003 "QUATCAT.spad" 1654918 1654929 1656678 1656743) (-1002 "QUATCAT.spad" 1652839 1652852 1654601 1654606) (-1001 "QUAGG.spad" 1651666 1651677 1652807 1652834) (-1000 "QQUTAST.spad" 1651434 1651443 1651656 1651661) (-999 "QFORM.spad" 1650899 1650913 1651424 1651429) (-998 "QFCAT.spad" 1649602 1649612 1650801 1650894) (-997 "QFCAT.spad" 1647896 1647908 1649097 1649102) (-996 "QFCAT2.spad" 1647589 1647605 1647886 1647891) (-995 "QEQUAT.spad" 1647148 1647156 1647579 1647584) (-994 "QCMPACK.spad" 1641895 1641914 1647138 1647143) (-993 "QALGSET.spad" 1637974 1638006 1641809 1641814) (-992 "QALGSET2.spad" 1635970 1635988 1637964 1637969) (-991 "PWFFINTB.spad" 1633386 1633407 1635960 1635965) (-990 "PUSHVAR.spad" 1632725 1632744 1633376 1633381) (-989 "PTRANFN.spad" 1628853 1628863 1632715 1632720) (-988 "PTPACK.spad" 1625941 1625951 1628843 1628848) (-987 "PTFUNC2.spad" 1625764 1625778 1625931 1625936) (-986 "PTCAT.spad" 1625019 1625029 1625732 1625759) (-985 "PSQFR.spad" 1624326 1624350 1625009 1625014) (-984 "PSEUDLIN.spad" 1623212 1623222 1624316 1624321) (-983 "PSETPK.spad" 1608645 1608661 1623090 1623095) (-982 "PSETCAT.spad" 1602565 1602588 1608625 1608640) (-981 "PSETCAT.spad" 1596459 1596484 1602521 1602526) (-980 "PSCURVE.spad" 1595442 1595450 1596449 1596454) (-979 "PSCAT.spad" 1594225 1594254 1595340 1595437) (-978 "PSCAT.spad" 1593098 1593129 1594215 1594220) (-977 "PRTITION.spad" 1592059 1592067 1593088 1593093) (-976 "PRTDAST.spad" 1591778 1591786 1592049 1592054) (-975 "PRS.spad" 1581340 1581357 1591734 1591739) (-974 "PRQAGG.spad" 1580775 1580785 1581308 1581335) (-973 "PROPLOG.spad" 1580074 1580082 1580765 1580770) (-972 "PROPFRML.spad" 1578642 1578653 1580064 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1446103) (-896 "PATTERN1.spad" 1444182 1444198 1445836 1445841) (-895 "PATRES.spad" 1441757 1441769 1444172 1444177) (-894 "PATRES2.spad" 1441429 1441443 1441747 1441752) (-893 "PATMATCH.spad" 1439626 1439657 1441137 1441142) (-892 "PATMAB.spad" 1439055 1439065 1439616 1439621) (-891 "PATLRES.spad" 1438141 1438155 1439045 1439050) (-890 "PATAB.spad" 1437905 1437915 1438131 1438136) (-889 "PARTPERM.spad" 1435305 1435313 1437895 1437900) (-888 "PARSURF.spad" 1434739 1434767 1435295 1435300) (-887 "PARSU2.spad" 1434536 1434552 1434729 1434734) (-886 "script-parser.spad" 1434056 1434064 1434526 1434531) (-885 "PARSCURV.spad" 1433490 1433518 1434046 1434051) (-884 "PARSC2.spad" 1433281 1433297 1433480 1433485) (-883 "PARPCURV.spad" 1432743 1432771 1433271 1433276) (-882 "PARPC2.spad" 1432534 1432550 1432733 1432738) (-881 "PARAMAST.spad" 1431662 1431670 1432524 1432529) (-880 "PAN2EXPR.spad" 1431074 1431082 1431652 1431657) (-879 "PALETTE.spad" 1430044 1430052 1431064 1431069) (-878 "PAIR.spad" 1429031 1429044 1429632 1429637) (-877 "PADICRC.spad" 1426365 1426383 1427536 1427629) (-876 "PADICRAT.spad" 1424380 1424392 1424601 1424694) (-875 "PADIC.spad" 1424075 1424087 1424306 1424375) (-874 "PADICCT.spad" 1422624 1422636 1424001 1424070) (-873 "PADEPAC.spad" 1421313 1421332 1422614 1422619) (-872 "PADE.spad" 1420065 1420081 1421303 1421308) (-871 "OWP.spad" 1419305 1419335 1419923 1419990) (-870 "OVERSET.spad" 1418878 1418886 1419295 1419300) (-869 "OVAR.spad" 1418659 1418682 1418868 1418873) (-868 "OUT.spad" 1417745 1417753 1418649 1418654) (-867 "OUTFORM.spad" 1407137 1407145 1417735 1417740) (-866 "OUTBFILE.spad" 1406555 1406563 1407127 1407132) (-865 "OUTBCON.spad" 1405561 1405569 1406545 1406550) (-864 "OUTBCON.spad" 1404565 1404575 1405551 1405556) (-863 "OSI.spad" 1404040 1404048 1404555 1404560) (-862 "OSGROUP.spad" 1403958 1403966 1404030 1404035) (-861 "ORTHPOL.spad" 1402443 1402453 1403875 1403880) (-860 "OREUP.spad" 1401896 1401924 1402123 1402162) (-859 "ORESUP.spad" 1401197 1401221 1401576 1401615) (-858 "OREPCTO.spad" 1399054 1399066 1401117 1401122) (-857 "OREPCAT.spad" 1393201 1393211 1399010 1399049) (-856 "OREPCAT.spad" 1387238 1387250 1393049 1393054) (-855 "ORDSET.spad" 1386410 1386418 1387228 1387233) (-854 "ORDSET.spad" 1385580 1385590 1386400 1386405) (-853 "ORDRING.spad" 1384970 1384978 1385560 1385575) (-852 "ORDRING.spad" 1384368 1384378 1384960 1384965) (-851 "ORDMON.spad" 1384223 1384231 1384358 1384363) (-850 "ORDFUNS.spad" 1383355 1383371 1384213 1384218) (-849 "ORDFIN.spad" 1383175 1383183 1383345 1383350) (-848 "ORDCOMP.spad" 1381640 1381650 1382722 1382751) (-847 "ORDCOMP2.spad" 1380933 1380945 1381630 1381635) (-846 "OPTPROB.spad" 1379571 1379579 1380923 1380928) (-845 "OPTPACK.spad" 1371980 1371988 1379561 1379566) (-844 "OPTCAT.spad" 1369659 1369667 1371970 1371975) (-843 "OPSIG.spad" 1369313 1369321 1369649 1369654) (-842 "OPQUERY.spad" 1368862 1368870 1369303 1369308) (-841 "OP.spad" 1368604 1368614 1368684 1368751) (-840 "OPERCAT.spad" 1368070 1368080 1368594 1368599) (-839 "OPERCAT.spad" 1367534 1367546 1368060 1368065) (-838 "ONECOMP.spad" 1366279 1366289 1367081 1367110) (-837 "ONECOMP2.spad" 1365703 1365715 1366269 1366274) (-836 "OMSERVER.spad" 1364709 1364717 1365693 1365698) (-835 "OMSAGG.spad" 1364497 1364507 1364665 1364704) (-834 "OMPKG.spad" 1363113 1363121 1364487 1364492) (-833 "OM.spad" 1362086 1362094 1363103 1363108) (-832 "OMLO.spad" 1361511 1361523 1361972 1362011) (-831 "OMEXPR.spad" 1361345 1361355 1361501 1361506) (-830 "OMERR.spad" 1360890 1360898 1361335 1361340) (-829 "OMERRK.spad" 1359924 1359932 1360880 1360885) (-828 "OMENC.spad" 1359268 1359276 1359914 1359919) (-827 "OMDEV.spad" 1353577 1353585 1359258 1359263) (-826 "OMCONN.spad" 1352986 1352994 1353567 1353572) (-825 "OINTDOM.spad" 1352749 1352757 1352912 1352981) (-824 "OFMONOID.spad" 1350872 1350882 1352705 1352710) (-823 "ODVAR.spad" 1350133 1350143 1350862 1350867) (-822 "ODR.spad" 1349777 1349803 1349945 1350094) (-821 "ODPOL.spad" 1347159 1347169 1347499 1347626) (-820 "ODP.spad" 1337006 1337026 1337379 1337510) (-819 "ODETOOLS.spad" 1335655 1335674 1336996 1337001) (-818 "ODESYS.spad" 1333349 1333366 1335645 1335650) (-817 "ODERTRIC.spad" 1329358 1329375 1333306 1333311) (-816 "ODERED.spad" 1328757 1328781 1329348 1329353) (-815 "ODERAT.spad" 1326372 1326389 1328747 1328752) (-814 "ODEPRRIC.spad" 1323409 1323431 1326362 1326367) (-813 "ODEPROB.spad" 1322666 1322674 1323399 1323404) (-812 "ODEPRIM.spad" 1320000 1320022 1322656 1322661) (-811 "ODEPAL.spad" 1319386 1319410 1319990 1319995) (-810 "ODEPACK.spad" 1306052 1306060 1319376 1319381) (-809 "ODEINT.spad" 1305487 1305503 1306042 1306047) (-808 "ODEIFTBL.spad" 1302882 1302890 1305477 1305482) (-807 "ODEEF.spad" 1298373 1298389 1302872 1302877) (-806 "ODECONST.spad" 1297910 1297928 1298363 1298368) (-805 "ODECAT.spad" 1296508 1296516 1297900 1297905) (-804 "OCT.spad" 1294644 1294654 1295358 1295397) (-803 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"NREP.spad" 1241062 1241076 1242674 1242679) (-783 "NPCOEF.spad" 1240308 1240328 1241052 1241057) (-782 "NORMRETR.spad" 1239906 1239945 1240298 1240303) (-781 "NORMPK.spad" 1237808 1237827 1239896 1239901) (-780 "NORMMA.spad" 1237496 1237522 1237798 1237803) (-779 "NONE.spad" 1237237 1237245 1237486 1237491) (-778 "NONE1.spad" 1236913 1236923 1237227 1237232) (-777 "NODE1.spad" 1236400 1236416 1236903 1236908) (-776 "NNI.spad" 1235295 1235303 1236374 1236395) (-775 "NLINSOL.spad" 1233921 1233931 1235285 1235290) (-774 "NIPROB.spad" 1232462 1232470 1233911 1233916) (-773 "NFINTBAS.spad" 1230022 1230039 1232452 1232457) (-772 "NETCLT.spad" 1229996 1230007 1230012 1230017) (-771 "NCODIV.spad" 1228212 1228228 1229986 1229991) (-770 "NCNTFRAC.spad" 1227854 1227868 1228202 1228207) (-769 "NCEP.spad" 1226020 1226034 1227844 1227849) (-768 "NASRING.spad" 1225616 1225624 1226010 1226015) (-767 "NASRING.spad" 1225210 1225220 1225606 1225611) (-766 "NARNG.spad" 1224562 1224570 1225200 1225205) (-765 "NARNG.spad" 1223912 1223922 1224552 1224557) (-764 "NAGSP.spad" 1222989 1222997 1223902 1223907) (-763 "NAGS.spad" 1212650 1212658 1222979 1222984) (-762 "NAGF07.spad" 1211081 1211089 1212640 1212645) (-761 "NAGF04.spad" 1205483 1205491 1211071 1211076) (-760 "NAGF02.spad" 1199552 1199560 1205473 1205478) (-759 "NAGF01.spad" 1195313 1195321 1199542 1199547) (-758 "NAGE04.spad" 1189013 1189021 1195303 1195308) (-757 "NAGE02.spad" 1179673 1179681 1189003 1189008) (-756 "NAGE01.spad" 1175675 1175683 1179663 1179668) (-755 "NAGD03.spad" 1173679 1173687 1175665 1175670) (-754 "NAGD02.spad" 1166426 1166434 1173669 1173674) (-753 "NAGD01.spad" 1160719 1160727 1166416 1166421) (-752 "NAGC06.spad" 1156594 1156602 1160709 1160714) (-751 "NAGC05.spad" 1155095 1155103 1156584 1156589) (-750 "NAGC02.spad" 1154362 1154370 1155085 1155090) (-749 "NAALG.spad" 1153903 1153913 1154330 1154357) (-748 "NAALG.spad" 1153464 1153476 1153893 1153898) (-747 "MULTSQFR.spad" 1150422 1150439 1153454 1153459) (-746 "MULTFACT.spad" 1149805 1149822 1150412 1150417) (-745 "MTSCAT.spad" 1147899 1147920 1149703 1149800) (-744 "MTHING.spad" 1147558 1147568 1147889 1147894) (-743 "MSYSCMD.spad" 1146992 1147000 1147548 1147553) (-742 "MSET.spad" 1144950 1144960 1146698 1146737) (-741 "MSETAGG.spad" 1144795 1144805 1144918 1144945) (-740 "MRING.spad" 1141772 1141784 1144503 1144570) (-739 "MRF2.spad" 1141342 1141356 1141762 1141767) (-738 "MRATFAC.spad" 1140888 1140905 1141332 1141337) (-737 "MPRFF.spad" 1138928 1138947 1140878 1140883) (-736 "MPOLY.spad" 1136399 1136414 1136758 1136885) (-735 "MPCPF.spad" 1135663 1135682 1136389 1136394) (-734 "MPC3.spad" 1135480 1135520 1135653 1135658) (-733 "MPC2.spad" 1135126 1135159 1135470 1135475) (-732 "MONOTOOL.spad" 1133477 1133494 1135116 1135121) (-731 "MONOID.spad" 1132796 1132804 1133467 1133472) (-730 "MONOID.spad" 1132113 1132123 1132786 1132791) (-729 "MONOGEN.spad" 1130861 1130874 1131973 1132108) (-728 "MONOGEN.spad" 1129631 1129646 1130745 1130750) (-727 "MONADWU.spad" 1127661 1127669 1129621 1129626) (-726 "MONADWU.spad" 1125689 1125699 1127651 1127656) (-725 "MONAD.spad" 1124849 1124857 1125679 1125684) (-724 "MONAD.spad" 1124007 1124017 1124839 1124844) (-723 "MOEBIUS.spad" 1122743 1122757 1123987 1124002) (-722 "MODULE.spad" 1122613 1122623 1122711 1122738) (-721 "MODULE.spad" 1122503 1122515 1122603 1122608) (-720 "MODRING.spad" 1121838 1121877 1122483 1122498) (-719 "MODOP.spad" 1120503 1120515 1121660 1121727) (-718 "MODMONOM.spad" 1120234 1120252 1120493 1120498) (-717 "MODMON.spad" 1117029 1117045 1117748 1117901) (-716 "MODFIELD.spad" 1116391 1116430 1116931 1117024) (-715 "MMLFORM.spad" 1115251 1115259 1116381 1116386) (-714 "MMAP.spad" 1114993 1115027 1115241 1115246) (-713 "MLO.spad" 1113452 1113462 1114949 1114988) (-712 "MLIFT.spad" 1112064 1112081 1113442 1113447) (-711 "MKUCFUNC.spad" 1111599 1111617 1112054 1112059) (-710 "MKRECORD.spad" 1111203 1111216 1111589 1111594) (-709 "MKFUNC.spad" 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1046105) (-671 "LSAGG.spad" 1043597 1043607 1043896 1043923) (-670 "LSAGG.spad" 1043286 1043298 1043587 1043592) (-669 "LPOLY.spad" 1042240 1042259 1043142 1043211) (-668 "LPEFRAC.spad" 1041511 1041521 1042230 1042235) (-667 "LO.spad" 1040912 1040926 1041445 1041472) (-666 "LOGIC.spad" 1040514 1040522 1040902 1040907) (-665 "LOGIC.spad" 1040114 1040124 1040504 1040509) (-664 "LODOOPS.spad" 1039044 1039056 1040104 1040109) (-663 "LODO.spad" 1038428 1038444 1038724 1038763) (-662 "LODOF.spad" 1037474 1037491 1038385 1038390) (-661 "LODOCAT.spad" 1036140 1036150 1037430 1037469) (-660 "LODOCAT.spad" 1034804 1034816 1036096 1036101) (-659 "LODO2.spad" 1034077 1034089 1034484 1034523) (-658 "LODO1.spad" 1033477 1033487 1033757 1033796) (-657 "LODEEF.spad" 1032279 1032297 1033467 1033472) (-656 "LNAGG.spad" 1028111 1028121 1032269 1032274) (-655 "LNAGG.spad" 1023907 1023919 1028067 1028072) (-654 "LMOPS.spad" 1020675 1020692 1023897 1023902) (-653 "LMODULE.spad" 1020443 1020453 1020665 1020670) (-652 "LMDICT.spad" 1019730 1019740 1019994 1020021) (-651 "LLINSET.spad" 1019127 1019137 1019720 1019725) (-650 "LITERAL.spad" 1019033 1019044 1019117 1019122) (-649 "LIST.spad" 1016768 1016778 1018180 1018207) (-648 "LIST3.spad" 1016079 1016093 1016758 1016763) (-647 "LIST2.spad" 1014781 1014793 1016069 1016074) (-646 "LIST2MAP.spad" 1011684 1011696 1014771 1014776) (-645 "LINSET.spad" 1011306 1011316 1011674 1011679) (-644 "LINEXP.spad" 1010740 1010750 1011286 1011301) (-643 "LINDEP.spad" 1009549 1009561 1010652 1010657) (-642 "LIMITRF.spad" 1007477 1007487 1009539 1009544) (-641 "LIMITPS.spad" 1006380 1006393 1007467 1007472) (-640 "LIE.spad" 1004396 1004408 1005670 1005815) (-639 "LIECAT.spad" 1003872 1003882 1004322 1004391) (-638 "LIECAT.spad" 1003376 1003388 1003828 1003833) (-637 "LIB.spad" 1001426 1001434 1002035 1002050) (-636 "LGROBP.spad" 998779 998798 1001416 1001421) (-635 "LF.spad" 997734 997750 998769 998774) (-634 "LFCAT.spad" 996793 996801 997724 997729) (-633 "LEXTRIPK.spad" 992296 992311 996783 996788) (-632 "LEXP.spad" 990299 990326 992276 992291) (-631 "LETAST.spad" 989998 990006 990289 990294) (-630 "LEADCDET.spad" 988396 988413 989988 989993) (-629 "LAZM3PK.spad" 987100 987122 988386 988391) (-628 "LAUPOL.spad" 985793 985806 986693 986762) (-627 "LAPLACE.spad" 985376 985392 985783 985788) (-626 "LA.spad" 984816 984830 985298 985337) (-625 "LALG.spad" 984592 984602 984796 984811) (-624 "LALG.spad" 984376 984388 984582 984587) (-623 "KVTFROM.spad" 984111 984121 984366 984371) (-622 "KTVLOGIC.spad" 983623 983631 984101 984106) (-621 "KRCFROM.spad" 983361 983371 983613 983618) (-620 "KOVACIC.spad" 982084 982101 983351 983356) (-619 "KONVERT.spad" 981806 981816 982074 982079) (-618 "KOERCE.spad" 981543 981553 981796 981801) (-617 "KERNEL.spad" 980198 980208 981327 981332) (-616 "KERNEL2.spad" 979901 979913 980188 980193) (-615 "KDAGG.spad" 979010 979032 979881 979896) (-614 "KDAGG.spad" 978127 978151 979000 979005) (-613 "KAFILE.spad" 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"INTPM.spad" 925250 925266 926508 926513) (-571 "INTPAF.spad" 923114 923132 925182 925187) (-570 "INTPACK.spad" 913488 913496 923104 923109) (-569 "INT.spad" 912936 912944 913342 913483) (-568 "INTHERTR.spad" 912210 912227 912926 912931) (-567 "INTHERAL.spad" 911880 911904 912200 912205) (-566 "INTHEORY.spad" 908319 908327 911870 911875) (-565 "INTG0.spad" 902052 902070 908251 908256) (-564 "INTFTBL.spad" 896081 896089 902042 902047) (-563 "INTFACT.spad" 895140 895150 896071 896076) (-562 "INTEF.spad" 893525 893541 895130 895135) (-561 "INTDOM.spad" 892148 892156 893451 893520) (-560 "INTDOM.spad" 890833 890843 892138 892143) (-559 "INTCAT.spad" 889092 889102 890747 890828) (-558 "INTBIT.spad" 888599 888607 889082 889087) (-557 "INTALG.spad" 887787 887814 888589 888594) (-556 "INTAF.spad" 887287 887303 887777 887782) (-555 "INTABL.spad" 885805 885836 885968 885995) (-554 "INT8.spad" 885685 885693 885795 885800) (-553 "INT64.spad" 885564 885572 885675 885680) (-552 "INT32.spad" 885443 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862788) (-531 "INBCON.spad" 859371 859381 861073 861078) (-530 "INAST.spad" 859032 859040 859361 859366) (-529 "IMPTAST.spad" 858740 858748 859022 859027) (-528 "IMATRIX.spad" 857685 857711 858197 858224) (-527 "IMATQF.spad" 856779 856823 857641 857646) (-526 "IMATLIN.spad" 855384 855408 856735 856740) (-525 "ILIST.spad" 854042 854057 854567 854594) (-524 "IIARRAY2.spad" 853430 853468 853649 853676) (-523 "IFF.spad" 852840 852856 853111 853204) (-522 "IFAST.spad" 852454 852462 852830 852835) (-521 "IFARRAY.spad" 849947 849962 851637 851664) (-520 "IFAMON.spad" 849809 849826 849903 849908) (-519 "IEVALAB.spad" 849214 849226 849799 849804) (-518 "IEVALAB.spad" 848617 848631 849204 849209) (-517 "IDPO.spad" 848415 848427 848607 848612) (-516 "IDPOAMS.spad" 848171 848183 848405 848410) (-515 "IDPOAM.spad" 847891 847903 848161 848166) (-514 "IDPC.spad" 846829 846841 847881 847886) (-513 "IDPAM.spad" 846574 846586 846819 846824) (-512 "IDPAG.spad" 846321 846333 846564 846569) (-511 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(-470 "GRALG.spad" 774690 774702 775603 775608) (-469 "GRALG.spad" 773765 773779 774680 774685) (-468 "GPOLSET.spad" 773219 773242 773447 773474) (-467 "GOSPER.spad" 772488 772506 773209 773214) (-466 "GMODPOL.spad" 771636 771663 772456 772483) (-465 "GHENSEL.spad" 770719 770733 771626 771631) (-464 "GENUPS.spad" 767012 767025 770709 770714) (-463 "GENUFACT.spad" 766589 766599 767002 767007) (-462 "GENPGCD.spad" 766175 766192 766579 766584) (-461 "GENMFACT.spad" 765627 765646 766165 766170) (-460 "GENEEZ.spad" 763578 763591 765617 765622) (-459 "GDMP.spad" 760634 760651 761408 761535) (-458 "GCNAALG.spad" 754557 754584 760428 760495) (-457 "GCDDOM.spad" 753733 753741 754483 754552) (-456 "GCDDOM.spad" 752971 752981 753723 753728) (-455 "GB.spad" 750497 750535 752927 752932) (-454 "GBINTERN.spad" 746517 746555 750487 750492) (-453 "GBF.spad" 742284 742322 746507 746512) (-452 "GBEUCLID.spad" 740166 740204 742274 742279) (-451 "GAUSSFAC.spad" 739479 739487 740156 740161) (-450 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"DLAGG.spad" 293747 293757 295320 295325) (-244 "DIVRING.spad" 293289 293297 293691 293742) (-243 "DIVRING.spad" 292875 292885 293279 293284) (-242 "DISPLAY.spad" 291065 291073 292865 292870) (-241 "DIRPROD.spad" 280645 280661 281285 281416) (-240 "DIRPROD2.spad" 279463 279481 280635 280640) (-239 "DIRPCAT.spad" 278407 278423 279327 279458) (-238 "DIRPCAT.spad" 277080 277098 278002 278007) (-237 "DIOSP.spad" 275905 275913 277070 277075) (-236 "DIOPS.spad" 274901 274911 275885 275900) (-235 "DIOPS.spad" 273871 273883 274857 274862) (-234 "DIFRING.spad" 273167 273175 273851 273866) (-233 "DIFRING.spad" 272471 272481 273157 273162) (-232 "DIFEXT.spad" 271642 271652 272451 272466) (-231 "DIFEXT.spad" 270730 270742 271541 271546) (-230 "DIAGG.spad" 270360 270370 270710 270725) (-229 "DIAGG.spad" 269998 270010 270350 270355) (-228 "DHMATRIX.spad" 268310 268320 269455 269482) (-227 "DFSFUN.spad" 261950 261958 268300 268305) (-226 "DFLOAT.spad" 258681 258689 261840 261945) (-225 "DFINTTLS.spad" 256912 256928 258671 258676) (-224 "DERHAM.spad" 254826 254858 256892 256907) (-223 "DEQUEUE.spad" 254150 254160 254433 254460) (-222 "DEGRED.spad" 253767 253781 254140 254145) (-221 "DEFINTRF.spad" 251304 251314 253757 253762) (-220 "DEFINTEF.spad" 249814 249830 251294 251299) (-219 "DEFAST.spad" 249182 249190 249804 249809) (-218 "DECIMAL.spad" 247288 247296 247649 247742) (-217 "DDFACT.spad" 245101 245118 247278 247283) (-216 "DBLRESP.spad" 244701 244725 245091 245096) (-215 "DBASE.spad" 243365 243375 244691 244696) (-214 "DATAARY.spad" 242827 242840 243355 243360) (-213 "D03FAFA.spad" 242655 242663 242817 242822) (-212 "D03EEFA.spad" 242475 242483 242645 242650) (-211 "D03AGNT.spad" 241561 241569 242465 242470) (-210 "D02EJFA.spad" 241023 241031 241551 241556) (-209 "D02CJFA.spad" 240501 240509 241013 241018) (-208 "D02BHFA.spad" 239991 239999 240491 240496) (-207 "D02BBFA.spad" 239481 239489 239981 239986) (-206 "D02AGNT.spad" 234295 234303 239471 239476) (-205 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"CTORCAT.spad" 215702 215712 216445 216450) (-184 "CTORCALL.spad" 215291 215301 215692 215697) (-183 "CSTTOOLS.spad" 214536 214549 215281 215286) (-182 "CRFP.spad" 208260 208273 214526 214531) (-181 "CRCEAST.spad" 207980 207988 208250 208255) (-180 "CRAPACK.spad" 207031 207041 207970 207975) (-179 "CPMATCH.spad" 206535 206550 206956 206961) (-178 "CPIMA.spad" 206240 206259 206525 206530) (-177 "COORDSYS.spad" 201249 201259 206230 206235) (-176 "CONTOUR.spad" 200660 200668 201239 201244) (-175 "CONTFRAC.spad" 196410 196420 200562 200655) (-174 "CONDUIT.spad" 196168 196176 196400 196405) (-173 "COMRING.spad" 195842 195850 196106 196163) (-172 "COMPPROP.spad" 195360 195368 195832 195837) (-171 "COMPLPAT.spad" 195127 195142 195350 195355) (-170 "COMPLEX.spad" 189264 189274 189508 189769) (-169 "COMPLEX2.spad" 188979 188991 189254 189259) (-168 "COMPILER.spad" 188528 188536 188969 188974) (-167 "COMPFACT.spad" 188130 188144 188518 188523) (-166 "COMPCAT.spad" 186202 186212 187864 188125) (-165 "COMPCAT.spad" 184002 184014 185666 185671) (-164 "COMMUPC.spad" 183750 183768 183992 183997) (-163 "COMMONOP.spad" 183283 183291 183740 183745) (-162 "COMM.spad" 183094 183102 183273 183278) (-161 "COMMAAST.spad" 182857 182865 183084 183089) (-160 "COMBOPC.spad" 181772 181780 182847 182852) (-159 "COMBINAT.spad" 180539 180549 181762 181767) (-158 "COMBF.spad" 177921 177937 180529 180534) (-157 "COLOR.spad" 176758 176766 177911 177916) (-156 "COLONAST.spad" 176424 176432 176748 176753) (-155 "CMPLXRT.spad" 176135 176152 176414 176419) (-154 "CLLCTAST.spad" 175797 175805 176125 176130) (-153 "CLIP.spad" 171905 171913 175787 175792) (-152 "CLIF.spad" 170560 170576 171861 171900) (-151 "CLAGG.spad" 167065 167075 170550 170555) (-150 "CLAGG.spad" 163441 163453 166928 166933) (-149 "CINTSLPE.spad" 162772 162785 163431 163436) (-148 "CHVAR.spad" 160910 160932 162762 162767) (-147 "CHARZ.spad" 160825 160833 160890 160905) (-146 "CHARPOL.spad" 160335 160345 160815 160820) (-145 "CHARNZ.spad" 160088 160096 160315 160330) (-144 "CHAR.spad" 157962 157970 160078 160083) (-143 "CFCAT.spad" 157290 157298 157952 157957) (-142 "CDEN.spad" 156486 156500 157280 157285) (-141 "CCLASS.spad" 154635 154643 155897 155936) (-140 "CATEGORY.spad" 153677 153685 154625 154630) (-139 "CATCTOR.spad" 153568 153576 153667 153672) (-138 "CATAST.spad" 153186 153194 153558 153563) (-137 "CASEAST.spad" 152900 152908 153176 153181) (-136 "CARTEN.spad" 148187 148211 152890 152895) (-135 "CARTEN2.spad" 147577 147604 148177 148182) (-134 "CARD.spad" 144872 144880 147551 147572) (-133 "CAPSLAST.spad" 144646 144654 144862 144867) (-132 "CACHSET.spad" 144270 144278 144636 144641) (-131 "CABMON.spad" 143825 143833 144260 144265) (-130 "BYTEORD.spad" 143500 143508 143815 143820) (-129 "BYTE.spad" 142927 142935 143490 143495) (-128 "BYTEBUF.spad" 140786 140794 142096 142123) (-127 "BTREE.spad" 139859 139869 140393 140420) (-126 "BTOURN.spad" 138864 138874 139466 139493) (-125 "BTCAT.spad" 138256 138266 138832 138859) (-124 "BTCAT.spad" 137668 137680 138246 138251) (-123 "BTAGG.spad" 136796 136804 137636 137663) (-122 "BTAGG.spad" 135944 135954 136786 136791) (-121 "BSTREE.spad" 134685 134695 135551 135578) (-120 "BRILL.spad" 132882 132893 134675 134680) (-119 "BRAGG.spad" 131822 131832 132872 132877) (-118 "BRAGG.spad" 130726 130738 131778 131783) (-117 "BPADICRT.spad" 128707 128719 128962 129055) (-116 "BPADIC.spad" 128371 128383 128633 128702) (-115 "BOUNDZRO.spad" 128027 128044 128361 128366) (-114 "BOP.spad" 123209 123217 128017 128022) (-113 "BOP1.spad" 120675 120685 123199 123204) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 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93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 57dff726..18c8f05a 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(188562 . 3477887514) -(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((#0=(-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) #0#) |has| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (-312 (-2 (|:| -1963 |#1|) (|:| -2179 |#2|))))) -((((-569)) . T) (($) -2718 (|has| |#1| (-310)) (|has| |#1| (-367)) (|has| |#1| (-353)) (|has| |#1| (-561))) (((-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-353)) (|has| |#1| (-1044 (-412 (-569))))) ((|#1|) . T)) +(188562 . 3479296395) +(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((#0=(-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) #0#) |has| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (-312 (-2 (|:| -2003 |#1|) (|:| -2214 |#2|))))) +((((-569)) . 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T)) (|has| (-412 |#2|) (-147)) (|has| (-412 |#2|) (-145)) @@ -854,15 +854,15 @@ (|has| |#1| (-561)) (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) ((((-867)) . T)) -((((-2 (|:| -1963 (-1165)) (|:| -2179 |#1|))) . T)) +((((-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))) . T)) (|has| |#1| (-38 (-412 (-569)))) -((((-393) (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|))) . T)) +((((-393) (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))) . T)) (|has| |#1| (-38 (-412 (-569)))) (|has| |#2| (-1158)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) ((((-867)) . T) (((-1188)) . T)) ((((-867)) . T) (((-1188)) . T)) ((((-867)) . T) (((-1188)) . T)) @@ -880,7 +880,7 @@ ((((-393) (-1165)) . T)) (|has| |#1| (-561)) ((((-569) |#1|) . T)) -(-2718 (|has| |#1| (-173)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) +(-2774 (|has| |#1| (-173)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((((-569)) . T) (($) . T) (((-412 (-569))) . T)) ((((-569)) . T) (($) . T) (((-412 (-569))) . T)) (((|#2|) . T)) @@ -896,7 +896,7 @@ ((((-649 |#1|)) . T)) ((((-867)) . T)) ((((-541)) |has| |#1| (-619 (-541)))) -(-2718 (|has| |#1| (-855)) (|has| |#1| (-1106))) +(-2774 (|has| |#1| (-855)) (|has| |#1| (-1106))) (((|#2|) |has| |#2| (-312 |#2|))) (((#0=(-569) #0#) . T) ((#1=(-412 (-569)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -906,14 +906,14 @@ (((#0=(-569) #0#) . T) ((#1=(-412 (-569)) #1#) . T) (($ $) . T)) ((($) . T) (((-569)) . T) (((-412 (-569))) . T)) (|has| |#2| (-372)) -(-2718 (|has| |#1| (-855)) (|has| |#1| (-1106))) +(-2774 (|has| |#1| (-855)) (|has| |#1| (-1106))) (((|#1|) . T) (((-412 (-569))) . T) (($) . T)) (((|#1|) . T) (((-412 (-569))) . T) (($) . T)) (((|#1|) . T) (((-412 (-569))) . T) (($) . T)) ((((-569)) . T) (((-412 (-569))) . T) (($) . T)) -((($) -2718 (|has| |#1| (-367)) (|has| |#1| (-561))) (((-412 (-569))) -2718 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) ((|#1|) |has| |#1| (-173))) +((($) -2774 (|has| |#1| (-367)) (|has| |#1| (-561))) (((-412 (-569))) -2774 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) ((|#1|) |has| |#1| (-173))) (((|#1| |#2|) . T)) -((((-412 (-569))) -2718 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) (($) -2718 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-561))) ((|#1|) . T)) +((((-412 (-569))) -2774 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) (($) -2774 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-561))) ((|#1|) . T)) ((((-569)) . T) (((-412 (-569))) . T) (($) . T)) (((|#1| |#2|) . T)) ((((-867)) . T)) @@ -921,8 +921,8 @@ ((((-867)) . T)) ((((-867)) . T)) ((((-541)) |has| |#1| (-619 (-541)))) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) -((($) . T) (((-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) +((($) . T) (((-412 (-569))) -2774 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) ((((-867)) . T)) ((((-1181 |#1| |#2| |#3|) $) -12 (|has| (-1181 |#1| |#2| |#3|) (-289 (-1181 |#1| |#2| |#3|) (-1181 |#1| |#2| |#3|))) (|has| |#1| (-367))) (($ $) . T)) ((($ $) . T)) @@ -934,14 +934,14 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-569)) . T) (($) . T)) -((($) -2718 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) +((($) -2774 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) ((($) . T) (((-569)) . T) ((|#2|) . T)) ((((-569)) . T) (($) . T) ((|#2|) . T) (((-412 (-569))) |has| |#2| (-38 (-412 (-569))))) ((((-412 (-569))) . T) (((-569)) . T)) ((((-569) (-144)) . T)) ((((-144)) . T)) (((|#1|) . T)) -(-2718 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-173)) (|has| |#1| (-561)) (|has| |#1| (-1055))) +(-2774 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-173)) (|has| |#1| (-561)) (|has| |#1| (-1055))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) ((((-112)) . T)) @@ -950,31 +950,31 @@ ((((-867)) . T)) ((((-1188)) . T)) (|has| |#1| (-825)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) -((($) -2718 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-561))) (((-412 (-569))) -2718 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) ((|#2|) |has| |#1| (-367)) ((|#1|) . T)) -((((-412 (-569))) -2718 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) (($) -2718 (|has| |#1| (-367)) (|has| |#1| (-561))) ((|#2|) |has| |#1| (-367)) ((|#1|) |has| |#1| (-173))) -(((|#1|) . 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T)) -(-2718 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-561))) -(-2718 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-561))) -(-2718 (|has| |#1| (-173)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-173)) (|has| |#1| (-561))) ((((-867)) . T)) ((((-867)) . T)) ((((-867)) . T)) (((|#1| (-1273 |#1|) (-1273 |#1|)) . T)) ((((-569) (-144)) . T)) ((($) . T)) -(-2718 (|has| |#4| (-173)) (|has| |#4| (-853)) (|has| |#4| (-1055))) -(-2718 (|has| |#3| (-173)) (|has| |#3| (-853)) (|has| |#3| (-1055))) +(-2774 (|has| |#4| (-173)) (|has| |#4| (-853)) (|has| |#4| (-1055))) +(-2774 (|has| |#3| (-173)) (|has| |#3| (-853)) (|has| |#3| (-1055))) ((((-1188)) . T) (((-867)) . T)) ((((-1188)) . T)) ((((-867)) . T)) @@ -982,20 +982,20 @@ (((|#1| (-977)) . T)) (((|#1| |#1|) . T)) ((($) . 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T)) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) (|has| |#2| (-853)) (-12 (|has| |#1| (-798)) (|has| |#2| (-798))) (-12 (|has| |#1| (-798)) (|has| |#2| (-798))) -(-2718 (-12 (|has| |#1| (-478)) (|has| |#2| (-478))) (-12 (|has| |#1| (-731)) (|has| |#2| (-731)))) +(-2774 (-12 (|has| |#1| (-478)) (|has| |#2| (-478))) (-12 (|has| |#1| (-731)) (|has| |#2| (-731)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-173)) ((|#4|) . T) (((-569)) . T)) (((|#2|) |has| |#2| (-173))) @@ -1007,7 +1007,7 @@ (((|#1|) . T)) ((((-412 (-569))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-412 (-569))) . T)) -((($) . T) (((-412 (-569))) -2718 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) ((|#1|) . T)) +((($) . T) (((-412 (-569))) -2774 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) ((|#1|) . T)) (|has| |#1| (-833)) ((((-412 (-569))) |has| |#1| (-1044 (-412 (-569)))) (((-569)) |has| |#1| (-1044 (-569))) ((|#1|) . T)) (|has| |#1| (-1106)) @@ -1018,13 +1018,13 @@ (((|#4|) |has| |#4| (-1106))) (((|#3|) |has| |#3| (-1106))) (|has| |#3| (-372)) -((($) |has| |#1| (-561)) ((|#1|) . T) (((-412 (-569))) -2718 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-1044 (-412 (-569))))) (((-569)) . T)) -((((-412 (-569))) -2718 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) (($) -2718 (|has| |#1| (-367)) (|has| |#1| (-561))) (((-1265 |#1| |#2| |#3|)) |has| |#1| (-367)) ((|#1|) |has| |#1| (-173))) +((($) |has| |#1| (-561)) ((|#1|) . T) (((-412 (-569))) -2774 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-1044 (-412 (-569))))) (((-569)) . T)) +((((-412 (-569))) -2774 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) (($) -2774 (|has| |#1| (-367)) (|has| |#1| (-561))) (((-1265 |#1| |#2| |#3|)) |has| |#1| (-367)) ((|#1|) |has| |#1| (-173))) ((((-867)) . T)) ((((-867)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-173)) (((-412 (-569))) -2718 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) (($) -2718 (|has| |#1| (-367)) (|has| |#1| (-561)))) +(((|#1|) |has| |#1| (-173)) (((-412 (-569))) -2774 (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-367))) (($) -2774 (|has| |#1| (-367)) (|has| |#1| (-561)))) ((($) |has| |#1| (-561)) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) (((|#1| |#1|) |has| |#1| (-173))) (|has| |#2| (-367)) @@ -1032,19 +1032,19 @@ (((|#1|) |has| |#1| (-173))) ((((-412 (-569))) . T) (((-569)) . T)) ((($) . T) (((-569)) . T) (((-412 (-569))) |has| |#2| (-38 (-412 (-569)))) ((|#2|) . T)) -((($ $) -2718 (|has| |#1| (-173)) (|has| |#1| (-561))) ((|#1| |#1|) . T) ((#0=(-412 (-569)) #0#) |has| |#1| (-38 (-412 (-569))))) +((($ $) -2774 (|has| |#1| (-173)) (|has| |#1| (-561))) ((|#1| |#1|) . T) ((#0=(-412 (-569)) #0#) |has| |#1| (-38 (-412 (-569))))) ((($) . T) (((-569)) . 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T)) -(-2718 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-173)) (|has| |#1| (-561)) (|has| |#1| (-1055))) +(-2774 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-173)) (|has| |#1| (-561)) (|has| |#1| (-1055))) (((|#1|) |has| |#1| (-173))) (|has| $ (-147)) (|has| $ (-147)) @@ -1054,15 +1054,15 @@ ((((-867)) . T)) (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-173)) (|has| |#1| (-478)) (|has| |#1| (-561)) (|has| |#1| (-1055)) (|has| |#1| (-1118))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-173)) (|has| |#1| (-478)) (|has| |#1| (-561)) (|has| |#1| (-1055)) (|has| |#1| (-1118))) ((($ $) |has| |#1| (-289 $ $)) ((|#1| $) |has| |#1| (-289 |#1| |#1|))) (((|#1| (-412 (-569))) . T)) (((|#1|) . T)) ((((-412 (-569))) . T) (((-569)) . T) (($) . T)) ((((-1183)) . T)) (|has| |#1| (-561)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) (|has| |#1| (-561)) (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) @@ -1073,7 +1073,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-853)) -(((|#2| (-241 (-2394 |#1|) (-776)) (-869 |#1|)) . T)) +(((|#2| (-241 (-2426 |#1|) (-776)) (-869 |#1|)) . T)) (|has| |#3| (-853)) (((|#1| (-536 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -1088,20 +1088,20 @@ (|has| |#1| (-145)) ((((-412 (-569))) |has| |#2| (-367)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) -(-2718 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) -(-2718 (|has| |#1| (-353)) (|has| |#1| (-372))) +(-2774 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) +(-2774 (|has| |#1| (-353)) (|has| |#1| (-372))) ((((-1148 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-173)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-234)) (|has| |#2| (-1055))) -(((|#2|) . T) (((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) -(-2718 (|has| |#3| (-798)) (|has| |#3| (-853))) -(-2718 (|has| |#3| (-798)) (|has| |#3| (-853))) +(((|#2|) . T) (((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) +(-2774 (|has| |#3| (-798)) (|has| |#3| (-853))) +(-2774 (|has| |#3| (-798)) (|has| |#3| (-853))) ((((-867)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-704)) . T)) -(-2718 (|has| |#2| (-173)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2774 (|has| |#2| (-173)) (|has| |#2| (-853)) (|has| |#2| (-1055))) (|has| |#1| (-561)) (((|#1|) . T)) (((|#1|) . T)) @@ -1125,11 +1125,11 @@ (((|#1| (-412 (-569))) . T)) (((|#3|) . T) (((-617 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) (((|#1|) . 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T)) -(((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) (((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) |has| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (-312 (-2 (|:| -1963 |#1|) (|:| -2179 |#2|))))) -(((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106))) (((-2 (|:| -1963 (-1165)) (|:| -2179 |#1|))) |has| (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|)) (-312 (-2 (|:| -1963 (-1165)) (|:| -2179 |#1|))))) +(((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) (((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) |has| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (-312 (-2 (|:| -2003 |#1|) (|:| -2214 |#2|))))) +(((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106))) (((-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))) |has| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (-312 (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))))) ((((-867)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1152,10 +1152,10 @@ ((($) . T) (((-569)) . T) (((-412 (-569))) |has| |#1| (-38 (-412 (-569)))) ((|#1|) . T)) ((((-569)) . T) (($) . 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T)) -((($) -2718 (|has| |#1| (-310)) (|has| |#1| (-367)) (|has| |#1| (-353)) (|has| |#1| (-561))) (((-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) +((($) -2774 (|has| |#1| (-310)) (|has| |#1| (-367)) (|has| |#1| (-353)) (|has| |#1| (-561))) (((-412 (-569))) -2774 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) ((((-569) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -1213,41 +1213,41 @@ (-12 (|has| |#1| (-372)) (|has| |#2| (-372))) ((((-867)) . T)) ((((-1183) |#1|) |has| |#1| (-519 (-1183) |#1|)) ((|#1| |#1|) |has| |#1| (-312 |#1|))) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) (((|#1|) . 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T)) -(-2718 (|has| |#1| (-855)) (|has| |#1| (-1106))) -(((|#2| |#2|) -2718 (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-1055))) (($ $) |has| |#2| (-173))) +(-2774 (|has| |#1| (-855)) (|has| |#1| (-1106))) +(((|#2| |#2|) -2774 (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-1055))) (($ $) |has| |#2| (-173))) (((|#2|) . T) (((-569)) . T)) ((((-867)) . T)) ((((-867)) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T) ((|#2|) . T)) ((((-867)) . T)) ((((-867)) . T)) ((((-1165) (-1183) (-569) (-226) (-867)) . T)) @@ -1472,9 +1472,9 @@ ((((-412 (-569))) . T) (($) . T)) ((((-867)) . T)) ((((-541)) |has| |#1| (-619 (-541)))) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) ((($) . T) (((-412 (-569))) . T)) -(((|#2|) -2718 (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-1055))) (($) |has| |#2| (-173))) +(((|#2|) -2774 (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-1055))) (($) |has| |#2| (-173))) (|has| $ (-147)) ((((-412 |#2|)) . T)) ((((-412 (-569))) |has| #0=(-412 |#2|) (-1044 (-412 (-569)))) (((-569)) |has| #0# (-1044 (-569))) ((#0#) . T)) @@ -1485,11 +1485,11 @@ (((|#3|) |has| |#3| (-173))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) (|has| |#1| (-147)) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) (|has| |#1| (-147)) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-234)) @@ -1527,7 +1527,7 @@ ((((-1005 |#1|)) . T) ((|#1|) . T)) ((((-867)) . T)) ((((-867)) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) ((((-412 (-569))) . T) (((-412 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1179 |#1|)) . T)) ((((-569)) . T) (($) . T) (((-412 (-569))) . T)) @@ -1536,8 +1536,8 @@ (((|#1|) . T) (((-569)) . T) (($) . T)) (((|#2|) . T)) ((((-569)) . T) (($) . T) (((-412 (-569))) . T)) -((((-2 (|:| -1963 (-1165)) (|:| -2179 |#1|))) . T)) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) +((((-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))) . T)) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) ((((-569) |#2|) . T)) (((|#1|) . T) (((-412 (-569))) . T) (((-569)) . T) (($) . T)) ((($) . T) (((-569)) . T) (((-412 (-569))) . T)) @@ -1550,7 +1550,7 @@ (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) ((((-1265 |#1| |#2| |#3|)) |has| |#1| (-367))) -(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((#0=(-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) #0#) |has| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (-312 (-2 (|:| -1963 |#1|) (|:| -2179 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((#0=(-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) #0#) |has| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (-312 (-2 (|:| -2003 |#1|) (|:| -2214 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1106)) (|has| |#1| (-38 (-412 (-569)))) @@ -1561,15 +1561,15 @@ (|has| |#1| (-38 (-412 (-569)))) (((|#2|) . 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T)) (|has| |#2| (-147)) (|has| |#1| (-478)) -(-2718 (|has| |#1| (-478)) (|has| |#1| (-731)) (|has| |#1| (-906 (-1183))) (|has| |#1| (-1055))) +(-2774 (|has| |#1| (-478)) (|has| |#1| (-731)) (|has| |#1| (-906 (-1183))) (|has| |#1| (-1055))) (|has| |#1| (-367)) ((((-867)) . T)) (|has| |#1| (-38 (-412 (-569)))) @@ -1668,8 +1668,8 @@ (|has| |#1| (-853)) ((((-867)) . T)) (((|#2|) . 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T)) (((|#1| (-607 |#1| |#3|) (-607 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-173))) (((|#1|) . T)) @@ -2173,12 +2173,12 @@ (((|#2|) |has| |#2| (-173))) (|has| |#2| (-853)) ((((-569)) . T) ((|#2|) . T) (((-412 (-569))) |has| |#2| (-1044 (-412 (-569))))) -((((-112)) |has| |#1| (-1106)) (((-867)) -2718 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-478)) (|has| |#1| (-731)) (|has| |#1| (-906 (-1183))) (|has| |#1| (-1055)) (|has| |#1| (-1118)) (|has| |#1| (-1106)))) +((((-112)) |has| |#1| (-1106)) (((-867)) -2774 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-478)) (|has| |#1| (-731)) (|has| |#1| (-906 (-1183))) (|has| |#1| (-1055)) (|has| |#1| (-1118)) (|has| |#1| (-1106)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-569)) . T) (((-412 (-569))) . T)) ((((-569)) . T) (($) . T) (((-412 (-569))) . T)) -((((-2 (|:| -1963 (-1165)) (|:| -2179 (-52)))) . T)) +((((-2 (|:| -2003 (-1165)) (|:| -2214 (-52)))) . T)) (((|#1|) . T) (((-412 (-569))) . T) (((-569)) . T) (($) . T)) (((|#1|) . T) (((-412 (-569))) . T) (((-569)) . T) (($) . T)) (((|#1|) . T) (((-412 (-569))) . T) (((-569)) . T) (($) . T)) @@ -2190,17 +2190,17 @@ ((((-704)) . T) (((-412 (-569))) . T) (((-569)) . T)) (((|#1| |#1|) |has| |#1| (-173))) (((|#2|) . T)) -((($) . T) (((-569)) . T) (((-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) +((($) . T) (((-569)) . T) (((-412 (-569))) -2774 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) ((((-569) |#1|) . 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T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) ((((-412 (-569))) . T) (($) . T)) (|has| |#1| (-478)) (|has| |#1| (-372)) (|has| |#1| (-372)) (|has| |#1| (-372)) (|has| |#1| (-367)) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-173)) (|has| |#1| (-478)) (|has| |#1| (-561)) (|has| |#1| (-1055)) (|has| |#1| (-1118))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-173)) (|has| |#1| (-478)) (|has| |#1| (-561)) (|has| |#1| (-1055)) (|has| |#1| (-1118))) (|has| |#1| (-38 (-412 (-569)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2237,12 +2237,12 @@ (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-855)) -((((-2 (|:| -1963 (-1165)) (|:| -2179 |#1|))) . T)) +((((-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-569)) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) |has| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (-312 (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)))) ((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106)))) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) |has| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (-312 (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)))) ((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2262,12 +2262,12 @@ ((((-541)) |has| |#1| (-619 (-541))) (((-898 (-569))) |has| |#1| (-619 (-898 (-569)))) (((-898 (-383))) |has| |#1| (-619 (-898 (-383)))) (((-383)) . #0=(|has| |#1| (-1028))) (((-226)) . #0#)) (((|#1|) |has| |#1| (-367))) ((((-867)) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) ((($ $) . T) (((-617 $) $) . T)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) ((($) . 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T)) ((((-569)) . T)) (|has| |#1| (-367)) -(-2718 (-12 (|has| (-1265 |#1| |#2| |#3|) (-147)) (|has| |#1| (-367))) (|has| |#1| (-147))) -(-2718 (-12 (|has| (-1265 |#1| |#2| |#3|) (-145)) (|has| |#1| (-367))) (|has| |#1| (-145))) +(-2774 (-12 (|has| (-1265 |#1| |#2| |#3|) (-147)) (|has| |#1| (-367))) (|has| |#1| (-147))) +(-2774 (-12 (|has| (-1265 |#1| |#2| |#3|) (-145)) (|has| |#1| (-367))) (|has| |#1| (-145))) (|has| |#1| (-367)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2322,25 +2322,25 @@ (|has| |#1| (-1106)) ((((-1148 |#2| |#1|)) . T) ((|#1|) . T) (((-569)) . T)) (((|#1| |#2|) . T)) -((((-569)) . T) ((|#1|) . T) (((-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-1044 (-412 (-569)))))) +((((-569)) . T) ((|#1|) . T) (((-412 (-569))) -2774 (|has| |#1| (-367)) (|has| |#1| (-1044 (-412 (-569)))))) (((|#1|) . T) (((-569)) |has| |#1| (-644 (-569)))) (((|#3|) |has| |#3| (-173))) (((|#2|) . T) (($) . T) (((-569)) . T)) (((|#1|) . T) (($) . T) (((-569)) . 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T)) ((((-569) |#1|) . T)) ((((-1183)) |has| (-412 |#2|) (-906 (-1183)))) -(((|#1|) . T) (($) -2718 (|has| |#1| (-293)) (|has| |#1| (-367))) (((-412 (-569))) |has| |#1| (-367))) +(((|#1|) . T) (($) -2774 (|has| |#1| (-293)) (|has| |#1| (-367))) (((-412 (-569))) |has| |#1| (-367))) ((((-541)) |has| |#2| (-619 (-541)))) ((((-694 |#2|)) . T) (((-867)) . T)) (((|#1|) . T)) @@ -2348,22 +2348,22 @@ (((|#4|) -12 (|has| |#4| (-312 |#4|)) (|has| |#4| (-1106)))) ((((-875 |#1|)) . T)) (((|#1|) |has| |#1| (-173))) -(-2718 (|has| |#4| (-798)) (|has| |#4| (-853))) -(-2718 (|has| |#3| (-798)) (|has| |#3| (-853))) +(-2774 (|has| |#4| (-798)) (|has| |#4| (-853))) +(-2774 (|has| |#3| (-798)) (|has| |#3| (-853))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) ((((-867)) . T)) ((((-867)) . T)) (((|#1|) . T)) ((($) . T) (((-569)) . T) ((|#2|) . T)) (((|#4|) -12 (|has| |#4| (-312 |#4|)) (|has| |#4| (-1106)))) -(((|#3|) -2718 (|has| |#3| (-173)) (|has| |#3| (-367)))) +(((|#3|) -2774 (|has| |#3| (-173)) (|has| |#3| (-367)))) (((|#2|) |has| |#2| (-1055))) (((|#3|) . T)) (((|#1|) . T)) ((((-412 |#2|)) . T)) -(((|#2|) -2718 (|has| |#2| (-173)) (|has| |#2| (-367)))) +(((|#2|) -2774 (|has| |#2| (-173)) (|has| |#2| (-367)))) (((|#1|) . T)) -(((|#2|) -2718 (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-1055))) (($) |has| |#2| (-173))) +(((|#2|) -2774 (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-1055))) (($) |has| |#2| (-173))) (((|#3|) -12 (|has| |#3| (-312 |#3|)) (|has| |#3| (-1106)))) ((((-569) |#1|) . T)) (((|#1|) . T)) @@ -2372,17 +2372,17 @@ ((((-412 (-569))) . T) (($) . T)) ((((-412 (-569))) . T) (($) . T)) ((((-412 (-569))) . T) (($) . T)) -(-2718 (|has| |#1| (-457)) (|has| |#1| (-1227))) +(-2774 (|has| |#1| (-457)) (|has| |#1| (-1227))) ((($) . 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T)) @@ -2473,10 +2473,10 @@ ((((-867)) . T)) ((((-867)) . T)) ((((-541)) |has| |#1| (-619 (-541)))) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) ((((-569)) . T) (($) . T) (((-412 (-569))) . T)) ((((-1183) |#1|) |has| |#1| (-519 (-1183) |#1|)) ((|#1| |#1|) |has| |#1| (-312 |#1|))) -(((|#1|) -2718 (|has| |#1| (-173)) (|has| |#1| (-367)))) +(((|#1|) -2774 (|has| |#1| (-173)) (|has| |#1| (-367)))) (((|#1|) . T) (((-412 (-569))) . T) (($) . T)) ((((-569)) . T) (((-412 (-569))) . T) (($) . T)) (((|#1|) . T) (((-412 (-569))) . T) (($) . T)) @@ -2486,10 +2486,10 @@ (((|#1|) . T) (($) . T) (((-412 (-569))) . T)) (((|#1|) . T) (($) . T) (((-412 (-569))) . T)) (((|#2|) |has| |#2| (-367))) -((($) -2718 (|has| |#1| (-367)) (|has| |#1| (-353))) (((-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) +((($) -2774 (|has| |#1| (-367)) (|has| |#1| (-353))) (((-412 (-569))) -2774 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) (((|#2|) . T)) ((((-412 (-569))) . T) (((-704)) . T) (($) . T)) -((($) . T) (((-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) +((($) . T) (((-412 (-569))) -2774 (|has| |#1| (-367)) (|has| |#1| (-353))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) (((#0=(-785 |#1| (-869 |#2|)) #0#) |has| (-785 |#1| (-869 |#2|)) (-312 (-785 |#1| (-869 |#2|))))) ((((-569)) . T) (($) . T)) @@ -2508,13 +2508,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . 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T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) ((((-867)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-569)) . T)) (((|#1| (-412 (-569))) . T)) (((|#1|) . T)) -(-2718 (|has| |#1| (-293)) (|has| |#1| (-367))) +(-2774 (|has| |#1| (-293)) (|has| |#1| (-367))) ((((-144)) . T)) ((((-412 |#2|)) . T) (((-412 (-569))) . T) (($) . T)) (|has| |#1| (-853)) @@ -2682,7 +2682,7 @@ ((((-867)) . T)) ((((-867)) . T)) ((((-188)) . T) (((-867)) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-867)) . T)) ((((-867)) . T)) @@ -2695,7 +2695,7 @@ ((((-867)) . T)) ((((-1165)) . T)) ((((-1183) |#1|) |has| |#1| (-519 (-1183) |#1|)) ((|#1| |#1|) |has| |#1| (-312 |#1|))) -((((-2 (|:| -1963 (-1165)) (|:| -2179 |#1|))) . T)) +((((-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))) . T)) (|has| |#1| (-855)) ((((-867)) . T)) ((((-541)) |has| |#1| (-619 (-541)))) @@ -2707,16 +2707,16 @@ (((|#2|) . T)) ((((-916 |#1|)) . T) (((-412 (-569))) . T) (($) . T)) ((($) . T) (((-569)) . T) (((-412 (-569))) . T) (((-617 $)) . T)) -(-2718 (|has| |#4| (-173)) (|has| |#4| (-731)) (|has| |#4| (-853)) (|has| |#4| (-1055))) -(-2718 (|has| |#3| (-173)) (|has| |#3| (-731)) (|has| |#3| (-853)) (|has| |#3| (-1055))) +(-2774 (|has| |#4| (-173)) (|has| |#4| (-731)) (|has| |#4| (-853)) (|has| |#4| (-1055))) +(-2774 (|has| |#3| (-173)) (|has| |#3| (-731)) (|has| |#3| (-853)) (|has| |#3| (-1055))) ((((-1183) (-52)) . T)) -(-2718 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) +(-2774 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2718 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) -(-2718 (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2774 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2774 (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-853)) (|has| |#2| (-1055))) (|has| |#1| (-915)) ((((-916 |#1|)) . T) (((-412 (-569))) . T) (($) . T) (((-569)) . T)) (|has| |#1| (-915)) @@ -2733,12 +2733,12 @@ (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) (|has| |#1| (-825)) (((#0=(-916 |#1|) #0#) . T) (($ $) . T) ((#1=(-412 (-569)) #1#) . T)) ((((-412 |#2|)) . T)) (|has| |#1| (-853)) -((((-1209 |#1|)) . T) (((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) +((((-1209 |#1|)) . T) (((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) (((|#1| |#1|) . T) ((#0=(-412 (-569)) #0#) . T) ((#1=(-569) #1#) . T) (($ $) . T)) ((((-916 |#1|)) . T) (($) . T) (((-412 (-569))) . T)) (((|#2|) |has| |#2| (-1055)) (((-569)) -12 (|has| |#2| (-644 (-569))) (|has| |#2| (-1055)))) @@ -2754,28 +2754,28 @@ (((|#2|) |has| |#2| (-173))) (((|#1|) . T)) (((|#2|) . T)) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) -((((-2 (|:| -1963 (-1183)) (|:| -2179 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1963 (-1183)) (|:| -2179 #0#))) . T)) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) +((((-2 (|:| -2003 (-1183)) (|:| -2214 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2003 (-1183)) (|:| -2214 #0#))) . T)) (|has| |#1| (-353)) ((((-569)) . T)) ((((-867)) . T)) (((|#1|) . T)) (((#0=(-1259 |#1| |#2| |#3| |#4|) $) |has| #0# (-289 #0# #0#))) (|has| |#1| (-367)) -(((|#1|) -2718 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-1055))) (($) -2718 (|has| |#1| (-906 (-1183))) (|has| |#1| (-1055))) (((-569)) -2718 (|has| |#1| (-21)) (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-906 (-1183))) (|has| |#1| (-1055)))) +(((|#1|) -2774 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-1055))) (($) -2774 (|has| |#1| (-906 (-1183))) (|has| |#1| (-1055))) (((-569)) -2774 (|has| |#1| (-21)) (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-906 (-1183))) (|has| |#1| (-1055)))) (((#0=(-1088) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-353))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-353))) (((#0=(-412 (-569)) #0#) . T) ((#1=(-704) #1#) . T) (($ $) . T)) ((((-319 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-412 (-569))) |has| |#1| (-367))) ((((-867)) . T)) (|has| |#1| (-1106)) (((|#1|) . T)) -(((|#1|) -2718 (|has| |#2| (-371 |#1|)) (|has| |#2| (-422 |#1|)))) -(((|#1|) -2718 (|has| |#2| (-371 |#1|)) (|has| |#2| (-422 |#1|)))) +(((|#1|) -2774 (|has| |#2| (-371 |#1|)) (|has| |#2| (-422 |#1|)))) +(((|#1|) -2774 (|has| |#2| (-371 |#1|)) (|has| |#2| (-422 |#1|)))) (((|#2|) . T)) ((((-412 (-569))) . T) (((-704)) . T) (($) . T)) ((((-584)) . T)) @@ -2800,7 +2800,7 @@ (((|#1|) . T)) ((((-569)) . T)) (((|#2|) . T) (((-412 (-569))) |has| |#1| (-1044 (-412 (-569)))) ((|#1|) . T) (($) . T) (((-569)) . T)) -(-2718 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) +(-2774 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) (((|#2|) . T) (((-569)) |has| |#2| (-644 (-569)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2844,7 +2844,7 @@ (|has| |#2| (-1028)) ((($) . T)) (|has| |#1| (-915)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2853,10 +2853,10 @@ (|has| |#1| (-367)) ((((-916 |#1|)) . T)) ((($) . T) (((-569)) . T) ((|#1|) . T) (((-412 (-569))) . T)) -((($) -2718 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) -((($) |has| |#1| (-853)) (((-569)) -2718 (|has| |#1| (-21)) (|has| |#1| (-853)))) +((($) -2774 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) +((($) |has| |#1| (-853)) (((-569)) -2774 (|has| |#1| (-21)) (|has| |#1| (-853)))) ((($ $) . T) ((#0=(-412 (-569)) #0#) . T)) -(-2718 (|has| |#1| (-372)) (|has| |#1| (-855))) +(-2774 (|has| |#1| (-372)) (|has| |#1| (-855))) (((|#1|) . T)) ((((-776)) . T)) ((((-867)) . T)) @@ -2867,17 +2867,17 @@ ((((-569)) . T) (($) . T)) ((((-569)) . T) (($) . T)) ((((-776) |#1|) . T)) -(((|#2| (-241 (-2394 |#1|) (-776))) . T)) +(((|#2| (-241 (-2426 |#1|) (-776))) . T)) (((|#1| (-536 |#3|)) . T)) ((((-412 (-569))) . T)) -(-2718 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) +(-2774 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((((-1165)) . T) (((-867)) . T)) -(((#0=(-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) #0#) |has| (-2 (|:| -1963 (-1183)) (|:| -2179 (-52))) (-312 (-2 (|:| -1963 (-1183)) (|:| -2179 (-52)))))) +(((#0=(-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) #0#) |has| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (-312 (-2 (|:| -2003 (-1183)) (|:| -2214 (-52)))))) ((((-1165)) . T)) (|has| |#1| (-915)) (|has| |#2| (-367)) (((|#1|) . T) (($) . T) (((-569)) . T)) -(-2718 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2774 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) ((((-170 (-383))) . T) (((-226)) . T) (((-383)) . T)) ((((-867)) . T)) (((|#1|) . T)) @@ -2894,11 +2894,11 @@ (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) -(-2718 (|has| |#1| (-310)) (|has| |#1| (-367)) (|has| |#1| (-353))) +(-2774 (|has| |#1| (-310)) (|has| |#1| (-367)) (|has| |#1| (-353))) (|has| |#1| (-38 (-412 (-569)))) (-12 (|has| |#1| (-550)) (|has| |#1| (-833))) ((((-867)) . T)) -((((-1183)) -2718 (-12 (|has| |#1| (-15 * (|#1| (-569) |#1|))) (|has| |#1| (-906 (-1183)))) (-12 (|has| |#1| (-367)) (|has| |#2| (-906 (-1183)))))) +((((-1183)) -2774 (-12 (|has| |#1| (-15 * (|#1| (-569) |#1|))) (|has| |#1| (-906 (-1183)))) (-12 (|has| |#1| (-367)) (|has| |#2| (-906 (-1183)))))) (|has| |#1| (-367)) ((((-1183)) -12 (|has| |#1| (-15 * (|#1| (-412 (-569)) |#1|))) (|has| |#1| (-906 (-1183))))) (|has| |#1| (-367)) @@ -2910,7 +2910,7 @@ (((|#2|) |has| |#1| (-367))) (((|#2|) |has| |#1| (-367))) ((((-569)) . T) (($) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-173))) (((|#1|) . T)) @@ -2940,11 +2940,11 @@ (((|#2|) |has| |#1| (-367))) ((((-383)) -12 (|has| |#1| (-367)) (|has| |#2| (-892 (-383)))) (((-569)) -12 (|has| |#1| (-367)) (|has| |#2| (-892 (-569))))) (|has| |#1| (-367)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) (|has| |#1| (-367)) (((|#1|) . T)) ((($) . T) (((-569)) . T) ((|#2|) . T)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) (|has| |#1| (-367)) (((|#3|) . T)) ((((-1165)) . T) (((-511)) . T) (((-226)) . T) (((-569)) . T)) @@ -2952,23 +2952,23 @@ (|has| |#1| (-561)) (((|#4| |#4|) -12 (|has| |#4| (-312 |#4|)) (|has| |#4| (-1106)))) ((((-412 |#2|)) . T) (((-412 (-569))) . T) (($) . T) (((-569)) . T)) -(-2718 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2774 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) (((|#2|) . T)) (((|#2|) . T)) -(-2718 (|has| |#2| (-173)) (|has| |#2| (-731)) (|has| |#2| (-853)) (|has| |#2| (-1055))) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) -((((-2 (|:| -1963 (-1165)) (|:| -2179 |#1|))) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +(-2774 (|has| |#2| (-173)) (|has| |#2| (-731)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) +((((-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) (|has| |#1| (-38 (-412 (-569)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-412 (-569)))) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) ((($) . T)) ((((-1165) |#1|) . T)) (|has| |#1| (-147)) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) (|has| |#1| (-147)) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-372))) ((($) . T)) (|has| |#1| (-147)) ((((-586 |#1|)) . T)) @@ -2982,7 +2982,7 @@ ((((-412 (-569))) |has| |#2| (-1044 (-569))) (((-569)) |has| |#2| (-1044 (-569))) (((-1183)) |has| |#2| (-1044 (-1183))) ((|#2|) . T)) (((#0=(-412 |#2|) #0#) . T) ((#1=(-412 (-569)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2718 (|has| |#1| (-145)) (|has| |#1| (-353))) +(-2774 (|has| |#1| (-145)) (|has| |#1| (-353))) (|has| |#1| (-147)) ((((-867)) . T)) ((($) . T)) @@ -3007,7 +3007,7 @@ ((((-867)) . T)) ((((-916 |#1|)) . T) (((-412 (-569))) . T) (($) . T) (((-569)) . T)) ((((-541)) |has| |#1| (-619 (-541)))) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-855)) (|has| |#1| (-1106)))) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-855)) (|has| |#1| (-1106)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3029,7 +3029,7 @@ ((((-569)) . T)) ((((-867)) . T)) ((((-569)) . T)) -(-2718 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-2774 (|has| |#2| (-798)) (|has| |#2| (-853))) ((((-170 (-383))) . T) (((-226)) . T) (((-383)) . T)) ((((-867)) . T)) ((((-867)) . T)) @@ -3041,9 +3041,9 @@ (((|#1|) . T) (($) . T) (((-412 (-569))) . 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T)) (|has| |#1| (-367)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) (|has| |#1| (-367)) (|has| |#1| (-561)) (|has| |#1| (-1106)) ((((-785 |#1| (-869 |#2|))) |has| (-785 |#1| (-869 |#2|)) (-312 (-785 |#1| (-869 |#2|))))) -(-2718 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) +(-2774 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3090,13 +3090,13 @@ (|has| |#2| (-367)) ((((-586 |#1|)) . T) (((-412 (-569))) . T) (($) . T) (((-569)) . T)) ((((-569)) . T) (((-412 (-569))) . T) (($) . T)) -((((-2 (|:| -1963 (-1165)) (|:| -2179 (-52)))) . T)) +((((-2 (|:| -2003 (-1165)) (|:| -2214 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-569)) . T)) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) ((((-867)) . T)) ((((-867)) . T)) -(-2718 (|has| |#3| (-798)) (|has| |#3| (-853))) +(-2774 (|has| |#3| (-798)) (|has| |#3| (-853))) ((((-867)) . 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T)) -(-2718 (|has| |#2| (-798)) (|has| |#2| (-853))) -(-2718 (-12 (|has| |#1| (-798)) (|has| |#2| (-798))) (-12 (|has| |#1| (-855)) (|has| |#2| (-855)))) +(-2774 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-2774 (-12 (|has| |#1| (-798)) (|has| |#2| (-798))) (-12 (|has| |#1| (-855)) (|has| |#2| (-855)))) ((((-875 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-372)) @@ -3283,7 +3283,7 @@ (((|#1|) . T)) ((((-867)) . T)) (|has| |#2| (-915)) -((((-2 (|:| -1963 (-1183)) (|:| -2179 (-52)))) . T)) +((((-2 (|:| -2003 (-1183)) (|:| -2214 (-52)))) . T)) ((((-541)) |has| |#2| (-619 (-541))) (((-898 (-383))) |has| |#2| (-619 (-898 (-383)))) (((-898 (-569))) |has| |#2| (-619 (-898 (-569))))) ((((-867)) . T)) ((((-867)) . T)) @@ -3310,7 +3310,7 @@ ((((-1188)) . T)) ((((-649 |#1|)) . T)) ((($) . T) (((-569)) . T) (((-1259 |#1| |#2| |#3| |#4|)) . T) (((-412 (-569))) . 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T)) -(-2718 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) -(-2718 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-798)) (|has| |#2| (-798)))) +(-2774 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2774 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-798)) (|has| |#2| (-798)))) ((((-1265 |#1| |#2| |#3|)) |has| |#1| (-367))) ((($) . T) (((-875 |#1|)) . T) (((-412 (-569))) . T)) ((((-1265 |#1| |#2| |#3|)) |has| |#1| (-367))) @@ -3583,15 +3583,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-412 |#2|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-412 (-569)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-412 (-569))) . T) (($) . T)) @@ -3621,21 +3621,21 @@ ((($) . T) (((-569)) . T) (((-116 |#1|)) . T) (((-412 (-569))) . T)) (((|#1| |#2| (-241 |#1| |#2|) (-241 |#1| |#2|)) . T)) ((((-867)) . T)) -((((-412 (-569))) |has| |#2| (-38 (-412 (-569)))) ((|#2|) |has| |#2| (-173)) (($) -2718 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915)))) +((((-412 (-569))) |has| |#2| (-38 (-412 (-569)))) ((|#2|) |has| |#2| (-173)) (($) -2774 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-412 (-569))) |has| |#2| (-38 (-412 (-569)))) ((|#2|) . T)) ((($) . T) (((-569)) . 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T)) -((($) -2718 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) +((($) -2774 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) ((($ $) . T) (((-1183) $) . T)) ((((-1265 |#1| |#2| |#3|)) . T)) (|has| |#2| (-915)) @@ -3649,7 +3649,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-173))) ((((-704)) . T)) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) ((((-1188)) . T)) (((|#1|) |has| |#1| (-173))) ((((-1188)) . T)) @@ -3666,13 +3666,13 @@ ((((-1188)) . T)) ((((-1188)) . T)) ((((-1188)) . T)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-353))) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-353))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-353))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-353))) ((((-1188)) . T)) ((((-1188)) . T)) (|has| |#1| (-367)) (|has| |#1| (-367)) -(-2718 (|has| |#1| (-173)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-173)) (|has| |#1| (-561))) (((|#1| (-569)) . T)) (((|#1| (-412 (-569))) . T)) (((|#1| (-776)) . T)) @@ -3687,16 +3687,16 @@ ((((-898 (-383))) . T) (((-898 (-569))) . T) (((-1183)) . T) (((-541)) . T)) (((|#1|) . T)) ((((-867)) . T)) -(-2718 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) -(-2718 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-798)) (|has| |#2| (-798)))) +(-2774 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2774 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-798)) (|has| |#2| (-798)))) ((((-569)) . T)) ((((-569)) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2718 (|has| |#2| (-173)) (|has| |#2| (-731)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2774 (|has| |#2| (-173)) (|has| |#2| (-731)) (|has| |#2| (-853)) (|has| |#2| (-1055))) ((((-1183)) -12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055)))) -(-2718 (-12 (|has| |#1| (-478)) (|has| |#2| (-478))) (-12 (|has| |#1| (-731)) (|has| |#2| (-731)))) +(-2774 (-12 (|has| |#1| (-478)) (|has| |#2| (-478))) (-12 (|has| |#1| (-731)) (|has| |#2| (-731)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-367)) @@ -3727,7 +3727,7 @@ (((|#1| |#2|) . T)) ((((-569)) . T) ((|#2|) |has| |#2| (-173))) ((((-114)) . T) ((|#1|) . T) (((-569)) . T)) -(-2718 (|has| |#1| (-353)) (|has| |#1| (-372))) +(-2774 (|has| |#1| (-353)) (|has| |#1| (-372))) (((|#1| |#2|) . T)) ((((-226)) . T)) ((((-412 (-569))) . T) (($) . T) (((-569)) . T)) @@ -3739,7 +3739,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-541)) |has| |#1| (-619 (-541)))) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-855)) (|has| |#1| (-1106)))) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-855)) (|has| |#1| (-1106)))) ((($) . T) (((-412 (-569))) . T)) (|has| |#1| (-915)) (|has| |#1| (-915)) @@ -3750,14 +3750,14 @@ (((|#1| |#1|) |has| |#1| (-173))) (((|#1|) . T) (((-569)) . T)) ((((-1188)) . T)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-561))) -(-2718 (|has| |#1| (-21)) (|has| |#1| (-853))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2774 (|has| |#1| (-21)) (|has| |#1| (-853))) (((|#2|) . T)) -(-2718 (|has| |#1| (-21)) (|has| |#1| (-853))) +(-2774 (|has| |#1| (-21)) (|has| |#1| (-853))) (((|#1|) |has| |#1| (-173))) (((|#1|) . T)) (((|#1|) . T)) -((((-867)) -2718 (-12 (|has| |#1| (-618 (-867))) (|has| |#2| (-618 (-867)))) (-12 (|has| |#1| (-1106)) (|has| |#2| (-1106))))) +((((-867)) -2774 (-12 (|has| |#1| (-618 (-867))) (|has| |#2| (-618 (-867)))) (-12 (|has| |#1| (-1106)) (|has| |#2| (-1106))))) ((((-412 |#2|) |#3|) . T)) ((((-412 (-569))) . T) (($) . T)) (|has| |#1| (-38 (-412 (-569)))) @@ -3771,19 +3771,19 @@ (((|#1|) . T) (((-412 (-569))) . T) (((-569)) . T) (($) . T)) (((#0=(-569) #0#) . T)) ((($) . T) (((-412 (-569))) . T)) -(-2718 (|has| |#4| (-173)) (|has| |#4| (-731)) (|has| |#4| (-853)) (|has| |#4| (-1055))) -(-2718 (|has| |#3| (-173)) (|has| |#3| (-731)) (|has| |#3| (-853)) (|has| |#3| (-1055))) +(-2774 (|has| |#4| (-173)) (|has| |#4| (-731)) (|has| |#4| (-853)) (|has| |#4| (-1055))) +(-2774 (|has| |#3| (-173)) (|has| |#3| (-731)) (|has| |#3| (-853)) (|has| |#3| (-1055))) ((((-867)) . T) (((-1188)) . 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T)) ((((-1181 |#1| |#2| |#3|)) |has| |#1| (-367))) -(((|#2|) . T) (((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) -((((-2 (|:| -1963 (-1183)) (|:| -2179 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) +((((-2 (|:| -2003 (-1183)) (|:| -2214 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1028)) -(((|#2|) . T) (((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) ((((-867)) . T)) ((((-541)) |has| |#2| (-619 (-541))) (((-898 (-569))) |has| |#2| (-619 (-898 (-569)))) (((-898 (-383))) |has| |#2| (-619 (-898 (-383)))) (((-383)) . #0=(|has| |#2| (-1028))) (((-226)) . #0#)) ((((-297 |#3|)) . T)) @@ -3819,15 +3819,15 @@ ((((-1181 |#1| |#2| |#3|)) . T)) ((((-1181 |#1| |#2| |#3|)) . T) (((-1174 |#1| |#2| |#3|)) . T)) ((((-867)) . T)) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) ((((-569) |#1|) . 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T)) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) ((((-129)) . T) (((-867)) . T)) ((((-569) |#1|) . T)) ((((-129)) . T)) @@ -3851,13 +3851,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-367)) (|has| |#2| (-289 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-915))) -(-2718 (|has| |#1| (-855)) (|has| |#1| (-1106))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-915))) +(-2774 (|has| |#1| (-855)) (|has| |#1| (-1106))) ((((-867)) . T)) ((((-867)) . T)) ((((-867)) . T)) (((|#1| (-536 |#2|)) . T)) -((((-2 (|:| -1963 (-1183)) (|:| -2179 (-52)))) . T)) +((((-2 (|:| -2003 (-1183)) (|:| -2214 (-52)))) . T)) ((((-569) (-129)) . T)) (((|#1| (-569)) . T)) (((|#1| (-412 (-569))) . T)) @@ -3872,8 +3872,8 @@ ((((-1188)) . T)) ((((-867)) . T) (((-1188)) . T)) ((((-867)) . T) (((-1188)) . T)) -(-2718 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) -(-2718 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) +(-2774 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) +(-2774 (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((($) . T)) (((|#2| (-536 (-869 |#1|))) . T)) ((((-1188)) . T)) @@ -3888,13 +3888,13 @@ ((((-1188)) . T)) ((((-867)) . T) (((-1188)) . T)) ((((-1188)) . T)) -((((-867)) -2718 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) +((((-867)) -2774 (|has| |#1| (-618 (-867))) (|has| |#1| (-1106)))) (((|#1|) . T)) (((|#2| (-776)) . T)) (((|#1| |#2|) . T)) ((((-1165) |#1|) . T)) ((((-412 |#2|)) . T)) -((((-2 (|:| -1963 |#1|) (|:| -2179 |#2|))) . T)) +((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) (|has| |#1| (-561)) (|has| |#1| (-561)) ((($) . T) ((|#2|) . T)) @@ -3905,14 +3905,14 @@ ((((-569)) . T) (($) . T)) (((|#2| $) |has| |#2| (-289 |#2| |#2|))) (((|#1| (-649 |#1|)) |has| |#1| (-853))) -(-2718 (|has| |#1| (-234)) (|has| |#1| (-353))) -(-2718 (|has| |#1| (-367)) (|has| |#1| (-353))) +(-2774 (|has| |#1| (-234)) (|has| |#1| (-353))) +(-2774 (|has| |#1| (-367)) (|has| |#1| (-353))) ((((-1269 |#1|)) . T) (((-569)) . T) ((|#2|) . T) (((-412 (-569))) |has| |#2| (-1044 (-412 (-569))))) (|has| |#1| (-1106)) (((|#1|) . T)) -((((-1269 |#1|)) . T) (((-569)) . T) (($) -2718 (|has| |#2| (-367)) (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) (((-1088)) . T) ((|#2|) . T) (((-412 (-569))) -2718 (|has| |#2| (-38 (-412 (-569)))) (|has| |#2| (-1044 (-412 (-569)))))) +((((-1269 |#1|)) . T) (((-569)) . T) (($) -2774 (|has| |#2| (-367)) (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) (((-1088)) . T) ((|#2|) . T) (((-412 (-569))) -2774 (|has| |#2| (-38 (-412 (-569)))) (|has| |#2| (-1044 (-412 (-569)))))) ((((-412 (-569))) . T) (($) . T)) -((((-1005 |#1|)) . T) ((|#1|) . T) (((-569)) -2718 (|has| (-1005 |#1|) (-1044 (-569))) (|has| |#1| (-1044 (-569)))) (((-412 (-569))) -2718 (|has| (-1005 |#1|) (-1044 (-412 (-569)))) (|has| |#1| (-1044 (-412 (-569)))))) +((((-1005 |#1|)) . T) ((|#1|) . T) (((-569)) -2774 (|has| (-1005 |#1|) (-1044 (-569))) (|has| |#1| (-1044 (-569)))) (((-412 (-569))) -2774 (|has| (-1005 |#1|) (-1044 (-412 (-569)))) (|has| |#1| (-1044 (-412 (-569)))))) ((((-916 |#1|)) . T) (((-412 (-569))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) @@ -3928,10 +3928,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1146 |#1| |#2|) #0#) |has| (-1146 |#1| |#2|) (-312 (-1146 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((#0=(-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) #0#) |has| (-2 (|:| -1963 |#1|) (|:| -2179 |#2|)) (-312 (-2 (|:| -1963 |#1|) (|:| -2179 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((#0=(-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) #0#) |has| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (-312 (-2 (|:| -2003 |#1|) (|:| -2214 |#2|))))) (((#0=(-116 |#1|)) |has| #0# (-312 #0#))) ((($ $) . T)) -(-2718 (|has| |#1| (-855)) (|has| |#1| (-1106))) +(-2774 (|has| |#1| (-855)) (|has| |#1| (-1106))) ((($ $) . T) ((#0=(-869 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-234)) ((|#2| |#1|) |has| |#1| (-234)) ((|#3| |#1|) . T) ((|#3| $) . 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. -618) 184616) ((-393 . -102) T) ((-1126 . -143) T) ((-126 . -618) 184548) ((-879 . -1106) T) ((-663 . -416) 184532) ((-719 . -618) 184514) ((-250 . -618) 184481) ((-188 . -618) 184463) ((-162 . -618) 184445) ((-157 . -618) 184427) ((-1288 . -731) T) ((-1108 . -34) T) ((-876 . -800) NIL) ((-876 . -797) NIL) ((-863 . -855) T) ((-736 . -892) NIL) ((-1297 . -131) T) ((-385 . -131) T) ((-898 . -621) 184395) ((-910 . -102) T) ((-736 . -1044) 184271) ((-536 . -131) T) ((-1093 . -416) 184255) ((-1006 . -494) 184239) ((-117 . -405) 184216) ((-1174 . -1223) 184195) ((-787 . -416) 184179) ((-785 . -416) 184163) ((-949 . -34) T) ((-699 . -1158) NIL) ((-253 . -653) 183998) ((-252 . -653) 183820) ((-822 . -926) 183799) ((-459 . -416) 183783) ((-607 . -19) 183767) ((-1152 . -1216) 183736) ((-1174 . -892) NIL) ((-1174 . -890) 183688) ((-607 . -609) 183665) ((-1209 . -618) 183597) ((-1182 . -618) 183579) ((-62 . -400) T) ((-1180 . -1044) 183514) ((-1174 . -1044) 183480) ((-699 . -38) 183430) ((-40 . 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. -93) T) ((-325 . -1062) 181999) ((-253 . -796) 181978) ((-253 . -799) 181929) ((-31 . -495) 181910) ((-253 . -798) 181889) ((-252 . -796) 181868) ((-252 . -799) 181819) ((-252 . -798) 181798) ((-31 . -618) 181764) ((-50 . -1064) T) ((-253 . -731) 181674) ((-252 . -731) 181584) ((-1217 . -1106) T) ((-675 . -23) T) ((-586 . -1064) T) ((-523 . -1064) T) ((-383 . -1062) 181549) ((-325 . -111) 181524) ((-73 . -387) T) ((-73 . -400) T) ((-1030 . -38) 181461) ((-699 . -405) 181443) ((-99 . -102) T) ((-716 . -1106) T) ((-1301 . -1057) 181430) ((-1009 . -145) 181402) ((-1009 . -147) 181374) ((-875 . -651) 181346) ((-383 . -111) 181302) ((-322 . -1227) 181281) ((-479 . -1008) 181247) ((-358 . -38) 181212) ((-40 . -374) 181184) ((-878 . -618) 181056) ((-127 . -125) 181040) ((-121 . -125) 181024) ((-841 . -1062) 180994) ((-838 . -21) 180946) ((-832 . -1062) 180930) ((-838 . -25) 180882) ((-322 . -561) 180833) ((-522 . -621) 180814) ((-569 . -833) T) ((-241 . -1223) T) ((-1040 . -621) 180783) 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-25) T) ((-820 . -23) 177825) ((-1183 . -618) 177807) ((-59 . -19) 177791) ((-1183 . -619) 177713) ((-1179 . -731) T) ((-1131 . -731) T) ((-521 . -19) 177697) ((-501 . -19) 177681) ((-59 . -609) 177658) ((-1093 . -1106) T) ((-907 . -102) 177636) ((-859 . -731) T) ((-787 . -1106) T) ((-521 . -609) 177613) ((-501 . -609) 177590) ((-785 . -1106) T) ((-785 . -1071) 177557) ((-466 . -1106) T) ((-459 . -1106) T) ((-591 . -722) 177532) ((-654 . -1106) T) ((-1265 . -47) 177509) ((-1259 . -102) T) ((-1258 . -47) 177479) ((-1237 . -47) 177456) ((-1217 . -173) 177407) ((-1180 . -310) 177386) ((-1174 . -310) 177365) ((-1102 . -621) 177346) ((-1096 . -621) 177327) ((-1086 . -561) 177278) ((-1010 . -906) NIL) ((-1086 . -1227) 177229) ((-675 . -131) T) ((-632 . -1118) T) ((-1079 . -621) 177210) ((-1072 . -621) 177191) ((-1042 . -621) 177172) ((-1025 . -621) 177153) ((-704 . -651) 177103) ((-277 . -1106) T) ((-85 . -446) T) ((-85 . -400) T) ((-719 . -1062) 177073) ((-716 . -173) T) ((-50 . -1106) T) ((-600 . -47) 177050) ((-226 . -653) 177015) ((-586 . -1106) T) ((-523 . -1106) T) ((-492 . -825) T) ((-492 . -926) T) ((-363 . -1227) T) ((-357 . -1227) T) ((-349 . -1227) T) ((-322 . -1118) T) ((-319 . -1057) 176925) ((-316 . -1057) 176854) ((-108 . -1227) T) ((-631 . -621) 176835) ((-363 . -561) T) ((-218 . -926) T) ((-218 . -825) T) ((-319 . -645) 176745) ((-316 . -645) 176674) ((-357 . -561) T) ((-349 . -561) T) ((-488 . -621) 176655) ((-108 . -561) T) ((-663 . -722) 176625) ((-1174 . -1028) NIL) ((-219 . -621) 176606) ((-322 . -23) T) ((-67 . -1223) T) ((-1006 . -618) 176538) ((-699 . -232) 176520) ((-719 . -111) 176485) ((-649 . -34) T) ((-246 . -494) 176469) ((-1108 . -1104) 176453) ((-172 . -1106) T) ((-1301 . -1158) T) ((-1297 . -21) T) ((-1297 . -25) T) ((-1295 . -131) T) ((-1293 . -131) T) ((-958 . -915) 176432) ((-1286 . -102) T) ((-1269 . -618) 176398) ((-1258 . -1044) 176333) ((-520 . -621) 176317) ((-1237 . -1223) 176296) ((-1237 . -892) NIL) ((-1237 . -890) 176248) ((-486 . -915) 176227) ((-1237 . -1044) 176193) ((-1217 . -519) 176160) ((-1093 . -722) 176009) ((-1068 . -653) 175996) ((-958 . -653) 175921) ((-602 . -495) 175902) ((-590 . -495) 175883) ((-787 . -722) 175712) ((-602 . -618) 175678) ((-590 . -618) 175644) ((-541 . -618) 175626) ((-541 . -619) 175607) ((-785 . -722) 175456) ((-1083 . -102) T) ((-385 . -25) T) ((-628 . -651) 175428) ((-385 . -21) T) ((-486 . -653) 175353) ((-466 . -722) 175324) ((-459 . -722) 175173) ((-993 . -102) T) ((-1196 . -619) NIL) ((-1196 . -618) 175155) ((-1148 . -1129) 175100) ((-742 . -102) T) ((-117 . -651) 175030) ((-610 . -621) 175012) ((-1052 . -1216) 174941) ((-907 . -312) 174879) ((-536 . -25) T) ((-881 . -93) T) ((-719 . -621) 174833) ((-686 . -93) T) ((-650 . -495) 174814) ((-141 . -102) T) ((-44 . -131) T) ((-681 . -93) T) ((-669 . -618) 174796) ((-347 . -1064) T) ((-292 . -1118) T) ((-650 . -618) 174749) ((-483 . -93) T) ((-359 . -618) 174731) ((-356 . -618) 174713) ((-348 . -618) 174695) ((-266 . -619) 174443) ((-266 . -618) 174425) ((-248 . -618) 174407) ((-248 . -619) 174268) ((-133 . -93) T) ((-138 . -93) T) ((-137 . -93) T) ((-1147 . -618) 174250) ((-1126 . -645) 174237) ((-1126 . -1057) 174224) ((-824 . -731) T) ((-824 . -862) T) ((-607 . -291) 174201) ((-586 . -722) 174166) ((-484 . -619) NIL) ((-484 . -618) 174148) ((-523 . -722) 174093) ((-319 . -102) T) ((-316 . -102) T) ((-292 . -23) T) ((-152 . -131) T) ((-916 . -618) 174075) ((-916 . -619) 174057) ((-391 . -731) T) ((-877 . -1062) 174009) ((-877 . -111) 173947) ((-719 . -1055) T) ((-717 . -1249) 173931) ((-699 . -353) NIL) ((-136 . -102) T) ((-114 . -102) T) ((-139 . -102) T) ((-524 . -618) 173863) ((-383 . -800) T) ((-224 . -1106) T) ((-168 . -1223) T) ((-383 . -797) T) ((-226 . -799) T) ((-226 . -796) T) ((-59 . -619) 173824) ((-59 . -618) 173736) ((-226 . -731) T) ((-521 . -619) 173697) ((-521 . -618) 173609) ((-502 . -618) 173541) ((-501 . -619) 173502) ((-501 . -618) 173414) ((-1086 . -367) 173365) ((-40 . -416) 173342) ((-77 . -1223) T) ((-876 . -915) NIL) ((-363 . -332) 173326) ((-363 . -367) T) ((-357 . -332) 173310) ((-357 . -367) T) ((-349 . -332) 173294) ((-349 . -367) T) ((-319 . -287) 173273) ((-108 . -367) T) ((-70 . -1223) T) ((-1237 . -342) 173225) ((-876 . -653) 173170) ((-1237 . -381) 173122) ((-970 . -131) 172977) ((-820 . -131) 172847) ((-964 . -656) 172831) ((-1093 . -173) 172742) ((-964 . -377) 172726) ((-1068 . -799) T) ((-1068 . -796) T) ((-877 . -621) 172624) ((-787 . -173) 172515) ((-785 . -173) 172426) ((-821 . -47) 172388) ((-1068 . -731) T) ((-330 . -494) 172372) ((-958 . -731) T) ((-1286 . -312) 172310) ((-459 . -173) 172221) ((-246 . -289) 172198) ((-1265 . -906) 172111) ((-1258 . -906) 172017) ((-1257 . -1062) 171852) ((-486 . -731) T) ((-1237 . -906) 171685) ((-1236 . -1062) 171493) ((-1217 . -293) 171472) ((-1193 . -1223) T) ((-1190 . -372) T) ((-1189 . -372) T) ((-1152 . -151) 171456) ((-1126 . -102) T) ((-1124 . -1106) T) ((-1086 . -23) T) ((-1086 . -1118) T) ((-1081 . -102) T) ((-1063 . -618) 171423) ((-933 . -961) T) ((-742 . -312) 171361) ((-75 . -1223) T) ((-669 . -386) 171333) ((-170 . -915) 171286) ((-30 . -961) T) ((-112 . -849) T) ((-1 . -618) 171268) ((-1009 . -414) 171240) ((-128 . -656) 171222) ((-50 . -625) 171206) ((-699 . -651) 171141) ((-600 . -906) 171054) ((-443 . -102) T) ((-128 . -377) 171036) ((-141 . -312) NIL) ((-877 . -1055) T) ((-838 . -855) 171015) ((-81 . -1223) T) ((-716 . -293) T) ((-40 . -1064) T) ((-586 . -173) T) ((-523 . -173) T) ((-516 . -618) 170997) ((-170 . -653) 170907) ((-512 . -618) 170889) ((-355 . -147) 170871) ((-355 . -145) T) ((-363 . -1118) T) ((-357 . -1118) T) ((-349 . -1118) T) ((-1010 . -310) T) ((-920 . -310) T) ((-877 . -244) T) ((-108 . -1118) T) ((-877 . -234) 170850) ((-1257 . -111) 170671) ((-1236 . -111) 170460) ((-246 . -1261) 170444) ((-569 . -853) T) ((-363 . -23) T) ((-358 . -353) T) ((-319 . -312) 170431) ((-316 . -312) 170372) ((-357 . -23) T) ((-322 . -131) T) ((-349 . -23) T) ((-1010 . -1028) T) ((-31 . -621) 170353) ((-108 . -23) T) ((-659 . -1057) 170337) ((-246 . -609) 170314) ((-336 . -1106) T) ((-659 . -645) 170284) ((-1259 . -38) 170176) ((-1246 . -915) 170155) ((-112 . -1106) T) ((-1041 . -102) T) ((-1246 . -653) 170080) ((-876 . -799) NIL) ((-860 . -653) 170054) ((-876 . -796) NIL) ((-821 . -892) NIL) ((-876 . -731) T) ((-1093 . -519) 169927) ((-787 . -519) 169874) ((-785 . -519) 169826) ((-576 . -653) 169813) ((-821 . -1044) 169641) ((-459 . -519) 169584) ((-393 . -394) T) ((-1257 . -621) 169397) ((-1236 . -621) 169145) ((-60 . -1223) T) ((-626 . -855) 169124) ((-505 . -666) T) ((-1152 . -982) 169093) ((-1030 . -651) 169030) ((-1009 . -457) T) ((-704 . -853) T) ((-515 . -797) T) ((-479 . -1062) 168865) ((-347 . -1106) T) ((-316 . -1158) NIL) ((-292 . -131) T) ((-399 . -1106) T) ((-875 . -1064) T) ((-699 . -374) 168832) ((-358 . -651) 168762) ((-224 . -625) 168739) ((-330 . -289) 168716) ((-479 . -111) 168537) ((-1257 . -1055) T) ((-1236 . -1055) T) ((-821 . -381) 168521) ((-170 . -731) T) ((-659 . -102) T) ((-1257 . -244) 168500) ((-1257 . -234) 168452) ((-1236 . -234) 168357) ((-1236 . -244) 168336) ((-1009 . -407) NIL) ((-675 . -644) 168284) ((-319 . -38) 168194) ((-316 . -38) 168123) ((-69 . -618) 168105) ((-322 . -498) 168071) ((-48 . -651) 168021) ((-1196 . -291) 168000) ((-1231 . -855) T) ((-1119 . -1118) 167910) ((-83 . -1223) T) ((-61 . -618) 167892) ((-484 . -291) 167871) ((-1288 . -1044) 167848) ((-1171 . -1106) T) ((-1119 . -23) 167718) ((-821 . -906) 167654) ((-1246 . -731) T) ((-1108 . -1223) T) ((-479 . -621) 167480) ((-1093 . -293) 167411) ((-972 . -1106) T) ((-899 . -102) T) ((-787 . -293) 167322) ((-330 . -19) 167306) ((-59 . -291) 167283) ((-785 . -293) 167214) ((-860 . -731) T) ((-117 . -853) NIL) ((-521 . -291) 167191) ((-330 . -609) 167168) ((-501 . -291) 167145) ((-459 . -293) 167076) ((-1041 . -312) 166927) ((-881 . -495) 166908) ((-881 . -618) 166874) ((-686 . -495) 166855) ((-576 . -731) T) ((-681 . -495) 166836) ((-686 . -618) 166786) ((-681 . -618) 166752) ((-667 . -618) 166734) ((-483 . -495) 166715) ((-483 . -618) 166681) ((-246 . -619) 166642) ((-246 . -495) 166619) ((-138 . -495) 166600) ((-137 . -495) 166581) ((-133 . -495) 166562) ((-246 . -618) 166454) ((-214 . -102) T) ((-138 . -618) 166420) ((-137 . -618) 166386) ((-133 . -618) 166352) ((-1153 . -34) T) ((-949 . -1223) T) ((-347 . -722) 166297) ((-675 . -25) T) ((-675 . -21) T) ((-1183 . -621) 166278) ((-479 . -1055) T) ((-640 . -422) 166243) ((-612 . -422) 166208) ((-1126 . -1158) T) ((-717 . -1057) 166031) ((-586 . -293) T) ((-523 . -293) T) ((-1258 . -310) 166010) ((-479 . -234) 165962) ((-479 . -244) 165941) ((-1237 . -310) 165920) ((-717 . -645) 165749) ((-1237 . -1028) NIL) ((-1086 . -131) T) ((-877 . -800) 165728) ((-144 . -102) T) ((-40 . -1106) T) ((-877 . -797) 165707) ((-649 . -1016) 165691) ((-585 . -1064) T) ((-569 . -1064) T) ((-500 . -1064) T) ((-412 . -457) T) ((-363 . -131) T) ((-319 . -405) 165675) ((-316 . -405) 165636) ((-357 . -131) T) ((-349 . -131) T) ((-1188 . -1106) T) ((-1126 . -38) 165623) ((-1100 . -618) 165590) ((-108 . -131) T) ((-960 . -1106) T) ((-927 . -1106) T) ((-776 . -1106) T) ((-677 . -1106) T) ((-706 . -147) T) ((-116 . -147) T) ((-1295 . -21) T) ((-1295 . -25) T) ((-1293 . -21) T) ((-1293 . -25) T) ((-669 . -1062) 165574) ((-536 . -855) T) ((-505 . -855) T) ((-359 . -1062) 165526) ((-356 . -1062) 165478) ((-348 . -1062) 165430) ((-253 . -1223) T) ((-252 . -1223) T) ((-266 . -1062) 165273) ((-248 . -1062) 165116) ((-669 . -111) 165095) ((-552 . -849) T) ((-359 . -111) 165033) ((-356 . -111) 164971) ((-348 . -111) 164909) ((-266 . -111) 164738) ((-248 . -111) 164567) ((-822 . -1227) 164546) ((-628 . -416) 164530) ((-44 . -21) T) ((-44 . -25) T) ((-820 . -644) 164436) ((-822 . -561) 164415) ((-253 . -1044) 164242) ((-252 . -1044) 164069) ((-126 . -119) 164053) ((-916 . -1062) 164018) ((-717 . -102) T) ((-704 . -1064) T) ((-602 . -621) 163999) ((-590 . -621) 163980) ((-541 . -623) 163883) ((-347 . -173) T) ((-88 . -618) 163865) ((-152 . -21) T) ((-152 . -25) T) ((-916 . -111) 163821) ((-40 . -722) 163766) ((-875 . -1106) T) ((-669 . -621) 163743) ((-650 . -621) 163724) ((-359 . -621) 163661) ((-356 . -621) 163598) ((-552 . -1106) T) ((-348 . -621) 163535) ((-330 . -619) 163496) ((-330 . -618) 163408) ((-266 . -621) 163161) ((-248 . -621) 162946) ((-1236 . -797) 162899) ((-1236 . -800) 162852) ((-253 . -381) 162821) ((-252 . -381) 162790) ((-659 . -38) 162760) ((-613 . -34) T) ((-487 . -1118) 162670) ((-480 . -34) T) ((-1119 . -131) 162540) ((-970 . -25) 162351) ((-916 . -621) 162301) ((-879 . -618) 162283) ((-970 . -21) 162238) ((-820 . -21) 162148) ((-820 . -25) 161999) ((-1229 . -372) T) ((-628 . -1064) T) ((-1185 . -561) 161978) ((-1179 . -47) 161955) ((-359 . -1055) T) ((-356 . -1055) T) ((-487 . -23) 161825) ((-348 . -1055) T) ((-266 . -1055) T) ((-248 . -1055) T) ((-1131 . -47) 161797) ((-117 . -1064) T) ((-1040 . -653) 161771) ((-964 . -34) T) ((-359 . -234) 161750) ((-359 . -244) T) ((-356 . -234) 161729) ((-356 . -244) T) ((-348 . -234) 161708) ((-348 . -244) T) ((-266 . -329) 161680) ((-248 . -329) 161637) ((-266 . -234) 161616) ((-1163 . -151) 161600) ((-253 . -906) 161532) ((-252 . -906) 161464) ((-1088 . -855) T) ((-419 . -1118) T) ((-1060 . -23) T) ((-916 . -1055) T) ((-325 . -653) 161446) ((-1030 . -853) T) ((-1217 . -1008) 161412) ((-1180 . -926) 161391) ((-1174 . -926) 161370) ((-1174 . -825) NIL) ((-1005 . -1057) 161266) ((-916 . -244) T) ((-822 . -367) 161245) ((-389 . -23) T) ((-127 . -1106) 161223) ((-121 . -1106) 161201) ((-916 . -234) T) ((-128 . -34) T) ((-383 . -653) 161166) ((-1005 . -645) 161114) ((-875 . -722) 161101) ((-1301 . -651) 161073) ((-1052 . -151) 161038) ((-40 . -173) T) ((-699 . -416) 161020) ((-717 . -312) 161007) ((-841 . -653) 160967) ((-832 . -653) 160941) ((-322 . -25) T) ((-322 . -21) T) ((-663 . -289) 160920) ((-585 . -1106) T) ((-569 . -1106) T) ((-500 . -1106) T) ((-246 . -291) 160897) ((-316 . -232) 160858) ((-1179 . -892) NIL) ((-55 . -1106) T) ((-1131 . -892) 160717) ((-129 . -855) T) ((-1179 . -1044) 160597) ((-1131 . -1044) 160480) ((-184 . -618) 160462) ((-859 . -1044) 160358) ((-787 . -289) 160285) ((-822 . -1118) T) ((-1040 . -731) T) ((-607 . -656) 160269) ((-1052 . -982) 160198) ((-1005 . -102) T) ((-822 . -23) T) ((-717 . -1158) 160176) ((-699 . -1064) T) ((-607 . -377) 160160) ((-355 . -457) T) ((-347 . -293) T) ((-1274 . -1106) T) ((-249 . -1106) T) ((-404 . -102) T) ((-292 . -21) T) ((-292 . -25) T) ((-365 . -731) T) ((-715 . -1106) T) ((-704 . -1106) T) ((-365 . -478) T) ((-1217 . -618) 160142) ((-1179 . -381) 160126) ((-1131 . -381) 160110) ((-1030 . -416) 160072) ((-141 . -230) 160054) ((-383 . -799) T) ((-383 . -796) T) ((-875 . -173) T) ((-383 . -731) T) ((-716 . -618) 160036) ((-717 . -38) 159865) ((-1273 . -1271) 159849) ((-355 . -407) T) ((-1273 . -1106) 159799) ((-585 . -722) 159786) ((-569 . -722) 159773) ((-500 . -722) 159738) ((-1259 . -651) 159628) ((-319 . -634) 159607) ((-841 . -731) T) ((-832 . -731) T) ((-649 . -1223) T) ((-1086 . -644) 159555) ((-1179 . -906) 159498) ((-1131 . -906) 159482) ((-667 . -1062) 159466) ((-108 . -644) 159448) ((-487 . -131) 159318) ((-1185 . -1118) T) ((-958 . -47) 159287) ((-628 . -1106) T) ((-667 . -111) 159266) ((-496 . -618) 159232) ((-330 . -291) 159209) ((-486 . -47) 159166) ((-1185 . -23) T) ((-117 . -1106) T) ((-103 . -102) 159144) ((-1285 . -1118) T) ((-553 . -855) T) ((-1060 . -131) T) ((-1030 . -1064) T) ((-824 . -1044) 159128) ((-1009 . -729) 159100) ((-1285 . -23) T) ((-704 . -722) 159065) ((-591 . -618) 159047) ((-391 . -1044) 159031) ((-358 . -1064) T) ((-389 . -131) T) ((-327 . -1044) 159015) ((-1203 . -618) 158997) ((-1126 . -833) T) ((-1111 . -1106) T) ((-226 . -892) 158979) ((-1010 . -926) T) ((-91 . -34) T) ((-1010 . -825) T) ((-920 . -926) T) ((-1086 . -21) T) ((-1086 . -25) T) ((-492 . -1227) T) ((-1005 . -312) 158944) ((-881 . -621) 158925) ((-719 . -653) 158885) ((-218 . -1227) T) ((-686 . -621) 158866) ((-226 . -1044) 158826) ((-40 . -293) T) ((-681 . -621) 158807) ((-492 . -561) T) ((-483 . -621) 158788) ((-319 . -651) 158472) ((-316 . -651) 158386) ((-363 . -25) T) ((-363 . -21) T) ((-357 . -25) T) ((-218 . -561) T) ((-357 . -21) T) ((-349 . -25) T) ((-349 . -21) T) ((-246 . -621) 158363) ((-138 . -621) 158344) ((-137 . -621) 158325) ((-133 . -621) 158306) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1064) T) ((-585 . -173) T) ((-569 . -173) T) ((-500 . -173) T) ((-663 . -618) 158288) ((-742 . -741) 158272) ((-340 . -618) 158254) ((-68 . -387) T) ((-68 . -400) T) ((-1108 . -107) 158238) ((-1068 . -892) 158220) ((-958 . -892) 158145) ((-658 . -1118) T) ((-628 . -722) 158132) ((-486 . -892) NIL) ((-1152 . -102) T) ((-1100 . -623) 158116) ((-1068 . -1044) 158098) ((-97 . -618) 158080) ((-482 . -147) T) ((-958 . -1044) 157960) ((-117 . -722) 157905) ((-658 . -23) T) ((-486 . -1044) 157781) ((-1093 . -619) NIL) ((-1093 . -618) 157763) ((-787 . -619) NIL) ((-787 . -618) 157724) ((-785 . -619) 157358) ((-785 . -618) 157272) ((-1119 . -644) 157178) ((-466 . -618) 157160) ((-459 . -618) 157142) ((-459 . -619) 157003) ((-1041 . -230) 156949) ((-877 . -915) 156928) ((-126 . -34) T) ((-822 . -131) T) ((-654 . -618) 156910) ((-583 . -102) T) ((-359 . -1292) 156894) ((-356 . -1292) 156878) ((-348 . -1292) 156862) ((-127 . -519) 156795) ((-121 . -519) 156728) ((-516 . -797) T) ((-516 . -800) T) ((-515 . -799) T) ((-103 . -312) 156666) ((-223 . -102) 156644) ((-704 . -173) T) ((-699 . -1106) T) ((-877 . -653) 156596) ((-65 . -388) T) ((-277 . -618) 156578) ((-65 . -400) T) ((-958 . -381) 156562) ((-875 . -293) T) ((-50 . -618) 156544) ((-1005 . -38) 156492) ((-1126 . -651) 156464) ((-586 . -618) 156446) ((-486 . -381) 156430) ((-586 . -619) 156412) ((-523 . -618) 156394) ((-916 . -1292) 156381) ((-876 . -1223) T) ((-706 . -457) T) ((-500 . -519) 156347) ((-492 . -367) T) ((-359 . -372) 156326) ((-356 . -372) 156305) ((-348 . -372) 156284) ((-719 . -731) T) ((-218 . -367) T) ((-116 . -457) T) ((-1296 . -1287) 156268) ((-876 . -890) 156245) ((-876 . -892) NIL) ((-970 . -855) 156144) ((-820 . -855) 156095) ((-1230 . -102) T) ((-659 . -661) 156079) ((-1209 . -34) T) ((-172 . -618) 156061) ((-1119 . -21) 155971) ((-1119 . -25) 155822) ((-876 . -1044) 155799) ((-958 . -906) 155780) ((-1246 . -47) 155757) ((-916 . -372) T) ((-59 . -656) 155741) ((-521 . -656) 155725) ((-486 . -906) 155702) ((-71 . -446) T) ((-71 . -400) T) ((-501 . -656) 155686) ((-59 . -377) 155670) ((-628 . -173) T) ((-521 . -377) 155654) ((-501 . -377) 155638) ((-832 . -713) 155622) ((-1179 . -310) 155601) ((-1185 . -131) T) ((-1148 . -1057) 155585) ((-117 . -173) T) ((-1148 . -645) 155517) ((-1152 . -312) 155455) ((-170 . -1223) T) ((-1285 . -131) T) ((-871 . -1057) 155425) ((-640 . -749) 155409) ((-612 . -749) 155393) ((-1258 . -926) 155372) ((-1237 . -926) 155351) ((-1237 . -825) NIL) ((-871 . -645) 155321) ((-699 . -722) 155271) ((-1236 . -915) 155224) ((-1030 . -1106) T) ((-876 . -381) 155201) ((-876 . -342) 155178) ((-911 . -1118) T) ((-170 . -890) 155162) ((-170 . -892) 155087) ((-492 . -1118) T) ((-358 . -1106) T) ((-218 . -1118) T) ((-76 . -446) T) ((-76 . -400) T) ((-170 . -1044) 154983) ((-322 . -855) T) ((-1273 . -519) 154916) ((-1257 . -653) 154813) ((-1236 . -653) 154683) ((-877 . -799) 154662) ((-877 . -796) 154641) ((-877 . -731) T) ((-492 . -23) T) ((-224 . -618) 154623) ((-175 . -457) T) ((-223 . -312) 154561) ((-86 . -446) T) ((-86 . -400) T) ((-218 . -23) T) ((-1297 . -1290) 154540) ((-682 . -1044) 154524) ((-585 . -293) T) ((-569 . -293) T) ((-500 . -293) T) ((-136 . -475) 154479) ((-659 . -651) 154438) ((-48 . -1106) T) ((-717 . -232) 154422) ((-876 . -906) NIL) ((-1246 . -892) NIL) ((-895 . -102) T) ((-891 . -102) T) ((-393 . -1106) T) ((-170 . -381) 154406) ((-170 . -342) 154390) ((-1246 . -1044) 154270) ((-860 . -1044) 154166) ((-1148 . -102) T) ((-667 . -797) 154145) ((-658 . 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149788) ((-1273 . -494) 149772) ((-1148 . -38) 149732) ((-969 . -23) T) ((-916 . -653) 149697) ((-870 . -1106) T) ((-848 . -102) T) ((-822 . -21) T) ((-640 . -1057) 149681) ((-612 . -1057) 149665) ((-822 . -25) T) ((-740 . -23) T) ((-720 . -23) T) ((-640 . -645) 149649) ((-110 . -666) T) ((-612 . -645) 149633) ((-586 . -1062) 149598) ((-523 . -1062) 149543) ((-228 . -57) 149501) ((-458 . -23) T) ((-412 . -102) T) ((-265 . -102) T) ((-699 . -293) T) ((-871 . -38) 149471) ((-586 . -111) 149427) ((-523 . -111) 149356) ((-1093 . -621) 149092) ((-423 . -1118) T) ((-319 . -1064) 148982) ((-316 . -1064) T) ((-128 . -1223) T) ((-787 . -621) 148730) ((-785 . -621) 148496) ((-663 . -1055) T) ((-1301 . -1106) T) ((-459 . -621) 148281) ((-170 . -310) 148212) ((-423 . -23) T) ((-40 . -618) 148194) ((-40 . -619) 148178) ((-108 . -998) 148160) ((-116 . -874) 148144) ((-654 . -621) 148128) ((-48 . -519) 148094) ((-1209 . -1016) 148078) ((-1188 . -618) 148045) ((-1196 . -34) T) ((-960 . -618) 148011) 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T) ((-1181 . -561) 147215) ((-1180 . -1227) 147194) ((-1180 . -561) 147145) ((-586 . -1055) T) ((-523 . -1055) T) ((-1174 . -1227) 147124) ((-365 . -1044) 147108) ((-325 . -1044) 147092) ((-1030 . -293) T) ((-383 . -892) 147074) ((-1174 . -561) 147025) ((-1009 . -38) 146970) ((-1005 . -651) 146893) ((-804 . -1118) T) ((-916 . -731) T) ((-586 . -244) T) ((-586 . -234) T) ((-523 . -234) T) ((-523 . -244) T) ((-1132 . -561) 146872) ((-358 . -293) T) ((-652 . -700) 146856) ((-383 . -1044) 146816) ((-297 . -1057) 146737) ((-1126 . -1064) T) ((-103 . -125) 146721) ((-297 . -645) 146663) ((-804 . -23) T) ((-1295 . -1290) 146639) ((-1273 . -289) 146616) ((-412 . -312) 146581) ((-1293 . -1290) 146560) ((-1259 . -1106) T) ((-875 . -618) 146542) ((-841 . -1044) 146511) ((-204 . -792) T) ((-203 . -792) T) ((-202 . -792) T) ((-201 . -792) T) ((-200 . -792) T) ((-199 . -792) T) ((-198 . -792) T) ((-197 . -792) T) ((-196 . -792) T) ((-195 . -792) T) ((-552 . -618) 146493) ((-500 . -1008) T) ((-276 . 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144021) ((-717 . -1064) T) ((-699 . -1008) NIL) ((-1257 . -47) 143991) ((-1236 . -47) 143968) ((-1147 . -1016) 143939) ((-3 . |UnionCategory|) T) ((-1126 . -722) 143926) ((-1111 . -618) 143908) ((-1086 . -147) 143887) ((-1086 . -145) 143838) ((-972 . -621) 143822) ((-226 . -926) T) ((-40 . -111) 143751) ((-877 . -1044) 143615) ((-1010 . -367) T) ((-1009 . -232) 143592) ((-706 . -1057) 143579) ((-920 . -367) T) ((-706 . -645) 143566) ((-322 . -1211) 143532) ((-383 . -310) T) ((-322 . -1208) 143498) ((-319 . -173) 143477) ((-316 . -173) T) ((-586 . -1292) 143464) ((-523 . -1292) 143441) ((-363 . -147) 143420) ((-116 . -1057) 143407) ((-363 . -145) 143358) ((-357 . -147) 143337) ((-357 . -145) 143288) ((-349 . -147) 143267) ((-613 . -1199) 143243) ((-116 . -645) 143230) ((-349 . -145) 143181) ((-322 . -35) 143147) ((-480 . -1199) 143126) ((0 . |EnumerationCategory|) T) ((-322 . -95) 143092) ((-383 . -1028) T) ((-108 . -147) T) ((-108 . -145) NIL) ((-45 . -236) 143042) ((-659 . -1106) T) 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140670) ((-1009 . -651) 140600) ((-969 . -21) T) ((-969 . -25) T) ((-740 . -21) T) ((-740 . -25) T) ((-720 . -21) T) ((-720 . -25) T) ((-716 . -653) 140565) ((-458 . -21) T) ((-458 . -25) T) ((-343 . -102) T) ((-175 . -102) T) ((-1005 . -1064) T) ((-875 . -1055) T) ((-779 . -102) T) ((-1258 . -367) 140544) ((-1257 . -906) 140450) ((-1237 . -367) 140429) ((-1236 . -906) 140280) ((-1030 . -618) 140262) ((-412 . -833) 140215) ((-1181 . -498) 140181) ((-170 . -926) 140112) ((-1180 . -498) 140078) ((-1174 . -498) 140044) ((-717 . -1106) T) ((-1132 . -498) 140010) ((-585 . -1062) 139997) ((-569 . -1062) 139984) ((-500 . -1062) 139949) ((-319 . -293) 139928) ((-316 . -293) T) ((-358 . -618) 139910) ((-423 . -25) T) ((-423 . -21) T) ((-99 . -289) 139889) ((-585 . -111) 139874) ((-569 . -111) 139859) ((-500 . -111) 139815) ((-1183 . -892) 139782) ((-907 . -494) 139766) ((-48 . -618) 139748) ((-48 . -619) 139693) ((-241 . -131) 139563) ((-1296 . -651) 139522) ((-1246 . -926) 139501) ((-821 . -1227) 139480) ((-393 . -495) 139461) ((-1041 . -519) 139305) ((-393 . -618) 139271) ((-821 . -561) 139202) ((-591 . -653) 139177) ((-266 . -47) 139149) ((-248 . -47) 139106) ((-536 . -514) 139083) ((-585 . -621) 139055) ((-569 . -621) 139027) ((-500 . -621) 138960) ((-1080 . -1223) T) ((-1006 . -1223) T) ((-1265 . -23) T) ((-704 . -1062) 138925) ((-1265 . -1118) T) ((-1258 . -1118) T) ((-1258 . -23) T) ((-1237 . -1118) T) ((-1237 . -23) T) ((-1009 . -374) 138897) ((-112 . -372) T) ((-479 . -906) 138803) ((-1217 . -731) T) ((-910 . -618) 138785) ((-55 . -621) 138767) ((-91 . -107) 138751) ((-1126 . -293) T) ((-911 . -855) 138702) ((-706 . -1158) T) ((-704 . -111) 138658) ((-848 . -651) 138575) ((-601 . -1118) T) ((-600 . -1118) T) ((-717 . -722) 138404) ((-716 . -731) T) ((-1010 . -131) T) ((-977 . -131) T) ((-492 . -855) T) ((-920 . -131) T) ((-804 . -25) T) ((-804 . -21) T) ((-218 . -855) T) ((-412 . -651) 138341) ((-585 . -1055) T) ((-569 . -1055) T) ((-500 . -1055) T) ((-601 . -23) T) ((-347 . -1292) 138318) ((-322 . -457) 138297) ((-343 . -312) 138284) ((-600 . -23) T) ((-432 . -131) T) ((-663 . -653) 138258) ((-246 . -1016) 138242) ((-877 . -310) T) ((-1297 . -1287) 138226) ((-776 . -797) T) ((-776 . -800) T) ((-706 . -38) 138213) ((-569 . -234) T) ((-500 . -244) T) ((-500 . -234) T) ((-1156 . -236) 138163) ((-1093 . -915) 138142) ((-116 . -38) 138129) ((-210 . -805) T) ((-209 . -805) T) ((-208 . -805) T) ((-207 . -805) T) ((-877 . -1028) 138107) ((-1286 . -494) 138091) ((-787 . -915) 138070) ((-785 . -915) 138049) ((-1196 . -1223) T) ((-459 . -915) 138028) ((-742 . -494) 138012) ((-1093 . -653) 137937) ((-704 . -621) 137872) ((-787 . -653) 137797) ((-628 . -1062) 137784) ((-484 . -1223) T) ((-347 . -372) T) ((-141 . -494) 137766) ((-785 . -653) 137691) ((-1147 . -1223) T) ((-554 . -855) T) ((-466 . -653) 137662) ((-266 . -892) 137521) ((-248 . -892) NIL) ((-117 . -1062) 137466) ((-459 . -653) 137391) ((-669 . -1044) 137368) ((-628 . -111) 137353) ((-395 . 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-21) T) ((-870 . -618) 135322) ((-1005 . -722) 135270) ((-224 . -653) 135237) ((-699 . -111) 135171) ((-50 . -731) T) ((-1180 . -25) T) ((-355 . -353) T) ((-1174 . -21) T) ((-1086 . -457) 135122) ((-1174 . -25) T) ((-717 . -519) 135069) ((-586 . -731) T) ((-523 . -731) T) ((-1132 . -21) T) ((-1132 . -25) T) ((-601 . -131) T) ((-297 . -651) 134804) ((-600 . -131) T) ((-363 . -457) T) ((-357 . -457) T) ((-349 . -457) T) ((-479 . -310) 134783) ((-1231 . -102) T) ((-316 . -289) 134718) ((-108 . -457) T) ((-79 . -446) T) ((-79 . -400) T) ((-482 . -102) T) ((-696 . -621) 134702) ((-1301 . -618) 134684) ((-1301 . -619) 134666) ((-1086 . -407) 134645) ((-1041 . -494) 134576) ((-569 . -800) T) ((-569 . -797) T) ((-1069 . -236) 134522) ((-363 . -407) 134473) ((-357 . -407) 134424) ((-349 . -407) 134375) ((-1288 . -1118) T) ((-1297 . -1057) 134359) ((-385 . -1057) 134343) ((-1297 . -645) 134313) ((-385 . -645) 134283) ((-699 . -621) 134218) ((-1288 . -23) T) ((-1275 . -102) T) ((-176 . -618) 134200) ((-1148 . -1064) T) ((-552 . -372) T) ((-675 . -749) 134184) ((-1185 . -145) 134163) ((-1185 . -147) 134142) ((-1152 . -1106) T) ((-1152 . -1077) 134111) ((-69 . -1223) T) ((-1030 . -1062) 134048) ((-355 . -651) 133978) ((-871 . -1064) T) ((-241 . -644) 133884) ((-699 . -1055) T) ((-358 . -1062) 133829) ((-61 . -1223) T) ((-1030 . -111) 133745) ((-907 . -618) 133656) ((-699 . -244) T) ((-699 . -234) NIL) ((-848 . -853) 133635) ((-704 . -800) T) ((-704 . -797) T) ((-1009 . -416) 133612) ((-358 . -111) 133541) ((-383 . -926) T) ((-412 . -853) 133520) ((-717 . -293) 133431) ((-224 . -731) T) ((-1265 . -498) 133397) ((-1258 . -498) 133363) ((-1237 . -498) 133329) ((-583 . -1106) T) ((-319 . -1008) 133308) ((-223 . -1106) 133286) ((-1230 . -849) T) ((-322 . -979) 133248) ((-105 . -102) T) ((-48 . -1062) 133213) ((-1297 . -102) T) ((-385 . -102) T) ((-48 . -111) 133169) ((-1010 . -644) 133151) ((-1259 . -618) 133133) ((-536 . -102) T) ((-505 . -102) T) ((-1139 . -1140) 133117) ((-152 . -1280) 133101) ((-246 . -1223) T) ((-1222 . -102) T) ((-1030 . -621) 133038) ((-1179 . -1227) 133017) ((-358 . -621) 132947) ((-1131 . -1227) 132926) ((-241 . -21) 132836) ((-241 . -25) 132687) ((-127 . -119) 132671) ((-121 . -119) 132655) ((-44 . -749) 132639) ((-1179 . -561) 132550) ((-1131 . -561) 132481) ((-1230 . -1106) T) ((-1041 . -289) 132456) ((-1173 . -1089) T) ((-1000 . -1089) T) ((-821 . -131) T) ((-117 . -800) NIL) ((-117 . -797) NIL) ((-359 . -310) T) ((-356 . -310) T) ((-348 . -310) T) ((-253 . -1118) 132366) ((-252 . -1118) 132276) ((-1030 . -1055) T) ((-1009 . -1064) T) ((-48 . -621) 132209) ((-347 . -653) 132154) ((-626 . -38) 132138) ((-1286 . -618) 132100) ((-1286 . -619) 132061) ((-1083 . -618) 132043) ((-1030 . -244) T) ((-358 . -1055) T) ((-820 . -1280) 132013) ((-253 . -23) T) ((-252 . -23) T) ((-993 . -618) 131995) ((-742 . -619) 131956) ((-742 . -618) 131938) ((-804 . -855) 131917) ((-1166 . -151) 131864) ((-1005 . -519) 131776) ((-358 . -234) T) ((-358 . -244) T) ((-393 . -621) 131757) ((-1010 . -25) T) ((-141 . -618) 131739) ((-141 . -619) 131698) ((-916 . -310) T) ((-1010 . -21) T) ((-977 . -25) T) ((-920 . -21) T) ((-920 . -25) T) ((-432 . -21) T) ((-432 . -25) T) ((-848 . -416) 131682) ((-48 . -1055) T) ((-1295 . -1287) 131666) ((-1293 . -1287) 131650) ((-1041 . -609) 131625) ((-319 . -619) 131486) ((-319 . -618) 131468) ((-316 . -619) NIL) ((-316 . -618) 131450) ((-48 . -244) T) ((-48 . -234) T) ((-659 . -289) 131411) ((-555 . -236) 131361) ((-139 . -618) 131328) ((-136 . -618) 131310) ((-114 . -618) 131292) ((-482 . -38) 131257) ((-1297 . -1294) 131236) ((-1288 . -131) T) ((-1296 . -1064) T) ((-1088 . -102) T) ((-88 . -1223) T) ((-505 . -312) NIL) ((-1006 . -107) 131220) ((-895 . -1106) T) ((-891 . -1106) T) ((-1273 . -656) 131204) ((-1273 . -377) 131188) ((-330 . -1223) T) ((-598 . -855) T) ((-1148 . -1106) T) ((-1148 . -1059) 131128) ((-103 . -519) 131061) ((-933 . -618) 131043) ((-347 . -731) T) ((-30 . -618) 131025) ((-871 . -1106) T) ((-848 . -1064) 131004) ((-40 . -653) 130949) ((-226 . -1227) T) ((-412 . -1064) T) ((-1165 . -151) 130931) ((-1005 . -293) 130882) ((-622 . -1106) T) ((-226 . -561) T) ((-322 . -1254) 130866) ((-322 . -1251) 130836) ((-706 . -651) 130808) ((-1196 . -1199) 130787) ((-1081 . -618) 130769) ((-1196 . -107) 130719) ((-652 . -151) 130703) ((-637 . -151) 130649) ((-116 . -651) 130621) ((-484 . -1199) 130600) ((-492 . -147) T) ((-492 . -145) NIL) ((-1126 . -619) 130515) ((-443 . -618) 130497) ((-218 . -147) T) ((-218 . -145) NIL) ((-1126 . -618) 130479) ((-129 . -102) T) ((-52 . -102) T) ((-1237 . -644) 130431) ((-484 . -107) 130381) ((-999 . -23) T) ((-1297 . -38) 130351) ((-1179 . -1118) T) ((-1131 . -1118) T) ((-1068 . -1227) T) ((-314 . -102) T) ((-859 . -1118) T) ((-958 . -1227) 130330) ((-486 . -1227) 130309) ((-1068 . -561) T) ((-958 . -561) 130240) ((-1179 . -23) T) ((-1157 . -1089) T) ((-1131 . -23) T) ((-859 . -23) T) ((-486 . -561) 130171) ((-1148 . -722) 130103) ((-675 . -1057) 130087) ((-1152 . -519) 130020) ((-675 . -645) 130004) ((-1041 . -619) NIL) ((-1041 . -618) 129986) ((-96 . -1089) T) ((-871 . -722) 129956) ((-1217 . -47) 129925) ((-253 . -131) T) ((-252 . -131) T) ((-1110 . -1106) T) ((-1009 . -1106) T) ((-62 . -618) 129907) ((-1174 . -855) NIL) ((-1030 . -797) T) ((-1030 . -800) T) ((-1301 . -1062) 129894) ((-1301 . -111) 129879) ((-1265 . -25) T) ((-1265 . -21) T) ((-875 . -653) 129866) ((-1258 . -21) T) ((-1258 . -25) T) ((-1237 . -21) T) ((-1237 . -25) T) ((-1033 . -151) 129850) ((-877 . -825) 129829) ((-877 . -926) T) ((-717 . -289) 129756) ((-601 . -21) T) ((-343 . -651) 129715) ((-601 . -25) T) ((-600 . -21) T) ((-175 . -651) 129632) ((-40 . -731) T) ((-223 . -519) 129565) ((-600 . -25) T) ((-481 . -151) 129549) ((-468 . -151) 129533) ((-927 . -799) T) ((-927 . -731) T) ((-776 . -798) T) ((-776 . -799) T) ((-511 . -1106) T) ((-507 . -1106) T) ((-776 . -731) T) ((-226 . -367) T) ((-1295 . -1057) 129517) ((-1293 . -1057) 129501) ((-1295 . -645) 129471) ((-1163 . -1106) 129449) ((-876 . -1227) T) ((-1293 . -645) 129419) ((-659 . -618) 129401) ((-876 . -561) T) ((-699 . -372) NIL) ((-44 . -1057) 129385) ((-1301 . -621) 129367) ((-1296 . -1106) T) ((-675 . -102) T) ((-363 . -1280) 129351) ((-357 . -1280) 129335) ((-44 . -645) 129319) ((-349 . -1280) 129303) ((-553 . -102) T) ((-525 . -855) 129282) ((-1052 . -1106) T) ((-822 . -457) 129261) ((-152 . -1057) 129245) ((-1052 . -1077) 129174) ((-1033 . -982) 129143) ((-824 . -1118) T) ((-1009 . -722) 129088) ((-152 . -645) 129072) ((-391 . -1118) T) ((-481 . -982) 129041) ((-468 . -982) 129010) ((-110 . -151) 128992) ((-73 . -618) 128974) ((-899 . -618) 128956) ((-1086 . -729) 128935) ((-1301 . -1055) T) ((-821 . -644) 128883) ((-297 . -1064) 128825) ((-170 . -1227) 128730) ((-226 . -1118) T) ((-327 . -23) T) ((-1174 . -998) 128682) ((-848 . -1106) T) ((-1259 . -1062) 128587) ((-1132 . -745) 128566) ((-1257 . -926) 128545) ((-1236 . -926) 128524) ((-875 . -731) T) ((-170 . -561) 128435) ((-585 . -653) 128422) ((-569 . -653) 128409) ((-412 . -1106) T) ((-265 . -1106) T) ((-214 . -618) 128391) ((-500 . -653) 128356) ((-226 . -23) T) ((-1236 . -825) 128309) ((-1295 . -102) T) ((-358 . -1292) 128286) ((-1293 . -102) T) ((-1259 . -111) 128178) ((-820 . -1057) 128075) ((-820 . -645) 128017) ((-144 . -618) 127999) ((-999 . -131) T) ((-44 . -102) T) ((-241 . -855) 127950) ((-1246 . -1227) 127929) ((-103 . -494) 127913) ((-1296 . -722) 127883) ((-1093 . -47) 127844) ((-1068 . -1118) T) ((-958 . -1118) T) ((-127 . -34) T) ((-121 . -34) T) ((-787 . -47) 127821) ((-785 . -47) 127793) ((-1246 . -561) 127704) ((-358 . -372) T) ((-486 . -1118) T) ((-1179 . -131) T) ((-1131 . -131) T) ((-459 . -47) 127683) ((-876 . -367) T) ((-859 . -131) T) ((-152 . -102) T) ((-1068 . -23) T) ((-958 . -23) T) ((-576 . -561) T) ((-821 . -25) T) ((-821 . -21) T) ((-1148 . -519) 127616) ((-597 . -1089) T) ((-591 . -1044) 127600) ((-1259 . -621) 127474) ((-486 . -23) T) ((-355 . -1064) T) 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123899) ((-459 . -381) 123883) ((-412 . -173) T) ((-319 . -244) 123862) ((-316 . -244) T) ((-316 . -234) NIL) ((-297 . -1106) 123644) ((-226 . -131) T) ((-1126 . -111) 123629) ((-170 . -23) T) ((-804 . -147) 123608) ((-804 . -145) 123587) ((-253 . -644) 123493) ((-252 . -644) 123399) ((-322 . -287) 123365) ((-1163 . -519) 123298) ((-482 . -651) 123248) ((-1139 . -1106) T) ((-226 . -1066) T) ((-820 . -312) 123186) ((-1093 . -906) 123121) ((-787 . -906) 123064) ((-785 . -906) 123048) ((-1295 . -38) 123018) ((-1293 . -38) 122988) ((-1246 . -1118) T) ((-860 . -1118) T) ((-459 . -906) 122965) ((-863 . -1106) T) ((-1246 . -23) T) ((-1126 . -621) 122937) ((-576 . -1118) T) ((-860 . -23) T) ((-628 . -731) T) ((-359 . -926) T) ((-356 . -926) T) ((-292 . -102) T) ((-348 . -926) T) ((-1068 . -131) T) ((-976 . -1089) T) ((-958 . -131) T) ((-117 . -799) NIL) ((-117 . -796) NIL) ((-117 . -731) T) ((-699 . -915) NIL) ((-1052 . -519) 122838) ((-486 . -131) T) ((-576 . -23) T) ((-680 . -312) 122776) ((-640 . -766) T) ((-612 . -766) T) ((-1237 . -855) NIL) ((-1086 . -1057) 122686) ((-1009 . -293) T) ((-699 . -653) 122636) ((-253 . -21) T) ((-355 . -1106) T) ((-253 . -25) T) ((-252 . -21) T) ((-252 . -25) T) ((-152 . -38) 122620) ((-2 . -102) T) ((-916 . -926) T) ((-1086 . -645) 122488) ((-487 . -1280) 122458) ((-1126 . -1055) T) ((-716 . -310) T) ((-363 . -1057) 122410) ((-357 . -1057) 122362) ((-349 . -1057) 122314) ((-363 . -645) 122266) ((-224 . -1044) 122243) ((-357 . -645) 122195) ((-108 . -1057) 122145) ((-349 . -645) 122097) ((-297 . -722) 122039) ((-706 . -1064) T) ((-492 . -457) T) ((-412 . -519) 121951) ((-108 . -645) 121901) ((-218 . -457) T) ((-1126 . -234) T) ((-298 . -151) 121851) ((-1005 . -619) 121812) ((-1005 . -618) 121794) ((-995 . -618) 121776) ((-116 . -1064) T) ((-659 . -1062) 121760) ((-226 . -498) T) ((-404 . -618) 121742) ((-404 . -619) 121719) ((-1060 . -1280) 121689) ((-659 . -111) 121668) ((-1148 . -494) 121652) ((-1297 . -651) 121611) ((-385 . -651) 121580) ((-820 . -38) 121550) ((-63 . -446) T) ((-63 . -400) T) ((-1166 . -102) T) ((-876 . -131) T) ((-489 . -102) 121528) ((-1301 . -372) T) ((-1086 . -102) T) ((-1067 . -102) T) ((-355 . -722) 121473) ((-736 . -147) 121452) ((-736 . -145) 121431) ((-659 . -621) 121349) ((-1030 . -653) 121286) ((-528 . -1106) 121264) ((-363 . -102) T) ((-357 . -102) T) ((-349 . -102) T) ((-108 . -102) T) ((-509 . -1106) T) ((-358 . -653) 121209) ((-1179 . -644) 121157) ((-1131 . -644) 121105) ((-389 . -514) 121084) ((-838 . -853) 121063) ((-383 . -1227) T) ((-699 . -731) T) ((-343 . -1064) T) ((-1237 . -998) 121015) ((-175 . -1064) T) ((-103 . -618) 120947) ((-1181 . -145) 120926) ((-1181 . -147) 120905) ((-383 . -561) T) ((-1180 . -147) 120884) ((-1180 . -145) 120863) ((-1174 . -145) 120770) ((-412 . -293) T) ((-1174 . -147) 120677) ((-1132 . -147) 120656) ((-1132 . -145) 120635) ((-322 . -38) 120476) ((-170 . -131) T) ((-316 . -800) NIL) ((-316 . -797) NIL) ((-659 . -1055) T) ((-48 . -653) 120441) 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116142) ((-468 . -312) 116080) ((-355 . -293) T) ((-1163 . -1261) 116064) ((-1148 . -618) 116026) ((-1148 . -619) 115987) ((-1146 . -102) T) ((-1005 . -1062) 115883) ((-40 . -906) 115835) ((-1163 . -609) 115812) ((-1301 . -653) 115799) ((-871 . -495) 115776) ((-1069 . -151) 115722) ((-877 . -1227) T) ((-1005 . -111) 115604) ((-343 . -722) 115588) ((-871 . -618) 115550) ((-175 . -722) 115482) ((-412 . -289) 115440) ((-877 . -561) T) ((-108 . -405) 115422) ((-84 . -388) T) ((-84 . -400) T) ((-706 . -173) T) ((-622 . -618) 115404) ((-99 . -731) T) ((-487 . -102) 115194) ((-99 . -478) T) ((-116 . -173) T) ((-1295 . -651) 115153) ((-1293 . -651) 115112) ((-1119 . -38) 115082) ((-170 . -644) 115030) ((-1060 . -102) T) ((-1005 . -621) 114920) ((-876 . -25) T) ((-820 . -239) 114899) ((-876 . -21) T) ((-823 . -102) T) ((-44 . -651) 114842) ((-419 . -102) T) ((-389 . -102) T) ((-110 . -312) NIL) ((-228 . -102) 114820) ((-127 . -1223) T) ((-121 . -1223) T) ((-822 . -1057) 114771) ((-822 . -645) 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. -651) 113814) ((-719 . -23) T) ((-511 . -618) 113780) ((-507 . -618) 113762) ((-820 . -651) 113512) ((-1297 . -1064) T) ((-383 . -1066) T) ((-1032 . -1106) 113490) ((-55 . -1044) 113472) ((-907 . -34) T) ((-487 . -312) 113410) ((-597 . -102) T) ((-1163 . -619) 113371) ((-1163 . -618) 113303) ((-1185 . -1057) 113186) ((-45 . -102) T) ((-822 . -102) T) ((-1185 . -645) 113083) ((-1246 . -25) T) ((-1246 . -21) T) ((-860 . -25) T) ((-44 . -371) 113067) ((-860 . -21) T) ((-736 . -457) 113018) ((-1296 . -618) 113000) ((-1285 . -1057) 112970) ((-1060 . -312) 112908) ((-676 . -1089) T) ((-611 . -1089) T) ((-395 . -1106) T) ((-576 . -25) T) ((-576 . -21) T) ((-181 . -1089) T) ((-161 . -1089) T) ((-156 . -1089) T) ((-154 . -1089) T) ((-1285 . -645) 112878) ((-626 . -1106) T) ((-704 . -892) 112860) ((-1273 . -1223) T) ((-228 . -312) 112798) ((-144 . -372) T) ((-1052 . -619) 112740) ((-1052 . -618) 112683) ((-316 . -915) NIL) ((-1231 . -849) T) ((-704 . -1044) 112628) ((-716 . -926) T) ((-479 . -1227) 112607) ((-1180 . -457) 112586) ((-1174 . -457) 112565) ((-333 . -102) T) ((-877 . -1118) T) ((-322 . -651) 112447) ((-319 . -653) 112268) ((-316 . -653) 112197) ((-479 . -561) 112148) ((-343 . -519) 112114) ((-555 . -151) 112064) ((-40 . -310) T) ((-848 . -618) 112046) ((-706 . -293) T) ((-877 . -23) T) ((-383 . -498) T) ((-1086 . -232) 112016) ((-517 . -102) T) ((-412 . -619) 111823) ((-412 . -618) 111805) ((-265 . -618) 111787) ((-116 . -293) T) ((-1259 . -731) T) ((-1257 . -367) 111766) ((-1236 . -367) 111745) ((-1286 . -34) T) ((-1231 . -1106) T) ((-117 . -1223) T) ((-108 . -232) 111727) ((-1185 . -102) T) ((-482 . -1106) T) ((-528 . -494) 111711) ((-742 . -34) T) ((-658 . -1057) 111695) ((-487 . -38) 111665) ((-658 . -645) 111635) ((-141 . -34) T) ((-117 . -890) 111612) ((-117 . -892) NIL) ((-628 . -1044) 111495) ((-649 . -855) 111474) ((-1285 . -102) T) ((-298 . -102) T) ((-717 . -372) 111453) ((-117 . -1044) 111430) ((-395 . -722) 111414) ((-626 . -722) 111398) ((-45 . -312) 111202) ((-821 . -145) 111181) ((-821 . -147) 111160) ((-292 . -651) 111132) ((-1296 . -386) 111111) ((-824 . -855) T) ((-1275 . -1106) T) ((-1166 . -230) 111058) ((-391 . -855) 111037) ((-1265 . -1211) 111003) ((-1265 . -1208) 110969) ((-1258 . -1208) 110935) ((-520 . -131) T) ((-1258 . -1211) 110901) ((-1237 . -1208) 110867) ((-1237 . -1211) 110833) ((-1265 . -35) 110799) ((-1265 . -95) 110765) ((-640 . -618) 110734) ((-612 . -618) 110703) ((-226 . -855) T) ((-1258 . -95) 110669) ((-1258 . -35) 110635) ((-1257 . -1118) T) ((-1126 . -653) 110622) ((-1237 . -95) 110588) ((-1236 . -1118) T) ((-598 . -151) 110570) ((-1086 . -353) 110549) ((-175 . -293) T) ((-117 . -381) 110526) ((-117 . -342) 110503) ((-1237 . -35) 110469) ((-875 . -310) T) ((-316 . -799) NIL) ((-316 . -796) NIL) ((-319 . -731) 110318) ((-316 . -731) T) ((-479 . -367) 110297) ((-363 . -353) 110276) ((-357 . -353) 110255) ((-349 . -353) 110234) ((-319 . -478) 110213) ((-1257 . -23) T) ((-1236 . -23) T) ((-723 . 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109290) ((-871 . -111) 109255) ((-1010 . -457) T) ((-699 . -1044) 109200) ((-916 . -561) T) ((-538 . -618) 109182) ((-586 . -926) T) ((-492 . -1057) 109132) ((-479 . -1118) T) ((-523 . -926) T) ((-920 . -457) T) ((-65 . -618) 109114) ((-218 . -1057) 109064) ((-492 . -645) 109014) ((-363 . -651) 108951) ((-357 . -651) 108888) ((-349 . -651) 108825) ((-637 . -230) 108771) ((-218 . -645) 108721) ((-108 . -651) 108671) ((-479 . -23) T) ((-1126 . -799) T) ((-877 . -131) T) ((-1126 . -796) T) ((-1288 . -1290) 108650) ((-1126 . -731) T) ((-659 . -653) 108624) ((-297 . -618) 108365) ((-1148 . -621) 108283) ((-1041 . -34) T) ((-820 . -853) 108262) ((-585 . -310) T) ((-569 . -310) T) ((-500 . -310) T) ((-1297 . -722) 108232) ((-699 . -381) 108214) ((-699 . -342) 108196) ((-482 . -173) T) ((-385 . -722) 108166) ((-871 . -621) 108101) ((-876 . -855) NIL) ((-569 . -1028) T) ((-500 . -1028) T) ((-1139 . -618) 108083) ((-1119 . -239) 108062) ((-215 . -102) T) ((-1156 . -102) T) ((-71 . -618) 108044) 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-1118) T) ((-1258 . -457) 106235) ((-1237 . -457) 106214) ((-528 . -618) 106146) ((-717 . -653) 106071) ((-412 . -1062) 106023) ((-509 . -618) 106005) ((-916 . -23) T) ((-492 . -312) NIL) ((-1296 . -621) 105961) ((-479 . -131) T) ((-218 . -312) NIL) ((-412 . -111) 105899) ((-820 . -1064) 105829) ((-742 . -1104) 105813) ((-1257 . -498) 105779) ((-1236 . -498) 105745) ((-553 . -849) T) ((-141 . -1104) 105727) ((-482 . -293) T) ((-1296 . -1055) T) ((-1228 . -102) T) ((-1069 . -102) T) ((-848 . -621) 105595) ((-505 . -519) NIL) ((-487 . -239) 105574) ((-412 . -621) 105472) ((-969 . -1057) 105355) ((-740 . -1057) 105325) ((-969 . -645) 105222) ((-1179 . -145) 105201) ((-740 . -645) 105171) ((-458 . -1057) 105141) ((-1179 . -147) 105120) ((-1131 . -147) 105099) ((-1131 . -145) 105078) ((-640 . -1062) 105062) ((-612 . -1062) 105046) ((-458 . -645) 105016) ((-1181 . -1264) 105000) ((-1181 . -1251) 104977) ((-675 . -1106) T) ((-675 . -1059) 104917) ((-1180 . -1256) 104878) ((-553 . -1106) T) 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T) ((-821 . -457) 103978) ((-44 . -1106) T) ((-1094 . -855) T) ((-1069 . -312) 103829) ((-669 . -131) T) ((-1060 . -651) 103798) ((-675 . -722) 103782) ((-292 . -1064) T) ((-359 . -131) T) ((-356 . -131) T) ((-348 . -131) T) ((-266 . -131) T) ((-248 . -131) T) ((-389 . -651) 103751) ((-423 . -102) T) ((-152 . -1106) T) ((-45 . -230) 103701) ((-804 . -1057) 103685) ((-964 . -855) 103664) ((-1005 . -653) 103602) ((-804 . -645) 103586) ((-241 . -1280) 103556) ((-1030 . -310) T) ((-297 . -1062) 103477) ((-916 . -131) T) ((-40 . -926) T) ((-492 . -405) 103459) ((-358 . -310) T) ((-218 . -405) 103441) ((-1086 . -416) 103425) ((-297 . -111) 103341) ((-1190 . -855) T) ((-1189 . -855) T) ((-877 . -25) T) ((-877 . -21) T) ((-343 . -618) 103323) ((-1259 . -47) 103267) ((-226 . -147) T) ((-175 . -618) 103249) ((-1119 . -853) 103228) ((-779 . -618) 103210) ((-128 . -855) T) ((-613 . -236) 103157) ((-480 . -236) 103107) ((-1295 . -722) 103077) ((-48 . -310) T) ((-1293 . -722) 103047) ((-65 . -621) 102976) ((-970 . -1106) T) ((-820 . -1106) 102766) ((-315 . -102) T) ((-907 . -1223) T) ((-48 . -1028) T) ((-1236 . -644) 102674) ((-694 . -102) 102652) ((-44 . -722) 102636) ((-555 . -102) T) ((-297 . -621) 102567) ((-67 . -387) T) ((-67 . -400) T) ((-667 . -23) T) ((-822 . -651) 102503) ((-675 . -766) T) ((-1220 . -1106) 102481) ((-355 . -1062) 102426) ((-680 . -1106) 102404) ((-1068 . -147) T) ((-958 . -147) 102383) ((-958 . -145) 102362) ((-804 . -102) T) ((-152 . -722) 102346) ((-486 . -147) 102325) ((-486 . -145) 102304) ((-355 . -111) 102233) ((-1086 . -1064) T) ((-325 . -855) 102212) ((-1265 . -979) 102181) ((-632 . -1106) T) ((-1258 . -979) 102143) ((-516 . -131) T) ((-512 . -131) T) ((-298 . -230) 102093) ((-363 . -1064) T) ((-357 . -1064) T) ((-349 . -1064) T) ((-297 . -1055) 102035) ((-1237 . -979) 102004) ((-383 . -855) T) ((-108 . -1064) T) ((-1005 . -731) T) ((-875 . -926) T) ((-848 . -800) 101983) ((-848 . -797) 101962) ((-423 . -312) 101901) ((-473 . -102) T) ((-600 . 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-234) T) ((-355 . -244) T) ((-316 . -1223) T) ((-292 . -1106) T) ((-1180 . -1057) 100390) ((-1174 . -1057) 100180) ((-1132 . -1057) 100063) ((-1181 . -645) 99960) ((-1180 . -645) 99801) ((-716 . -1227) T) ((-1174 . -645) 99597) ((-1163 . -656) 99581) ((-1132 . -645) 99478) ((-1217 . -561) 99457) ((-824 . -390) 99441) ((-716 . -561) T) ((-319 . -890) 99425) ((-319 . -892) 99350) ((-316 . -890) 99311) ((-316 . -892) NIL) ((-804 . -312) 99276) ((-322 . -722) 99117) ((-391 . -390) 99101) ((-327 . -326) 99078) ((-490 . -102) T) ((-479 . -25) T) ((-479 . -21) T) ((-423 . -38) 99052) ((-319 . -1044) 98715) ((-226 . -1208) T) ((-226 . -1211) T) ((-3 . -618) 98697) ((-316 . -1044) 98627) ((-2 . -1106) T) ((-2 . |RecordCategory|) T) ((-838 . -618) 98609) ((-1119 . -1064) 98539) ((-585 . -926) T) ((-569 . -825) T) ((-569 . -926) T) ((-500 . -926) T) ((-136 . -1044) 98523) ((-226 . -95) T) ((-170 . -147) 98502) ((-75 . -446) T) ((0 . -618) 98484) ((-75 . -400) T) ((-170 . -145) 98435) ((-226 . 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T) ((-1093 . -23) T) ((-822 . -1064) T) ((-787 . -23) T) ((-785 . -23) T) ((-486 . -457) 92105) ((-1166 . -519) 91888) ((-385 . -386) 91867) ((-1185 . -416) 91851) ((-466 . -23) T) ((-459 . -23) T) ((-96 . -1106) T) ((-489 . -519) 91784) ((-1265 . -1057) 91667) ((-1265 . -645) 91564) ((-1258 . -645) 91405) ((-1258 . -1057) 91240) ((-292 . -293) T) ((-1237 . -1057) 91030) ((-1088 . -618) 91012) ((-1088 . -619) 90993) ((-412 . -915) 90972) ((-1237 . -645) 90768) ((-50 . -1118) T) ((-1217 . -131) T) ((-1030 . -926) T) ((-1009 . -731) T) ((-848 . -653) 90741) ((-717 . -892) NIL) ((-601 . -1057) 90701) ((-586 . -1118) T) ((-523 . -1118) T) ((-600 . -1057) 90584) ((-1174 . -405) 90536) ((-1010 . -312) NIL) ((-820 . -494) 90520) ((-601 . -645) 90493) ((-358 . -926) T) ((-600 . -645) 90390) ((-1163 . -34) T) ((-412 . -653) 90342) ((-50 . -23) T) ((-716 . -131) T) ((-717 . -1044) 90222) ((-586 . -23) T) ((-108 . -519) NIL) ((-523 . -23) T) ((-170 . -414) 90193) ((-1146 . -1106) T) ((-1288 . -1287) 90177) ((-706 . -800) T) ((-706 . -797) T) ((-1126 . -310) T) ((-383 . -147) T) ((-283 . -618) 90159) ((-282 . -618) 90141) ((-1236 . -998) 90111) ((-48 . -926) T) ((-680 . -494) 90095) ((-253 . -1280) 90065) ((-252 . -1280) 90035) ((-1183 . -855) T) ((-1119 . -173) 90014) ((-1126 . -1028) T) ((-1052 . -34) T) ((-841 . -147) 89993) ((-841 . -145) 89972) ((-742 . -107) 89956) ((-617 . -132) T) ((-487 . -1106) 89746) ((-1185 . -1064) T) ((-876 . -457) T) ((-85 . -1223) T) ((-241 . -38) 89716) ((-141 . -107) 89698) ((-717 . -381) 89682) ((-838 . -621) 89550) ((-1296 . -731) T) ((-1285 . -1064) T) ((-1126 . -550) T) ((-584 . -102) T) ((-129 . -495) 89532) ((-1265 . -102) T) ((-395 . -1062) 89516) ((-1258 . -102) T) ((-1179 . -955) 89485) ((-129 . -618) 89452) ((-52 . -618) 89434) ((-1131 . -955) 89401) ((-658 . -416) 89385) ((-1237 . -102) T) ((-1165 . -519) NIL) ((-667 . -25) T) ((-626 . -1062) 89369) ((-667 . -21) T) ((-969 . -651) 89279) ((-740 . -651) 89224) ((-720 . -651) 89196) ((-395 . -111) 89175) ((-223 . -256) 89159) ((-1060 . -1059) 89099) ((-1060 . -1106) T) ((-1010 . -1158) T) ((-823 . -1106) T) ((-458 . -651) 89014) ((-347 . -1227) T) ((-640 . -653) 88998) ((-626 . -111) 88977) ((-612 . -653) 88961) ((-601 . -102) T) ((-314 . -495) 88942) ((-591 . -131) T) ((-600 . -102) T) ((-419 . -1106) T) ((-389 . -1106) T) ((-314 . -618) 88908) ((-228 . -1106) 88886) ((-652 . -519) 88819) ((-637 . -519) 88663) ((-838 . -1055) 88642) ((-649 . -151) 88626) ((-347 . -561) T) ((-717 . -906) 88569) ((-555 . -230) 88519) ((-1265 . -287) 88485) ((-1258 . -287) 88451) ((-1086 . -293) 88402) ((-492 . -853) T) ((-224 . -1118) T) ((-1237 . -287) 88368) ((-1217 . -498) 88334) ((-1010 . -38) 88284) ((-218 . -853) T) ((-423 . -651) 88243) ((-920 . -38) 88195) ((-848 . -799) 88174) ((-848 . -796) 88153) ((-848 . -731) 88132) ((-363 . -293) T) ((-357 . -293) T) ((-349 . -293) T) ((-170 . -457) 88063) ((-432 . -38) 88047) ((-108 . -293) T) ((-224 . -23) T) ((-412 . -799) 88026) ((-412 . -796) 88005) ((-412 . -731) T) ((-505 . -291) 87980) ((-482 . -1062) 87945) ((-663 . -131) T) ((-626 . -621) 87914) ((-1119 . -519) 87847) ((-340 . -131) T) ((-170 . -407) 87826) ((-487 . -722) 87768) ((-820 . -289) 87745) ((-482 . -111) 87701) ((-658 . -1064) T) ((-821 . -1057) 87544) ((-1284 . -1089) T) ((-1246 . -457) 87475) ((-821 . -645) 87324) ((-1283 . -1089) T) ((-1093 . -131) T) ((-1060 . -722) 87266) ((-787 . -131) T) ((-785 . -131) T) ((-576 . -457) T) ((-1033 . -519) 87199) ((-626 . -1055) T) ((-597 . -1106) T) ((-538 . -174) T) ((-466 . -131) T) ((-459 . -131) T) ((-45 . -1106) T) ((-389 . -722) 87169) ((-822 . -1106) T) ((-481 . -519) 87102) ((-468 . -519) 87035) ((-458 . -371) 87005) ((-45 . -615) 86984) ((-319 . -305) T) ((-482 . -621) 86934) ((-1237 . -312) 86819) ((-675 . -618) 86781) ((-59 . -855) 86760) ((-1010 . -405) 86742) ((-553 . -618) 86724) ((-804 . -651) 86683) ((-820 . -609) 86660) ((-521 . -855) 86639) ((-501 . -855) 86618) ((-40 . -1227) T) ((-1005 . -1044) 86514) ((-50 . -131) T) ((-586 . -131) T) ((-523 . -131) T) ((-297 . -653) 86374) ((-347 . -332) 86351) ((-347 . -367) T) ((-325 . -326) 86328) ((-322 . -289) 86313) ((-40 . -561) T) ((-383 . -1208) T) ((-383 . -1211) T) ((-1041 . -1199) 86288) ((-1196 . -236) 86238) ((-1174 . -232) 86190) ((-333 . -1106) T) ((-383 . -95) T) ((-383 . -35) T) ((-1041 . -107) 86136) ((-482 . -1055) T) ((-1297 . -1062) 86120) ((-484 . -236) 86070) ((-1166 . -494) 86004) ((-1288 . -1057) 85988) ((-385 . -1062) 85972) ((-1288 . -645) 85942) ((-482 . -244) T) ((-821 . -102) T) ((-719 . -147) 85921) ((-719 . -145) 85900) ((-489 . -494) 85884) ((-490 . -339) 85853) ((-1297 . -111) 85832) ((-517 . -1106) T) ((-487 . -173) 85811) ((-1005 . -381) 85795) ((-418 . -102) T) ((-385 . -111) 85774) ((-1005 . -342) 85758) ((-281 . -989) 85742) ((-280 . -989) 85726) ((-1295 . -618) 85708) ((-1293 . -618) 85690) ((-110 . -519) NIL) ((-1179 . -1249) 85674) ((-859 . -857) 85658) ((-1185 . -1106) T) 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. -1106) T) ((-412 . -1044) 72457) ((-322 . -111) 72278) ((-699 . -367) T) ((-226 . -287) T) ((-1220 . -621) 72255) ((-48 . -1227) T) ((-820 . -1055) 72185) ((-1179 . -1158) 72163) ((-585 . -131) T) ((-569 . -131) T) ((-500 . -131) T) ((-1166 . -291) 72139) ((-48 . -561) T) ((-1068 . -102) T) ((-958 . -102) T) ((-876 . -1057) 72084) ((-319 . -27) 72063) ((-820 . -234) 72015) ((-250 . -840) 71997) ((-241 . -853) 71976) ((-188 . -840) 71958) ((-718 . -102) T) ((-298 . -494) 71895) ((-876 . -645) 71840) ((-486 . -102) T) ((-736 . -1064) T) ((-617 . -618) 71822) ((-617 . -619) 71683) ((-412 . -381) 71667) ((-412 . -342) 71651) ((-322 . -621) 71477) ((-1179 . -38) 71306) ((-1131 . -38) 71155) ((-859 . -38) 71125) ((-395 . -653) 71109) ((-649 . -312) 71047) ((-1157 . -495) 71028) ((-1157 . -618) 70994) ((-969 . -722) 70891) ((-740 . -722) 70861) ((-223 . -107) 70845) ((-45 . -289) 70770) ((-626 . -653) 70744) ((-315 . -1106) T) ((-292 . -1062) 70731) ((-110 . -618) 70713) ((-110 . -619) 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. -102) T) ((-482 . -653) 69743) ((-473 . -1106) T) ((-45 . -609) 69668) ((-1165 . -291) 69643) ((-292 . -621) 69615) ((-40 . -644) 69554) ((-1246 . -1057) 69377) ((-860 . -1057) 69361) ((-48 . -367) T) ((-1112 . -618) 69343) ((-1246 . -645) 69172) ((-860 . -645) 69142) ((-637 . -291) 69117) ((-821 . -651) 69027) ((-576 . -1057) 69014) ((-487 . -618) 68745) ((-241 . -416) 68714) ((-958 . -312) 68701) ((-576 . -645) 68688) ((-65 . -1223) T) ((-1069 . -519) 68532) ((-676 . -1106) T) ((-628 . -131) T) ((-486 . -312) 68519) ((-611 . -1106) T) ((-551 . -102) T) ((-117 . -131) T) ((-292 . -1055) T) ((-181 . -1106) T) ((-161 . -1106) T) ((-156 . -1106) T) ((-154 . -1106) T) ((-458 . -766) T) ((-31 . -1089) T) ((-969 . -173) 68470) ((-976 . -93) T) ((-1086 . -1062) 68380) ((-626 . -799) 68359) ((-598 . -1106) T) ((-626 . -796) 68338) ((-626 . -731) T) ((-298 . -289) 68317) ((-297 . -1223) T) ((-1060 . -618) 68279) ((-1060 . -619) 68240) ((-1030 . -1118) T) ((-170 . -102) T) ((-277 . -855) 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 f323d7c2..d754c03e 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3477887505) -(4446 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3479296386) +(4447 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -483,666 +483,667 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |ipow| |critM| |initializeGroupForWordProblem| - |e02ajf| |stoseInvertible?| |cond| |simplifyPower| |cCosh| - |asechIfCan| |factorial| |critB| |e02akf| |movedPoints| - |stoseInvertibleSet| |generate| |number?| |cSinh| |acschIfCan| |map| - |sec2cos| |multinomial| |critBonD| |wordInGenerators| |e02baf| - |stoseSquareFreePart| |kernel| |seriesSolve| |cAcsc| |pushdown| - |permutation| |sech2cosh| |previous| |isQuotient| |critMTonD1| - |incrementBy| |e02bbf| |wordInStrongGenerators| |coleman| - |outerProduct| |log10| |draw| |constantToUnaryFunction| |cAsec| - |pushup| |sin2csc| |stirling1| |critMonD1| |e02bcf| |orbits| - |inverseColeman| |expand| |bitand| |tubePlot| |cAcot| - |reducedDiscriminant| |sinh2csch| |stirling2| |currentEnv| |redPo| - |e02bdf| |orbit| |listYoungTableaus| |filterWhile| |bitior| - |exponentialOrder| |cAtan| |idealSimplify| |tan2trig| |summation| - |hMonic| |e02bef| |makeYoungTableau| |permutationGroup| |filterUntil| - |symbol| |completeEval| |cAcos| |definingInequation| |convert| - |tanh2trigh| |factorials| |updatF| |e02daf| |nextColeman| - |wordsForStrongGenerators| |select| |expression| |makeObject| - |lowerPolynomial| |cAsin| |definingEquations| |tan2cot| - |setProperties| |height| |mkcomm| |sPol| |e02dcf| |strongGenerators| - |nextLatticePermutation| |integer| |coef| |raisePolynomial| |cCsc| - |setStatus| |setright!| |tanh2coth| |setProperty| |polarCoordinates| - |updatD| |generators| |e02ddf| |nextPartition| |normalDeriv| |cSec| - |quasiAlgebraicSet| |setleft!| |cot2tan| |imaginary| |minGbasis| - |bivariateSLPEBR| |e02def| |numberOfImproperPartitions| |ran| |cCot| - |radicalSimplify| |brillhartIrreducible?| |coth2tanh| |elaborateFile| - |lepol| |solveLinearPolynomialEquationByRecursion| |e02dff| |subSet| - |highCommonTerms| |cTan| |denominator| |brillhartTrials| |removeCosSq| - |elaborate| |prinshINFO| |factorByRecursion| |e02gaf| - |unrankImproperPartitions0| |mapCoef| |cCos| |numerator| ** - |removeSinSq| |solid| |prindINFO| |makeRecord| |e02zaf| - |factorSquareFreeByRecursion| |lo| |unrankImproperPartitions1| - |nthCoef| |cSin| |quadraticForm| |removeCoshSq| |solid?| |fprindINFO| - |e04dgf| |randomR| |incr| |subresultantSequence| |acsch| - |binomThmExpt| |label| |cLog| |back| |removeSinhSq| |initial| - |denominators| |prinpolINFO| |factorSFBRlcUnit| |e04fdf| - |SturmHabichtSequence| |pomopo!| |cExp| |front| |expandTrigProducts| - |numerators| |prinb| |charthRoot| |e04gcf| |SturmHabichtCoefficients| - |mapExponents| |cRationalPower| |rotate!| |fintegrate| |convergents| - |critpOrder| |conditionP| |e04jaf| |SturmHabicht| - |linearAssociatedLog| |cPower| |dequeue!| |coefficient| |approximants| - |makeCrit| |solveLinearPolynomialEquation| |e04mbf| |countRealRoots| - |linearAssociatedOrder| |seriesToOutputForm| |enqueue!| |coHeight| - |reducedForm| |virtualDegree| |factorSquareFreePolynomial| |e04naf| - |SturmHabichtMultiple| |linearAssociatedExp| |iCompose| |quatern| - |extendIfCan| Y |partialQuotients| |conditionsForIdempotents| - |factorPolynomial| |e04ucf| |countRealRootsMultiple| |tail| - |createNormalElement| |taylorQuoByVar| |imagK| |algebraicVariables| - |partialDenominators| |constructor| |rules| |genericRightDiscriminant| - |squareFreePolynomial| |e04ycf| |signatureAst| |zeroOf| - |setLabelValue| |iExquo| |imagJ| |zeroSetSplitIntoTriangularSystems| - |partialNumerators| |genericRightTraceForm| |gcdPolynomial| |f01brf| - |pop!| |rootsOf| |option| |getCode| |getStream| |imagI| |zeroSetSplit| - |reducedContinuedFraction| |showSummary| |genericLeftDiscriminant| - |torsion?| |f01bsf| |push!| |makeSketch| |printCode| |getRef| - |conjugate| |inc| |reduceByQuasiMonic| |push| |genericLeftTraceForm| - |torsionIfCan| |f01maf| |minordet| |inrootof| |printStatement| - |makeSeries| |queue| |collectQuasiMonic| |bindings| |showAttributes| - |genericRightNorm| |getGoodPrime| |f01mcf| |determinant| |droot| - |unknown| |putProperty| |block| |mappingMode| |nthRoot| |removeZero| - |macroExpand| |cartesian| |genericRightTrace| |f01qcf| |badNum| - |diagonalProduct| |rightTrim| |iroot| |putProperties| |returns| - |categoryMode| |fractRadix| |initiallyReduce| |polar| - |genericRightMinimalPolynomial| |f01qdf| |mix| |diagonal| |leftTrim| - |size?| |goto| |voidMode| |wholeRadix| |headReduce| |cylindrical| - |rightRankPolynomial| |doubleDisc| |f01qef| |diagonalMatrix| |eq?| - |repeatUntilLoop| |noValueMode| |cycleRagits| |stronglyReduce| - |spherical| |say| |genericLeftNorm| |polyred| |f01rcf| |scalarMatrix| - |doublyTransitive?| |whileLoop| |jokerMode| |prefixRagits| - |rewriteSetWithReduction| |parabolic| |genericLeftTrace| - |padicFraction| |f01rdf| |hermite| |knownInfBasis| |forLoop| GF2FG - |fractRagits| |autoReduced?| |parabolicCylindrical| - |genericLeftMinimalPolynomial| |padicallyExpand| F |f01ref| - |completeHermite| |rootSplit| |sin?| FG2F |wholeRagits| - |initiallyReduced?| |paraboloidal| |leftRankPolynomial| - |numberOfFractionalTerms| |f02aaf| |smith| |ratDenom| |zeroVector| - F2FG |radix| |result| |headReduced?| |ellipticCylindrical| |generic| - |nthFractionalTerm| |f02abf| |completeSmith| |ratPoly| - |zeroSquareMatrix| |open| |explogs2trigs| |randnum| |remove| |eval| - |stronglyReduced?| |reset| |prolateSpheroidal| |rightUnits| - |firstNumer| |f02adf| |diophantineSystem| |rootPower| - |identitySquareMatrix| |trigs2explogs| |reseed| |reduced?| - |oblateSpheroidal| |leftUnits| |firstDenom| |f02aef| |csubst| - |rootProduct| |lookupFunction| |swap!| |pattern| |seed| |last| - |normalized?| |write| |bipolar| |compBound| |compactFraction| |f02aff| - |particularSolution| |assoc| |rootSimp| |encodingDirectory| |fill!| - |null| |rational| |quasiComponent| |save| |bipolarCylindrical| - |tablePow| |partialFraction| |f02agf| |mapSolve| |rootKerSimp| - |operations| |attributeData| |minIndex| |rational?| |not| |taylor| - |initials| |toroidal| |solveid| |gcdPrimitive| |f02ajf| |quadratic| - |leftRank| |domainTemplate| |maxIndex| |and| |rationalIfCan| |laurent| - |basicSet| |conical| |testModulus| |symmetricGroup| |f02akf| |cubic| - |rightRank| |lSpaceBasis| |entry?| |message| |or| |setvalue!| - |puiseux| |infRittWu?| |HenselLift| |alternatingGroup| |f02awf| - |quartic| |doubleRank| |finiteBasis| |indices| |setchildren!| |xor| - |getCurve| |completeHensel| |f02axf| |abelianGroup| |hi| |aLinear| - |weakBiRank| |principal?| |index?| |node?| |case| |inv| |listLoops| - |multMonom| |cyclicGroup| |f02bbf| |aQuadratic| |biRank| |divisor| - |entries| |child?| |Zero| |ground?| |closed?| |build| |dihedralGroup| - |f02bjf| |aCubic| |basisOfCommutingElements| |ground| |key?| |One| - |distance| |lcm| |open?| |leadingIndex| |mathieu11| |f02fjf| - |aQuartic| |basisOfLeftAnnihilator| |elaboration| |symbolIfCan| - |nodes| |leadingMonomial| |setClosed| |leadingExponent| |mathieu12| - |cons| |f02wef| |radicalSolve| |basisOfRightAnnihilator| |select!| - |argument| |append| |rename| |leadingCoefficient| |tube| - |GospersMethod| |mathieu22| |f02xef| |radicalRoots| - |basisOfLeftNucleus| |delete!| |constantKernel| |primitiveMonomials| - |gcd| |rename!| |output| |unitVector| |integerBound| |f04adf| - |contractSolve| |basisOfRightNucleus| |dn| |constantIfCan| |false| - |mainValue| |reductum| |cosSinInfo| |iiabs| |quotientByP| |f04arf| - |decomposeFunc| |basisOfMiddleNucleus| |sncndn| |kovacic| - |mainDefiningPolynomial| |elt| |loopPoints| |bringDown| |moduloP| - |f04asf| |unvectorise| |basisOfNucleus| |categoryFrame| |laplace| - |mainForm| |generalTwoFactor| |newReduc| |modulus| |f04atf| - |bubbleSort!| |basisOfCenter| |interactiveEnv| |generalSqFr| - |logical?| |digits| |f04axf| |insertionSort!| |basisOfLeftNucloid| - |limitedint| |selectPolynomials| |twoFactor| |character?| - |continuedFraction| |f04faf| |check| |basisOfRightNucloid| - |getProperties| |integerIfCan| |selectOrPolynomials| |setOrder| - |doubleComplex?| |light| |f04jgf| |lprop| |basisOfCentroid| - |internalIntegrate| |selectAndPolynomials| |categories| |getOrder| - |complex?| |pastel| |radicalOfLeftTraceForm| |getProperty| - |infieldIntegrate| |quasiMonicPolynomials| |less?| |double?| |dark| - |coefChoose| |currentScope| |applyRules| |scopes| |limitedIntegrate| - |univariate?| |userOrdered?| |ffactor| |getSyntaxFormsFromFile| - |myDegree| |pushNewContour| |localUnquote| |eigenvalues| - |extendedIntegrate| |univariatePolynomials| |largest| |qfactor| - |surface| |normDeriv2| |findBinding| |arbitrary| |eigenvector| - |varselect| |linear?| |UP2ifCan| |coordinate| |plenaryPower| - |contours| |setColumn!| |generalizedEigenvector| |kmax| - |linearPolynomials| |maxrow| |anfactor| |partitions| |c02aff| - |structuralConstants| |generalizedEigenvectors| |ksec| |bivariate?| - |tableau| |fortranCharacter| |conjugates| |c02agf| |coordinates| - |plusInfinity| |eigenvectors| |vark| |bivariatePolynomials| - |listOfLists| |fortranDoubleComplex| |shuffle| |c05adf| |bounds| - |minusInfinity| |factorAndSplit| |removeConstantTerm| - |removeRoughlyRedundantFactorsInPols| |key| |tanSum| |fortranComplex| - |shufflein| |c05nbf| |high| |inGroundField?| |rightOne| |mkPrim| - |removeRoughlyRedundantFactorsInPol| |tanAn| |fortranLogical| - |sequences| |c05pbf| |low| |transcendent?| |leftOne| |filename| - |intPatternMatch| |interReduce| |tanNa| |fortranInteger| - |permutations| |c06eaf| |subset?| |algebraic?| |rightZero| - |primintegrate| |roughBasicSet| |initTable!| |fortranDouble| |atoms| - |c06ebf| |symmetricDifference| |sh| |leftZero| |expintegrate| - |crushedSet| |parse| |printInfo!| |fortranReal| |makeResult| |c06ecf| - |difference| |type| |mirror| |setRow!| |swap| |tanintegrate| - |rewriteSetByReducingWithParticularGenerators| |next| |startStats!| - |external?| |is?| |c06ekf| |intersect| |monomial?| - |oneDimensionalArray| |minPoly| |primextendedint| - |rewriteIdealWithQuasiMonicGenerators| |printStats!| |point| - |scalarTypeOf| |Is| |c06fpf| |part?| |rquo| |freeOf?| |expextendedint| - |squareFreeFactors| |clearTable!| |associatedEquations| - |fortranCarriageReturn| |c06fqf| |addMatchRestricted| |checkPrecision| - |before?| |lquo| |operators| |primlimitedint| - |univariatePolynomialsGcds| |usingTable?| |arrayStack| - |fortranLiteral| |insertMatch| |c06frf| |latex| |mindegTerm| - |mainKernel| |explimitedint| |removeRoughlyRedundantFactorsInContents| - |printingInfo?| |series| |fortranLiteralLine| |addMatch| |c06fuf| - |member?| |product| |distribute| |primextintfrac| - |removeRedundantFactorsInContents| |lhs| |makingStats?| - |processTemplate| |c06gbf| |getMatch| |enumerate| EQ |LiePolyIfCan| - |functionIsFracPolynomial?| |primlimintfrac| - |removeRedundantFactorsInPols| |rhs| |extractIfCan| |makeFR| |failed?| - |c06gcf| |setOfMinN| |trunc| |problemPoints| |primintfldpoly| - |irreducibleFactors| |insert!| |musserTrials| |optpair| |c06gqf| - |elements| |degree| |zerosOf| |expintfldpoly| |lazyIrreducibleFactors| - |min| |interpretString| |stopMusserTrials| |getBadValues| |c06gsf| - |replaceKthElement| |rule| |quasiRegular| |singularitiesOf| - |monomialIntegrate| |removeIrreducibleRedundantFactors| - |stripCommentsAndBlanks| |numberOfFactors| |resetBadValues| |d01ajf| - |incrementKthElement| |quasiRegular?| |polynomialZeros| - |monomialIntPoly| |index| |normalForm| |setPrologue!| |modularFactor| - |hasTopPredicate?| |d01akf| |float?| |constant?| |f2df| - |inverseLaplace| |changeBase| |setTex!| |useSingleFactorBound?| - |topPredicate| |d01alf| |integer?| |mindeg| |ef2edf| |center| - |inputOutputBinaryFile| |companionBlocks| |setEpilogue!| - |useSingleFactorBound| |setTopPredicate| |d01amf| |symbol?| |maxdeg| - |ocf2ocdf| |bothWays| |pair| |xCoord| |prologue| - |useEisensteinCriterion?| |d01anf| |patternVariable| |string?| |value| - |RemainderList| |socf2socdf| |bytes| |yCoord| |epilogue| - |useEisensteinCriterion| |withPredicates| |d01apf| |list?| |unexpand| - |df2fi| |ip4Address| |zCoord| |endOfFile?| |eisensteinIrreducible?| - |setPredicates| |d01aqf| |pair?| |triangSolve| |edf2fi| |iprint| - |rCoord| |readIfCan!| |parents| |tryFunctionalDecomposition?| - |predicates| |d01asf| |atom?| |entry| |univariateSolve| |edf2df| - |elem?| |thetaCoord| |readLineIfCan!| |tryFunctionalDecomposition| - |hasPredicate?| |d01bbf| |null?| |realSolve| |expenseOfEvaluation| - |notelem| |phiCoord| |readLine!| |btwFact| |optional?| |d01fcf| - |startTable!| |positiveSolve| |numberOfOperations| |logpart| |color| - |writeLine!| |beauzamyBound| |multiple?| |d01gaf| |stopTable!| - |squareFree| |edf2efi| |ratpart| |hue| |sign| |sn| |bombieriNorm| - |reverse| |generic?| |d01gbf| |supDimElseRittWu?| - |linearlyDependentOverZ?| |dfRange| |mkAnswer| |shade| |nonQsign| - |rootBound| |quoted?| |d02bbf| |algebraicSort| |linearDependenceOverZ| - |dflist| |call| |irDef| |nthRootIfCan| |direction| |singleFactorBound| - |inR?| |d02bhf| |moreAlgebraic?| |solveLinearlyOverQ| |leaves| |df2mf| - |tree| |irCtor| |expIfCan| |createThreeSpace| |quadraticNorm| |isList| - |d02cjf| |subTriSet?| |ldf2vmf| |irVar| |logIfCan| |cyclicParents| - |infinityNorm| |isOp| |d02ejf| |subPolSet?| |edf2ef| - |perfectNthPower?| |sinIfCan| |cyclicEqual?| |scaleRoots| |satisfy?| - |d02gaf| |internalSubPolSet?| |vedf2vef| |perfectNthRoot| |cosIfCan| - |init| |cyclicEntries| |shiftRoots| |addBadValue| |d02gbf| - |internalInfRittWu?| |df2st| |approxNthRoot| |tanIfCan| |cyclicCopy| - |degreePartition| |badValues| |d02kef| |internalSubQuasiComponent?| - |f2st| |perfectSquare?| |cotIfCan| |cyclic?| |factorOfDegree| - |retractable?| |d02raf| |subQuasiComponent?| |ldf2lst| |generator| - |perfectSqrt| |secIfCan| |complexNormalize| |factorsOfDegree| - |ListOfTerms| |d03edf| |removeSuperfluousQuasiComponents| |sdf2lst| - |approxSqrt| |cscIfCan| |complexElementary| |pascalTriangle| - |PDESolve| |d03eef| |subCase?| |getlo| |generateIrredPoly| |asinIfCan| - |trigs| |rangePascalTriangle| |search| |leftFactor| |d03faf| - |removeSuperfluousCases| |gethi| |complexExpand| |acosIfCan| |real?| - |stack| |sizePascalTriangle| |rightFactorCandidate| |e01baf| - |prepareDecompose| |outputMeasure| |complexIntegrate| |atanIfCan| - |complexForm| |fillPascalTriangle| |measure| |e01bef| |branchIfCan| - |dimensionOfIrreducibleRepresentation| |acotIfCan| |UpTriBddDenomInv| - |condition| |safeCeiling| |e01bff| |coerceImages| |rem| - |startTableGcd!| |weight| |irreducibleRepresentation| |asecIfCan| - |LowTriBddDenomInv| |safeFloor| |e01bgf| |fixedPoints| |quo| - |stopTableGcd!| |makeVariable| |checkRur| |acscIfCan| |simplify| - |safetyMargin| |odd?| |e01bhf| |startTableInvSet!| |dim| |finiteBound| - |cAcsch| |sinhIfCan| |htrigs| |e01daf| |div| |stopTableInvSet!| - |sortConstraints| |cAsech| |coshIfCan| |simplifyExp| |hclf| - |rightRemainder| |e01saf| |stosePrepareSubResAlgo| |exquo| |matrix| - |sumOfSquares| |cAcoth| |tanhIfCan| |simplifyLog| |writable?| - |rightQuotient| |e01sbf| ~= |stoseInternalLastSubResultant| - |splitLinear| |cAtanh| |cothIfCan| |coerce| |expandPower| |readable?| - |rightLcm| |e01sef| |stoseIntegralLastSubResultant| |#| - |simpleBounds?| |bezoutResultant| |expandLog| |exists?| - |leftExtendedGcd| ~ |e01sff| |stoseLastSubResultant| |printInfo| - |linearMatrix| |submod| |max| |bezoutDiscriminant| |clearCache| - |cos2sec| |extension| |leftGcd| |level| |e02adf| - |stoseInvertible?sqfreg| |linearPart| |addmod| |resultantEuclidean| - |cosh2sech| |shallowExpand| |leftExactQuotient| |e02aef| - |stoseInvertibleSetsqfreg| |nonLinearPart| |symmetricRemainder| - |semiResultantEuclidean2| |linear| |cot2trig| |deepExpand| - |leftRemainder| |substring?| |quadratic?| |positiveRemainder| - |semiResultantEuclidean1| |char| |coth2trigh| - |clearFortranOutputStack| |leftQuotient| |linears| - |extendedSubResultantGcd| |changeNameToObjf| |bit?| - |indiceSubResultant| |leader| |csc2sin| |polynomial| - |showFortranOutputStack| |ddFact| |monicLeftDivide| |exactQuotient!| - |suffix?| |optAttributes| |algint| |indiceSubResultantEuclidean| - |csch2sinh| |topFortranOutputStack| |monicRightDivide| |failed| - |separateFactors| |exactQuotient| |Nul| |algintegrate| - |semiIndiceSubResultantEuclidean| |setFormula!| |compile| |exptMod| - |leftDivide| |primPartElseUnitCanonical!| |prefix?| |status| - |exponents| |formula| |palgintegrate| |degreeSubResultant| - |shallowCopy| |linkToFortran| |rightDivide| |meshPar2Var| - |primPartElseUnitCanonical| |iisqrt2| |palginfieldint| - |degreeSubResultantEuclidean| |numberOfChildren| - |setLegalFortranSourceExtensions| |hermiteH| |meshFun2Var| - |lazyResidueClass| |second| |iisqrt3| |bitLength| - |semiDegreeSubResultantEuclidean| |erf| |children| |float| |fracPart| - |laguerreL| |meshPar1Var| |monicModulo| |third| |iiexp| |bitCoef| - |lastSubResultantEuclidean| |child| |polyPart| |legendreP| |ptFunc| - |lazyPseudoDivide| |hitherPlane| |iilog| |bitTruth| - |semiLastSubResultantEuclidean| |nrows| |birth| |void| - |fullPartialFraction| |writeBytes!| |minimumExponent| - |lazyPremWithDefault| |eyeDistance| |iisin| |contains?| - |subResultantGcdEuclidean| |ncols| |dilog| |internal?| - |primeFrobenius| |maximumExponent| |writeUInt8!| |lazyPquo| |infix?| - |perspective| |iicos| |inf| |semiSubResultantGcdEuclidean2| |sin| - |root?| |discreteLog| |mask| |writeInt8!| |rowEch| |lazyPrem| |zoom| - |iitan| |qinterval| |semiSubResultantGcdEuclidean1| |cos| |leaf?| - |decreasePrecision| |writeByte!| |rowEchLocal| |pquo| |rotate| |iicot| - |interval| |discriminantEuclidean| |expr| |tan| |outputForm| - |increasePrecision| |isOpen?| |rowEchelonLocal| |prem| |drawStyle| - |iisec| |unit?| |semiDiscriminantEuclidean| |cot| |argscript| |bits| - |outputBinaryFile| |normalizedDivide| |supRittWu?| |outlineRender| - |iicsc| |associates?| |chainSubResultants| |sec| |superscript| GE - |unitNormalize| |maxint| |blankSeparate| |double| |RittWuCompare| - |diagonals| |iiasin| |unitCanonical| |schema| |csc| |subscript| GT - |unit| |semicolonSeparate| |binaryFunction| |mainMonomials| |axes| - |bfEntry| |iiacos| |unitNormal| |variable| |resultantReduit| |asin| - |scripted?| LE |flagFactor| |commaSeparate| |makeFloatFunction| - |mainCoefficients| |controlPanel| |bfKeys| |iiatan| |lfextendedint| - |resetNew| |iterators| |resultantReduitEuclidean| |acos| |log| LT - |sqfrFactor| |pile| |unaryFunction| |leastMonomial| |viewpoint| - |iiacot| |lflimitedint| |semiResultantReduitEuclidean| |symFunc| - |atan| |primeFactor| |paren| |compiledFunction| |mainMonomial| - |dimensions| |iiasec| |lfinfieldint| BY |divide| |symbolTableOf| - |acot| |nthFlag| |bracket| |corrPoly| |quasiMonic?| |resize| |iiacsc| - |lfintegrate| |Lazard| |argumentListOf| |asec| |nthExponent| |prod| - |lifting| |monic?| |move| |iisinh| |lfextlimint| |Lazard2| - |returnTypeOf| |acsc| |irreducibleFactor| |lifting1| |overlabel| - |deepestInitial| |declare!| |modifyPointData| |iicosh| |BasicMethod| - |nextsousResultant2| |printHeader| |sinh| |sylvesterMatrix| |factors| - |overbar| |exprex| |iteratedInitials| |subspace| |iitanh| - |PollardSmallFactor| |resultantnaif| |returnType!| |cosh| - |bezoutMatrix| |nilFactor| |prime| |coerceL| |deepestTail| - |makeViewport3D| |iicoth| |showTheFTable| |resultantEuclideannaif| - |argumentList!| |tanh| |regularRepresentation| |quote| |coerceS| - |head| |viewport3D| |iisech| |clearTheFTable| - |semiResultantEuclideannaif| |endSubProgram| |coth| |traceMatrix| - |frobenius| |supersub| |mdeg| NOT |viewDeltaYDefault| |iicsch| - |fTable| |pdct| |currentSubProgram| |sech| |randomLC| |computePowers| - |keys| |presuper| |mvar| OR |viewDeltaXDefault| |iiasinh| |palgint0| - |powers| |depth| |newSubProgram| |csch| |minimize| |pow| |presub| - |relativeApprox| AND |viewZoomDefault| |iiacosh| |palgextint0| - |partition| |clearTheSymbolTable| |module| |An| |sub| |debug| |rootOf| - |segment| |viewPhiDefault| |iiatanh| |palglimint0| |complete| - |showTheSymbolTable| |rightRegularRepresentation| |rarrow| D - |UnVectorise| |allRootsOf| |viewThetaDefault| |iiacoth| |palgRDE0| - |pole?| |printTypes| |leftRegularRepresentation| |assign| |Vectorise| - |definingPolynomial| |pointColorDefault| |iiasech| |palgLODE0| - |listBranches| |newTypeLists| |rightTraceMatrix| |slash| |setPoly| - |positive?| |lineColorDefault| |iiacsch| |chineseRemainder| - |triangular?| |typeLists| |leftTraceMatrix| |over| |exponent| - |negative?| |associatedSystem| |axesColorDefault| |specialTrigs| - |divisors| |rewriteIdealWithRemainder| |externalList| |function| - |rightDiscriminant| |zag| |exQuo| |zero?| |uncouplingMatrices| - |unitsColorDefault| |localReal?| |eulerPhi| - |rewriteIdealWithHeadRemainder| |typeList| |parts| |leftDiscriminant| - |postfix| |moebius| |augment| |pointSizeDefault| |rischNormalize| - |fibonacci| |remainder| |parametersOf| |represents| |infix| - |rightRecip| |lastSubResultant| |viewPosDefault| |realElementary| - |harmonic| |headRemainder| |fortranTypeOf| |properties| |mergeFactors| - |leftRecip| |vconcat| |lastSubResultantElseSplit| * |viewSizeDefault| - |validExponential| |jacobi| |roughUnitIdeal?| |empty| |translate| - |isMult| |hconcat| |leftPower| |invertibleSet| |viewDefaults| - |rootNormalize| |moebiusMu| |roughEqualIdeals?| |compound?| - |exprToXXP| |optimize| |rspace| |print| |rightPower| |invertible?| - |viewWriteDefault| |tanQ| |numberOfDivisors| |roughSubIdeal?| - |getOperands| |operation| |exprToUPS| |resolve| |vspace| - |derivationCoordinates| |invertibleElseSplit?| = |viewWriteAvailable| - |callForm?| |sumOfDivisors| |roughBase?| |getOperator| |exprToGenUPS| - |hspace| |one?| |purelyAlgebraicLeadingMonomial?| |var1StepsDefault| - |getIdentifier| |sumOfKthPowerDivisors| |trivialIdeal?| |nil?| - |localAbs| |superHeight| |splitSquarefree| |algebraicCoefficients?| < - |var2StepsDefault| |variable?| |HermiteIntegrate| |collectUpper| - |buildSyntax| |universe| |subHeight| |normalDenom| - |purelyTranscendental?| > |tubePointsDefault| |setleaves!| - |getConstant| |palgint| |collect| |solve| |complement| - |doubleFloatFormat| |totalfract| |purelyAlgebraic?| <= - |tubeRadiusDefault| |balancedBinaryTree| |environment| |palgextint| - |collectUnder| |triangularSystems| |cardinality| |messagePrint| - |pushdterm| |prepareSubResAlgo| >= |dimension| |irForm| |palglimint| - |mainVariable?| |nativeModuleExtension| |interpret| - |internalIntegrate0| |members| |pushucoef| |internalLastSubResultant| - |crest| |palgRDE| |mainVariables| |hostByteOrder| |true| |makeCos| - |padecf| |pushuconst| |integralLastSubResultant| |cfirst| - |totalDifferential| |cn| |palgLODE| |removeSquaresIfCan| - |hostPlatform| |makeSin| |mantissa| |pade| |numberOfMonomials| - |toseLastSubResultant| + |sts2stst| |homogeneous?| |splitConstant| - |unprotectedRemoveRedundantFactors| |rootDirectory| - |resetAttributeButtons| |iiGamma| |root| |multiset| |toseInvertible?| - - |clikeUniv| |leadingBasisTerm| |pmComplexintegrate| - |removeRedundantFactors| |bumprow| |getButtonValue| |mergeDifference| - |toseInvertibleSet| |weierstrass| / |ignore?| |pmintegrate| - |certainlySubVariety?| |bumptab| |leastAffineMultiple| |OMgetEndAtp| - |squareFreePrim| |toseSquareFreePart| |qqq| |computeInt| |infieldint| - |possiblyNewVariety?| |bumptab1| |category| |reducedQPowers| - |OMgetEndAttr| |nil| |compdegd| |quotedOperators| |integralBasis| - |checkForZero| |extendedint| |shift| |probablyZeroDim?| |untab| - |domain| |rootOfIrreduciblePoly| |OMgetEndBind| |univcase| |rur| - |localIntegralBasis| |logGamma| |bat1| |package| |write!| - |OMgetEndBVar| |consnewpol| |create| |qualifier| |varList| - |hypergeometric0F1| |zeroDimPrime?| |pointPlot| |bat| |read!| - |OMgetEndError| |dec| |nsqfree| |enterInCache| |approximate| |qelt| - |mainExpression| |rotatez| |zeroDimPrimary?| |delta| |calcRanges| - |tab1| |iomode| |OMgetEndObject| |complex| |property| |intChoose| - |currentCategoryFrame| |qsetelt| |changeWeightLevel| |rotatey| - |primaryDecomp| |fixPredicate| |tab| |close!| |OMgetInteger| |xRange| - |characteristicSerie| |rotatex| |contract| |patternMatch| |show| |lex| - |reopen!| |OMgetFloat| |lyndonIfCan| |binomial| |yRange| - |characteristicSet| |identity| |gensym| |retract| |patternMatchTimes| - |slex| |deleteProperty!| |rightUnit| |lyndon| |OMgetVariable| - |poisson| |units| |zRange| |medialSet| |dictionary| |leadingSupport| - |bernoulli| |trace| |typeForm| |inverse| |has?| |leftUnit| - |OMgetString| |lyndon?| |geometric| |map!| |Hausdorff| |dioSolve| - |shrinkable| |chebyshevT| |rightMinimalPolynomial| |OMgetSymbol| - |numberOfComputedEntries| |ridHack1| |qsetelt!| |Frobenius| |newLine| - |physicalLength!| |chebyshevU| |isConnected?| - |transcendentalDecompose| |leftMinimalPolynomial| |OMgetType| |rst| - |interpolate| |transcendenceDegree| |copies| |physicalLength| |lambda| - |cyclotomic| |connectTo| |internalDecompose| |associatorDependence| - |OMencodingBinary| |frst| |nullSpace| |extensionDegree| |sayLength| - |flexibleArray| |euler| |normalizedAssociate| |decompose| |code| - |lieAlgebra?| |OMencodingSGML| |lazyEvaluate| |nullity| |setnext!| - |elseBranch| |fixedDivisor| |normalize| |upDateBranches| - |jordanAlgebra?| |OMencodingXML| |lazy?| |rowEchelon| |setrest!| - |setprevious!| |thenBranch| |laguerre| |outputArgs| |preprocess| - |datalist| |noncommutativeJordanAlgebra?| |OMencodingUnknown| - |explicitlyEmpty?| |column| |setfirst!| |shanksDiscLogAlgorithm| - |generalizedInverse| |legendre| |normInvertible?| - |internalZeroSetSplit| |jordanAdmissible?| |omError| - |explicitEntries?| |row| |cycleSplit!| |plus| |reflect| |imports| - |dmpToHdmp| |normFactors| |internalAugment| |comparison| - |lieAdmissible?| |errorInfo| |matrixDimensions| |maxColIndex| - |concat!| |reify| |sequence| |hdmpToDmp| |npcoef| |possiblyInfinite?| - |dom| |equality| |jacobiIdentity?| |errorKind| |matrixConcat3D| - |minColIndex| |cycleTail| |functorData| |readBytes!| |listexp| - |pToHdmp| |explicitlyFinite?| |sum| |powerAssociative?| |OMReadError?| - |setelt!| |maxRowIndex| |cycleLength| |separant| |readUInt32!| - |hdmpToP| |characteristicPolynomial| |nextItem| |alternative?| - |OMUnknownSymbol?| |identityMatrix| |minRowIndex| |cycleEntry| |times| - |isobaric?| |readInt32!| |dmpToP| |realEigenvalues| |upperBound| - |flexible?| |OMUnknownCD?| |zeroMatrix| |antisymmetric?| - |invmultisect| |morphism| |weights| |readUInt16!| |pToDmp| - |realEigenvectors| |lowerBound| |setButtonValue| |top| - |rightAlternative?| |OMParseError?| |mappingAst| |symmetric?| - |multisect| |lp| |systemCommand| |balancedFactorisation| - |differentialVariables| |readInt16!| |sylvesterSequence| - |halfExtendedResultant2| |iterationVar| |setAttributeButtonStep| - |leftAlternative?| |nullary| |OMwrite| |diagonal?| |symbolTable| - |title| |comp| |revert| |extractBottom!| |readUInt8!| |sturmSequence| - |halfExtendedResultant1| |infiniteProduct| |decrease| - |antiAssociative?| |po| |fixedPoint| |square?| |generalLambert| |node| - |monom| |extractTop!| |options| |readInt8!| |boundOfCauchy| - |extendedResultant| |evenInfiniteProduct| |increase| |continue| - |associative?| |sort| |pushFortranOutputStack| |OMread| |recur| - |rectangularMatrix| |evenlambert| |normal| |insertBottom!| |readByte!| - |sturmVariationsOf| |subResultantsChain| |oddInfiniteProduct| |e| - |antiCommutative?| |popFortranOutputStack| |OMreadFile| |const| - |characteristic| |oddlambert| |insertTop!| |setFieldInfo| - |lazyVariations| |lazyPseudoQuotient| |generalInfiniteProduct| - |commutative?| |list| |curry| |OMreadStr| |round| |outputAsFortran| - |lambert| |common| |bottom!| |string| |pol| |content| - |lazyPseudoRemainder| |showAll?| |car| |rightCharacteristicPolynomial| - |OMlistCDs| |diag| |fractionPart| |lagrange| |top!| |xn| |totalDegree| - |bernoulliB| |showAllElements| |random| |cdr| - |leftCharacteristicPolynomial| |OMlistSymbols| |curryRight| - |wholePart| |univariatePolynomial| |dequeue| |dAndcExp| - |minimumDegree| |eulerE| |delay| |rightNorm| |setDifference| - |curryLeft| |OMsupportsCD?| |nothing| |floor| |integrate| |recolor| - |repSq| |monomials| |numericIfCan| |findCycle| |setIntersection| - |leftNorm| |OMsupportsSymbol?| |constantRight| |ceiling| - |multiplyCoefficients| |drawComplex| |expPot| |isPlus| - |complexNumericIfCan| |repeating?| |setUnion| |rightTrace| - |OMunhandledSymbol| |constantLeft| |norm| |quoByVar| - |drawComplexVectorField| |qPot| |isTimes| |FormatArabic| |repeating| - |apply| |leftTrace| |OMreceive| |twist| |mightHaveRoots| - |coefficients| |setRealSteps| |lookup| |isExpt| |ScanArabic| |recip| - |someBasis| |OMsend| |setsubMatrix!| |refine| |stFunc1| |zero| - |setImagSteps| |normal?| |isPower| |FormatRoman| |integers| |size| - |sort!| |OMserve| |subMatrix| |middle| |stFunc2| |numeric| - |setClipValue| |basis| |ScanRoman| |rroot| |width| |oddintegers| - |copyInto!| |makeop| |swapColumns!| |roman| |stFuncN| |radical| |And| - |option?| |normalElement| |ScanFloatIgnoreSpaces| |qroot| |equation| - |mapmult| |sorted?| |precision| |opeval| |swapRows!| - |recoverAfterFail| |fixedPointExquo| |Or| |range| |minimalPolynomial| - |froot| |ScanFloatIgnoreSpacesIfCan| |deriv| |first| |LiePoly| - |evaluateInverse| |vertConcat| |showTheRoutinesTable| |ode1| |Not| - |colorFunction| |position!| |nthr| |numericalIntegration| |gderiv| - |quickSort| |rest| |horizConcat| |evaluate| |deleteRoutine!| |vector| - |ode2| |curveColor| |eof?| |firstUncouplingMatrix| |rk4| |compose| - |heapSort| |substitute| |squareTop| |conjug| |getExplanations| - |differentiate| |ode| |pointColor| |inputBinaryFile| |integral| |rk4a| - |addiag| |removeDuplicates| |shellSort| |adjoint| |elRow1!| - |getMeasure| |mpsode| |clip| |increment| |primitiveElement| |rk4qc| - |lazyIntegrate| |outputSpacing| |elRow2!| |arity| |mr| |changeMeasure| - |clipBoolean| UP2UTS |charpol| |nextPrime| |super| |name| |rk4f| - |optional| |hash| |nlde| |outputGeneral| |getDatabase| |elColumn2!| - |changeThreshhold| UTS2UP |style| |count| |solve1| |prevPrime| |lift| - |body| |aromberg| |powern| |outputFixed| |numericalOptimization| - |fractionFreeGauss!| |selectMultiDimensionalRoutines| LODO2FUN - |inspect| |toScale| |innerEigenvectors| |primes| |reduce| |asimpson| - |mapdiv| |outputFloating| |goodnessOfFit| |invertIfCan| - |selectNonFiniteRoutines| RF2UTS |extract!| |pointColorPalette| - |parseString| |selectsecond| |atrapezoidal| |lazyGintegrate| |exp1| - |whatInfinity| |copy!| |selectSumOfSquaresRoutines| |magnitude| - |curveColorPalette| |unparse| |selectfirst| |romberg| |power| |log2| - |infinite?| |plus!| |selectFiniteRoutines| |cross| |var1Steps| - |binary| |makeprod| |simpson| |sincos| |rationalApproximation| - |finite?| |minus!| |selectODEIVPRoutines| |dot| |var2Steps| - |packageCall| |disjunction| |trapezoidal| |sinhcosh| |relerror| - |leftScalarTimes!| |pureLex| |selectPDERoutines| SEGMENT |error| - |scan| |space| |innerSolve1| |conjunction| |port| |rombergo| - |subresultantVector| |constantOpIfCan| |any| |complexSolve| |totalLex| - |rightScalarTimes!| |selectOptimizationRoutines| |assert| - |graphCurves| |tower| |bag| |tubePoints| |innerSolve| |isEquiv| - |simpsono| |primitivePart| |complexRoots| |reverseLex| |times!| - |selectIntegrationRoutines| |drawCurves| |binding| |tubeRadius| - |makeEq| |isImplies| |t| |trapezoidalo| |pointData| |realRoots| - |leftLcm| |power!| |routines| |scale| |modularGcdPrimitive| |isOr| - |sup| |parent| |leadingTerm| |rightExtendedGcd| |just| - |mainSquareFreePart| |connect| |modTree| |modularGcd| |isAnd| |imagE| - |extractProperty| |overlap| |rightGcd| |gradient| |mainPrimitivePart| - |region| |multiEuclideanTree| |reduction| |isNot| |imagk| - |extractClosed| |hcrf| |loadNativeModule| |constant| - |rightExactQuotient| |divergence| |mainContent| |points| - |complexZeros| |complexNumeric| |mapDown!| |signAround| |isTerm| - |imagj| |extractIndex| |laplacian| |primitivePart!| |getGraph| - |mapUp!| |divisorCascade| |byte| |predicate| |invmod| |equiv| |imagi| - |extractPoint| |useNagFunctions| |algDsolve| |hessian| - |nextsubResultant2| |putGraph| |graeffe| |kernels| |powmod| |implies| - |concat| |octon| |traverse| |rationalPoints| |denomLODE| - |noLinearFactor?| |bandedHessian| |LazardQuotient2| |graphs| - |pleskenSplit| |operator| |mulmod| |merge!| |ODESolve| - |defineProperty| |nonSingularModel| |indicialEquations| |insertRoot!| - |jacobian| |LazardQuotient| |graphStates| |reciprocalPolynomial| - |constDsolve| |closeComponent| |algSplitSimple| |indicialEquation| - |binarySearchTree| |bandedJacobian| |subResultantChain| |graphState| - |rootRadius| |univariate| |nextSubsetGray| |mathieu23| - |showTheIFTable| |modifyPoint| |hyperelliptic| |denomRicDE| |nor| - |comment| |duplicates| |halfExtendedSubResultantGcd2| |schwerpunkt| - |makeViewport2D| |directory| |script| |firstSubsetGray| |mathieu24| - |clearTheIFTable| |step| |addPointLast| |elliptic| - |leadingCoefficientRicDE| |nand| |removeDuplicates!| - |halfExtendedSubResultantGcd1| |viewport2D| |setErrorBound| - |clipPointsDefault| |janko2| |iFTable| |addPoint2| - |integralDerivationMatrix| |constantCoefficientRicDE| - |binaryTournament| |getPickedPoints| |startPolynomial| |factor| - |drawToScale| |rubiksGroup| |showIntensityFunctions| |addPoint| |int| - |integralRepresents| |trailingCoefficient| |changeVar| |rischDE| - |construct| |binaryTree| |cycleElt| |adaptive| |colorDef| |sqrt| |tex| - |youngGroup| |source| |expint| |merge| |integralCoordinates| - |ratDsolve| |normalizeIfCan| |rischDEsys| |setLength!| - |computeCycleLength| |intensity| |figureUnits| |real| |parameters| - |lexGroebner| |diff| |deepCopy| |yCoordinates| - |indicialEquationAtInfinity| |polCase| |monomRDE| |capacity| - |lighting| |computeCycleEntry| |imag| |putColorInfo| |totalGroebner| - |inverseIntegralMatrixAtInfinity| |distFact| |reduceLODE| |baseRDE| - |length| |byteBuffer| |clipSurface| |findConstructor| |directProduct| - |appendPoint| |expressIdealMember| |f04maf| |llprop| - |integralMatrixAtInfinity| |identification| |singRicDE| |polyRDE| - |scripts| |unknownEndian| |showClipRegion| |dualSignature| |component| - |principalIdeal| |f04mbf| |lllp| |inverseIntegralMatrix| |polyRicDE| - |LyndonCoordinates| |monomRDEsys| |bigEndian| |coerceP| |ranges| - |showRegion| |brace| |LagrangeInterpolation| |target| |ptree| |f04mcf| - |lllip| |integralMatrix| |ricDsolve| |LyndonBasis| |baseRDEsys| - |littleEndian| |derivative| |powerSum| |destruct| |pointLists| - |psolve| |f04qaf| |mesh?| |reduceBasisAtInfinity| |triangulate| - |zeroDimensional?| |weighted| |subtractIfCan| |more?| - |constantOperator| |elementary| |makeGraphImage| |wrregime| |f07adf| - |mesh| |kind| |normalizeAtInfinity| |solveInField| |fglmIfCan| - |rdHack1| |setPosition| |setVariableOrder| |alternating| |graphImage| - |rdregime| |f07aef| |polygon?| |op| |complementaryBasis| - |wronskianMatrix| |groebner| |midpoint| - |generalizedContinuumHypothesisAssumed| |getVariableOrder| |cyclic| - |groebSolve| |bsolve| |f07fdf| |polygon| |integral?| - |variationOfParameters| |lexTriangular| |midpoints| - |generalizedContinuumHypothesisAssumed?| |resetVariableOrder| |ravel| - |dihedral| |monomial| |testDim| |dmp2rfi| |f07fef| |closedCurve?| - |integralAtInfinity?| |lexico| |squareFreeLexTriangular| |realZeros| - |countable?| |prime?| |cap| |genericPosition| |multivariate| |reshape| - |se2rfi| |s01eaf| |closedCurve| |arguments| |integralBasisAtInfinity| - |belong?| |OMmakeConn| |mainCharacterization| |setelt| |Aleph| - |sample| |cup| |variables| |lfunc| |pr2dmp| |s13aaf| |curve?| - |ramified?| |OMcloseConn| |Ci| |algebraicOf| |unravel| - |rationalFunction| |wreath| |inHallBasis?| |hasoln| |s13acf| |curve| - |ramifiedAtInfinity?| |Si| |OMconnInDevice| |ReduceOrder| |copy| - |leviCivitaSymbol| |taylorIfCan| |SFunction| |reorder| |ParCondList| - |s13adf| |point?| |union| |singular?| |OMconnOutDevice| |Ei| |setref| - |kroneckerDelta| |removeZeroes| |skewSFunction| |headAst| |s14aaf| - |redpps| |rank| |enterPointData| |singularAtInfinity?| |OMconnectTCP| - |linGenPos| |deref| |reindex| |taylorRep| |cyclotomicDecomposition| - |heap| |s14abf| |B1solve| |composites| |update| |branchPoint?| - |groebgen| |OMbindTCP| |ref| |autoCoerce| |principalAncestors| - |factorSquareFree| |cyclotomicFactorization| |gcdprim| |factorset| - |s14baf| |components| |branchPointAtInfinity?| |OMopenFile| |totolex| - |radicalEigenvectors| |exportedOperators| |henselFact| |rangeIsFinite| - |gcdcofact| |maxrank| |s15adf| |numberOfComposites| |rationalPoint?| - |OMopenString| |minPol| |radicalEigenvector| |alphanumeric| |hasHi| - |functionIsContinuousAtEndPoints| |gcdcofactprim| |minrank| |s15aef| - |numberOfComponents| |absolutelyIrreducible?| |OMclose| |computeBasis| - |radicalEigenvalues| |alphabetic| |fmecg| |functionIsOscillatory| - |lintgcd| |minset| |s17acf| |create3Space| |hexDigit| |genus| - |OMsetEncoding| |coord| |eigenMatrix| |digit?| |commonDenominator| - |changeName| |hex| |s17adf| |nextSublist| |outputAsScript| |position| - |getZechTable| |OMputApp| |anticoord| |normalise| |digit| - |clearDenominator| |exprHasWeightCosWXorSinWX| |every?| |s17aef| - |overset?| |match?| |lists| |outputAsTex| |createZechTable| |OMputAtp| - |intcompBasis| |gramschmidt| |charClass| |splitDenominator| - |exprHasAlgebraicWeight| |any?| |ParCond| |s17aff| |abs| - |createMultiplicationTable| |OMputAttr| |choosemon| |orthonormalBasis| - |alphanumeric?| |monicRightFactorIfCan| |exprHasLogarithmicWeights| - |host| |redmat| |s17agf| |Beta| |createMultiplicationMatrix| - |OMputBind| |transform| |antisymmetricTensors| |lowerCase?| - |rightFactorIfCan| |combineFeatureCompatibility| |trueEqual| |declare| - |regime| |s17ahf| |digamma| |createLowComplexityTable| |OMputBVar| - |pack!| |createGenericMatrix| |upperCase?| |leftFactorIfCan| - |sparsityIF| |factorList| |sqfree| |s17ajf| |polygamma| - |createLowComplexityNormalBasis| |OMputError| |complexLimit| - |symmetricTensors| |alphabetic?| |monicDecomposeIfCan| - |stiffnessAndStabilityFactor| |listConjugateBases| |inconsistent?| - |s17akf| |Gamma| |representationType| |OMputObject| |limit| - |tensorProduct| |hexDigit?| |monicCompleteDecompose| - |stiffnessAndStabilityOfODEIF| |matrixGcd| |numFunEvals| |s17dcf| - |besselJ| |createPrimitiveElement| |arg1| |OMputEndApp| - |linearlyDependent?| |permutationRepresentation| |escape| - |divideIfCan| |systemSizeIF| |divideIfCan!| |setAdaptive| |s17def| - |besselY| |tableForDiscreteLogarithm| |arg2| |OMputEndAtp| - |linearDependence| |completeEchelonBasis| |ord| |noKaratsuba| - |expenseOfEvaluationIF| |leastPower| |adaptive?| |s17dgf| |besselI| - |factorsOfCyclicGroupSize| |OMputEndAttr| |solveLinear| - |createRandomElement| |karatsubaOnce| |accuracyIF| |idealiser| - |setScreenResolution| |s17dhf| |besselK| |sizeMultiplication| - |reducedSystem| |conditions| |OMputEndBind| |asinh| |cyclicSubmodule| - |karatsuba| |intermediateResultsIF| |idealiserMatrix| - |screenResolution| |s17dlf| |airyAi| |getMultiplicationMatrix| - |duplicates?| |match| |OMputEndBVar| |acosh| - |standardBasisOfCyclicSubmodule| |separate| |subscriptedVariables| - |stop| |moduleSum| |setMaxPoints| |close| |s18acf| |airyBi| - |getMultiplicationTable| |mapGen| |OMputEndError| |atanh| - |areEquivalent?| |pseudoDivide| |central?| |mapUnivariate| |maxPoints| - |s18adf| |subNode?| |primitive?| |li| |mapExpon| |OMputEndObject| - |acoth| |isAbsolutelyIrreducible?| |pseudoQuotient| |elliptic?| - |mapUnivariateIfCan| |s18aef| |setMinPoints| |display| |infLex?| - |bright| |numberOfIrreduciblePoly| |commutativeEquality| - |OMputInteger| |asech| |meatAxe| |composite| |doubleResultant| - |mapMatrixIfCan| |minPoints| |s18aff| |setEmpty!| - |numberOfPrimitivePoly| |OMputFloat| |leftMult| |scanOneDimSubspaces| - |subResultantGcd| |distdfact| |mapBivariate| |parametric?| |s18dcf| - |setStatus!| |numberOfNormalPoly| |fortran| |rightMult| - |OMputVariable| |multiple| |expt| |resultant| |separateDegrees| - |fullDisplay| |plotPolar| |s18def| |setCondition!| - |createIrreduciblePoly| |applyQuote| |box| |OMputString| |makeUnit| - |showArrayValues| |discriminant| |trace2PowMod| |relationsIdeal| - |debug3D| |s19aaf| |setValue!| |createPrimitivePoly| |OMputSymbol| - |reverse!| |showScalarValues| |pseudoRemainder| |tracePowMod| - |saturate| |input| |numFunEvals3D| |s19abf| |empty?| - |createNormalPoly| |OMgetApp| |nthFactor| |solveRetract| |shiftLeft| - |irreducible?| |groebner?| |library| |setAdaptive3D| |s19acf| - |splitNodeOf!| |createNormalPrimitivePoly| |nthExpon| |OMgetAtp| - |ruleset| |mainVariable| |shiftRight| |decimal| |groebnerIdeal| - |adaptive3D?| |s19adf| |remove!| |createPrimitiveNormalPoly| - |OMgetAttr| |makeMulti| |uniform01| |karatsubaDivide| |innerint| - |ideal| |setScreenResolution3D| |s20acf| |subNodeOf?| - |nextIrreduciblePoly| |OMgetBind| |makeTerm| |normal01| |nary?| - |monicDivide| |test| |exteriorDifferential| |leadingIdeal| |id| - |screenResolution3D| |s20adf| |nodeOf?| |nextPrimitivePoly| - |listOfMonoms| |OMgetBVar| |suchThat| |exponential1| |divideExponents| - |backOldPos| |setMaxPoints3D| |set| |s21baf| |updateStatus!| - |nextNormalPoly| |OMgetError| |symmetricSquare| |chiSquare1| |unary?| - |unmakeSUP| |mkIntegral| |generalPosition| |table| |maxPoints3D| - |s21bbf| |extractSplittingLeaf| |nextNormalPrimitivePoly| - |OMgetObject| |factor1| |exponential| |nullary?| |makeSUP| |radPoly| - |subst| |quotient| |insert| |new| |setMinPoints3D| |s21bcf| - |squareMatrix| |obj| |nextPrimitiveNormalPoly| |OMgetEndApp| - |symmetricProduct| |chiSquare| |vectorise| |rootPoly| |zeroDim?| - |s21bdf| |minPoints3D| |eq| |transpose| |prefix| |symmetricPower| - |cache| |factorFraction| |extend| |goodPoint| |inRadical?| |iter| - |tValues| |fortranCompilerName| |trim| |measure2Result| |directSum| - |componentUpperBound| |truncate| |chvar| |in?| |fortranLinkerArgs| - |tRange| |split| |signature| |att2Result| - |solveLinearPolynomialEquationByFractions| |blue| |order| |find| - |element?| |plot| |aspFilename| |replace| |iflist2Result| - |hasSolution?| |green| |terms| |clipParametric| |delete| - |dimensionsOf| |upperCase!| |pdf2ef| |linSolve| |red| |squareFreePart| - |clipWithRanges| |objects| |sumSquares| |even?| |restorePrecision| - |upperCase| |pdf2df| |LyndonWordsList| |whitePoint| |BumInSepFFE| - |numberOfHues| |base| |euclideanNormalForm| |numberOfCycles| - |antiCommutator| |lowerCase!| |df2ef| |LyndonWordsList1| |uniform| - |multiplyExponents| |yellow| |euclideanGroebner| |cyclePartition| - |commutator| |lowerCase| |fi2df| |retractIfCan| |laurentIfCan| - |iifact| |factorGroebnerBasis| |coerceListOfPairs| |flatten| - |associator| |KrullNumber| |exp| |mat| |cAcosh| |sechIfCan| - |laurentRep| |iibinom| |groebnerFactorize| |coercePreimagesImages| - |left| |complexEigenvalues| |numberOfVariables| |numer| |neglist| - |cAsinh| |cschIfCan| |rationalPower| |iiperm| |credPol| - |listRepresentation| |right| |complexEigenvectors| - |algebraicDecompose| |outputList| |denom| |multiEuclidean| |cCsch| - |asinhIfCan| |dominantTerm| |iipow| |redPol| |permanent| - |extendedEuclidean| |cSech| |acoshIfCan| |limitPlus| |iidsum| |gbasis| - |/\\| |cycles| |e02agf| |stoseInvertible?reg| |pi| |euclideanSize| - |cCoth| |atanhIfCan| |split!| |iidprod| |critT| |\\/| |cycle| |e02ahf| - |stoseInvertibleSetreg| |infinity| |sizeLess?| |cTanh| |acothIfCan| - |setlast!| |nil| |infinite| |arbitraryExponent| |approximate| + |Record| |Union| |c06fpf| |outputArgs| |lifting1| |showClipRegion| + |pi| |rational| |primitiveElement| |complexForm| |cot2tan| |part?| + |preprocess| |dualSignature| |overlabel| |infinity| |quasiComponent| + |fillPascalTriangle| |rk4qc| |imaginary| |divideIfCan!| + |noncommutativeJordanAlgebra?| |rquo| |component| |deepestInitial| + |cond| |bipolarCylindrical| |measure| |lazyIntegrate| |minGbasis| + |setAdaptive| |freeOf?| |principalIdeal| |OMencodingUnknown| + |generate| |modifyPointData| |log10| |outputSpacing| |tablePow| + |e01bef| |map| |s17def| |bivariateSLPEBR| |expextendedint| + |explicitlyEmpty?| |iicosh| |f04mbf| |bitand| |kernel| + |partialFraction| |elRow2!| |branchIfCan| |e02def| |besselY| + |previous| |isQuotient| |incrementBy| |BasicMethod| + |squareFreeFactors| |column| |lllp| |outerProduct| + |complexEigenvectors| |bitior| |draw| |f02agf| + |dimensionOfIrreducibleRepresentation| |arity| + |tableForDiscreteLogarithm| |numberOfImproperPartitions| + |inverseIntegralMatrix| |clearTable!| |setfirst!| |nextsousResultant2| + |expand| |algebraicDecompose| |mapSolve| |acotIfCan| |changeMeasure| + |ran| |OMputEndAtp| |associatedEquations| |currentEnv| + |shanksDiscLogAlgorithm| |polyRicDE| |filterWhile| |printHeader| + |multiEuclidean| |rootKerSimp| |clipBoolean| |UpTriBddDenomInv| |cCot| + |linearDependence| |sylvesterMatrix| |fortranCarriageReturn| + |generalizedInverse| |LyndonCoordinates| |filterUntil| |symbol| + |cCsch| |attributeData| |safeCeiling| |setStatus| UP2UTS |convert| + |completeEchelonBasis| |radicalSimplify| |factors| |c06fqf| + |monomRDEsys| |legendre| |select| |expression| |asinhIfCan| + |makeObject| |setright!| |minIndex| |charpol| |e01bff| + |brillhartIrreducible?| |ord| |height| |bigEndian| + |wordsForStrongGenerators| |normInvertible?| |addMatchRestricted| + |overbar| |integer| |dominantTerm| |coef| |rational?| |tanh2coth| + |coerceImages| |nextPrime| |noKaratsuba| |coth2tanh| |lowerPolynomial| + |before?| |internalZeroSetSplit| |coerceP| |exprex| |iipow| + |setProperty| |initials| |rk4f| |startTableGcd!| |elaborateFile| + |expenseOfEvaluationIF| |jordanAdmissible?| |lquo| |ranges| + |iteratedInitials| |redPol| |toroidal| |weight| |nlde| ** |lepol| + |leastPower| |operators| |omError| |showRegion| |subspace| |permanent| + |solveid| |outputGeneral| |irreducibleRepresentation| |adaptive?| + |solveLinearPolynomialEquationByRecursion| |primlimitedint| + |explicitEntries?| |iitanh| |LagrangeInterpolation| + |extendedEuclidean| |gcdPrimitive| |getDatabase| |asecIfCan| |e02dff| + |s17dgf| |PollardSmallFactor| |makeRecord| |univariatePolynomialsGcds| + |row| |f04mcf| |lo| |cSech| |f02ajf| |elColumn2!| |LowTriBddDenomInv| + |besselI| |subSet| |resultantnaif| |usingTable?| |cycleSplit!| |incr| + |lllip| |acoshIfCan| |acsch| |label| |quadratic| |safeFloor| + |changeThreshhold| |highCommonTerms| |factorsOfCyclicGroupSize| + |initial| |arrayStack| |reflect| |integralMatrix| |returnType!| + |limitPlus| |leftRank| |e01bgf| UTS2UP |cTan| |OMputEndAttr| + |fortranLiteral| |imports| |bezoutMatrix| |ricDsolve| |iidsum| + |domainTemplate| |style| |fixedPoints| |solveLinear| |denominator| + |insertMatch| |dmpToHdmp| |nilFactor| |LyndonBasis| |gbasis| + |brillhartTrials| |maxIndex| |solve1| |stopTableGcd!| + |createRandomElement| Y |c06frf| |normFactors| |prime| |baseRDEsys| + |cycles| |rationalIfCan| |makeVariable| |prevPrime| |karatsubaOnce| + |removeCosSq| |latex| |internalAugment| |littleEndian| |coerceL| + |e02agf| |basicSet| |checkRur| |aromberg| |elaborate| |accuracyIF| + |comparison| |mindegTerm| |derivative| |deepestTail| + |stoseInvertible?reg| |critM| |tail| |conical| |acscIfCan| |powern| + |prinshINFO| |idealiser| |constructor| |rules| |mainKernel| + |lieAdmissible?| |powerSum| |makeViewport3D| |euclideanSize| + |initializeGroupForWordProblem| |testModulus| |outputFixed| |simplify| + |setScreenResolution| |factorByRecursion| |explimitedint| |nothing| + |errorInfo| |iicoth| |pointLists| |cCoth| |e02ajf| |option| + |symmetricGroup| |safetyMargin| |numericalOptimization| |e02gaf| + |s17dhf| |showSummary| |matrixDimensions| + |removeRoughlyRedundantFactorsInContents| |showTheFTable| |psolve| + |atanhIfCan| |stoseInvertible?| |f02akf| |fractionFreeGauss!| |odd?| + |besselK| |maxColIndex| |printingInfo?| |f04qaf| + |resultantEuclideannaif| |split!| |simplifyPower| |cubic| |e01bhf| + |selectMultiDimensionalRoutines| |sizeMultiplication| |showAttributes| + |fortranLiteralLine| |concat!| |mesh?| |argumentList!| |iidprod| + |cCosh| |unknown| |rightRank| |startTableInvSet!| LODO2FUN + |reducedSystem| |macroExpand| |reify| |reduceBasisAtInfinity| + |addMatch| |regularRepresentation| |rightTrim| |critT| |asechIfCan| + |lSpaceBasis| |inspect| |finiteBound| |OMputEndBind| |sequence| + |c06fuf| |triangulate| |quote| |leftTrim| |cycle| |factorial| |entry?| + |toScale| |cAcsch| |cyclicSubmodule| |hdmpToDmp| |member?| + |zeroDimensional?| |coerceS| |e02ahf| |critB| |setvalue!| + |innerEigenvectors| |sinhIfCan| |karatsuba| |say| |npcoef| F |product| + |weighted| |head| |stoseInvertibleSetreg| |e02akf| |infRittWu?| + |primes| |htrigs| |intermediateResultsIF| |distribute| + |possiblyInfinite?| |subtractIfCan| |viewport3D| |sizeLess?| + |movedPoints| |HenselLift| |e01daf| |asimpson| |idealiserMatrix| + |equality| |primextintfrac| |iisech| |more?| |cTanh| |function| + |stoseInvertibleSet| |alternatingGroup| |stopTableInvSet!| |mapdiv| + |remove| |multivariate| |screenResolution| |jacobiIdentity?| + |removeRedundantFactorsInContents| |constantOperator| |clearTheFTable| + |acothIfCan| |number?| |fortran| |sortConstraints| |f02awf| + |outputFloating| |s17dlf| |variables| |result| |errorKind| + |makingStats?| |elementary| |semiResultantEuclideannaif| |setlast!| + |open| |cSinh| |cAsech| |quartic| |goodnessOfFit| |last| |eval| + |airyAi| |reset| |processTemplate| |matrixConcat3D| |makeGraphImage| + |endSubProgram| |assoc| |acschIfCan| |doubleRank| |null| |invertIfCan| + |coshIfCan| |getMultiplicationMatrix| |c06gbf| |minColIndex| + |traceMatrix| |wrregime| |finiteBasis| |sec2cos| |pattern| + |selectNonFiniteRoutines| |not| |simplifyExp| |duplicates?| |write| + |getMatch| |cycleTail| |frobenius| |f07adf| |multinomial| |hclf| + |indices| |and| RF2UTS |OMputEndBVar| |save| |functorData| |enumerate| + |supersub| |mesh| |extract!| |critBonD| |operations| |setchildren!| + |rightRemainder| |or| |taylor| |standardBasisOfCyclicSubmodule| + |readBytes!| |LiePolyIfCan| |normalizeAtInfinity| |mdeg| + |wordInGenerators| |pointColorPalette| |getCurve| |e01saf| |xor| + |laurent| |separate| |functionIsFracPolynomial?| |listexp| + |solveInField| |viewDeltaYDefault| |completeHensel| |e02baf| + |parseString| |message| |stosePrepareSubResAlgo| |case| + |subscriptedVariables| |puiseux| |primlimintfrac| |pToHdmp| |iicsch| + |fglmIfCan| |stoseSquareFreePart| |sumOfSquares| |f02axf| + |selectsecond| |Zero| |moduleSum| |fTable| + |removeRedundantFactorsInPols| |explicitlyFinite?| |rdHack1| |hi| + |seriesSolve| |cAcoth| |atrapezoidal| |One| |inv| |setMaxPoints| + |powerAssociative?| |extractIfCan| |setPosition| |pdct| |cAcsc| + |rewriteSetWithReduction| |tanhIfCan| |lazyGintegrate| |ground?| + |s18acf| |makeFR| |OMReadError?| |currentSubProgram| + |setVariableOrder| |parabolic| |pushdown| |exp1| |ground| + |simplifyLog| |lcm| |airyBi| |setelt!| |failed?| |alternating| + |randomLC| |permutation| |genericLeftTrace| |writable?| |whatInfinity| + |getMultiplicationTable| |leadingMonomial| |graphImage| + |computePowers| |padicFraction| |sech2cosh| |append| |copy!| + |rightQuotient| |mapGen| |leadingCoefficient| |rightUnit| |shuffle| + |presuper| |rdregime| |critMTonD1| |e01sbf| |f01rdf| + |primitiveMonomials| |gcd| |selectSumOfSquaresRoutines| |elt| |output| + |OMputEndError| |lyndon| |c05adf| |cCsc| |f07aef| |mvar| |e02bbf| + |hermite| |false| |stoseInternalLastSubResultant| |magnitude| + |reductum| |areEquivalent?| |OMgetVariable| |bounds| |polygon?| + |viewDeltaXDefault| |knownInfBasis| |wordInStrongGenerators| + |pseudoDivide| |factorAndSplit| |poisson| |iiasinh| + |complementaryBasis| |forLoop| |coleman| |setClipValue| |satisfy?| + |central?| |removeConstantTerm| |medialSet| |palgint0| + |wronskianMatrix| |constantToUnaryFunction| GF2FG |basis| |d02gaf| + |mapUnivariate| |dictionary| |removeRoughlyRedundantFactorsInPols| + |groebner| |powers| |cAsec| |fractRagits| |ScanRoman| + |internalSubPolSet?| |maxPoints| |leadingSupport| |tanSum| + |autoReduced?| |pushup| |vedf2vef| |rroot| |s18adf| |fortranComplex| + |bernoulli| |iFTable| |subscript| |parabolicCylindrical| |sin2csc| + |perfectNthRoot| |oddintegers| |categories| |subNode?| |shufflein| + |inverse| |unit| |addPoint2| |stirling1| + |genericLeftMinimalPolynomial| |copyInto!| |cosIfCan| |primitive?| + |has?| |c05nbf| |integralDerivationMatrix| |semicolonSeparate| + |critMonD1| |padicallyExpand| |makeop| |cyclicEntries| |leftUnit| + |high| |binaryFunction| |constantCoefficientRicDE| |e02bcf| |f01ref| + |shiftRoots| |swapColumns!| |exprHasLogarithmicWeights| |OMgetString| + |inGroundField?| |binaryTournament| |mainMonomials| |completeHermite| + |orbits| |addBadValue| |roman| |host| |rightOne| |lyndon?| + |getPickedPoints| |axes| |plusInfinity| |rootSplit| |inverseColeman| + |d02gbf| |stFuncN| |redmat| |mkPrim| |geometric| |bfEntry| + |startPolynomial| |minusInfinity| |sin?| |option?| + |internalInfRittWu?| |s17agf| |removeRoughlyRedundantFactorsInPol| + |Hausdorff| |iiacos| |drawToScale| |hasSolution?| FG2F |df2st| + |normalElement| |Beta| |dioSolve| |tanAn| |unitNormal| |rubiksGroup| + |green| |approxNthRoot| |wholeRagits| |ScanFloatIgnoreSpaces| |key| + |createMultiplicationMatrix| |fortranLogical| |shrinkable| + |showIntensityFunctions| |resultantReduit| |terms| |initiallyReduced?| + |qroot| |tanIfCan| |OMputBind| |sequences| |chebyshevT| |addPoint| + |scripted?| |clipParametric| |paraboloidal| |filename| |mapmult| + |cyclicCopy| |transform| |rightMinimalPolynomial| |c05pbf| + |integralRepresents| |flagFactor| |type| |dimensionsOf| + |leftRankPolynomial| |sorted?| |degreePartition| + |antisymmetricTensors| |OMgetSymbol| |low| |trailingCoefficient| + |commaSeparate| |upperCase!| |opeval| |numberOfFractionalTerms| + |badValues| |parse| |lowerCase?| |numberOfComputedEntries| + |transcendent?| |makeFloatFunction| |changeVar| |pdf2ef| |f02aaf| + |swapRows!| |d02kef| |next| |rightFactorIfCan| |leftOne| |ridHack1| + |rischDE| |mainCoefficients| |linSolve| |smith| |recoverAfterFail| + |internalSubQuasiComponent?| |combineFeatureCompatibility| + |intPatternMatch| |Frobenius| |binaryTree| |controlPanel| |red| + |ratDenom| |f2st| |fixedPointExquo| |trueEqual| |bfKeys| |cycleElt| + |newLine| |interReduce| |checkPrecision| |reducedDiscriminant| + |squareFreePart| |zeroVector| |range| |perfectSquare?| |regime| + |iiatan| |adaptive| |physicalLength!| |tanNa| EQ |sinh2csch| + |clipWithRanges| F2FG |minimalPolynomial| |cotIfCan| |s17ahf| + |fortranInteger| |chebyshevU| |lfextendedint| |colorDef| |sumSquares| + |froot| |radix| |lhs| |cyclic?| |digamma| |isConnected?| + |permutations| |youngGroup| |resetNew| |even?| |factorOfDegree| + |headReduced?| |ScanFloatIgnoreSpacesIfCan| |rhs| + |createLowComplexityTable| |c06eaf| |transcendentalDecompose| |expint| + |resultantReduitEuclidean| |restorePrecision| |ellipticCylindrical| + |retractable?| |deriv| |OMputBVar| |leftMinimalPolynomial| |subset?| + |sqfrFactor| |merge| |upperCase| |generic| |LiePoly| |d02raf| |pack!| + |OMgetType| |algebraic?| |integralCoordinates| |pile| |pdf2df| |rule| + |nthFractionalTerm| |evaluateInverse| |subQuasiComponent?| + |createGenericMatrix| |rightZero| |rst| |unaryFunction| |ratDsolve| + |LyndonWordsList| |ldf2lst| |f02abf| |vertConcat| |index| |upperCase?| + |primintegrate| |interpolate| |normalizeIfCan| |leastMonomial| + |whitePoint| |completeSmith| |perfectSqrt| |showTheRoutinesTable| + |leftFactorIfCan| |roughBasicSet| |transcendenceDegree| |rischDEsys| + |viewpoint| |BumInSepFFE| |ratPoly| |center| |secIfCan| |ode1| + |sparsityIF| |copies| |initTable!| |setLength!| |iiacot| + |numberOfHues| |colorFunction| |zeroSquareMatrix| |pair| + |complexNormalize| |factorList| |computeCycleLength| |fortranDouble| + |physicalLength| |lflimitedint| |value| |euclideanNormalForm| |closed| + |explogs2trigs| |factorsOfDegree| |position!| |sqfree| |atoms| + |cyclotomic| |semiResultantReduitEuclidean| |intensity| + |numberOfCycles| |randnum| |ListOfTerms| |nthr| |s17ajf| |c06ebf| + |connectTo| |figureUnits| |symFunc| |antiCommutator| + |stronglyReduced?| |d03edf| |numericalIntegration| |polygamma| + |symmetricDifference| |internalDecompose| |primeFactor| |lexGroebner| + |entry| |lowerCase!| |prolateSpheroidal| + |removeSuperfluousQuasiComponents| |gderiv| + |createLowComplexityNormalBasis| |associatorDependence| |sh| |diff| + |paren| |df2ef| |rightUnits| |sdf2lst| |quickSort| |OMputError| + |leftZero| |OMencodingBinary| |compiledFunction| |deepCopy| + |LyndonWordsList1| |firstNumer| |approxSqrt| |horizConcat| + |complexLimit| |expintegrate| |frst| |yCoordinates| |mainMonomial| + |uniform| |f02adf| |evaluate| |cscIfCan| |symmetricTensors| |sn| + |reverse| |crushedSet| |nullSpace| |indicialEquationAtInfinity| + |dimensions| |multiplyExponents| |diophantineSystem| |deleteRoutine!| + |complexElementary| |alphabetic?| |printInfo!| |extensionDegree| + |iiasec| |polCase| |yellow| |rootPower| |call| |pascalTriangle| |ode2| + |monicDecomposeIfCan| |sayLength| |fortranReal| |lfinfieldint| + |monomRDE| |euclideanGroebner| |leaves| |identitySquareMatrix| |tree| + |curveColor| |PDESolve| |stiffnessAndStabilityFactor| |flexibleArray| + |makeResult| |capacity| |divide| |cyclePartition| |trigs2explogs| + |eof?| |d03eef| |listConjugateBases| |c06ecf| |euler| |symbolTableOf| + |lighting| |commutator| |reseed| |firstUncouplingMatrix| |subCase?| + |inconsistent?| |normalizedAssociate| |difference| |computeCycleEntry| + |nthFlag| |lowerCase| |getlo| |reduced?| |rk4| |init| |s17akf| + |decompose| |mirror| |putColorInfo| |bracket| |fi2df| + |oblateSpheroidal| |generateIrredPoly| |compose| |Gamma| |setRow!| + |lieAlgebra?| |corrPoly| |totalGroebner| |laurentIfCan| |leftUnits| + |heapSort| |asinIfCan| |representationType| |swap| |OMencodingSGML| + |inverseIntegralMatrixAtInfinity| |quasiMonic?| |iifact| |generator| + |firstDenom| |squareTop| |trigs| |OMputObject| |tanintegrate| + |lazyEvaluate| |distFact| |resize| |factorGroebnerBasis| |f02aef| + |rangePascalTriangle| |conjug| |limit| + |rewriteSetByReducingWithParticularGenerators| |nullity| |iiacsc| + |reduceLODE| |coerceListOfPairs| |csubst| |leftFactor| + |getExplanations| |tensorProduct| |setnext!| |lfintegrate| + |startStats!| |search| |baseRDE| |associator| |d03faf| |ode| + |hexDigit?| |stack| |byteBuffer| |external?| |elseBranch| |rem| + |Lazard| |KrullNumber| |inrootof| |pointColor| + |removeSuperfluousCases| |monicCompleteDecompose| |quo| |is?| + |fixedDivisor| |argumentListOf| |clipSurface| |mat| |printStatement| + |gethi| |inputBinaryFile| |stiffnessAndStabilityOfODEIF| |condition| + |c06ekf| |normalize| |findConstructor| |nthExponent| |cAcosh| + |makeSeries| |complexExpand| |integral| |matrixGcd| |appendPoint| + |div| |prod| |sechIfCan| |queue| |rk4a| |acosIfCan| |numFunEvals| + |getProperty| |integralBasis| |lifting| |expressIdealMember| |exquo| + |dim| |laurentRep| |collectQuasiMonic| |addiag| |real?| |s17dcf| + |checkForZero| |infieldIntegrate| |f04maf| ~= |monic?| |iibinom| + |bindings| |shellSort| |sizePascalTriangle| |besselJ| |extendedint| + |quasiMonicPolynomials| |llprop| |move| |#| |groebnerFactorize| + |matrix| |genericRightNorm| |createPrimitiveElement| |dec| + |probablyZeroDim?| |less?| |iisinh| |integralMatrixAtInfinity| ~ + |coercePreimagesImages| |logpart| |getGoodPrime| |delay| |concat| + |OMputEndApp| |double?| |untab| |lfextlimint| |identification| + |complexEigenvalues| |f01mcf| |rightNorm| |color| |linearlyDependent?| + |rootOfIrreduciblePoly| |dark| |singRicDE| |Lazard2| |printInfo| + |numberOfVariables| |determinant| |curryLeft| |writeLine!| + |clearCache| |permutationRepresentation| |coefChoose| |OMgetEndBind| + |level| |neglist| |droot| |beauzamyBound| |OMsupportsCD?| |escape| + |univcase| |currentScope| |graeffe| |contains?| |cAsinh| |putProperty| + |multiple?| |floor| |divideIfCan| |applyRules| |powmod| |rur| + |subResultantGcdEuclidean| |substring?| |cschIfCan| |block| |d01gaf| + |integrate| |char| |systemSizeIF| |scopes| |failed| + |localIntegralBasis| |implies| |internal?| |rationalPower| + |mappingMode| |recolor| |stopTable!| |logGamma| |primeFrobenius| + |limitedIntegrate| |octon| |suffix?| |iiperm| |nthRoot| |repSq| + |squareFree| |vspace| |hasHi| |univariate?| |bat1| |maximumExponent| + |traverse| |credPol| |removeZero| |edf2efi| |monomials| + |functionIsContinuousAtEndPoints| |derivationCoordinates| + |rationalPoints| |compile| |write!| |userOrdered?| |writeUInt8!| + |prefix?| |status| |listRepresentation| |cartesian| |ratpart| + |numericIfCan| |gcdcofactprim| |invertibleElseSplit?| |ffactor| + |OMgetEndBVar| |denomLODE| |lazyPquo| |genericRightTrace| |hue| + |findCycle| |minrank| |viewWriteAvailable| |consnewpol| + |getSyntaxFormsFromFile| |noLinearFactor?| |perspective| |chiSquare1| + |second| |callForm?| |f01qcf| |leftNorm| |sign| |erf| |s15aef| |float| + |myDegree| |create| |iicos| |bandedHessian| |unary?| |third| |badNum| + |bombieriNorm| |OMsupportsSymbol?| |sumOfDivisors| + |numberOfComponents| |pushNewContour| |qualifier| |inf| + |LazardQuotient2| |unmakeSUP| |diagonalProduct| |constantRight| + |generic?| |absolutelyIrreducible?| |roughBase?| |void| |localUnquote| + |hypergeometric0F1| |semiSubResultantGcdEuclidean2| |graphs| + |mkIntegral| |iroot| |dilog| |d01gbf| |ceiling| |OMclose| + |getOperator| |pleskenSplit| |eigenvalues| |zeroDimPrime?| |root?| + |infix?| |generalPosition| |putProperties| |exprToGenUPS| + |supDimElseRittWu?| |multiplyCoefficients| |computeBasis| |sin| + |discreteLog| |extendedIntegrate| |pointPlot| |mulmod| |mask| + |maxPoints3D| |drawComplex| |returns| |cos| |linearlyDependentOverZ?| + |hspace| |radicalEigenvalues| |univariatePolynomials| |bat| + |writeInt8!| |merge!| |s21bbf| |alphabetic| |dfRange| |categoryMode| + |expPot| |expr| |one?| |tan| |read!| |largest| |rowEch| |ODESolve| + |extractSplittingLeaf| |mkAnswer| |fractRadix| |cot| |isPlus| + |purelyAlgebraicLeadingMonomial?| |fmecg| |qfactor| |OMgetEndError| + |lazyPrem| |defineProperty| |nextNormalPrimitivePoly| + |functionIsOscillatory| |initiallyReduce| |complexNumericIfCan| + |shade| |sec| |var1StepsDefault| GE |nonSingularModel| |nsqfree| + |surface| |double| |zoom| |OMgetObject| |polar| |getIdentifier| + |lintgcd| |repeating?| |nonQsign| |csc| |log| GT |normDeriv2| + |enterInCache| |iitan| |indicialEquations| |factor1| |rightTrace| + |rootBound| |genericRightMinimalPolynomial| |sumOfKthPowerDivisors| + |variable| |minset| |asin| LE |findBinding| |mainExpression| + |insertRoot!| |qinterval| |exponential| |f01qdf| |s17acf| |iterators| + BY |OMunhandledSymbol| |quoted?| |trivialIdeal?| |acos| LT |arbitrary| + |rotatez| |jacobian| |semiSubResultantGcdEuclidean1| |nullary?| + |constantLeft| |mix| |d02bbf| |create3Space| |nil?| |atan| + |eigenvector| |zeroDimPrimary?| |LazardQuotient| |leaf?| |makeSUP| + |hexDigit| |diagonal| |norm| |algebraicSort| |localAbs| |acot| + |varselect| |calcRanges| |decreasePrecision| |graphStates| |radPoly| + |size?| |genus| |quoByVar| |linearDependenceOverZ| |superHeight| + |asec| |linear?| |tab1| |reciprocalPolynomial| |writeByte!| |quotient| + |drawComplexVectorField| |goto| |dflist| |splitSquarefree| + |OMsetEncoding| |acsc| |iomode| |UP2ifCan| |rowEchLocal| |constDsolve| + |declare!| |setMinPoints3D| |qPot| |voidMode| |irDef| |coord| + |algebraicCoefficients?| |sinh| |makeYoungTableau| |OMgetEndObject| + |coordinate| |pquo| |closeComponent| |s21bcf| |wholeRadix| + |eigenMatrix| |isTimes| |nthRootIfCan| |var2StepsDefault| |cosh| + |algSplitSimple| |permutationGroup| |intChoose| |plenaryPower| NOT + |rotate| |squareMatrix| |variable?| |headReduce| |FormatArabic| + |direction| |commonDenominator| |tanh| |iicot| |currentCategoryFrame| + |contours| |indicialEquation| OR |nextPrimitiveNormalPoly| + |cylindrical| |changeName| |singleFactorBound| |repeating| + |HermiteIntegrate| |coth| |setColumn!| |binarySearchTree| + |changeWeightLevel| |interval| AND |OMgetEndApp| |rightRankPolynomial| + |leftTrace| |inR?| |hex| |collectUpper| |rotatey| + |generalizedEigenvector| |bandedJacobian| |keys| + |discriminantEuclidean| |symmetricProduct| |d02bhf| |doubleDisc| + |OMreceive| |depth| |s17adf| |buildSyntax| |primaryDecomp| |kmax| + |subResultantChain| |outputForm| |chiSquare| |f01qef| |twist| + |moreAlgebraic?| |universe| |nextSublist| |increasePrecision| + |fixPredicate| |linearPolynomials| |debug| |segment| |graphState| + |parents| |vectorise| |diagonalMatrix| |mightHaveRoots| + |solveLinearlyOverQ| |subHeight| |outputAsScript| |tab| |maxrow| D + |rootRadius| |isOpen?| |rootPoly| |eq?| |df2mf| |coefficients| + |getZechTable| |normalDenom| |close!| |anfactor| |nextSubsetGray| + |rowEchelonLocal| |zeroDim?| |repeatUntilLoop| |setRealSteps| |irCtor| + |OMputApp| |purelyTranscendental?| |OMgetInteger| |partitions| + |mathieu23| |prem| |s21bdf| |noValueMode| |lookup| |expIfCan| + |anticoord| |tubePointsDefault| |c02aff| |characteristicSerie| + |showTheIFTable| |drawStyle| |minPoints3D| |cycleRagits| |isExpt| + |createThreeSpace| |setleaves!| |normalise| |rotatex| + |structuralConstants| |iisec| |modifyPoint| |transpose| + |stronglyReduce| |quadraticNorm| |ScanArabic| |digit| |getConstant| + |generalizedEigenvectors| |parts| |hyperelliptic| |contract| |unit?| * + |symmetricPower| |spherical| |isList| |recip| |palgint| + |clearDenominator| |ksec| |patternMatch| |denomRicDE| + |semiDiscriminantEuclidean| |factorFraction| |genericLeftNorm| + |someBasis| |d02cjf| |exprHasWeightCosWXorSinWX| |collect| + |properties| |optimize| |bivariate?| |lex| |nor| |argscript| |extend| + |polyred| |OMsend| |subTriSet?| |every?| |solve| |translate| |reopen!| + |tableau| |bits| |duplicates| |goodPoint| = |f01rcf| |ldf2vmf| + |setsubMatrix!| |complement| |s17aef| |fortranCharacter| |OMgetFloat| + |print| |outputBinaryFile| |halfExtendedSubResultantGcd2| |inRadical?| + |scalarMatrix| |irVar| |refine| |doubleFloatFormat| |overset?| + |schwerpunkt| |resolve| |lyndonIfCan| |conjugates| |operation| + |normalizedDivide| < |tValues| |doublyTransitive?| |logIfCan| + |stFunc1| |totalfract| |outputAsTex| |c02agf| |binomial| |supRittWu?| + |makeViewport2D| |fortranCompilerName| > |whileLoop| |setImagSteps| + |cyclicParents| |createZechTable| |purelyAlgebraic?| |coordinates| + |characteristicSet| |firstSubsetGray| |outlineRender| <= |trim| + |jokerMode| |infinityNorm| |normal?| |OMputAtp| |tubeRadiusDefault| + |identity| |eigenvectors| |iicsc| |mathieu24| |measure2Result| >= + |hMonic| |prefixRagits| |isOp| |isPower| |balancedBinaryTree| + |intcompBasis| |gensym| |vark| |associates?| |clearTheIFTable| + |directSum| |e02bef| |d02ejf| |FormatRoman| |environment| + |gramschmidt| |patternMatchTimes| |bivariatePolynomials| + |chainSubResultants| |addPointLast| |componentUpperBound| + |seriesToOutputForm| |subPolSet?| |integers| |charClass| |palgextint| + |interpret| |slex| |listOfLists| |elliptic| |superscript| |truncate| + + |enqueue!| |edf2ef| |sort!| |collectUnder| |splitDenominator| |true| + |deleteProperty!| |fortranDoubleComplex| |unitNormalize| + |leadingCoefficientRicDE| |chvar| - |cn| |coHeight| |perfectNthPower?| + |OMserve| |exprHasAlgebraicWeight| |triangularSystems| |nand| |in?| + |maxint| |mantissa| / |reducedForm| |subMatrix| |sinIfCan| + |cardinality| |any?| |e02bdf| |constantIfCan| |members| + |removeDuplicates!| |blankSeparate| |fortranLinkerArgs| + |virtualDegree| |middle| |cyclicEqual?| |messagePrint| |ParCond| + |category| |orbit| |pushucoef| |mainValue| |nil| + |halfExtendedSubResultantGcd1| |RittWuCompare| |tRange| + |factorSquareFreePolynomial| |scaleRoots| |stFunc2| |pushdterm| + |s17aff| |domain| |internalLastSubResultant| |cosSinInfo| |viewport2D| + |diagonals| |split| |e04naf| |prepareSubResAlgo| |abs| |package| + |iiabs| |crest| |setErrorBound| |iiasin| |att2Result| + |SturmHabichtMultiple| |definingInequation| |generalLambert| |maxdeg| + |shift| |createMultiplicationTable| |dimension| |palgRDE| + |quotientByP| |clipPointsDefault| |unitCanonical| |approximate| + |solveLinearPolynomialEquationByFractions| |extractTop!| + |linearAssociatedExp| |ocf2ocdf| |tanh2trigh| |irForm| |OMputAttr| + |f04arf| |mainVariables| |complex| |janko2| |schema| |blue| |varList| + |iCompose| |readInt8!| |bothWays| |palglimint| |choosemon| + |decomposeFunc| |hostByteOrder| |order| |delta| |quatern| + |boundOfCauchy| |xCoord| |show| |mainVariable?| |orthonormalBasis| + |basisOfMiddleNucleus| |makeCos| |trapezoidalo| + |indiceSubResultantEuclidean| |property| |find| |extendIfCan| + |extendedResultant| |prologue| |alphanumeric?| |nativeModuleExtension| + |sncndn| |padecf| |pointData| |csch2sinh| |element?| + |partialQuotients| |useEisensteinCriterion?| |trace| + |evenInfiniteProduct| |internalIntegrate0| |monicRightFactorIfCan| + |kovacic| |pushuconst| |realRoots| |topFortranOutputStack| |plot| + |increase| |conditionsForIdempotents| |d01anf| |retract| |leader| + |mainDefiningPolynomial| |integralLastSubResultant| |leftLcm| + |monicRightDivide| |units| |aspFilename| |leviCivitaSymbol| + |factorPolynomial| |associative?| |patternVariable| |typeForm| + |rightDiscriminant| |loopPoints| |cfirst| |power!| |separateFactors| + |replace| |e04ucf| |OMread| |string?| |zag| |taylorIfCan| + |totalDifferential| |bringDown| |routines| |exactQuotient| + |iflist2Result| |formula| |countRealRootsMultiple| |recur| + |RemainderList| |SFunction| |exQuo| |palgLODE| |moduloP| |Nul| |scale| + |socf2socdf| |createNormalElement| |lambda| |rectangularMatrix| + |reorder| |zero?| |f04asf| |removeSquaresIfCan| |modularGcdPrimitive| + |algintegrate| |numFunEvals3D| |taylorQuoByVar| |bytes| |evenlambert| + |uncouplingMatrices| |ParCondList| |code| |unvectorise| |hostPlatform| + |isOr| |semiIndiceSubResultantEuclidean| |s19abf| |imagK| + |insertBottom!| |yCoord| |s13adf| |unitsColorDefault| |basisOfNucleus| + |makeSin| |setFormula!| |sup| |empty?| |readByte!| + |algebraicVariables| |nrows| |epilogue| |localReal?| |point?| + |datalist| |categoryFrame| |pade| |exptMod| |parent| + |createNormalPoly| |partialDenominators| |useEisensteinCriterion| + |sturmVariationsOf| |ncols| |singular?| |eulerPhi| |laplace| + |numberOfMonomials| |leadingTerm| |leftDivide| |OMgetApp| |plus| + |genericRightDiscriminant| |subResultantsChain| |withPredicates| + |OMconnOutDevice| |rewriteIdealWithHeadRemainder| |mainForm| + |toseLastSubResultant| |rightExtendedGcd| |primPartElseUnitCanonical!| + |nthFactor| |squareFreePolynomial| |d01apf| |oddInfiniteProduct| |Ei| + |typeList| |dom| |generalTwoFactor| |sts2stst| |exponents| |just| + |solveRetract| |antiCommutative?| |e04ycf| |leftDiscriminant| |list?| + |setref| |sum| |homogeneous?| |newReduc| |palgintegrate| + |mainSquareFreePart| |shiftLeft| |polynomial| |kroneckerDelta| + |signatureAst| |OMreadFile| |unexpand| |postfix| |point| + |splitConstant| |modulus| |degreeSubResultant| |connect| + |irreducible?| |times| |zeroOf| |df2fi| |const| |moebius| + |removeZeroes| |modTree| |f04atf| |unprotectedRemoveRedundantFactors| + |shallowCopy| |symbolTable| |groebner?| |skewSFunction| + |setLabelValue| |ip4Address| |characteristic| |cAtan| |augment| + |stirling2| |factorials| |top| |bubbleSort!| |rootDirectory| + |linkToFortran| |modularGcd| |setAdaptive3D| |lp| |headAst| + |systemCommand| |iExquo| |series| |zCoord| |oddlambert| + |pointSizeDefault| |idealSimplify| |basisOfCenter| + |resetAttributeButtons| |pushFortranOutputStack| |redPo| |rightDivide| + |isAnd| |title| |comp| |s19acf| |insertTop!| |imagJ| |updatF| + |endOfFile?| |rischNormalize| |s14aaf| |interactiveEnv| + |listYoungTableaus| |popFortranOutputStack| |iiGamma| |meshPar2Var| + |imagE| |splitNodeOf!| |node| |monom| + |zeroSetSplitIntoTriangularSystems| |options| |eisensteinIrreducible?| + |setFieldInfo| |fibonacci| |redpps| |exponentialOrder| |continue| + |root| |sort| |generalSqFr| |primPartElseUnitCanonical| + |outputAsFortran| |extractProperty| |createNormalPrimitivePoly| + |normal| |partialNumerators| |setPredicates| |lazyVariations| + |remainder| |enterPointData| |e| |logical?| |multiset| |iisqrt2| + |overlap| |nthExpon| |singularAtInfinity?| |genericRightTraceForm| + |d01aqf| |lazyPseudoQuotient| |min| |parametersOf| |list| |digits| + |toseInvertible?| |palginfieldint| |rightGcd| |OMgetAtp| |common| + |gcdPolynomial| |string| |pair?| |generalInfiniteProduct| |represents| + |OMconnectTCP| |car| |f04axf| |clikeUniv| |gradient| + |degreeSubResultantEuclidean| |mainVariable| |f01brf| |commutative?| + |triangSolve| |linGenPos| |infix| |random| |cdr| |leadingBasisTerm| + |insertionSort!| |mainPrimitivePart| |numberOfChildren| |shiftRight| + |pop!| |edf2fi| |curry| |rightRecip| |deref| |setDifference| + |basisOfLeftNucloid| |pmComplexintegrate| + |setLegalFortranSourceExtensions| |region| |decimal| |rootsOf| + |iprint| |OMreadStr| |reindex| |lastSubResultant| |setIntersection| + |limitedint| |removeRedundantFactors| |multiEuclideanTree| |hermiteH| + |groebnerIdeal| |getCode| |rCoord| |round| |taylorRep| + |viewPosDefault| |setUnion| |selectPolynomials| |bumprow| |reduction| + |meshFun2Var| |adaptive3D?| |getStream| |readIfCan!| |lambert| + |cyclotomicDecomposition| |realElementary| |apply| |getButtonValue| + |twoFactor| |isNot| |lazyResidueClass| |s19adf| |imagI| |bottom!| + |tryFunctionalDecomposition?| |heap| |harmonic| |character?| + |mergeDifference| |iisqrt3| |imagk| |remove!| |zero| |zeroSetSplit| + |pol| |predicates| |s14abf| |headRemainder| |size| |continuedFraction| + |toseInvertibleSet| |bitLength| |extractClosed| + |createPrimitiveNormalPoly| |numeric| |reducedContinuedFraction| + |d01asf| |content| |width| |B1solve| |fortranTypeOf| |f04faf| + |weierstrass| |hcrf| |semiDegreeSubResultantEuclidean| |OMgetAttr| + |radical| |And| |mergeFactors| |genericLeftDiscriminant| + |lazyPseudoRemainder| |atom?| |equation| |composites| |ignore?| + |precision| |check| |rightExactQuotient| |children| |vector| + |makeMulti| |Or| |torsion?| |showAll?| |univariateSolve| + |branchPoint?| |leftRecip| |basisOfRightNucloid| |first| |fracPart| + |pmintegrate| |divergence| |differentiate| |uniform01| |Not| |f01bsf| + |edf2df| |rightCharacteristicPolynomial| |groebgen| |vconcat| |rest| + |getProperties| |certainlySubVariety?| |laguerreL| |mainContent| + |tubePlot| |karatsubaDivide| |push!| |elem?| |OMlistCDs| |OMbindTCP| + |lastSubResultantElseSplit| |substitute| |integerIfCan| |bumptab| + |meshPar1Var| |points| |innerint| |cAcot| |makeSketch| |diag| + |thetaCoord| |ref| |hash| |viewSizeDefault| |removeDuplicates| + |leastAffineMultiple| |selectOrPolynomials| |complexZeros| + |monicModulo| |ideal| |principalAncestors| |printCode| |fractionPart| + |readLineIfCan!| |validExponential| |count| |mapDown!| |OMgetEndAtp| + |setOrder| |iiexp| |mr| |setScreenResolution3D| + |tryFunctionalDecomposition| |jacobi| |getRef| |super| |lagrange| + |name| |optional| |factorSquareFree| |doubleComplex?| |squareFreePrim| + |signAround| |bitCoef| |s20acf| |cyclotomicFactorization| |top!| + |conjugate| |hasPredicate?| |lift| |body| |roughUnitIdeal?| |light| + |toseSquareFreePart| |isTerm| |lastSubResultantEuclidean| |inc| + |subNodeOf?| |gcdprim| |e02daf| |reduceByQuasiMonic| |xn| |d01bbf| + |reduce| |empty| |f04jgf| |qqq| |imagj| |child| |nextIrreduciblePoly| + |push| |nextColeman| |totalDegree| |null?| |isMult| |factorset| + |computeInt| |lprop| |polyPart| |extractIndex| |OMgetBind| + |genericLeftTraceForm| |bernoulliB| |realSolve| |s14baf| |hconcat| + |basisOfCentroid| |infieldint| |laplacian| |legendreP| |makeTerm| + |torsionIfCan| |expenseOfEvaluation| |showAllElements| |leftPower| + |components| |internalIntegrate| |possiblyNewVariety?| |ptFunc| + |primitivePart!| |normal01| |f01maf| |leftCharacteristicPolynomial| + |notelem| |branchPointAtInfinity?| |invertibleSet| + |selectAndPolynomials| |bumptab1| |lazyPseudoDivide| SEGMENT + |getGraph| |nary?| |error| |OMlistSymbols| |minordet| |phiCoord| + |port| |OMopenFile| |viewDefaults| |raisePolynomial| |any| + |reducedQPowers| |getOrder| |mapUp!| |hitherPlane| |assert| + |monicDivide| |tower| |curryRight| |readLine!| |rootNormalize| + |totolex| |complex?| |OMgetEndAttr| |divisorCascade| |iilog| + |exteriorDifferential| |unrankImproperPartitions0| |btwFact| + |moebiusMu| |wholePart| |t| |radicalEigenvectors| |compdegd| |pastel| + |invmod| |bitTruth| |leadingIdeal| |mapCoef| |optional?| + |univariatePolynomial| |exportedOperators| |roughEqualIdeals?| + |radicalOfLeftTraceForm| |loadNativeModule| |quotedOperators| |equiv| + |semiLastSubResultantEuclidean| |screenResolution3D| |cCos| |dequeue| + |d01fcf| |compound?| |henselFact| |imagi| |birth| |s20adf| |numerator| + |dAndcExp| |startTable!| |rangeIsFinite| |exprToXXP| |abelianGroup| + |constant| |fullPartialFraction| |extractPoint| |nodeOf?| + |complexNumeric| |removeSinSq| |minimumDegree| |positiveSolve| + |tan2trig| |gcdcofact| |rspace| |aLinear| |useNagFunctions| + |writeBytes!| |nextPrimitivePoly| |byte| |solid| |summation| + |predicate| |numberOfOperations| |eulerE| |rightPower| |maxrank| + |weakBiRank| |minimumExponent| |algDsolve| |listOfMonoms| |kernels| + |prindINFO| |s15adf| |invertible?| |principal?| |hessian| + |lazyPremWithDefault| |c06gcf| |OMgetBVar| |e02zaf| |operator| + |maxRowIndex| |cons| |numberOfComposites| |viewWriteDefault| |index?| + |nextsubResultant2| |eyeDistance| |exponential1| + |factorSquareFreeByRecursion| |setOfMinN| |cycleLength| |tanQ| + |completeEval| |rationalPoint?| |step| |node?| |iisin| |putGraph| + |divideExponents| |univariate| |unrankImproperPartitions1| |separant| + |trunc| |numberOfDivisors| |cAcos| |OMopenString| |listLoops| + |comment| |backOldPos| |qelt| |nthCoef| |problemPoints| |readUInt32!| + |minPol| |roughSubIdeal?| |multMonom| |curveColorPalette| + |splitLinear| |qsetelt| |setMaxPoints3D| |cSin| |primintfldpoly| + |hdmpToP| |radicalEigenvector| |linear| |getOperands| |unparse| + |cyclicGroup| |cAtanh| |coerce| |s21baf| |xRange| |factor| + |quadraticForm| |characteristicPolynomial| |irreducibleFactors| + |alphanumeric| |exprToUPS| |int| |f02bbf| |selectfirst| |cothIfCan| + |construct| |sqrt| |yRange| |updateStatus!| |source| |removeCoshSq| + |nextItem| |insert!| |cAsin| |aQuadratic| |romberg| |expandPower| + |solid?| |nextNormalPoly| |zRange| |alternative?| |real| + |musserTrials| |parameters| |midpoint| |newSubProgram| + |definingEquations| |biRank| |readable?| |power| |map!| |OMgetError| + |fprindINFO| |imag| |OMUnknownSymbol?| |optpair| + |generalizedContinuumHypothesisAssumed| |minimize| |divisor| |log2| + |rightLcm| |length| |qsetelt!| |symmetricSquare| |directProduct| + |e04dgf| |identityMatrix| |c06gqf| |pow| |getVariableOrder| |entries| + |e01sef| |infinite?| |scripts| |randomR| |minRowIndex| |elements| + |cyclic| |presub| |child?| |plus!| |stoseIntegralLastSubResultant| + |mapExpon| |brace| |target| |cycleEntry| |subresultantSequence| + |degree| |ptree| |groebSolve| |relativeApprox| |closed?| + |simpleBounds?| |selectFiniteRoutines| |OMputEndObject| |isobaric?| + |binomThmExpt| |destruct| |zerosOf| |strongGenerators| |bsolve| + |viewZoomDefault| |build| |bezoutResultant| |cross| + |isAbsolutelyIrreducible?| |readInt32!| |cLog| |expintfldpoly| + |nextLatticePermutation| |iiacosh| |f07fdf| |kind| |dihedralGroup| + |var1Steps| |expandLog| |pseudoQuotient| |back| |dmpToP| + |lazyIrreducibleFactors| |palgextint0| |polygon| |op| |f02bjf| + |exists?| |binary| |elliptic?| |removeSinhSq| |realEigenvalues| + |interpretString| |integral?| |partition| |tan2cot| |aCubic| + |leftExtendedGcd| |makeprod| |mapUnivariateIfCan| |ravel| + |denominators| |monomial| |stopMusserTrials| |upperBound| + |variationOfParameters| |clearTheSymbolTable| |setProperties| + |basisOfCommutingElements| |e01sff| |simpson| |s18aef| |flexible?| + |prinpolINFO| |module| |getBadValues| |lexTriangular| |reshape| + |arguments| |key?| |stoseLastSubResultant| |sincos| |setelt| + |setMinPoints| |factorSFBRlcUnit| |c06gsf| |OMUnknownCD?| |An| + |midpoints| |distance| |linearMatrix| |rationalApproximation| + |infLex?| |e04fdf| |zeroMatrix| |replaceKthElement| + |generalizedContinuumHypothesisAssumed?| |sub| |submod| |open?| + |finite?| |copy| |numberOfIrreduciblePoly| |SturmHabichtSequence| + |antisymmetric?| |quasiRegular| |rootOf| |resetVariableOrder| |union| + |leadingIndex| |minus!| |max| |commutativeEquality| |dihedral| + |pomopo!| |singularitiesOf| |invmultisect| |rank| |viewPhiDefault| + |mathieu11| |bezoutDiscriminant| |selectODEIVPRoutines| |OMputInteger| + |morphism| |cExp| |iiatanh| |monomialIntegrate| |testDim| |update| + |f02fjf| |autoCoerce| |cos2sec| |dot| |meatAxe| |front| |weights| + |removeIrreducibleRedundantFactors| |palglimint0| |dmp2rfi| |aQuartic| + |var2Steps| |extension| |composite| |expandTrigProducts| |readUInt16!| + |stripCommentsAndBlanks| |f07fef| |complete| |basisOfLeftAnnihilator| + |packageCall| |leftGcd| |doubleResultant| |numerators| + |numberOfFactors| |pToDmp| |closedCurve?| |showTheSymbolTable| + |elaboration| |e02adf| |disjunction| |mapMatrixIfCan| |prinb| + |realEigenvectors| |resetBadValues| |integralAtInfinity?| + |rightRegularRepresentation| |symbolIfCan| |trapezoidal| + |stoseInvertible?sqfreg| |digit?| |minPoints| |d01ajf| |charthRoot| + |lowerBound| |lexico| |rarrow| |position| |nodes| |linearPart| + |sinhcosh| |s18aff| |setButtonValue| |squareFreeLexTriangular| + |e04gcf| |incrementKthElement| |match?| |UnVectorise| |lists| + |setClosed| |relerror| |addmod| |setEmpty!| |SturmHabichtCoefficients| + |rightAlternative?| |quasiRegular?| |realZeros| |allRootsOf| + |leadingExponent| |leftScalarTimes!| |resultantEuclidean| + |numberOfPrimitivePoly| |mapExponents| |polynomialZeros| + |OMParseError?| |countable?| |viewThetaDefault| |mathieu12| |pureLex| + |cosh2sech| |OMputFloat| |iiacoth| |cRationalPower| |monomialIntPoly| + |mappingAst| |declare| |prime?| |f02wef| |shallowExpand| + |selectPDERoutines| |leftMult| |rotate!| |normalForm| |symmetric?| + |cap| |palgRDE0| |radicalSolve| |leftExactQuotient| |scan| + |scanOneDimSubspaces| |fintegrate| |setPrologue!| |multisect| + |genericPosition| |pole?| |basisOfRightAnnihilator| |space| |e02aef| + |subResultantGcd| |convergents| |balancedFactorisation| + |modularFactor| |se2rfi| |printTypes| |select!| |arg1| |innerSolve1| + |stoseInvertibleSetsqfreg| |distdfact| |critpOrder| + |differentialVariables| |hasTopPredicate?| |leftRegularRepresentation| + |s01eaf| |nonLinearPart| |argument| |arg2| |sech| |conjunction| + |mapBivariate| |conditionP| |readInt16!| |d01akf| |assign| + |closedCurve| |symmetricRemainder| |rename| |csch| |rombergo| + |parametric?| |e04jaf| |sylvesterSequence| |float?| |close| + |integralBasisAtInfinity| |Vectorise| |asinh| |conditions| |tube| + |semiResultantEuclidean2| |subresultantVector| |s18dcf| |SturmHabicht| + |halfExtendedResultant2| |constant?| |belong?| |definingPolynomial| + |constantOpIfCan| |GospersMethod| |match| |acosh| |cot2trig| + |setStatus!| |f2df| |linearAssociatedLog| |stop| |OMmakeConn| + |iterationVar| |display| |pointColorDefault| |bright| |complexSolve| + |mathieu22| |deepExpand| |atanh| |numberOfNormalPoly| |cPower| + |setAttributeButtonStep| |inverseLaplace| |iiasech| + |mainCharacterization| |li| |f02xef| |acoth| |totalLex| + |leftRemainder| |rightMult| |dequeue!| |leftAlternative?| |changeBase| + |Aleph| |palgLODE0| |quadratic?| |radicalRoots| |rightScalarTimes!| + |asech| |OMputVariable| |coefficient| |nullary| |setTex!| + |listBranches| |sample| |basisOfLeftNucleus| |positiveRemainder| + |selectOptimizationRoutines| |expt| |approximants| + |useSingleFactorBound?| |OMwrite| |cup| |newTypeLists| |delete!| + |multiple| |semiResultantEuclidean1| |graphCurves| |resultant| + |makeCrit| |input| |topPredicate| |diagonal?| |rightTraceMatrix| + |lfunc| |bag| |constantKernel| |box| |applyQuote| |coth2trigh| + |separateDegrees| |library| |solveLinearPolynomialEquation| |d01alf| + |revert| |slash| |pr2dmp| |rename!| |tubePoints| + |clearFortranOutputStack| |fullDisplay| |e04mbf| |extractBottom!| + |integer?| |setPoly| |s13aaf| |unitVector| |innerSolve| |leftQuotient| + |plotPolar| |countRealRoots| |readUInt8!| |mindeg| |positive?| + |curve?| |integerBound| |linears| |ruleset| |isEquiv| |s18def| + |linearAssociatedOrder| |ef2edf| |sturmSequence| |ramified?| + |lineColorDefault| |f04adf| |simpsono| |extendedSubResultantGcd| + |setCondition!| |inputOutputBinaryFile| |halfExtendedResultant1| |set| + |iiacsch| |OMcloseConn| |contractSolve| |changeNameToObjf| + |primitivePart| |mkcomm| |createIrreduciblePoly| |test| |id| + |companionBlocks| |infiniteProduct| |chineseRemainder| |Ci| + |basisOfRightNucleus| |complexRoots| |bit?| |suchThat| |OMputString| + |decrease| |setEpilogue!| |triangular?| |algebraicOf| |dn| + |reverseLex| |indiceSubResultant| |sPol| |makeUnit| |ipow| + |antiAssociative?| |useSingleFactorBound| |table| |unravel| + |typeLists| |times!| |csc2sin| |e02dcf| |showArrayValues| |subst| + |insert| |new| |po| |setTopPredicate| |leftTraceMatrix| + |rationalFunction| |rootProduct| |obj| |showFortranOutputStack| + |selectIntegrationRoutines| |discriminant| |wreath| |fixedPoint| + |d01amf| |over| |eq| |lookupFunction| |prefix| |ddFact| |cache| + |drawCurves| |trace2PowMod| |inHallBasis?| |square?| |symbol?| |iter| + |exponent| |swap!| |binding| |monicLeftDivide| |relationsIdeal| + |delete| |hasoln| |negative?| |signature| |seed| |tubeRadius| + |exactQuotient!| |debug3D| |intersect| |upDateBranches| + |associatedSystem| |s13acf| |normalized?| |polarCoordinates| + |optAttributes| |makeEq| |s19aaf| |jordanAlgebra?| |monomial?| |curve| + |axesColorDefault| |bipolar| |updatD| |algint| |isImplies| |setValue!| + |objects| |oneDimensionalArray| |OMencodingXML| |specialTrigs| + |ramifiedAtInfinity?| |compBound| |generators| |createPrimitivePoly| + |directory| |base| |script| |minPoly| |lazy?| |divisors| |Si| + |compactFraction| |adjoint| |rightFactorCandidate| |e02ddf| + |OMputSymbol| |primextendedint| |rowEchelon| |OMconnInDevice| + |rewriteIdealWithRemainder| |elRow1!| |f02aff| |e01baf| |retractIfCan| + |nextPartition| |reverse!| |rewriteIdealWithQuasiMonicGenerators| + |setrest!| |flatten| |ReduceOrder| |externalList| |exp| + |particularSolution| |getMeasure| |prepareDecompose| |normalDeriv| + |showScalarValues| |tex| |setprevious!| |printStats!| |left| |numer| + |rootSimp| |outputMeasure| |mpsode| |cSec| |pseudoRemainder| + |scalarTypeOf| |thenBranch| |/\\| |polyRDE| |returnTypeOf| |right| + |outputList| |denom| |encodingDirectory| |clip| |complexIntegrate| + |quasiAlgebraicSet| |tracePowMod| |unknownEndian| |Is| |laguerre| + |irreducibleFactor| |\\/| |fill!| |increment| |atanIfCan| |setleft!| + |saturate| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 8622df59..45739c74 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5356 +1,5356 @@ -(3226898 . 3477887529) -((-3389 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(|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-173)) ((-102) -2718 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2718 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-111 $ $) |has| |#2| (-173)) ((-131) -2718 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131))) ((-621 #0=(-412 (-569))) -12 (|has| |#2| (-1044 (-412 (-569)))) (|has| |#2| (-1106))) ((-621 (-569)) -2718 (|has| |#2| (-1055)) (-12 (|has| |#2| (-1044 (-569))) (|has| |#2| (-1106))) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-621 |#2|) -2718 (|has| |#2| (-1106)) (|has| |#2| (-173))) ((-618 (-867)) -2718 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-618 (-867))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-618 (-1273 |#2|)) . T) ((-173) |has| |#2| (-173)) ((-232 |#2|) |has| |#2| (-1055)) ((-234) -12 (|has| |#2| (-234)) (|has| |#2| (-1055))) ((-289 #1=(-569) |#2|) . T) ((-291 #1# |#2|) . T) ((-312 |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((-372) |has| |#2| (-372)) ((-381 |#2|) |has| |#2| (-1055)) ((-416 |#2|) |has| |#2| (-1106)) ((-494 |#2|) . T) ((-609 #1# |#2|) . T) ((-519 |#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((-651 (-569)) -2718 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 |#2|) -2718 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 $) -2718 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-653 |#2|) -2718 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-653 $) -2718 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-645 |#2|) -2718 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-644 (-569)) -12 (|has| |#2| (-644 (-569))) (|has| |#2| (-1055))) ((-644 |#2|) |has| |#2| (-1055)) ((-722 |#2|) -2718 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-731) -2718 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-796) |has| |#2| (-853)) ((-797) -2718 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-798) |has| |#2| (-798)) ((-799) -2718 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-800) -2718 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-853) |has| |#2| (-853)) ((-855) -2718 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-906 (-1183)) -12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055))) ((-1044 #0#) -12 (|has| |#2| (-1044 (-412 (-569)))) (|has| |#2| (-1106))) ((-1044 (-569)) -12 (|has| |#2| (-1044 (-569))) (|has| |#2| (-1106))) ((-1044 |#2|) |has| |#2| (-1106)) ((-1057 |#2|) -2718 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1057 $) |has| |#2| (-173)) ((-1062 |#2|) -2718 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1062 $) |has| |#2| (-173)) ((-1055) -2718 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1064) -2718 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1118) -2718 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-1106) -2718 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1223) . 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|%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-731)) (PROGN (-6 (-731)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-372)) (-6 (-372)) |%noBranch|) (IF (|has| |t#2| (-173)) (PROGN (-6 (-38 |t#2|)) (-6 (-173))) |%noBranch|) (IF (|has| |t#2| (-6 -4441)) (-6 -4441) |%noBranch|) (IF (|has| |t#2| (-853)) (-6 (-853)) |%noBranch|) (IF (|has| |t#2| (-798)) (-6 (-798)) |%noBranch|) (IF (|has| |t#2| (-367)) (-6 (-1280 |t#2|)) |%noBranch|))) +(((-21) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-23) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131))) ((-25) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-173)) ((-102) -2774 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-111 $ $) |has| |#2| (-173)) ((-131) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131))) ((-621 #0=(-412 (-569))) -12 (|has| |#2| (-1044 (-412 (-569)))) (|has| |#2| (-1106))) ((-621 (-569)) -2774 (|has| |#2| (-1055)) (-12 (|has| |#2| (-1044 (-569))) (|has| |#2| (-1106))) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-621 |#2|) -2774 (|has| |#2| (-1106)) (|has| |#2| (-173))) ((-618 (-867)) -2774 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-618 (-867))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-618 (-1273 |#2|)) . T) ((-173) |has| |#2| (-173)) ((-232 |#2|) |has| |#2| (-1055)) ((-234) -12 (|has| |#2| (-234)) (|has| |#2| (-1055))) ((-289 #1=(-569) |#2|) . T) ((-291 #1# |#2|) . T) ((-312 |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((-372) |has| |#2| (-372)) ((-381 |#2|) |has| |#2| (-1055)) ((-416 |#2|) |has| |#2| (-1106)) ((-494 |#2|) . T) ((-609 #1# |#2|) . T) ((-519 |#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((-651 (-569)) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 $) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-653 |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-653 $) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-645 |#2|) -2774 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-644 (-569)) -12 (|has| |#2| (-644 (-569))) (|has| |#2| (-1055))) ((-644 |#2|) |has| |#2| (-1055)) ((-722 |#2|) -2774 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-731) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-796) |has| |#2| (-853)) ((-797) -2774 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-798) |has| |#2| (-798)) ((-799) -2774 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-800) -2774 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-853) |has| |#2| (-853)) ((-855) -2774 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-906 (-1183)) -12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055))) ((-1044 #0#) -12 (|has| |#2| (-1044 (-412 (-569)))) (|has| |#2| (-1106))) ((-1044 (-569)) -12 (|has| |#2| (-1044 (-569))) (|has| |#2| (-1106))) ((-1044 |#2|) |has| |#2| (-1106)) ((-1057 |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1057 $) |has| |#2| (-173)) ((-1062 |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1062 $) |has| |#2| (-173)) ((-1055) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1064) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1118) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-1106) -2774 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1223) . T) ((-1280 |#2|) |has| |#2| (-367))) +((-4085 (((-241 |#1| |#3|) (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|) 21)) (-3596 ((|#3| (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|) 23)) (-1344 (((-241 |#1| |#3|) (-1 |#3| |#2|) (-241 |#1| |#2|)) 18))) +(((-240 |#1| |#2| |#3|) (-10 -7 (-15 -4085 ((-241 |#1| |#3|) (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|)) (-15 -3596 (|#3| (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|)) (-15 -1344 ((-241 |#1| |#3|) (-1 |#3| |#2|) (-241 |#1| |#2|)))) (-776) (-1223) (-1223)) (T -240)) +((-1344 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-241 *5 *6)) (-14 *5 (-776)) (-4 *6 (-1223)) (-4 *7 (-1223)) (-5 *2 (-241 *5 *7)) (-5 *1 (-240 *5 *6 *7)))) (-3596 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-241 *5 *6)) (-14 *5 (-776)) (-4 *6 (-1223)) (-4 *2 (-1223)) (-5 *1 (-240 *5 *6 *2)))) (-4085 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-241 *6 *7)) (-14 *6 (-776)) (-4 *7 (-1223)) (-4 *5 (-1223)) (-5 *2 (-241 *6 *5)) (-5 *1 (-240 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-412 (-569))) |has| |#1| (-38 (-412 (-569)))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-412 (-569)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #0#) -2774 (|has| |#1| (-1044 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569))))) ((-621 (-569)) . T) ((-621 |#1|) . T) ((-621 |#2|) . T) ((-621 |#3|) . T) ((-621 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457))) ((-618 (-867)) . 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T) ((-645 #0#) |has| |#1| (-38 (-412 (-569)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457))) ((-644 (-569)) |has| |#1| (-644 (-569))) ((-644 |#1|) . T) ((-722 #0#) |has| |#1| (-38 (-412 (-569)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457))) ((-731) . T) ((-906 (-1183)) |has| |#1| (-906 (-1183))) ((-906 |#3|) . T) ((-892 (-383)) -12 (|has| |#1| (-892 (-383))) (|has| |#3| (-892 (-383)))) ((-892 (-569)) -12 (|has| |#1| (-892 (-569))) (|has| |#3| (-892 (-569)))) ((-955 |#1| |#4| |#3|) . T) ((-915) |has| |#1| (-915)) ((-1044 (-412 (-569))) |has| |#1| (-1044 (-412 (-569)))) ((-1044 (-569)) |has| |#1| (-1044 (-569))) ((-1044 |#1|) . T) ((-1044 |#2|) . T) ((-1044 |#3|) . T) ((-1057 #0#) |has| |#1| (-38 (-412 (-569)))) ((-1057 |#1|) . T) ((-1057 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1062 #0#) |has| |#1| (-38 (-412 (-569)))) ((-1062 |#1|) . T) ((-1062 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1055) . T) ((-1064) . T) ((-1118) . T) ((-1106) . 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T) ((-107 |#1|) . T) ((-102) |has| |#1| (-1106)) ((-618 (-867)) -2718 (|has| |#1| (-1106)) (|has| |#1| (-618 (-867)))) ((-312 |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106))) ((-494 |#1|) . T) ((-519 |#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106))) ((-1001 |#1|) . T) ((-1106) |has| |#1| (-1106)) ((-1127 |#1|) . T) ((-1223) . 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T) ((-305) . T) ((-367) |has| |#1| (-561)) ((-381 |#1|) |has| |#1| (-1055)) ((-405 |#1|) . T) ((-416 |#1|) . T) ((-457) |has| |#1| (-561)) ((-478) |has| |#1| (-478)) ((-519 (-617 $) $) . T) ((-519 $ $) . T) ((-561) |has| |#1| (-561)) ((-651 #0#) |has| |#1| (-561)) ((-651 (-569)) -2718 (|has| |#1| (-1055)) (|has| |#1| (-561)) (|has| |#1| (-173)) (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#1| (-21))) ((-651 |#1|) |has| |#1| (-173)) ((-651 $) -2718 (|has| |#1| (-1055)) (|has| |#1| (-561)) (|has| |#1| (-173)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-653 #0#) |has| |#1| (-561)) ((-653 |#1|) |has| |#1| (-173)) ((-653 $) -2718 (|has| |#1| (-1055)) (|has| |#1| (-561)) (|has| |#1| (-173)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-645 #0#) |has| |#1| (-561)) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) |has| |#1| (-561)) ((-644 (-569)) -12 (|has| |#1| (-644 (-569))) (|has| |#1| (-1055))) ((-644 |#1|) |has| |#1| (-1055)) ((-722 #0#) |has| |#1| (-561)) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) |has| |#1| (-561)) ((-731) -2718 (|has| |#1| (-1118)) (|has| |#1| (-1055)) (|has| |#1| (-561)) (|has| |#1| (-478)) (|has| |#1| (-173)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-906 (-1183)) |has| |#1| (-1055)) ((-892 (-383)) |has| |#1| (-892 (-383))) ((-892 (-569)) |has| |#1| (-892 (-569))) ((-890 |#1|) . 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T) ((-645 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-722 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-731) . T) ((-906 (-1183)) -12 (|has| |#1| (-15 * (|#1| (-569) |#1|))) (|has| |#1| (-906 (-1183)))) ((-979 |#1| #0# (-1088)) . T) ((-926) |has| |#1| (-367)) ((-1008) |has| |#1| (-38 (-412 (-569)))) ((-1057 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-1057 |#1|) . T) ((-1057 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1062 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-1062 |#1|) . T) ((-1062 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1055) . T) ((-1064) . T) ((-1118) . T) ((-1106) . 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T) ((-23) . T) ((-47 |#1| #0=(-569)) . T) ((-25) . T) ((-38 #1=(-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 |#2|) |has| |#1| (-367)) ((-38 $) -2718 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-569)))) ((-95) |has| |#1| (-38 (-412 (-569)))) ((-102) . T) ((-111 #1# #1#) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-367)) ((-111 $ $) -2718 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) -2718 (-12 (|has| |#1| (-367)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2718 (-12 (|has| |#1| (-367)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-621 #1#) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-621 (-569)) . T) ((-621 #2=(-1183)) -12 (|has| |#1| (-367)) (|has| |#2| (-1044 (-1183)))) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . 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T) ((-651 |#1|) . T) ((-651 |#2|) |has| |#1| (-367)) ((-651 $) . T) ((-653 #1#) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-653 |#1|) . T) ((-653 |#2|) |has| |#1| (-367)) ((-653 $) . T) ((-645 #1#) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 |#2|) |has| |#1| (-367)) ((-645 $) -2718 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-644 (-569)) -12 (|has| |#1| (-367)) (|has| |#2| (-644 (-569)))) ((-644 |#2|) |has| |#1| (-367)) ((-722 #1#) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 |#2|) |has| |#1| (-367)) ((-722 $) -2718 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-731) . T) ((-796) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-797) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-799) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-800) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-825) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-853) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-855) -2718 (-12 (|has| |#1| (-367)) (|has| |#2| (-855))) (-12 (|has| |#1| (-367)) (|has| |#2| (-825)))) ((-906 (-1183)) -2718 (-12 (|has| |#1| (-367)) (|has| |#2| (-906 (-1183)))) (-12 (|has| |#1| (-15 * (|#1| (-569) |#1|))) (|has| |#1| (-906 (-1183))))) ((-892 (-383)) -12 (|has| |#1| (-367)) (|has| |#2| (-892 (-383)))) ((-892 (-569)) -12 (|has| |#1| (-367)) (|has| |#2| (-892 (-569)))) ((-890 |#2|) |has| |#1| (-367)) ((-915) -12 (|has| |#1| (-367)) (|has| |#2| (-915))) ((-979 |#1| #0# (-1088)) . 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T) ((-23) . T) ((-47 |#1| #0=(-569)) . T) ((-25) . T) ((-38 #1=(-412 (-569))) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 |#2|) |has| |#1| (-367)) ((-38 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-569)))) ((-95) |has| |#1| (-38 (-412 (-569)))) ((-102) . T) ((-111 #1# #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-367)) ((-111 $ $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) -2774 (-12 (|has| |#1| (-367)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2774 (-12 (|has| |#1| (-367)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-621 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-621 (-569)) . T) ((-621 #2=(-1183)) -12 (|has| |#1| (-367)) (|has| |#2| (-1044 (-1183)))) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . 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T) ((-651 |#1|) . T) ((-651 |#2|) |has| |#1| (-367)) ((-651 $) . T) ((-653 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-653 |#1|) . T) ((-653 |#2|) |has| |#1| (-367)) ((-653 $) . T) ((-645 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 |#2|) |has| |#1| (-367)) ((-645 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-644 (-569)) -12 (|has| |#1| (-367)) (|has| |#2| (-644 (-569)))) ((-644 |#2|) |has| |#1| (-367)) ((-722 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 |#2|) |has| |#1| (-367)) ((-722 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-731) . 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T) ((-23) . T) ((-47 |#1| #0=(-776)) . T) ((-25) . T) ((-38 #1=(-412 (-569))) |has| |#1| (-38 (-412 (-569)))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-412 (-569)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #1#) -2718 (|has| |#1| (-1044 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569))))) ((-621 (-569)) . T) ((-621 #2=(-1088)) . T) ((-621 |#1|) . T) ((-621 $) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-618 (-867)) . T) ((-173) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-619 (-541)) -12 (|has| (-1088) (-619 (-541))) (|has| |#1| (-619 (-541)))) ((-619 (-898 (-383))) -12 (|has| (-1088) (-619 (-898 (-383)))) (|has| |#1| (-619 (-898 (-383))))) ((-619 (-898 (-569))) -12 (|has| (-1088) (-619 (-898 (-569)))) (|has| |#1| (-619 (-898 (-569))))) ((-232 |#1|) . T) ((-234) . T) ((-289 (-412 $) (-412 $)) |has| |#1| (-561)) ((-289 |#1| |#1|) . T) ((-289 $ $) . T) ((-293) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-310) |has| |#1| (-367)) ((-312 $) . T) ((-329 |#1| #0#) . T) ((-381 |#1|) . T) ((-416 |#1|) . T) ((-457) -2718 (|has| |#1| (-915)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-519 #2# |#1|) . T) ((-519 #2# $) . T) ((-519 $ $) . T) ((-561) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-651 #1#) |has| |#1| (-38 (-412 (-569)))) ((-651 (-569)) . T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #1#) |has| |#1| (-38 (-412 (-569)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-569)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-644 (-569)) |has| |#1| (-644 (-569))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-569)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-731) . T) ((-906 #2#) . T) ((-906 (-1183)) |has| |#1| (-906 (-1183))) ((-892 (-383)) -12 (|has| (-1088) (-892 (-383))) (|has| |#1| (-892 (-383)))) ((-892 (-569)) -12 (|has| (-1088) (-892 (-569))) (|has| |#1| (-892 (-569)))) ((-955 |#1| #0# #2#) . T) ((-915) |has| |#1| (-915)) ((-926) |has| |#1| (-367)) ((-1044 (-412 (-569))) |has| |#1| (-1044 (-412 (-569)))) ((-1044 (-569)) |has| |#1| (-1044 (-569))) ((-1044 #2#) . T) ((-1044 |#1|) . T) ((-1057 #1#) |has| |#1| (-38 (-412 (-569)))) ((-1057 |#1|) . T) ((-1057 $) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1062 #1#) |has| |#1| (-38 (-412 (-569)))) ((-1062 |#1|) . T) ((-1062 $) -2718 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1055) . T) ((-1064) . T) ((-1118) . T) ((-1106) . T) ((-1158) |has| |#1| (-1158)) ((-1227) |has| |#1| (-915))) -((-3865 (((-649 (-1088)) $) 34)) (-1842 (($ $) 31)) (-3838 (($ |#2| |#3|) NIL) (($ $ (-1088) |#3|) 28) (($ $ (-649 (-1088)) (-649 |#3|)) 27)) (-1808 (($ $) 14)) (-1820 ((|#2| $) 12)) (-2091 ((|#3| $) 10))) -(((-1250 |#1| |#2| |#3|) (-10 -8 (-15 -3865 ((-649 (-1088)) |#1|)) (-15 -3838 (|#1| |#1| (-649 (-1088)) (-649 |#3|))) (-15 -3838 (|#1| |#1| (-1088) |#3|)) (-15 -1842 (|#1| |#1|)) (-15 -3838 (|#1| |#2| |#3|)) (-15 -2091 (|#3| |#1|)) (-15 -1808 (|#1| |#1|)) (-15 -1820 (|#2| |#1|))) (-1251 |#2| |#3|) (-1055) (-797)) (T -1250)) -NIL -(-10 -8 (-15 -3865 ((-649 (-1088)) |#1|)) (-15 -3838 (|#1| |#1| (-649 (-1088)) (-649 |#3|))) (-15 -3838 (|#1| |#1| (-1088) |#3|)) (-15 -1842 (|#1| |#1|)) (-15 -3838 (|#1| |#2| |#3|)) (-15 -2091 (|#3| |#1|)) (-15 -1808 (|#1| |#1|)) (-15 -1820 (|#2| |#1|))) -((-2383 (((-112) $ $) 7)) (-2789 (((-112) $) 17)) (-3865 (((-649 (-1088)) $) 86)) (-2599 (((-1183) $) 115)) (-2598 (((-2 (|:| -2591 $) (|:| 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(-412 (-569))))))) +(-13 (-955 |t#1| (-776) (-1088)) (-289 |t#1| |t#1|) (-289 $ $) (-234) (-232 |t#1|) (-10 -8 (-15 -2822 ((-1273 |t#1|) $ (-776))) (-15 -2704 ((-1179 |t#1|) $)) (-15 -2571 ($ (-1179 |t#1|))) (-15 -2253 ($ $ (-776))) (-15 -3762 ((-3 $ "failed") $ (-776))) (-15 -3659 ((-2 (|:| -2726 $) (|:| -3365 $)) $ $)) (-15 -3528 ((-2 (|:| -2726 $) (|:| -3365 $)) $ (-776))) (-15 -3409 ($ $ (-776))) (-15 -3274 ($ $ (-776))) (-15 -4401 ($ $ $)) (-15 -3514 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1158)) (-6 (-1158)) |%noBranch|) (IF (|has| |t#1| (-173)) (PROGN (-15 -4304 (|t#1| $)) (-15 -4202 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-561)) (PROGN (-6 (-289 (-412 $) (-412 $))) (-15 -1866 ((-412 $) (-412 $) (-412 $))) (-15 -3110 ((-776) $ $)) (-15 -4095 ($ $ $)) (-15 -4000 ((-3 $ "failed") $ $)) (-15 -4000 ((-3 (-412 $) "failed") (-412 $) $)) (-15 -3897 ($ $ $)) (-15 -1887 ((-2 (|:| -1433 |t#1|) (|:| -2726 $) (|:| -3365 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-457)) (-15 -1782 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-367)) (PROGN (-6 (-310)) (-6 -4440) (-15 -1866 (|t#1| (-412 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-412 (-569)))) (-15 -2488 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-776)) . T) ((-25) . T) ((-38 #1=(-412 (-569))) |has| |#1| (-38 (-412 (-569)))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-412 (-569)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #1#) -2774 (|has| |#1| (-1044 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569))))) ((-621 (-569)) . T) ((-621 #2=(-1088)) . T) ((-621 |#1|) . T) ((-621 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-618 (-867)) . T) ((-173) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-619 (-541)) -12 (|has| (-1088) (-619 (-541))) (|has| |#1| (-619 (-541)))) ((-619 (-898 (-383))) -12 (|has| (-1088) (-619 (-898 (-383)))) (|has| |#1| (-619 (-898 (-383))))) ((-619 (-898 (-569))) -12 (|has| (-1088) (-619 (-898 (-569)))) (|has| |#1| (-619 (-898 (-569))))) ((-232 |#1|) . T) ((-234) . T) ((-289 (-412 $) (-412 $)) |has| |#1| (-561)) ((-289 |#1| |#1|) . T) ((-289 $ $) . T) ((-293) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-310) |has| |#1| (-367)) ((-312 $) . T) ((-329 |#1| #0#) . T) ((-381 |#1|) . T) ((-416 |#1|) . T) ((-457) -2774 (|has| |#1| (-915)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-519 #2# |#1|) . T) ((-519 #2# $) . T) ((-519 $ $) . T) ((-561) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-651 #1#) |has| |#1| (-38 (-412 (-569)))) ((-651 (-569)) . T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #1#) |has| |#1| (-38 (-412 (-569)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-569)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-644 (-569)) |has| |#1| (-644 (-569))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-569)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-731) . T) ((-906 #2#) . T) ((-906 (-1183)) |has| |#1| (-906 (-1183))) ((-892 (-383)) -12 (|has| (-1088) (-892 (-383))) (|has| |#1| (-892 (-383)))) ((-892 (-569)) -12 (|has| (-1088) (-892 (-569))) (|has| |#1| (-892 (-569)))) ((-955 |#1| #0# #2#) . T) ((-915) |has| |#1| (-915)) ((-926) |has| |#1| (-367)) ((-1044 (-412 (-569))) |has| |#1| (-1044 (-412 (-569)))) ((-1044 (-569)) |has| |#1| (-1044 (-569))) ((-1044 #2#) . T) ((-1044 |#1|) . T) ((-1057 #1#) |has| |#1| (-38 (-412 (-569)))) ((-1057 |#1|) . T) ((-1057 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1062 #1#) |has| |#1| (-38 (-412 (-569)))) ((-1062 |#1|) . T) ((-1062 $) -2774 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1055) . T) ((-1064) . T) ((-1118) . T) ((-1106) . 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T) ((-23) . T) ((-47 |#1| #0=(-412 (-569))) . T) ((-25) . T) ((-38 #1=(-412 (-569))) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) -2718 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-569)))) ((-95) |has| |#1| (-38 (-412 (-569)))) ((-102) . T) ((-111 #1# #1#) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2718 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #1#) -2718 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-621 (-569)) . T) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . T) ((-621 $) -2718 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-618 (-867)) . 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(-3009 (($ $ $) 35)) (** (($ $ (-927)) NIL) (($ $ (-776)) 54)) (* (($ (-927) $) NIL) (($ (-776) $) NIL) (($ (-569) $) 44) (($ $ $) 43))) (((-1301 |#1|) (-13 (-173) (-372) (-619 (-569)) (-1158)) (-927)) (T -1301)) NIL (-13 (-173) (-372) (-619 (-569)) (-1158)) @@ -5366,4 +5366,4 @@ NIL NIL NIL NIL -((-3 3226883 3226888 3226893 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3226868 3226873 3226878 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3226853 3226858 3226863 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3226838 3226843 3226848 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1301 3225981 3226713 3226790 "ZMOD" 3226795 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1300 3225091 3225255 3225464 "ZLINDEP" 3225813 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1299 3214391 3216159 3218131 "ZDSOLVE" 3223221 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1298 3213637 3213778 3213967 "YSTREAM" 3214237 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1297 3211411 3212938 3213142 "XRPOLY" 3213480 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3207964 3209282 3209857 "XPR" 3210883 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1295 3205685 3207295 3207499 "XPOLY" 3207795 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1294 3203338 3204706 3204761 "XPOLYC" 3205049 NIL XPOLYC (NIL T T) -9 NIL 3205162 NIL) (-1293 3199714 3201855 3202243 "XPBWPOLY" 3202996 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1292 3195409 3197704 3197746 "XF" 3198367 NIL XF (NIL T) -9 NIL 3198767 NIL) (-1291 3195030 3195118 3195287 "XF-" 3195292 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1290 3190226 3191515 3191570 "XFALG" 3193742 NIL XFALG (NIL T T) -9 NIL 3194531 NIL) (-1289 3189359 3189463 3189668 "XEXPPKG" 3190118 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1288 3187468 3189209 3189305 "XDPOLY" 3189310 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3186275 3186875 3186918 "XALG" 3186923 NIL XALG (NIL T) -9 NIL 3187034 NIL) (-1286 3179717 3184252 3184746 "WUTSET" 3185867 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1285 3177973 3178769 3179092 "WP" 3179528 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1284 3177575 3177795 3177865 "WHILEAST" 3177925 T WHILEAST (NIL) -8 NIL NIL NIL) (-1283 3177047 3177292 3177386 "WHEREAST" 3177503 T WHEREAST (NIL) -8 NIL NIL NIL) (-1282 3175933 3176131 3176426 "WFFINTBS" 3176844 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1281 3173837 3174264 3174726 "WEIER" 3175505 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1280 3172883 3173333 3173375 "VSPACE" 3173511 NIL VSPACE (NIL T) -9 NIL 3173585 NIL) (-1279 3172721 3172748 3172839 "VSPACE-" 3172844 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1278 3172530 3172572 3172640 "VOID" 3172675 T VOID (NIL) -8 NIL NIL NIL) (-1277 3170666 3171025 3171431 "VIEW" 3172146 T VIEW (NIL) -7 NIL NIL NIL) (-1276 3167090 3167729 3168466 "VIEWDEF" 3169951 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1275 3156394 3158638 3160811 "VIEW3D" 3164939 T VIEW3D (NIL) -8 NIL NIL NIL) (-1274 3148645 3150305 3151884 "VIEW2D" 3154837 T VIEW2D (NIL) -8 NIL NIL NIL) (-1273 3143998 3148415 3148507 "VECTOR" 3148588 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1272 3142575 3142834 3143152 "VECTOR2" 3143728 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1271 3136049 3140356 3140399 "VECTCAT" 3141394 NIL VECTCAT (NIL T) -9 NIL 3141981 NIL) (-1270 3135063 3135317 3135707 "VECTCAT-" 3135712 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1269 3134517 3134714 3134834 "VARIABLE" 3134978 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1268 3134450 3134455 3134485 "UTYPE" 3134490 T UTYPE (NIL) -9 NIL NIL NIL) (-1267 3133280 3133434 3133696 "UTSODETL" 3134276 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1266 3130720 3131180 3131704 "UTSODE" 3132821 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1265 3122557 3128346 3128835 "UTS" 3130289 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1264 3113431 3118798 3118841 "UTSCAT" 3119953 NIL UTSCAT (NIL T) -9 NIL 3120711 NIL) (-1263 3110778 3111501 3112490 "UTSCAT-" 3112495 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1262 3110405 3110448 3110581 "UTS2" 3110729 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1261 3104631 3107243 3107286 "URAGG" 3109356 NIL URAGG (NIL T) -9 NIL 3110079 NIL) (-1260 3101570 3102433 3103556 "URAGG-" 3103561 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1259 3097279 3100205 3100670 "UPXSSING" 3101234 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1258 3089345 3096526 3096799 "UPXS" 3097064 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1257 3082418 3089249 3089321 "UPXSCONS" 3089326 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1256 3072163 3078956 3079018 "UPXSCCA" 3079592 NIL UPXSCCA (NIL T T) -9 NIL 3079825 NIL) (-1255 3071801 3071886 3072060 "UPXSCCA-" 3072065 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1254 3061398 3067964 3068007 "UPXSCAT" 3068655 NIL UPXSCAT (NIL T) -9 NIL 3069264 NIL) (-1253 3060828 3060907 3061086 "UPXS2" 3061313 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1252 3059482 3059735 3060086 "UPSQFREE" 3060571 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1251 3052903 3055960 3056015 "UPSCAT" 3057176 NIL UPSCAT (NIL T T) -9 NIL 3057950 NIL) (-1250 3052107 3052314 3052641 "UPSCAT-" 3052646 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 3037762 3045530 3045573 "UPOLYC" 3047674 NIL UPOLYC (NIL T) -9 NIL 3048895 NIL) (-1248 3029090 3031516 3034663 "UPOLYC-" 3034668 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1247 3028717 3028760 3028893 "UPOLYC2" 3029041 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1246 3020528 3028400 3028529 "UP" 3028636 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1245 3019867 3019974 3020138 "UPMP" 3020417 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1244 3019420 3019501 3019640 "UPDIVP" 3019780 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1243 3017988 3018237 3018553 "UPDECOMP" 3019169 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1242 3017223 3017335 3017520 "UPCDEN" 3017872 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1241 3016742 3016811 3016960 "UP2" 3017148 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1240 3015209 3015946 3016223 "UNISEG" 3016500 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1239 3014424 3014551 3014756 "UNISEG2" 3015052 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1238 3013484 3013664 3013890 "UNIFACT" 3014240 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1237 2997416 3012661 3012912 "ULS" 3013291 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1236 2985414 2997320 2997392 "ULSCONS" 2997397 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1235 2967433 2979418 2979480 "ULSCCAT" 2980118 NIL ULSCCAT (NIL T T) -9 NIL 2980406 NIL) (-1234 2966483 2966728 2967116 "ULSCCAT-" 2967121 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1233 2955857 2962337 2962380 "ULSCAT" 2963243 NIL ULSCAT (NIL T) -9 NIL 2963974 NIL) (-1232 2955287 2955366 2955545 "ULS2" 2955772 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1231 2954414 2954924 2955031 "UINT8" 2955142 T UINT8 (NIL) -8 NIL NIL 2955227) (-1230 2953540 2954050 2954157 "UINT64" 2954268 T UINT64 (NIL) -8 NIL NIL 2954353) (-1229 2952666 2953176 2953283 "UINT32" 2953394 T UINT32 (NIL) -8 NIL NIL 2953479) (-1228 2951792 2952302 2952409 "UINT16" 2952520 T UINT16 (NIL) -8 NIL NIL 2952605) (-1227 2950095 2951052 2951082 "UFD" 2951294 T UFD (NIL) -9 NIL 2951408 NIL) (-1226 2949889 2949935 2950030 "UFD-" 2950035 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1225 2948971 2949154 2949370 "UDVO" 2949695 T UDVO (NIL) -7 NIL NIL NIL) (-1224 2946787 2947196 2947667 "UDPO" 2948535 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1223 2946720 2946725 2946755 "TYPE" 2946760 T TYPE (NIL) -9 NIL NIL NIL) (-1222 2946480 2946675 2946706 "TYPEAST" 2946711 T TYPEAST (NIL) -8 NIL NIL NIL) (-1221 2945451 2945653 2945893 "TWOFACT" 2946274 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1220 2944474 2944860 2945095 "TUPLE" 2945251 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1219 2942165 2942684 2943223 "TUBETOOL" 2943957 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1218 2941014 2941219 2941460 "TUBE" 2941958 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1217 2935743 2939986 2940269 "TS" 2940766 NIL TS (NIL T) -8 NIL NIL NIL) (-1216 2924383 2928502 2928599 "TSETCAT" 2933868 NIL TSETCAT (NIL T T T T) -9 NIL 2935399 NIL) (-1215 2919115 2920715 2922606 "TSETCAT-" 2922611 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1214 2913754 2914601 2915530 "TRMANIP" 2918251 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1213 2913195 2913258 2913421 "TRIMAT" 2913686 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1212 2911061 2911298 2911655 "TRIGMNIP" 2912944 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1211 2910581 2910694 2910724 "TRIGCAT" 2910937 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1210 2910250 2910329 2910470 "TRIGCAT-" 2910475 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1209 2907095 2909108 2909389 "TREE" 2910004 NIL TREE (NIL T) -8 NIL NIL NIL) (-1208 2906369 2906897 2906927 "TRANFUN" 2906962 T TRANFUN (NIL) -9 NIL 2907028 NIL) (-1207 2905648 2905839 2906119 "TRANFUN-" 2906124 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1206 2905452 2905484 2905545 "TOPSP" 2905609 T TOPSP (NIL) -7 NIL NIL NIL) (-1205 2904800 2904915 2905069 "TOOLSIGN" 2905333 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1204 2903434 2903977 2904216 "TEXTFILE" 2904583 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1203 2901346 2901887 2902316 "TEX" 2903027 T TEX (NIL) -8 NIL NIL NIL) (-1202 2901127 2901158 2901230 "TEX1" 2901309 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1201 2900775 2900838 2900928 "TEMUTL" 2901059 T TEMUTL (NIL) -7 NIL NIL NIL) (-1200 2898929 2899209 2899534 "TBCMPPK" 2900498 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1199 2890706 2897089 2897145 "TBAGG" 2897545 NIL TBAGG (NIL T T) -9 NIL 2897756 NIL) (-1198 2885776 2887264 2889018 "TBAGG-" 2889023 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1197 2885160 2885267 2885412 "TANEXP" 2885665 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1196 2878550 2885017 2885110 "TABLE" 2885115 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1195 2877962 2878061 2878199 "TABLEAU" 2878447 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1194 2872570 2873790 2875038 "TABLBUMP" 2876748 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1193 2871792 2871939 2872120 "SYSTEM" 2872411 T SYSTEM (NIL) -8 NIL NIL NIL) (-1192 2868251 2868950 2869733 "SYSSOLP" 2871043 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1191 2868049 2868206 2868237 "SYSPTR" 2868242 T SYSPTR (NIL) -8 NIL NIL NIL) (-1190 2867093 2867598 2867717 "SYSNNI" 2867903 NIL SYSNNI (NIL NIL) -8 NIL NIL 2867988) (-1189 2866400 2866859 2866938 "SYSINT" 2866998 NIL SYSINT (NIL NIL) -8 NIL NIL 2867043) (-1188 2862732 2863678 2864388 "SYNTAX" 2865712 T SYNTAX (NIL) -8 NIL NIL NIL) (-1187 2859890 2860492 2861124 "SYMTAB" 2862122 T SYMTAB (NIL) -8 NIL NIL NIL) (-1186 2855139 2856041 2857024 "SYMS" 2858929 T SYMS (NIL) -8 NIL NIL NIL) (-1185 2852374 2854597 2854827 "SYMPOLY" 2854944 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1184 2851891 2851966 2852089 "SYMFUNC" 2852286 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1183 2847911 2849203 2850016 "SYMBOL" 2851100 T SYMBOL (NIL) -8 NIL NIL NIL) (-1182 2841450 2843139 2844859 "SWITCH" 2846213 T SWITCH (NIL) -8 NIL NIL NIL) (-1181 2834684 2840271 2840574 "SUTS" 2841205 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1180 2826750 2833931 2834204 "SUPXS" 2834469 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1179 2818509 2826368 2826494 "SUP" 2826659 NIL SUP (NIL T) -8 NIL NIL NIL) (-1178 2817668 2817795 2818012 "SUPFRACF" 2818377 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1177 2817289 2817348 2817461 "SUP2" 2817603 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1176 2815737 2816011 2816367 "SUMRF" 2816988 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1175 2815072 2815138 2815330 "SUMFS" 2815658 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1174 2799039 2814249 2814500 "SULS" 2814879 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1173 2798641 2798861 2798931 "SUCHTAST" 2798991 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1172 2797936 2798166 2798306 "SUCH" 2798549 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1171 2791802 2792842 2793801 "SUBSPACE" 2797024 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1170 2791232 2791322 2791486 "SUBRESP" 2791690 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1169 2784598 2785897 2787208 "STTF" 2789968 NIL STTF (NIL T) -7 NIL NIL NIL) (-1168 2778771 2779891 2781038 "STTFNC" 2783498 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1167 2770082 2771953 2773747 "STTAYLOR" 2777012 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1166 2763212 2769946 2770029 "STRTBL" 2770034 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1165 2758576 2763167 2763198 "STRING" 2763203 T STRING (NIL) -8 NIL NIL NIL) (-1164 2753437 2757949 2757979 "STRICAT" 2758038 T STRICAT (NIL) -9 NIL 2758100 NIL) (-1163 2746190 2751056 2751667 "STREAM" 2752861 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1162 2745700 2745777 2745921 "STREAM3" 2746107 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1161 2744682 2744865 2745100 "STREAM2" 2745513 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1160 2744370 2744422 2744515 "STREAM1" 2744624 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1159 2743386 2743567 2743798 "STINPROD" 2744186 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1158 2742938 2743148 2743178 "STEP" 2743258 T STEP (NIL) -9 NIL 2743336 NIL) (-1157 2742125 2742427 2742575 "STEPAST" 2742812 T STEPAST (NIL) -8 NIL NIL NIL) (-1156 2735557 2742024 2742101 "STBL" 2742106 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1155 2730683 2734778 2734821 "STAGG" 2734974 NIL STAGG (NIL T) -9 NIL 2735063 NIL) (-1154 2728385 2728987 2729859 "STAGG-" 2729864 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1153 2726532 2728155 2728247 "STACK" 2728328 NIL STACK (NIL T) -8 NIL NIL NIL) (-1152 2719227 2724673 2725129 "SREGSET" 2726162 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1151 2711652 2713021 2714534 "SRDCMPK" 2717833 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1150 2704569 2709092 2709122 "SRAGG" 2710425 T SRAGG (NIL) -9 NIL 2711033 NIL) (-1149 2703586 2703841 2704220 "SRAGG-" 2704225 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1148 2698046 2702533 2702954 "SQMATRIX" 2703212 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1147 2691731 2694764 2695491 "SPLTREE" 2697391 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1146 2687694 2688387 2689033 "SPLNODE" 2691157 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1145 2686741 2686974 2687004 "SPFCAT" 2687448 T SPFCAT (NIL) -9 NIL NIL NIL) (-1144 2685478 2685688 2685952 "SPECOUT" 2686499 T SPECOUT (NIL) -7 NIL NIL NIL) (-1143 2676588 2678460 2678490 "SPADXPT" 2683166 T SPADXPT (NIL) -9 NIL 2685330 NIL) (-1142 2676349 2676389 2676458 "SPADPRSR" 2676541 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1141 2674398 2676304 2676335 "SPADAST" 2676340 T SPADAST (NIL) -8 NIL NIL NIL) (-1140 2666343 2668116 2668159 "SPACEC" 2672532 NIL SPACEC (NIL T) -9 NIL 2674348 NIL) (-1139 2664473 2666275 2666324 "SPACE3" 2666329 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1138 2663225 2663396 2663687 "SORTPAK" 2664278 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1137 2661317 2661620 2662032 "SOLVETRA" 2662889 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1136 2660367 2660589 2660850 "SOLVESER" 2661090 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1135 2655671 2656559 2657554 "SOLVERAD" 2659419 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1134 2651486 2652095 2652824 "SOLVEFOR" 2655038 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1133 2645756 2650835 2650932 "SNTSCAT" 2650937 NIL SNTSCAT (NIL T T T T) -9 NIL 2651007 NIL) (-1132 2639862 2644079 2644470 "SMTS" 2645446 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1131 2634547 2639750 2639827 "SMP" 2639832 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1130 2632706 2633007 2633405 "SMITH" 2634244 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1129 2625419 2629615 2629718 "SMATCAT" 2631069 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631619 NIL) (-1128 2622359 2623182 2624360 "SMATCAT-" 2624365 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1127 2620025 2621595 2621638 "SKAGG" 2621899 NIL SKAGG (NIL T) -9 NIL 2622034 NIL) (-1126 2616336 2619441 2619636 "SINT" 2619823 T SINT (NIL) -8 NIL NIL 2619996) (-1125 2616108 2616146 2616212 "SIMPAN" 2616292 T SIMPAN (NIL) -7 NIL NIL NIL) (-1124 2615387 2615643 2615783 "SIG" 2615990 T SIG (NIL) -8 NIL NIL NIL) (-1123 2614225 2614446 2614721 "SIGNRF" 2615146 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1122 2613058 2613209 2613493 "SIGNEF" 2614054 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1121 2612364 2612641 2612765 "SIGAST" 2612956 T SIGAST (NIL) -8 NIL NIL NIL) (-1120 2610054 2610508 2611014 "SHP" 2611905 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1119 2603906 2609955 2610031 "SHDP" 2610036 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1118 2603479 2603671 2603701 "SGROUP" 2603794 T SGROUP (NIL) -9 NIL 2603856 NIL) (-1117 2603337 2603363 2603436 "SGROUP-" 2603441 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1116 2600172 2600870 2601593 "SGCF" 2602636 T SGCF (NIL) -7 NIL NIL NIL) (-1115 2594540 2599619 2599716 "SFRTCAT" 2599721 NIL SFRTCAT (NIL T T T T) -9 NIL 2599760 NIL) (-1114 2587961 2588979 2590115 "SFRGCD" 2593523 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1113 2581087 2582160 2583346 "SFQCMPK" 2586894 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1112 2580707 2580796 2580907 "SFORT" 2581028 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1111 2579825 2580547 2580668 "SEXOF" 2580673 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1110 2578932 2579706 2579774 "SEX" 2579779 T SEX (NIL) -8 NIL NIL NIL) (-1109 2574445 2575160 2575255 "SEXCAT" 2578192 NIL SEXCAT (NIL T T T T T) -9 NIL 2578770 NIL) (-1108 2571598 2574379 2574427 "SET" 2574432 NIL SET (NIL T) -8 NIL NIL NIL) (-1107 2569822 2570311 2570616 "SETMN" 2571339 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1106 2569318 2569470 2569500 "SETCAT" 2569676 T SETCAT (NIL) -9 NIL 2569786 NIL) (-1105 2569010 2569088 2569218 "SETCAT-" 2569223 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1104 2565371 2567471 2567514 "SETAGG" 2568384 NIL SETAGG (NIL T) -9 NIL 2568724 NIL) (-1103 2564829 2564945 2565182 "SETAGG-" 2565187 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1102 2564272 2564525 2564626 "SEQAST" 2564750 T SEQAST (NIL) -8 NIL NIL NIL) (-1101 2563471 2563765 2563826 "SEGXCAT" 2564112 NIL SEGXCAT (NIL T T) -9 NIL 2564232 NIL) (-1100 2562477 2563137 2563319 "SEG" 2563324 NIL SEG (NIL T) -8 NIL NIL NIL) (-1099 2561456 2561670 2561713 "SEGCAT" 2562235 NIL SEGCAT (NIL T) -9 NIL 2562456 NIL) (-1098 2560388 2560819 2561027 "SEGBIND" 2561283 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1097 2560009 2560068 2560181 "SEGBIND2" 2560323 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1096 2559582 2559810 2559887 "SEGAST" 2559954 T SEGAST (NIL) -8 NIL NIL NIL) (-1095 2558801 2558927 2559131 "SEG2" 2559426 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1094 2558211 2558736 2558783 "SDVAR" 2558788 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1093 2550738 2557981 2558111 "SDPOL" 2558116 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1092 2549331 2549597 2549916 "SCPKG" 2550453 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1091 2548495 2548667 2548859 "SCOPE" 2549161 T SCOPE (NIL) -8 NIL NIL NIL) (-1090 2547715 2547849 2548028 "SCACHE" 2548350 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1089 2547361 2547547 2547577 "SASTCAT" 2547582 T SASTCAT (NIL) -9 NIL 2547595 NIL) (-1088 2546848 2547196 2547272 "SAOS" 2547307 T SAOS (NIL) -8 NIL NIL NIL) (-1087 2546413 2546448 2546621 "SAERFFC" 2546807 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1086 2540352 2546310 2546390 "SAE" 2546395 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1085 2539945 2539980 2540139 "SAEFACT" 2540311 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1084 2538266 2538580 2538981 "RURPK" 2539611 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1083 2536903 2537209 2537514 "RULESET" 2538100 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1082 2534126 2534656 2535114 "RULE" 2536584 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1081 2533738 2533920 2534003 "RULECOLD" 2534078 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1080 2533528 2533556 2533627 "RTVALUE" 2533689 T RTVALUE (NIL) -8 NIL NIL NIL) (-1079 2532999 2533245 2533339 "RSTRCAST" 2533456 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1078 2527847 2528642 2529562 "RSETGCD" 2532198 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1077 2517077 2522156 2522253 "RSETCAT" 2526372 NIL RSETCAT (NIL T T T T) -9 NIL 2527469 NIL) (-1076 2515004 2515543 2516367 "RSETCAT-" 2516372 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1075 2507390 2508766 2510286 "RSDCMPK" 2513603 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1074 2505369 2505836 2505910 "RRCC" 2506996 NIL RRCC (NIL T T) -9 NIL 2507340 NIL) (-1073 2504720 2504894 2505173 "RRCC-" 2505178 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1072 2504163 2504416 2504517 "RPTAST" 2504641 T RPTAST (NIL) -8 NIL NIL NIL) (-1071 2478014 2487371 2487438 "RPOLCAT" 2498102 NIL RPOLCAT (NIL T T T) -9 NIL 2501261 NIL) (-1070 2469512 2471852 2474974 "RPOLCAT-" 2474979 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1069 2460443 2467723 2468205 "ROUTINE" 2469052 T ROUTINE (NIL) -8 NIL NIL NIL) (-1068 2457241 2460069 2460209 "ROMAN" 2460325 T ROMAN (NIL) -8 NIL NIL NIL) (-1067 2455485 2456101 2456361 "ROIRC" 2457046 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1066 2451717 2454001 2454031 "RNS" 2454335 T RNS (NIL) -9 NIL 2454609 NIL) (-1065 2450226 2450609 2451143 "RNS-" 2451218 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1064 2449629 2450037 2450067 "RNG" 2450072 T RNG (NIL) -9 NIL 2450093 NIL) (-1063 2448632 2448994 2449196 "RNGBIND" 2449480 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1062 2448031 2448419 2448462 "RMODULE" 2448467 NIL RMODULE (NIL T) -9 NIL 2448494 NIL) (-1061 2446867 2446961 2447297 "RMCAT2" 2447932 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1060 2443717 2446213 2446510 "RMATRIX" 2446629 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1059 2436544 2438804 2438919 "RMATCAT" 2442278 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443260 NIL) (-1058 2435919 2436066 2436373 "RMATCAT-" 2436378 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1057 2435320 2435541 2435584 "RLINSET" 2435778 NIL RLINSET (NIL T) -9 NIL 2435869 NIL) (-1056 2434887 2434962 2435090 "RINTERP" 2435239 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1055 2433945 2434499 2434529 "RING" 2434585 T RING (NIL) -9 NIL 2434677 NIL) (-1054 2433737 2433781 2433878 "RING-" 2433883 NIL RING- (NIL T) -8 NIL NIL NIL) (-1053 2432578 2432815 2433073 "RIDIST" 2433501 T RIDIST (NIL) -7 NIL NIL NIL) (-1052 2423867 2432046 2432252 "RGCHAIN" 2432426 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1051 2423217 2423623 2423664 "RGBCSPC" 2423722 NIL RGBCSPC (NIL T) -9 NIL 2423774 NIL) (-1050 2422375 2422756 2422797 "RGBCMDL" 2423029 NIL RGBCMDL (NIL T) -9 NIL 2423143 NIL) (-1049 2419369 2419983 2420653 "RF" 2421739 NIL RF (NIL T) -7 NIL NIL NIL) (-1048 2419015 2419078 2419181 "RFFACTOR" 2419300 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1047 2418740 2418775 2418872 "RFFACT" 2418974 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1046 2416857 2417221 2417603 "RFDIST" 2418380 T RFDIST (NIL) -7 NIL NIL NIL) (-1045 2416310 2416402 2416565 "RETSOL" 2416759 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1044 2415946 2416026 2416069 "RETRACT" 2416202 NIL RETRACT (NIL T) -9 NIL 2416289 NIL) (-1043 2415795 2415820 2415907 "RETRACT-" 2415912 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1042 2415397 2415617 2415687 "RETAST" 2415747 T RETAST (NIL) -8 NIL NIL NIL) (-1041 2408135 2415050 2415177 "RESULT" 2415292 T RESULT (NIL) -8 NIL NIL NIL) (-1040 2406726 2407404 2407603 "RESRING" 2408038 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1039 2406362 2406411 2406509 "RESLATC" 2406663 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1038 2406067 2406102 2406209 "REPSQ" 2406321 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1037 2403489 2404069 2404671 "REP" 2405487 T REP (NIL) -7 NIL NIL NIL) (-1036 2403186 2403221 2403332 "REPDB" 2403448 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1035 2397086 2398475 2399698 "REP2" 2401998 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1034 2393463 2394144 2394952 "REP1" 2396313 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1033 2386159 2391604 2392060 "REGSET" 2393093 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1032 2384924 2385307 2385557 "REF" 2385944 NIL REF (NIL T) -8 NIL NIL NIL) (-1031 2384301 2384404 2384571 "REDORDER" 2384808 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1030 2380269 2383514 2383741 "RECLOS" 2384129 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1029 2379321 2379502 2379717 "REALSOLV" 2380076 T REALSOLV (NIL) -7 NIL NIL NIL) (-1028 2379167 2379208 2379238 "REAL" 2379243 T REAL (NIL) -9 NIL 2379278 NIL) (-1027 2375650 2376452 2377336 "REAL0Q" 2378332 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1026 2371251 2372239 2373300 "REAL0" 2374631 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1025 2370722 2370968 2371062 "RDUCEAST" 2371179 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1024 2370127 2370199 2370406 "RDIV" 2370644 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1023 2369195 2369369 2369582 "RDIST" 2369949 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1022 2367792 2368079 2368451 "RDETRS" 2368903 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1021 2365604 2366058 2366596 "RDETR" 2367334 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1020 2364229 2364507 2364904 "RDEEFS" 2365320 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1019 2362738 2363044 2363469 "RDEEF" 2363917 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1018 2356799 2359719 2359749 "RCFIELD" 2361044 T RCFIELD (NIL) -9 NIL 2361775 NIL) (-1017 2354863 2355367 2356063 "RCFIELD-" 2356138 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1016 2351132 2352964 2353007 "RCAGG" 2354091 NIL RCAGG (NIL T) -9 NIL 2354556 NIL) (-1015 2350760 2350854 2351017 "RCAGG-" 2351022 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1014 2350095 2350207 2350372 "RATRET" 2350644 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1013 2349648 2349715 2349836 "RATFACT" 2350023 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1012 2348956 2349076 2349228 "RANDSRC" 2349518 T RANDSRC (NIL) -7 NIL NIL NIL) (-1011 2348690 2348734 2348807 "RADUTIL" 2348905 T RADUTIL (NIL) -7 NIL NIL NIL) (-1010 2341806 2347523 2347833 "RADIX" 2348414 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1009 2333425 2341648 2341778 "RADFF" 2341783 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1008 2333072 2333147 2333177 "RADCAT" 2333337 T RADCAT (NIL) -9 NIL NIL NIL) (-1007 2332854 2332902 2333002 "RADCAT-" 2333007 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1006 2330952 2332624 2332716 "QUEUE" 2332797 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1005 2327489 2330885 2330933 "QUAT" 2330938 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1004 2327120 2327163 2327294 "QUATCT2" 2327440 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1003 2320569 2323914 2323956 "QUATCAT" 2324747 NIL QUATCAT (NIL T) -9 NIL 2325513 NIL) (-1002 2316708 2317745 2319135 "QUATCAT-" 2319231 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1001 2314173 2315784 2315827 "QUAGG" 2316208 NIL QUAGG (NIL T) -9 NIL 2316383 NIL) (-1000 2313775 2313995 2314065 "QQUTAST" 2314125 T QQUTAST (NIL) -8 NIL NIL NIL) (-999 2312673 2313173 2313345 "QFORM" 2313647 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-998 2303678 2308917 2308957 "QFCAT" 2309615 NIL QFCAT (NIL T) -9 NIL 2310616 NIL) (-997 2299250 2300451 2302042 "QFCAT-" 2302136 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-996 2298888 2298931 2299058 "QFCAT2" 2299201 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-995 2298348 2298458 2298588 "QEQUAT" 2298778 T QEQUAT (NIL) -8 NIL NIL NIL) (-994 2291494 2292567 2293751 "QCMPACK" 2297281 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-993 2289043 2289491 2289919 "QALGSET" 2291149 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-992 2288288 2288462 2288694 "QALGSET2" 2288863 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-991 2286978 2287202 2287519 "PWFFINTB" 2288061 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-990 2285160 2285328 2285682 "PUSHVAR" 2286792 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-989 2281078 2282132 2282173 "PTRANFN" 2284057 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-988 2279480 2279771 2280093 "PTPACK" 2280789 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-987 2279112 2279169 2279278 "PTFUNC2" 2279417 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-986 2273589 2277984 2278025 "PTCAT" 2278321 NIL PTCAT (NIL T) -9 NIL 2278474 NIL) (-985 2273247 2273282 2273406 "PSQFR" 2273548 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-984 2271842 2272140 2272474 "PSEUDLIN" 2272945 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-983 2258605 2260976 2263300 "PSETPK" 2269602 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-982 2251623 2254363 2254459 "PSETCAT" 2257480 NIL PSETCAT (NIL T T T T) -9 NIL 2258294 NIL) (-981 2249459 2250093 2250914 "PSETCAT-" 2250919 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-980 2248808 2248973 2249001 "PSCURVE" 2249269 T PSCURVE (NIL) -9 NIL 2249436 NIL) (-979 2244806 2246322 2246387 "PSCAT" 2247231 NIL PSCAT (NIL T T T) -9 NIL 2247471 NIL) (-978 2243869 2244085 2244485 "PSCAT-" 2244490 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2242574 2243234 2243439 "PRTITION" 2243684 T PRTITION (NIL) -8 NIL NIL NIL) (-976 2242049 2242295 2242387 "PRTDAST" 2242502 T PRTDAST (NIL) -8 NIL NIL NIL) (-975 2231139 2233353 2235541 "PRS" 2239911 NIL PRS (NIL T T) -7 NIL NIL NIL) (-974 2228950 2230489 2230529 "PRQAGG" 2230712 NIL PRQAGG (NIL T) -9 NIL 2230814 NIL) (-973 2228154 2228459 2228487 "PROPLOG" 2228734 T PROPLOG (NIL) -9 NIL 2228900 NIL) (-972 2226335 2226901 2227198 "PROPFRML" 2227890 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-971 2225804 2225911 2226039 "PROPERTY" 2226227 T PROPERTY (NIL) -8 NIL NIL NIL) (-970 2219862 2223970 2224790 "PRODUCT" 2225030 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-969 2217140 2219320 2219554 "PR" 2219673 NIL PR (NIL T T) -8 NIL NIL NIL) (-968 2216936 2216968 2217027 "PRINT" 2217101 T PRINT (NIL) -7 NIL NIL NIL) (-967 2216276 2216393 2216545 "PRIMES" 2216816 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-966 2214341 2214742 2215208 "PRIMELT" 2215855 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-965 2214070 2214119 2214147 "PRIMCAT" 2214271 T PRIMCAT (NIL) -9 NIL NIL NIL) (-964 2210185 2214008 2214053 "PRIMARR" 2214058 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-963 2209192 2209370 2209598 "PRIMARR2" 2210003 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-962 2208835 2208891 2209002 "PREASSOC" 2209130 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-961 2208310 2208443 2208471 "PPCURVE" 2208676 T PPCURVE (NIL) -9 NIL 2208812 NIL) (-960 2207905 2208105 2208188 "PORTNUM" 2208247 T PORTNUM (NIL) -8 NIL NIL NIL) (-959 2205264 2205663 2206255 "POLYROOT" 2207486 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-958 2199446 2204868 2205028 "POLY" 2205137 NIL POLY (NIL T) -8 NIL NIL NIL) (-957 2198829 2198887 2199121 "POLYLIFT" 2199382 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-956 2195104 2195553 2196182 "POLYCATQ" 2198374 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-955 2181816 2186944 2187009 "POLYCAT" 2190523 NIL POLYCAT (NIL T T T) -9 NIL 2192401 NIL) (-954 2175265 2177127 2179511 "POLYCAT-" 2179516 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-953 2174852 2174920 2175040 "POLY2UP" 2175191 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-952 2174484 2174541 2174650 "POLY2" 2174789 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-951 2173169 2173408 2173684 "POLUTIL" 2174258 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-950 2171524 2171801 2172132 "POLTOPOL" 2172891 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-949 2166989 2171460 2171506 "POINT" 2171511 NIL POINT (NIL T) -8 NIL NIL NIL) (-948 2165176 2165533 2165908 "PNTHEORY" 2166634 T PNTHEORY (NIL) -7 NIL NIL NIL) (-947 2163634 2163931 2164330 "PMTOOLS" 2164874 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-946 2163227 2163305 2163422 "PMSYM" 2163550 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-945 2162737 2162806 2162980 "PMQFCAT" 2163152 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-944 2162092 2162202 2162358 "PMPRED" 2162614 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-943 2161485 2161571 2161733 "PMPREDFS" 2161993 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-942 2160149 2160357 2160735 "PMPLCAT" 2161247 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-941 2159681 2159760 2159912 "PMLSAGG" 2160064 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-940 2159154 2159230 2159412 "PMKERNEL" 2159599 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-939 2158771 2158846 2158959 "PMINS" 2159073 NIL PMINS (NIL T) -7 NIL NIL NIL) (-938 2158213 2158282 2158491 "PMFS" 2158696 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-937 2157441 2157559 2157764 "PMDOWN" 2158090 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-936 2156608 2156766 2156947 "PMASS" 2157280 T PMASS (NIL) -7 NIL NIL NIL) (-935 2155881 2155991 2156154 "PMASSFS" 2156495 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-934 2155536 2155604 2155698 "PLOTTOOL" 2155807 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-933 2150143 2151347 2152495 "PLOT" 2154408 T PLOT (NIL) -8 NIL NIL NIL) (-932 2145947 2146991 2147912 "PLOT3D" 2149242 T PLOT3D (NIL) -8 NIL NIL NIL) (-931 2144859 2145036 2145271 "PLOT1" 2145751 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-930 2120248 2124925 2129776 "PLEQN" 2140125 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-929 2119566 2119688 2119868 "PINTERP" 2120113 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-928 2119259 2119306 2119409 "PINTERPA" 2119513 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-927 2118480 2119028 2119115 "PI" 2119155 T PI (NIL) -8 NIL NIL 2119222) (-926 2116777 2117752 2117780 "PID" 2117962 T PID (NIL) -9 NIL 2118096 NIL) (-925 2116528 2116565 2116640 "PICOERCE" 2116734 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-924 2115848 2115987 2116163 "PGROEB" 2116384 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-923 2111435 2112249 2113154 "PGE" 2114963 T PGE (NIL) -7 NIL NIL NIL) (-922 2109558 2109805 2110171 "PGCD" 2111152 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-921 2108896 2108999 2109160 "PFRPAC" 2109442 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-920 2105536 2107444 2107797 "PFR" 2108575 NIL PFR (NIL T) -8 NIL NIL NIL) (-919 2103925 2104169 2104494 "PFOTOOLS" 2105283 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-918 2102458 2102697 2103048 "PFOQ" 2103682 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-917 2100959 2101171 2101527 "PFO" 2102242 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-916 2097512 2100848 2100917 "PF" 2100922 NIL PF (NIL NIL) -8 NIL NIL NIL) (-915 2094846 2096117 2096145 "PFECAT" 2096730 T PFECAT (NIL) -9 NIL 2097114 NIL) (-914 2094291 2094445 2094659 "PFECAT-" 2094664 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-913 2092894 2093146 2093447 "PFBRU" 2094040 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-912 2090760 2091112 2091544 "PFBR" 2092545 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-911 2086642 2088136 2088812 "PERM" 2090117 NIL PERM (NIL T) -8 NIL NIL NIL) (-910 2081876 2082849 2083719 "PERMGRP" 2085805 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-909 2079982 2080939 2080980 "PERMCAT" 2081426 NIL PERMCAT (NIL T) -9 NIL 2081731 NIL) (-908 2079635 2079676 2079800 "PERMAN" 2079935 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-907 2077123 2079300 2079422 "PENDTREE" 2079546 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-906 2075147 2075915 2075956 "PDRING" 2076613 NIL PDRING (NIL T) -9 NIL 2076899 NIL) (-905 2074250 2074468 2074830 "PDRING-" 2074835 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-904 2071465 2072243 2072911 "PDEPROB" 2073602 T PDEPROB (NIL) -8 NIL NIL NIL) (-903 2069010 2069514 2070069 "PDEPACK" 2070930 T PDEPACK (NIL) -7 NIL NIL NIL) (-902 2067922 2068112 2068363 "PDECOMP" 2068809 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-901 2065501 2066344 2066372 "PDECAT" 2067159 T PDECAT (NIL) -9 NIL 2067872 NIL) (-900 2065252 2065285 2065375 "PCOMP" 2065462 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-899 2063430 2064053 2064350 "PBWLB" 2064981 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-898 2055903 2057503 2058841 "PATTERN" 2062113 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-897 2055535 2055592 2055701 "PATTERN2" 2055840 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-896 2053292 2053680 2054137 "PATTERN1" 2055124 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-895 2050660 2051241 2051722 "PATRES" 2052857 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-894 2050224 2050291 2050423 "PATRES2" 2050587 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-893 2048107 2048512 2048919 "PATMATCH" 2049891 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-892 2047617 2047826 2047867 "PATMAB" 2047974 NIL PATMAB (NIL T) -9 NIL 2048057 NIL) (-891 2046135 2046471 2046729 "PATLRES" 2047422 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-890 2045681 2045804 2045845 "PATAB" 2045850 NIL PATAB (NIL T) -9 NIL 2046022 NIL) (-889 2043162 2043694 2044267 "PARTPERM" 2045128 T PARTPERM (NIL) -7 NIL NIL NIL) (-888 2042783 2042846 2042948 "PARSURF" 2043093 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-887 2042415 2042472 2042581 "PARSU2" 2042720 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-886 2042179 2042219 2042286 "PARSER" 2042368 T PARSER (NIL) -7 NIL NIL NIL) (-885 2041800 2041863 2041965 "PARSCURV" 2042110 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-884 2041432 2041489 2041598 "PARSC2" 2041737 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-883 2041071 2041129 2041226 "PARPCURV" 2041368 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-882 2040703 2040760 2040869 "PARPC2" 2041008 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-881 2039764 2040076 2040258 "PARAMAST" 2040541 T PARAMAST (NIL) -8 NIL NIL NIL) (-880 2039284 2039370 2039489 "PAN2EXPR" 2039665 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-879 2038061 2038405 2038633 "PALETTE" 2039076 T PALETTE (NIL) -8 NIL NIL NIL) (-878 2036454 2037066 2037426 "PAIR" 2037747 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-877 2030324 2035713 2035907 "PADICRC" 2036309 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-876 2023553 2029670 2029854 "PADICRAT" 2030172 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-875 2021868 2023490 2023535 "PADIC" 2023540 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-874 2018978 2020542 2020582 "PADICCT" 2021163 NIL PADICCT (NIL NIL) -9 NIL 2021445 NIL) (-873 2017935 2018135 2018403 "PADEPAC" 2018765 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-872 2017147 2017280 2017486 "PADE" 2017797 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-871 2015534 2016355 2016635 "OWP" 2016951 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-870 2015027 2015240 2015337 "OVERSET" 2015457 T OVERSET (NIL) -8 NIL NIL NIL) (-869 2014073 2014632 2014804 "OVAR" 2014895 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-868 2013337 2013458 2013619 "OUT" 2013932 T OUT (NIL) -7 NIL NIL NIL) (-867 2002209 2004446 2006646 "OUTFORM" 2011157 T OUTFORM (NIL) -8 NIL NIL NIL) (-866 2001545 2001806 2001933 "OUTBFILE" 2002102 T OUTBFILE (NIL) -8 NIL NIL NIL) (-865 2000852 2001017 2001045 "OUTBCON" 2001363 T OUTBCON (NIL) -9 NIL 2001529 NIL) (-864 2000453 2000565 2000722 "OUTBCON-" 2000727 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-863 1999833 2000182 2000271 "OSI" 2000384 T OSI (NIL) -8 NIL NIL NIL) (-862 1999363 1999701 1999729 "OSGROUP" 1999734 T OSGROUP (NIL) -9 NIL 1999756 NIL) (-861 1998108 1998335 1998620 "ORTHPOL" 1999110 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-860 1995659 1997943 1998064 "OREUP" 1998069 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-859 1993062 1995350 1995477 "ORESUP" 1995601 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-858 1990590 1991090 1991651 "OREPCTO" 1992551 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-857 1984276 1986477 1986518 "OREPCAT" 1988866 NIL OREPCAT (NIL T) -9 NIL 1989970 NIL) (-856 1981423 1982205 1983263 "OREPCAT-" 1983268 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-855 1980574 1980872 1980900 "ORDSET" 1981209 T ORDSET (NIL) -9 NIL 1981373 NIL) (-854 1980005 1980153 1980377 "ORDSET-" 1980382 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-853 1978570 1979361 1979389 "ORDRING" 1979591 T ORDRING (NIL) -9 NIL 1979716 NIL) (-852 1978215 1978309 1978453 "ORDRING-" 1978458 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-851 1977595 1978058 1978086 "ORDMON" 1978091 T ORDMON (NIL) -9 NIL 1978112 NIL) (-850 1976757 1976904 1977099 "ORDFUNS" 1977444 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-849 1976095 1976514 1976542 "ORDFIN" 1976607 T ORDFIN (NIL) -9 NIL 1976681 NIL) (-848 1972654 1974681 1975090 "ORDCOMP" 1975719 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-847 1971920 1972047 1972233 "ORDCOMP2" 1972514 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-846 1968501 1969411 1970225 "OPTPROB" 1971126 T OPTPROB (NIL) -8 NIL NIL NIL) (-845 1965303 1965942 1966646 "OPTPACK" 1967817 T OPTPACK (NIL) -7 NIL NIL NIL) (-844 1962990 1963756 1963784 "OPTCAT" 1964603 T OPTCAT (NIL) -9 NIL 1965253 NIL) (-843 1962374 1962667 1962772 "OPSIG" 1962905 T OPSIG (NIL) -8 NIL NIL NIL) (-842 1962142 1962181 1962247 "OPQUERY" 1962328 T OPQUERY (NIL) -7 NIL NIL NIL) (-841 1959273 1960453 1960957 "OP" 1961671 NIL OP (NIL T) -8 NIL NIL NIL) (-840 1958647 1958873 1958914 "OPERCAT" 1959126 NIL OPERCAT (NIL T) -9 NIL 1959223 NIL) (-839 1958402 1958458 1958575 "OPERCAT-" 1958580 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-838 1955215 1957199 1957568 "ONECOMP" 1958066 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-837 1954520 1954635 1954809 "ONECOMP2" 1955087 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-836 1953939 1954045 1954175 "OMSERVER" 1954410 T OMSERVER (NIL) -7 NIL NIL NIL) (-835 1950801 1953379 1953419 "OMSAGG" 1953480 NIL OMSAGG (NIL T) -9 NIL 1953544 NIL) (-834 1949424 1949687 1949969 "OMPKG" 1950539 T OMPKG (NIL) -7 NIL NIL NIL) (-833 1948854 1948957 1948985 "OM" 1949284 T OM (NIL) -9 NIL NIL NIL) (-832 1947401 1948403 1948572 "OMLO" 1948735 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-831 1946361 1946508 1946728 "OMEXPR" 1947227 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-830 1945652 1945907 1946043 "OMERR" 1946245 T OMERR (NIL) -8 NIL NIL NIL) (-829 1944803 1945073 1945233 "OMERRK" 1945512 T OMERRK (NIL) -8 NIL NIL NIL) (-828 1944254 1944480 1944588 "OMENC" 1944715 T OMENC (NIL) -8 NIL NIL NIL) (-827 1938149 1939334 1940505 "OMDEV" 1943103 T OMDEV (NIL) -8 NIL NIL NIL) (-826 1937218 1937389 1937583 "OMCONN" 1937975 T OMCONN (NIL) -8 NIL NIL NIL) (-825 1935739 1936715 1936743 "OINTDOM" 1936748 T OINTDOM (NIL) -9 NIL 1936769 NIL) (-824 1933077 1934427 1934764 "OFMONOID" 1935434 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-823 1932488 1933014 1933059 "ODVAR" 1933064 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-822 1929911 1932233 1932388 "ODR" 1932393 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-821 1922492 1929687 1929813 "ODPOL" 1929818 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-820 1916314 1922364 1922469 "ODP" 1922474 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-819 1915080 1915295 1915570 "ODETOOLS" 1916088 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-818 1912047 1912705 1913421 "ODESYS" 1914413 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-817 1906929 1907837 1908862 "ODERTRIC" 1911122 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-816 1906355 1906437 1906631 "ODERED" 1906841 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-815 1903243 1903791 1904468 "ODERAT" 1905778 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-814 1900200 1900667 1901264 "ODEPRRIC" 1902772 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-813 1898143 1898739 1899225 "ODEPROB" 1899734 T ODEPROB (NIL) -8 NIL NIL NIL) (-812 1894663 1895148 1895795 "ODEPRIM" 1897622 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-811 1893912 1894014 1894274 "ODEPAL" 1894555 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-810 1890074 1890865 1891729 "ODEPACK" 1893068 T ODEPACK (NIL) -7 NIL NIL NIL) (-809 1889135 1889242 1889464 "ODEINT" 1889963 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-808 1883236 1884661 1886108 "ODEIFTBL" 1887708 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-807 1878634 1879420 1880372 "ODEEF" 1882395 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-806 1877983 1878072 1878295 "ODECONST" 1878539 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-805 1876108 1876769 1876797 "ODECAT" 1877402 T ODECAT (NIL) -9 NIL 1877933 NIL) (-804 1872963 1875813 1875935 "OCT" 1876018 NIL OCT (NIL T) -8 NIL NIL NIL) (-803 1872601 1872644 1872771 "OCTCT2" 1872914 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-802 1867250 1869685 1869725 "OC" 1870822 NIL OC (NIL T) -9 NIL 1871680 NIL) (-801 1864477 1865225 1866215 "OC-" 1866309 NIL OC- (NIL T T) -8 NIL NIL NIL) (-800 1863829 1864297 1864325 "OCAMON" 1864330 T OCAMON (NIL) -9 NIL 1864351 NIL) (-799 1863360 1863701 1863729 "OASGP" 1863734 T OASGP (NIL) -9 NIL 1863754 NIL) (-798 1862621 1863110 1863138 "OAMONS" 1863178 T OAMONS (NIL) -9 NIL 1863221 NIL) (-797 1862035 1862468 1862496 "OAMON" 1862501 T OAMON (NIL) -9 NIL 1862521 NIL) (-796 1861293 1861811 1861839 "OAGROUP" 1861844 T OAGROUP (NIL) -9 NIL 1861864 NIL) (-795 1860983 1861033 1861121 "NUMTUBE" 1861237 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-794 1854556 1856074 1857610 "NUMQUAD" 1859467 T NUMQUAD (NIL) -7 NIL NIL NIL) (-793 1850312 1851300 1852325 "NUMODE" 1853551 T NUMODE (NIL) -7 NIL NIL NIL) (-792 1847667 1848547 1848575 "NUMINT" 1849498 T NUMINT (NIL) -9 NIL 1850262 NIL) (-791 1846615 1846812 1847030 "NUMFMT" 1847469 T NUMFMT (NIL) -7 NIL NIL NIL) (-790 1832974 1835919 1838451 "NUMERIC" 1844122 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-789 1827344 1832423 1832518 "NTSCAT" 1832523 NIL NTSCAT (NIL T T T T) -9 NIL 1832562 NIL) (-788 1826538 1826703 1826896 "NTPOLFN" 1827183 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-787 1814615 1823363 1824175 "NSUP" 1825759 NIL NSUP (NIL T) -8 NIL NIL NIL) (-786 1814247 1814304 1814413 "NSUP2" 1814552 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-785 1804475 1814021 1814154 "NSMP" 1814159 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-784 1802907 1803208 1803565 "NREP" 1804163 NIL NREP (NIL T) -7 NIL NIL NIL) (-783 1801498 1801750 1802108 "NPCOEF" 1802650 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-782 1800564 1800679 1800895 "NORMRETR" 1801379 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-781 1798605 1798895 1799304 "NORMPK" 1800272 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-780 1798290 1798318 1798442 "NORMMA" 1798571 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-779 1798090 1798247 1798276 "NONE" 1798281 T NONE (NIL) -8 NIL NIL NIL) (-778 1797879 1797908 1797977 "NONE1" 1798054 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-777 1797376 1797438 1797617 "NODE1" 1797811 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-776 1795661 1796512 1796767 "NNI" 1797114 T NNI (NIL) -8 NIL NIL 1797349) (-775 1794081 1794394 1794758 "NLINSOL" 1795329 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-774 1790322 1791317 1792216 "NIPROB" 1793202 T NIPROB (NIL) -8 NIL NIL NIL) (-773 1789079 1789313 1789615 "NFINTBAS" 1790084 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-772 1788253 1788729 1788770 "NETCLT" 1788942 NIL NETCLT (NIL T) -9 NIL 1789024 NIL) (-771 1786961 1787192 1787473 "NCODIV" 1788021 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-770 1786723 1786760 1786835 "NCNTFRAC" 1786918 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-769 1784903 1785267 1785687 "NCEP" 1786348 NIL NCEP (NIL T) -7 NIL NIL NIL) (-768 1783754 1784527 1784555 "NASRING" 1784665 T NASRING (NIL) -9 NIL 1784745 NIL) (-767 1783549 1783593 1783687 "NASRING-" 1783692 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-766 1782656 1783181 1783209 "NARNG" 1783326 T NARNG (NIL) -9 NIL 1783417 NIL) (-765 1782348 1782415 1782549 "NARNG-" 1782554 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-764 1781227 1781434 1781669 "NAGSP" 1782133 T NAGSP (NIL) -7 NIL NIL NIL) (-763 1772499 1774183 1775856 "NAGS" 1779574 T NAGS (NIL) -7 NIL NIL NIL) (-762 1771047 1771355 1771686 "NAGF07" 1772188 T NAGF07 (NIL) -7 NIL NIL NIL) (-761 1765585 1766876 1768183 "NAGF04" 1769760 T NAGF04 (NIL) -7 NIL NIL NIL) (-760 1758553 1760167 1761800 "NAGF02" 1763972 T NAGF02 (NIL) -7 NIL NIL NIL) (-759 1753777 1754877 1755994 "NAGF01" 1757456 T NAGF01 (NIL) -7 NIL NIL NIL) (-758 1747405 1748971 1750556 "NAGE04" 1752212 T NAGE04 (NIL) -7 NIL NIL NIL) (-757 1738574 1740695 1742825 "NAGE02" 1745295 T NAGE02 (NIL) -7 NIL NIL NIL) (-756 1734527 1735474 1736438 "NAGE01" 1737630 T NAGE01 (NIL) -7 NIL NIL NIL) (-755 1732322 1732856 1733414 "NAGD03" 1733989 T NAGD03 (NIL) -7 NIL NIL NIL) (-754 1724072 1726000 1727954 "NAGD02" 1730388 T NAGD02 (NIL) -7 NIL NIL NIL) (-753 1717883 1719308 1720748 "NAGD01" 1722652 T NAGD01 (NIL) -7 NIL NIL NIL) (-752 1714092 1714914 1715751 "NAGC06" 1717066 T NAGC06 (NIL) -7 NIL NIL NIL) (-751 1712557 1712889 1713245 "NAGC05" 1713756 T NAGC05 (NIL) -7 NIL NIL NIL) (-750 1711933 1712052 1712196 "NAGC02" 1712433 T NAGC02 (NIL) -7 NIL NIL NIL) (-749 1710892 1711475 1711515 "NAALG" 1711594 NIL NAALG (NIL T) -9 NIL 1711655 NIL) (-748 1710727 1710756 1710846 "NAALG-" 1710851 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-747 1704677 1705785 1706972 "MULTSQFR" 1709623 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-746 1703996 1704071 1704255 "MULTFACT" 1704589 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-745 1696720 1700633 1700686 "MTSCAT" 1701756 NIL MTSCAT (NIL T T) -9 NIL 1702271 NIL) (-744 1696432 1696486 1696578 "MTHING" 1696660 NIL MTHING (NIL T) -7 NIL NIL NIL) (-743 1696224 1696257 1696317 "MSYSCMD" 1696392 T MSYSCMD (NIL) -7 NIL NIL NIL) (-742 1692306 1694979 1695299 "MSET" 1695937 NIL MSET (NIL T) -8 NIL NIL NIL) (-741 1689375 1691867 1691908 "MSETAGG" 1691913 NIL MSETAGG (NIL T) -9 NIL 1691947 NIL) (-740 1685216 1686754 1687499 "MRING" 1688675 NIL MRING (NIL T T) -8 NIL NIL NIL) (-739 1684782 1684849 1684980 "MRF2" 1685143 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-738 1684400 1684435 1684579 "MRATFAC" 1684741 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-737 1682012 1682307 1682738 "MPRFF" 1684105 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-736 1676309 1681866 1681963 "MPOLY" 1681968 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-735 1675799 1675834 1676042 "MPCPF" 1676268 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-734 1675313 1675356 1675540 "MPC3" 1675750 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1674508 1674589 1674810 "MPC2" 1675228 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-732 1672809 1673146 1673536 "MONOTOOL" 1674168 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-731 1672034 1672351 1672379 "MONOID" 1672598 T MONOID (NIL) -9 NIL 1672745 NIL) (-730 1671580 1671699 1671880 "MONOID-" 1671885 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-729 1662055 1668006 1668065 "MONOGEN" 1668739 NIL MONOGEN (NIL T T) -9 NIL 1669195 NIL) (-728 1659273 1660008 1661008 "MONOGEN-" 1661127 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-727 1658106 1658552 1658580 "MONADWU" 1658972 T MONADWU (NIL) -9 NIL 1659210 NIL) (-726 1657478 1657637 1657885 "MONADWU-" 1657890 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-725 1656837 1657081 1657109 "MONAD" 1657316 T MONAD (NIL) -9 NIL 1657428 NIL) (-724 1656522 1656600 1656732 "MONAD-" 1656737 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-723 1654811 1655435 1655714 "MOEBIUS" 1656275 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-722 1654089 1654493 1654533 "MODULE" 1654538 NIL MODULE (NIL T) -9 NIL 1654577 NIL) (-721 1653657 1653753 1653943 "MODULE-" 1653948 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-720 1651337 1652021 1652348 "MODRING" 1653481 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-719 1648281 1649442 1649963 "MODOP" 1650866 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-718 1646869 1647348 1647625 "MODMONOM" 1648144 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-717 1636911 1645160 1645574 "MODMON" 1646506 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-716 1634067 1635755 1636031 "MODFIELD" 1636786 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1633044 1633348 1633538 "MMLFORM" 1633897 T MMLFORM (NIL) -8 NIL NIL NIL) (-714 1632570 1632613 1632792 "MMAP" 1632995 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-713 1630649 1631416 1631457 "MLO" 1631880 NIL MLO (NIL T) -9 NIL 1632122 NIL) (-712 1628015 1628531 1629133 "MLIFT" 1630130 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-711 1627406 1627490 1627644 "MKUCFUNC" 1627926 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-710 1627005 1627075 1627198 "MKRECORD" 1627329 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-709 1626052 1626214 1626442 "MKFUNC" 1626816 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-708 1625440 1625544 1625700 "MKFLCFN" 1625935 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-707 1624717 1624819 1625004 "MKBCFUNC" 1625333 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-706 1621424 1624271 1624407 "MINT" 1624601 T MINT (NIL) -8 NIL NIL NIL) (-705 1620236 1620479 1620756 "MHROWRED" 1621179 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-704 1615616 1618771 1619176 "MFLOAT" 1619851 T MFLOAT (NIL) -8 NIL NIL NIL) (-703 1614973 1615049 1615220 "MFINFACT" 1615528 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-702 1611288 1612136 1613020 "MESH" 1614109 T MESH (NIL) -7 NIL NIL NIL) (-701 1609678 1609990 1610343 "MDDFACT" 1610975 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-700 1606473 1608837 1608878 "MDAGG" 1609133 NIL MDAGG (NIL T) -9 NIL 1609276 NIL) (-699 1596213 1605766 1605973 "MCMPLX" 1606286 T MCMPLX (NIL) -8 NIL NIL NIL) (-698 1595354 1595500 1595700 "MCDEN" 1596062 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-697 1593244 1593514 1593894 "MCALCFN" 1595084 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-696 1592169 1592409 1592642 "MAYBE" 1593050 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-695 1589781 1590304 1590866 "MATSTOR" 1591640 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-694 1585738 1589153 1589401 "MATRIX" 1589566 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-693 1581502 1582211 1582947 "MATLIN" 1585095 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-692 1571608 1574794 1574871 "MATCAT" 1579751 NIL MATCAT (NIL T T T) -9 NIL 1581168 NIL) (-691 1567964 1568985 1570341 "MATCAT-" 1570346 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-690 1566558 1566711 1567044 "MATCAT2" 1567799 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-689 1564670 1564994 1565378 "MAPPKG3" 1566233 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-688 1563651 1563824 1564046 "MAPPKG2" 1564494 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-687 1562150 1562434 1562761 "MAPPKG1" 1563357 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-686 1561229 1561556 1561733 "MAPPAST" 1561993 T MAPPAST (NIL) -8 NIL NIL NIL) (-685 1560840 1560898 1561021 "MAPHACK3" 1561165 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-684 1560432 1560493 1560607 "MAPHACK2" 1560772 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-683 1559869 1559973 1560115 "MAPHACK1" 1560323 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-682 1557948 1558569 1558873 "MAGMA" 1559597 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-681 1557427 1557672 1557763 "MACROAST" 1557877 T MACROAST (NIL) -8 NIL NIL NIL) (-680 1553845 1555666 1556127 "M3D" 1556999 NIL M3D (NIL T) -8 NIL NIL NIL) (-679 1547951 1552214 1552255 "LZSTAGG" 1553037 NIL LZSTAGG (NIL T) -9 NIL 1553332 NIL) (-678 1543908 1545082 1546539 "LZSTAGG-" 1546544 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-677 1540995 1541799 1542286 "LWORD" 1543453 NIL LWORD (NIL T) -8 NIL NIL NIL) (-676 1540571 1540799 1540874 "LSTAST" 1540940 T LSTAST (NIL) -8 NIL NIL NIL) (-675 1533737 1540342 1540476 "LSQM" 1540481 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-674 1532961 1533100 1533328 "LSPP" 1533592 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-673 1530773 1531074 1531530 "LSMP" 1532650 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-672 1527552 1528226 1528956 "LSMP1" 1530075 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-671 1521429 1526719 1526760 "LSAGG" 1526822 NIL LSAGG (NIL T) -9 NIL 1526900 NIL) (-670 1518124 1519048 1520261 "LSAGG-" 1520266 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-669 1515723 1517268 1517517 "LPOLY" 1517919 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-668 1515305 1515390 1515513 "LPEFRAC" 1515632 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-667 1513626 1514399 1514652 "LO" 1515137 NIL LO (NIL T T T) -8 NIL NIL NIL) (-666 1513278 1513390 1513418 "LOGIC" 1513529 T LOGIC (NIL) -9 NIL 1513610 NIL) (-665 1513140 1513163 1513234 "LOGIC-" 1513239 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-664 1512333 1512473 1512666 "LODOOPS" 1512996 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-663 1509756 1512249 1512315 "LODO" 1512320 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-662 1508294 1508529 1508882 "LODOF" 1509503 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-661 1504512 1506943 1506984 "LODOCAT" 1507422 NIL LODOCAT (NIL T) -9 NIL 1507633 NIL) (-660 1504245 1504303 1504430 "LODOCAT-" 1504435 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-659 1501565 1504086 1504204 "LODO2" 1504209 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-658 1499000 1501502 1501547 "LODO1" 1501552 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-657 1497881 1498046 1498351 "LODEEF" 1498823 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-656 1493120 1496011 1496052 "LNAGG" 1496999 NIL LNAGG (NIL T) -9 NIL 1497443 NIL) (-655 1492267 1492481 1492823 "LNAGG-" 1492828 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-654 1488403 1489192 1489831 "LMOPS" 1491682 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-653 1487806 1488194 1488235 "LMODULE" 1488240 NIL LMODULE (NIL T) -9 NIL 1488266 NIL) (-652 1485004 1487451 1487574 "LMDICT" 1487716 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-651 1484410 1484631 1484672 "LLINSET" 1484863 NIL LLINSET (NIL T) -9 NIL 1484954 NIL) (-650 1484109 1484318 1484378 "LITERAL" 1484383 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-649 1477272 1483043 1483347 "LIST" 1483838 NIL LIST (NIL T) -8 NIL NIL NIL) (-648 1476797 1476871 1477010 "LIST3" 1477192 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-647 1475804 1475982 1476210 "LIST2" 1476615 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-646 1473938 1474250 1474649 "LIST2MAP" 1475451 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-645 1473534 1473771 1473812 "LINSET" 1473817 NIL LINSET (NIL T) -9 NIL 1473851 NIL) (-644 1472195 1472865 1472906 "LINEXP" 1473161 NIL LINEXP (NIL T) -9 NIL 1473310 NIL) (-643 1470842 1471102 1471399 "LINDEP" 1471947 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-642 1467609 1468328 1469105 "LIMITRF" 1470097 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-641 1465912 1466208 1466617 "LIMITPS" 1467304 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-640 1460340 1465423 1465651 "LIE" 1465733 NIL LIE (NIL T T) -8 NIL NIL NIL) (-639 1459288 1459757 1459797 "LIECAT" 1459937 NIL LIECAT (NIL T) -9 NIL 1460088 NIL) (-638 1459129 1459156 1459244 "LIECAT-" 1459249 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-637 1451625 1458578 1458743 "LIB" 1458984 T LIB (NIL) -8 NIL NIL NIL) (-636 1447260 1448143 1449078 "LGROBP" 1450742 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-635 1445258 1445532 1445882 "LF" 1446981 NIL LF (NIL T T) -7 NIL NIL NIL) (-634 1444098 1444790 1444818 "LFCAT" 1445025 T LFCAT (NIL) -9 NIL 1445164 NIL) (-633 1441000 1441630 1442318 "LEXTRIPK" 1443462 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-632 1437744 1438570 1439073 "LEXP" 1440580 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-631 1437220 1437465 1437557 "LETAST" 1437672 T LETAST (NIL) -8 NIL NIL NIL) (-630 1435618 1435931 1436332 "LEADCDET" 1436902 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-629 1434808 1434882 1435111 "LAZM3PK" 1435539 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-628 1429725 1432885 1433423 "LAUPOL" 1434320 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-627 1429304 1429348 1429509 "LAPLACE" 1429675 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-626 1427243 1428405 1428656 "LA" 1429137 NIL LA (NIL T T T) -8 NIL NIL NIL) (-625 1426237 1426821 1426862 "LALG" 1426924 NIL LALG (NIL T) -9 NIL 1426983 NIL) (-624 1425951 1426010 1426146 "LALG-" 1426151 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-623 1425786 1425810 1425851 "KVTFROM" 1425913 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-622 1424709 1425153 1425338 "KTVLOGIC" 1425621 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-621 1424544 1424568 1424609 "KRCFROM" 1424671 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-620 1423448 1423635 1423934 "KOVACIC" 1424344 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-619 1423283 1423307 1423348 "KONVERT" 1423410 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-618 1423118 1423142 1423183 "KOERCE" 1423245 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-617 1420948 1421711 1422088 "KERNEL" 1422774 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-616 1420444 1420525 1420657 "KERNEL2" 1420862 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-615 1414214 1418983 1419037 "KDAGG" 1419414 NIL KDAGG (NIL T T) -9 NIL 1419620 NIL) (-614 1413743 1413867 1414072 "KDAGG-" 1414077 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1406891 1413404 1413559 "KAFILE" 1413621 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-612 1401319 1406402 1406630 "JORDAN" 1406712 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-611 1400698 1400968 1401089 "JOINAST" 1401218 T JOINAST (NIL) -8 NIL NIL NIL) (-610 1400544 1400603 1400658 "JAVACODE" 1400663 T JAVACODE (NIL) -8 NIL NIL NIL) (-609 1396796 1398749 1398803 "IXAGG" 1399732 NIL IXAGG (NIL T T) -9 NIL 1400191 NIL) (-608 1395715 1396021 1396440 "IXAGG-" 1396445 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-607 1391245 1395637 1395696 "IVECTOR" 1395701 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-606 1390011 1390248 1390514 "ITUPLE" 1391012 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-605 1388513 1388690 1388985 "ITRIGMNP" 1389833 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-604 1387258 1387462 1387745 "ITFUN3" 1388289 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-603 1386890 1386947 1387056 "ITFUN2" 1387195 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-602 1386049 1386370 1386544 "ITFORM" 1386736 T ITFORM (NIL) -8 NIL NIL NIL) (-601 1384010 1385069 1385347 "ITAYLOR" 1385804 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-600 1372955 1378147 1379310 "ISUPS" 1382880 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-599 1372059 1372199 1372435 "ISUMP" 1372802 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-598 1367434 1372004 1372045 "ISTRING" 1372050 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-597 1366910 1367155 1367247 "ISAST" 1367362 T ISAST (NIL) -8 NIL NIL NIL) (-596 1366119 1366201 1366417 "IRURPK" 1366824 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-595 1365055 1365256 1365496 "IRSN" 1365899 T IRSN (NIL) -7 NIL NIL NIL) (-594 1363126 1363481 1363910 "IRRF2F" 1364693 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-593 1362873 1362911 1362987 "IRREDFFX" 1363082 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-592 1361488 1361747 1362046 "IROOT" 1362606 NIL IROOT (NIL T) -7 NIL NIL NIL) (-591 1358092 1359172 1359864 "IR" 1360828 NIL IR (NIL T) -8 NIL NIL NIL) (-590 1357297 1357585 1357736 "IRFORM" 1357961 T IRFORM (NIL) -8 NIL NIL NIL) (-589 1354910 1355405 1355971 "IR2" 1356775 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-588 1354010 1354123 1354337 "IR2F" 1354793 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-587 1353801 1353835 1353895 "IPRNTPK" 1353970 T IPRNTPK (NIL) -7 NIL NIL NIL) (-586 1350382 1353690 1353759 "IPF" 1353764 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-585 1348709 1350307 1350364 "IPADIC" 1350369 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-584 1348021 1348269 1348399 "IP4ADDR" 1348599 T IP4ADDR (NIL) -8 NIL NIL NIL) (-583 1347494 1347725 1347835 "IOMODE" 1347931 T IOMODE (NIL) -8 NIL NIL NIL) (-582 1346567 1347091 1347218 "IOBFILE" 1347387 T IOBFILE (NIL) -8 NIL NIL NIL) (-581 1346055 1346471 1346499 "IOBCON" 1346504 T IOBCON (NIL) -9 NIL 1346525 NIL) (-580 1345566 1345624 1345807 "INVLAPLA" 1345991 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-579 1335214 1337568 1339954 "INTTR" 1343230 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-578 1331549 1332291 1333156 "INTTOOLS" 1334399 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-577 1331135 1331226 1331343 "INTSLPE" 1331452 T INTSLPE (NIL) -7 NIL NIL NIL) (-576 1329088 1331058 1331117 "INTRVL" 1331122 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-575 1326690 1327202 1327777 "INTRF" 1328573 NIL INTRF (NIL T) -7 NIL NIL NIL) (-574 1326101 1326198 1326340 "INTRET" 1326588 NIL INTRET (NIL T) -7 NIL NIL NIL) (-573 1324098 1324487 1324957 "INTRAT" 1325709 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-572 1321361 1321944 1322563 "INTPM" 1323583 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-571 1318106 1318705 1319443 "INTPAF" 1320747 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-570 1313285 1314247 1315298 "INTPACK" 1317075 T INTPACK (NIL) -7 NIL NIL NIL) (-569 1310233 1313082 1313191 "INT" 1313196 T INT (NIL) -8 NIL NIL NIL) (-568 1309485 1309637 1309845 "INTHERTR" 1310075 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-567 1308924 1309004 1309192 "INTHERAL" 1309399 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-566 1306770 1307213 1307670 "INTHEORY" 1308487 T INTHEORY (NIL) -7 NIL NIL NIL) (-565 1298176 1299797 1301569 "INTG0" 1305122 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-564 1278749 1283539 1288349 "INTFTBL" 1293386 T INTFTBL (NIL) -8 NIL NIL NIL) (-563 1277998 1278136 1278309 "INTFACT" 1278608 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-562 1275425 1275871 1276428 "INTEF" 1277552 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-561 1273792 1274531 1274559 "INTDOM" 1274860 T INTDOM (NIL) -9 NIL 1275067 NIL) (-560 1273161 1273335 1273577 "INTDOM-" 1273582 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-559 1269549 1271477 1271531 "INTCAT" 1272330 NIL INTCAT (NIL T) -9 NIL 1272651 NIL) (-558 1269021 1269124 1269252 "INTBIT" 1269441 T INTBIT (NIL) -7 NIL NIL NIL) (-557 1267720 1267874 1268181 "INTALG" 1268866 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-556 1267203 1267293 1267450 "INTAF" 1267624 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-555 1260546 1267013 1267153 "INTABL" 1267158 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-554 1259887 1260353 1260418 "INT8" 1260452 T INT8 (NIL) -8 NIL NIL 1260497) (-553 1259227 1259693 1259758 "INT64" 1259792 T INT64 (NIL) -8 NIL NIL 1259837) (-552 1258567 1259033 1259098 "INT32" 1259132 T INT32 (NIL) -8 NIL NIL 1259177) (-551 1257907 1258373 1258438 "INT16" 1258472 T INT16 (NIL) -8 NIL NIL 1258517) (-550 1252817 1255530 1255558 "INS" 1256492 T INS (NIL) -9 NIL 1257157 NIL) (-549 1250057 1250828 1251802 "INS-" 1251875 NIL INS- (NIL T) -8 NIL NIL NIL) (-548 1248832 1249059 1249357 "INPSIGN" 1249810 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-547 1247950 1248067 1248264 "INPRODPF" 1248712 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-546 1246844 1246961 1247198 "INPRODFF" 1247830 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-545 1245844 1245996 1246256 "INNMFACT" 1246680 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-544 1245041 1245138 1245326 "INMODGCD" 1245743 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-543 1243549 1243794 1244118 "INFSP" 1244786 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-542 1242733 1242850 1243033 "INFPROD0" 1243429 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-541 1239588 1240798 1241313 "INFORM" 1242226 T INFORM (NIL) -8 NIL NIL NIL) (-540 1239198 1239258 1239356 "INFORM1" 1239523 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-539 1238721 1238810 1238924 "INFINITY" 1239104 T INFINITY (NIL) -7 NIL NIL NIL) (-538 1237897 1238441 1238542 "INETCLTS" 1238640 T INETCLTS (NIL) -8 NIL NIL NIL) (-537 1236513 1236763 1237084 "INEP" 1237645 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-536 1235762 1236410 1236475 "INDE" 1236480 NIL INDE (NIL T) -8 NIL NIL NIL) (-535 1235326 1235394 1235511 "INCRMAPS" 1235689 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-534 1234144 1234595 1234801 "INBFILE" 1235140 T INBFILE (NIL) -8 NIL NIL NIL) (-533 1229444 1230380 1231324 "INBFF" 1233232 NIL INBFF (NIL T) -7 NIL NIL NIL) (-532 1228352 1228621 1228649 "INBCON" 1229162 T INBCON (NIL) -9 NIL 1229428 NIL) (-531 1227604 1227827 1228103 "INBCON-" 1228108 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-530 1227083 1227328 1227419 "INAST" 1227533 T INAST (NIL) -8 NIL NIL NIL) (-529 1226510 1226762 1226868 "IMPTAST" 1226997 T IMPTAST (NIL) -8 NIL NIL NIL) (-528 1222956 1226354 1226458 "IMATRIX" 1226463 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-527 1221668 1221791 1222106 "IMATQF" 1222812 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-526 1219888 1220115 1220452 "IMATLIN" 1221424 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-525 1214466 1219812 1219870 "ILIST" 1219875 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-524 1212371 1214326 1214439 "IIARRAY2" 1214444 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-523 1207769 1212282 1212346 "IFF" 1212351 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-522 1207116 1207386 1207502 "IFAST" 1207673 T IFAST (NIL) -8 NIL NIL NIL) (-521 1202111 1206408 1206596 "IFARRAY" 1206973 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-520 1201291 1202015 1202088 "IFAMON" 1202093 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-519 1200875 1200940 1200994 "IEVALAB" 1201201 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-518 1200550 1200618 1200778 "IEVALAB-" 1200783 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-517 1200181 1200464 1200527 "IDPO" 1200532 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-516 1199431 1200070 1200145 "IDPOAMS" 1200150 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-515 1198738 1199320 1199395 "IDPOAM" 1199400 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-514 1197797 1198073 1198126 "IDPC" 1198539 NIL IDPC (NIL T T) -9 NIL 1198688 NIL) (-513 1197266 1197689 1197762 "IDPAM" 1197767 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-512 1196642 1197158 1197231 "IDPAG" 1197236 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-511 1196287 1196478 1196553 "IDENT" 1196587 T IDENT (NIL) -8 NIL NIL NIL) (-510 1192542 1193390 1194285 "IDECOMP" 1195444 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-509 1185380 1186465 1187512 "IDEAL" 1191578 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-508 1184544 1184656 1184855 "ICDEN" 1185264 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-507 1183615 1184024 1184171 "ICARD" 1184417 T ICARD (NIL) -8 NIL NIL NIL) (-506 1181675 1181988 1182393 "IBPTOOLS" 1183292 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-505 1177282 1181295 1181408 "IBITS" 1181594 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-504 1174005 1174581 1175276 "IBATOOL" 1176699 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-503 1171784 1172246 1172779 "IBACHIN" 1173540 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-502 1169613 1171630 1171733 "IARRAY2" 1171738 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-501 1165719 1169539 1169596 "IARRAY1" 1169601 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-500 1159828 1164131 1164612 "IAN" 1165258 T IAN (NIL) -8 NIL NIL NIL) (-499 1159339 1159396 1159569 "IALGFACT" 1159765 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-498 1158867 1158980 1159008 "HYPCAT" 1159215 T HYPCAT (NIL) -9 NIL NIL NIL) (-497 1158405 1158522 1158708 "HYPCAT-" 1158713 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-496 1158000 1158200 1158283 "HOSTNAME" 1158342 T HOSTNAME (NIL) -8 NIL NIL NIL) (-495 1157845 1157882 1157923 "HOMOTOP" 1157928 NIL HOMOTOP (NIL T) -9 NIL 1157961 NIL) (-494 1154477 1155855 1155896 "HOAGG" 1156877 NIL HOAGG (NIL T) -9 NIL 1157556 NIL) (-493 1153071 1153470 1153996 "HOAGG-" 1154001 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-492 1147075 1152666 1152815 "HEXADEC" 1152942 T HEXADEC (NIL) -8 NIL NIL NIL) (-491 1145823 1146045 1146308 "HEUGCD" 1146852 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-490 1144899 1145660 1145790 "HELLFDIV" 1145795 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-489 1143078 1144676 1144764 "HEAP" 1144843 NIL HEAP (NIL T) -8 NIL NIL NIL) (-488 1142341 1142630 1142764 "HEADAST" 1142964 T HEADAST (NIL) -8 NIL NIL NIL) (-487 1136207 1142256 1142318 "HDP" 1142323 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-486 1130195 1135842 1135994 "HDMP" 1136108 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-485 1129519 1129659 1129823 "HB" 1130051 T HB (NIL) -7 NIL NIL NIL) (-484 1122905 1129365 1129469 "HASHTBL" 1129474 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-483 1122381 1122626 1122718 "HASAST" 1122833 T HASAST (NIL) -8 NIL NIL NIL) (-482 1120159 1122003 1122185 "HACKPI" 1122219 T HACKPI (NIL) -8 NIL NIL NIL) (-481 1115827 1120012 1120125 "GTSET" 1120130 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-480 1109242 1115705 1115803 "GSTBL" 1115808 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-479 1101520 1108273 1108538 "GSERIES" 1109033 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-478 1100661 1101078 1101106 "GROUP" 1101309 T GROUP (NIL) -9 NIL 1101443 NIL) (-477 1100027 1100186 1100437 "GROUP-" 1100442 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-476 1098394 1098715 1099102 "GROEBSOL" 1099704 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-475 1097308 1097596 1097647 "GRMOD" 1098176 NIL GRMOD (NIL T T) -9 NIL 1098344 NIL) (-474 1097076 1097112 1097240 "GRMOD-" 1097245 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-473 1092366 1093430 1094430 "GRIMAGE" 1096096 T GRIMAGE (NIL) -8 NIL NIL NIL) (-472 1090832 1091093 1091417 "GRDEF" 1092062 T GRDEF (NIL) -7 NIL NIL NIL) (-471 1090276 1090392 1090533 "GRAY" 1090711 T GRAY (NIL) -7 NIL NIL NIL) (-470 1089463 1089869 1089920 "GRALG" 1090073 NIL GRALG (NIL T T) -9 NIL 1090166 NIL) (-469 1089124 1089197 1089360 "GRALG-" 1089365 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-468 1085901 1088709 1088887 "GPOLSET" 1089031 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-467 1085255 1085312 1085570 "GOSPER" 1085838 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-466 1080987 1081693 1082219 "GMODPOL" 1084954 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-465 1079992 1080176 1080414 "GHENSEL" 1080799 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-464 1074148 1074991 1076011 "GENUPS" 1079076 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-463 1073845 1073896 1073985 "GENUFACT" 1074091 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-462 1073257 1073334 1073499 "GENPGCD" 1073763 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-461 1072731 1072766 1072979 "GENMFACT" 1073216 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-460 1071297 1071554 1071861 "GENEEZ" 1072474 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-459 1065443 1070908 1071070 "GDMP" 1071220 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-458 1054785 1059214 1060320 "GCNAALG" 1064426 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-457 1053112 1053974 1054002 "GCDDOM" 1054257 T GCDDOM (NIL) -9 NIL 1054414 NIL) (-456 1052582 1052709 1052924 "GCDDOM-" 1052929 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-455 1051254 1051439 1051743 "GB" 1052361 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-454 1039870 1042200 1044592 "GBINTERN" 1048945 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-453 1037707 1037999 1038420 "GBF" 1039545 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-452 1036488 1036653 1036920 "GBEUCLID" 1037523 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-451 1035837 1035962 1036111 "GAUSSFAC" 1036359 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-450 1034204 1034506 1034820 "GALUTIL" 1035556 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-449 1032512 1032786 1033110 "GALPOLYU" 1033931 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-448 1029877 1030167 1030574 "GALFACTU" 1032209 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-447 1021682 1023182 1024790 "GALFACT" 1028309 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-446 1019070 1019728 1019756 "FVFUN" 1020912 T FVFUN (NIL) -9 NIL 1021632 NIL) (-445 1018336 1018518 1018546 "FVC" 1018837 T FVC (NIL) -9 NIL 1019020 NIL) (-444 1017979 1018161 1018229 "FUNDESC" 1018288 T FUNDESC (NIL) -8 NIL NIL NIL) (-443 1017594 1017776 1017857 "FUNCTION" 1017931 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-442 1015338 1015916 1016382 "FT" 1017148 T FT (NIL) -8 NIL NIL NIL) (-441 1014129 1014639 1014842 "FTEM" 1015155 T FTEM (NIL) -8 NIL NIL NIL) (-440 1012420 1012709 1013106 "FSUPFACT" 1013820 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-439 1010817 1011106 1011438 "FST" 1012108 T FST (NIL) -8 NIL NIL NIL) (-438 1010016 1010122 1010310 "FSRED" 1010699 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-437 1008715 1008971 1009318 "FSPRMELT" 1009731 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-436 1006021 1006459 1006945 "FSPECF" 1008278 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-435 987659 995990 996031 "FS" 999915 NIL FS (NIL T) -9 NIL 1002204 NIL) (-434 976302 979295 983352 "FS-" 983652 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 975830 975884 976054 "FSINT" 976243 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-432 974122 974823 975126 "FSERIES" 975609 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-431 973164 973280 973504 "FSCINT" 974002 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-430 969372 972108 972149 "FSAGG" 972519 NIL FSAGG (NIL T) -9 NIL 972778 NIL) (-429 967134 967735 968531 "FSAGG-" 968626 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-428 966176 966319 966546 "FSAGG2" 966987 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-427 963858 964138 964685 "FS2UPS" 965894 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-426 963492 963535 963664 "FS2" 963809 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-425 962370 962541 962843 "FS2EXPXP" 963317 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-424 961796 961911 962063 "FRUTIL" 962250 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-423 953209 957291 958649 "FR" 960470 NIL FR (NIL T) -8 NIL NIL NIL) (-422 948178 950852 950892 "FRNAALG" 952288 NIL FRNAALG (NIL T) -9 NIL 952895 NIL) (-421 943851 944927 946202 "FRNAALG-" 946952 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-420 943489 943532 943659 "FRNAAF2" 943802 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-419 941869 942343 942638 "FRMOD" 943301 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-418 939620 940252 940569 "FRIDEAL" 941660 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-417 938815 938902 939191 "FRIDEAL2" 939527 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-416 937948 938362 938403 "FRETRCT" 938408 NIL FRETRCT (NIL T) -9 NIL 938584 NIL) (-415 937060 937291 937642 "FRETRCT-" 937647 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-414 934148 935358 935417 "FRAMALG" 936299 NIL FRAMALG (NIL T T) -9 NIL 936591 NIL) (-413 932282 932737 933367 "FRAMALG-" 933590 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-412 926203 931757 932033 "FRAC" 932038 NIL FRAC (NIL T) -8 NIL NIL NIL) (-411 925839 925896 926003 "FRAC2" 926140 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-410 925475 925532 925639 "FR2" 925776 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-409 919988 922881 922909 "FPS" 924028 T FPS (NIL) -9 NIL 924585 NIL) (-408 919437 919546 919710 "FPS-" 919856 NIL FPS- (NIL T) -8 NIL NIL NIL) (-407 916739 918408 918436 "FPC" 918661 T FPC (NIL) -9 NIL 918803 NIL) (-406 916532 916572 916669 "FPC-" 916674 NIL FPC- (NIL T) -8 NIL NIL NIL) (-405 915322 916020 916061 "FPATMAB" 916066 NIL FPATMAB (NIL T) -9 NIL 916218 NIL) (-404 912995 913498 913924 "FPARFRAC" 914959 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-403 908389 908887 909569 "FORTRAN" 912427 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-402 906105 906605 907144 "FORT" 907870 T FORT (NIL) -7 NIL NIL NIL) (-401 903781 904343 904371 "FORTFN" 905431 T FORTFN (NIL) -9 NIL 906055 NIL) (-400 903545 903595 903623 "FORTCAT" 903682 T FORTCAT (NIL) -9 NIL 903744 NIL) (-399 901651 902161 902551 "FORMULA" 903175 T FORMULA (NIL) -8 NIL NIL NIL) (-398 901439 901469 901538 "FORMULA1" 901615 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-397 900962 901014 901187 "FORDER" 901381 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-396 900058 900222 900415 "FOP" 900789 T FOP (NIL) -7 NIL NIL NIL) (-395 898639 899338 899512 "FNLA" 899940 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-394 897368 897783 897811 "FNCAT" 898271 T FNCAT (NIL) -9 NIL 898531 NIL) (-393 896907 897327 897355 "FNAME" 897360 T FNAME (NIL) -8 NIL NIL NIL) (-392 895470 896433 896461 "FMTC" 896466 T FMTC (NIL) -9 NIL 896502 NIL) (-391 894216 895406 895452 "FMONOID" 895457 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-390 891044 892212 892253 "FMONCAT" 893470 NIL FMONCAT (NIL T) -9 NIL 894075 NIL) (-389 890236 890786 890935 "FM" 890940 NIL FM (NIL T T) -8 NIL NIL NIL) (-388 887660 888306 888334 "FMFUN" 889478 T FMFUN (NIL) -9 NIL 890186 NIL) (-387 886929 887110 887138 "FMC" 887428 T FMC (NIL) -9 NIL 887610 NIL) (-386 884008 884868 884922 "FMCAT" 886117 NIL FMCAT (NIL T T) -9 NIL 886612 NIL) (-385 882874 883774 883874 "FM1" 883953 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-384 880648 881064 881558 "FLOATRP" 882425 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-383 874222 878377 878998 "FLOAT" 880047 T FLOAT (NIL) -8 NIL NIL NIL) (-382 871660 872160 872738 "FLOATCP" 873689 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-381 870400 871238 871279 "FLINEXP" 871284 NIL FLINEXP (NIL T) -9 NIL 871377 NIL) (-380 869554 869789 870117 "FLINEXP-" 870122 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-379 868630 868774 868998 "FLASORT" 869406 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-378 865746 866614 866666 "FLALG" 867893 NIL FLALG (NIL T T) -9 NIL 868360 NIL) (-377 859482 863232 863273 "FLAGG" 864535 NIL FLAGG (NIL T) -9 NIL 865187 NIL) (-376 858208 858547 859037 "FLAGG-" 859042 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-375 857250 857393 857620 "FLAGG2" 858061 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-374 854101 855109 855168 "FINRALG" 856296 NIL FINRALG (NIL T T) -9 NIL 856804 NIL) (-373 853261 853490 853829 "FINRALG-" 853834 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-372 852641 852880 852908 "FINITE" 853104 T FINITE (NIL) -9 NIL 853211 NIL) (-371 844998 847185 847225 "FINAALG" 850892 NIL FINAALG (NIL T) -9 NIL 852345 NIL) (-370 840330 841380 842524 "FINAALG-" 843903 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-369 839698 840085 840188 "FILE" 840260 NIL FILE (NIL T) -8 NIL NIL NIL) (-368 838356 838694 838748 "FILECAT" 839432 NIL FILECAT (NIL T T) -9 NIL 839648 NIL) (-367 836072 837600 837628 "FIELD" 837668 T FIELD (NIL) -9 NIL 837748 NIL) (-366 834692 835077 835588 "FIELD-" 835593 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-365 832542 833327 833674 "FGROUP" 834378 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-364 831632 831796 832016 "FGLMICPK" 832374 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-363 827464 831557 831614 "FFX" 831619 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-362 827065 827126 827261 "FFSLPE" 827397 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-361 823055 823837 824633 "FFPOLY" 826301 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-360 822559 822595 822804 "FFPOLY2" 823013 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-359 818403 822478 822541 "FFP" 822546 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-358 813801 818314 818378 "FF" 818383 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-357 808927 813144 813334 "FFNBX" 813655 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-356 803855 808062 808320 "FFNBP" 808781 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-355 798488 803139 803350 "FFNB" 803688 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-354 797320 797518 797833 "FFINTBAS" 798285 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-353 793389 795609 795637 "FFIELDC" 796257 T FFIELDC (NIL) -9 NIL 796633 NIL) (-352 792051 792422 792919 "FFIELDC-" 792924 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-351 791620 791666 791790 "FFHOM" 791993 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-350 789315 789802 790319 "FFF" 791135 NIL FFF (NIL T) -7 NIL NIL NIL) (-349 784933 789057 789158 "FFCGX" 789258 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-348 780555 784665 784772 "FFCGP" 784876 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-347 775738 780282 780390 "FFCG" 780491 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-346 757134 766215 766301 "FFCAT" 771466 NIL FFCAT (NIL T T T) -9 NIL 772917 NIL) (-345 752331 753379 754693 "FFCAT-" 755923 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-344 751742 751785 752020 "FFCAT2" 752282 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 741065 744714 745934 "FEXPR" 750594 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-342 740065 740500 740541 "FEVALAB" 740625 NIL FEVALAB (NIL T) -9 NIL 740886 NIL) (-341 739224 739434 739772 "FEVALAB-" 739777 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-340 737790 738607 738810 "FDIV" 739123 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-339 734810 735551 735666 "FDIVCAT" 737234 NIL FDIVCAT (NIL T T T T) -9 NIL 737671 NIL) (-338 734572 734599 734769 "FDIVCAT-" 734774 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-337 733792 733879 734156 "FDIV2" 734479 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-336 732766 733087 733289 "FCTRDATA" 733610 T FCTRDATA (NIL) -8 NIL NIL NIL) (-335 731452 731711 732000 "FCPAK1" 732497 T FCPAK1 (NIL) -7 NIL NIL NIL) (-334 730551 730952 731093 "FCOMP" 731343 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-333 714256 717701 721239 "FC" 727033 T FC (NIL) -8 NIL NIL NIL) (-332 706619 710647 710687 "FAXF" 712489 NIL FAXF (NIL T) -9 NIL 713181 NIL) (-331 703895 704553 705378 "FAXF-" 705843 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-330 698947 703271 703447 "FARRAY" 703752 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-329 693841 695908 695961 "FAMR" 696984 NIL FAMR (NIL T T) -9 NIL 697444 NIL) (-328 692731 693033 693468 "FAMR-" 693473 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-327 691900 692653 692706 "FAMONOID" 692711 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-326 689686 690396 690449 "FAMONC" 691390 NIL FAMONC (NIL T T) -9 NIL 691776 NIL) (-325 688350 689440 689577 "FAGROUP" 689582 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-324 686145 686464 686867 "FACUTIL" 688031 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-323 685244 685429 685651 "FACTFUNC" 685955 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-322 677666 684547 684746 "EXPUPXS" 685100 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-321 675149 675689 676275 "EXPRTUBE" 677100 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-320 671420 672012 672742 "EXPRODE" 674488 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-319 656905 670069 670498 "EXPR" 671024 NIL EXPR (NIL T) -8 NIL NIL NIL) (-318 651459 652046 652852 "EXPR2UPS" 656203 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-317 651091 651148 651257 "EXPR2" 651396 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-316 642481 650244 650534 "EXPEXPAN" 650928 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-315 642281 642438 642467 "EXIT" 642472 T EXIT (NIL) -8 NIL NIL NIL) (-314 641761 642005 642096 "EXITAST" 642210 T EXITAST (NIL) -8 NIL NIL NIL) (-313 641388 641450 641563 "EVALCYC" 641693 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-312 640929 641047 641088 "EVALAB" 641258 NIL EVALAB (NIL T) -9 NIL 641362 NIL) (-311 640410 640532 640753 "EVALAB-" 640758 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-310 637778 639080 639108 "EUCDOM" 639663 T EUCDOM (NIL) -9 NIL 640013 NIL) (-309 636183 636625 637215 "EUCDOM-" 637220 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-308 623721 626481 629231 "ESTOOLS" 633453 T ESTOOLS (NIL) -7 NIL NIL NIL) (-307 623353 623410 623519 "ESTOOLS2" 623658 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-306 623104 623146 623226 "ESTOOLS1" 623305 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-305 617141 618749 618777 "ES" 621545 T ES (NIL) -9 NIL 622955 NIL) (-304 612088 613375 615192 "ES-" 615356 NIL ES- (NIL T) -8 NIL NIL NIL) (-303 608462 609223 610003 "ESCONT" 611328 T ESCONT (NIL) -7 NIL NIL NIL) (-302 608207 608239 608321 "ESCONT1" 608424 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-301 607882 607932 608032 "ES2" 608151 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-300 607512 607570 607679 "ES1" 607818 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-299 606728 606857 607033 "ERROR" 607356 T ERROR (NIL) -7 NIL NIL NIL) (-298 600120 606587 606678 "EQTBL" 606683 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-297 592623 595434 596883 "EQ" 598704 NIL -2071 (NIL T) -8 NIL NIL NIL) (-296 592255 592312 592421 "EQ2" 592560 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-295 587545 588593 589686 "EP" 591194 NIL EP (NIL T) -7 NIL NIL NIL) (-294 586145 586436 586742 "ENV" 587259 T ENV (NIL) -8 NIL NIL NIL) (-293 585239 585793 585821 "ENTIRER" 585826 T ENTIRER (NIL) -9 NIL 585872 NIL) (-292 581706 583194 583564 "EMR" 585038 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-291 580850 581035 581089 "ELTAGG" 581469 NIL ELTAGG (NIL T T) -9 NIL 581680 NIL) (-290 580569 580631 580772 "ELTAGG-" 580777 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-289 580358 580387 580441 "ELTAB" 580525 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-288 579484 579630 579829 "ELFUTS" 580209 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-287 579226 579282 579310 "ELEMFUN" 579415 T ELEMFUN (NIL) -9 NIL NIL NIL) (-286 579096 579117 579185 "ELEMFUN-" 579190 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-285 573940 577196 577237 "ELAGG" 578177 NIL ELAGG (NIL T) -9 NIL 578640 NIL) (-284 572225 572659 573322 "ELAGG-" 573327 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-283 571537 571674 571830 "ELABOR" 572089 T ELABOR (NIL) -8 NIL NIL NIL) (-282 570198 570477 570771 "ELABEXPR" 571263 T ELABEXPR (NIL) -8 NIL NIL NIL) (-281 563062 564865 565692 "EFUPXS" 569474 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-280 556512 558313 559123 "EFULS" 562338 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-279 553997 554355 554827 "EFSTRUC" 556144 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-278 543788 545354 546902 "EF" 552512 NIL EF (NIL T T) -7 NIL NIL NIL) (-277 542862 543273 543422 "EAB" 543659 T EAB (NIL) -8 NIL NIL NIL) (-276 542044 542821 542849 "E04UCFA" 542854 T E04UCFA (NIL) -8 NIL NIL NIL) (-275 541226 542003 542031 "E04NAFA" 542036 T E04NAFA (NIL) -8 NIL NIL NIL) (-274 540408 541185 541213 "E04MBFA" 541218 T E04MBFA (NIL) -8 NIL NIL NIL) (-273 539590 540367 540395 "E04JAFA" 540400 T E04JAFA (NIL) -8 NIL NIL NIL) (-272 538774 539549 539577 "E04GCFA" 539582 T E04GCFA (NIL) -8 NIL NIL NIL) (-271 537958 538733 538761 "E04FDFA" 538766 T E04FDFA (NIL) -8 NIL NIL NIL) (-270 537140 537917 537945 "E04DGFA" 537950 T E04DGFA (NIL) -8 NIL NIL NIL) (-269 531313 532665 534029 "E04AGNT" 535796 T E04AGNT (NIL) -7 NIL NIL NIL) (-268 529993 530499 530539 "DVARCAT" 531014 NIL DVARCAT (NIL T) -9 NIL 531213 NIL) (-267 529197 529409 529723 "DVARCAT-" 529728 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-266 522334 528996 529125 "DSMP" 529130 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-265 517115 518279 519347 "DROPT" 521286 T DROPT (NIL) -8 NIL NIL NIL) (-264 516780 516839 516937 "DROPT1" 517050 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-263 511895 513021 514158 "DROPT0" 515663 T DROPT0 (NIL) -7 NIL NIL NIL) (-262 510240 510565 510951 "DRAWPT" 511529 T DRAWPT (NIL) -7 NIL NIL NIL) (-261 504827 505750 506829 "DRAW" 509214 NIL DRAW (NIL T) -7 NIL NIL NIL) (-260 504460 504513 504631 "DRAWHACK" 504768 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-259 503191 503460 503751 "DRAWCX" 504189 T DRAWCX (NIL) -7 NIL NIL NIL) (-258 502706 502775 502926 "DRAWCURV" 503117 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-257 493174 495136 497251 "DRAWCFUN" 500611 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-256 489938 491867 491908 "DQAGG" 492537 NIL DQAGG (NIL T) -9 NIL 492811 NIL) (-255 478062 484531 484614 "DPOLCAT" 486466 NIL DPOLCAT (NIL T T T T) -9 NIL 487011 NIL) (-254 472898 474247 476205 "DPOLCAT-" 476210 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-253 466020 472759 472857 "DPMO" 472862 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-252 459045 465800 465967 "DPMM" 465972 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-251 458523 458737 458835 "DOMTMPLT" 458967 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-250 457956 458325 458405 "DOMCTOR" 458463 T DOMCTOR (NIL) -8 NIL NIL NIL) (-249 457168 457436 457587 "DOMAIN" 457825 T DOMAIN (NIL) -8 NIL NIL NIL) (-248 451156 456803 456955 "DMP" 457069 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-247 450756 450812 450956 "DLP" 451094 NIL DLP (NIL T) -7 NIL NIL NIL) (-246 444578 450083 450273 "DLIST" 450598 NIL DLIST (NIL T) -8 NIL NIL NIL) (-245 441375 443431 443472 "DLAGG" 444022 NIL DLAGG (NIL T) -9 NIL 444252 NIL) (-244 440051 440715 440743 "DIVRING" 440835 T DIVRING (NIL) -9 NIL 440918 NIL) (-243 439288 439478 439778 "DIVRING-" 439783 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-242 437390 437747 438153 "DISPLAY" 438902 T DISPLAY (NIL) -7 NIL NIL NIL) (-241 431278 437304 437367 "DIRPROD" 437372 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-240 430126 430329 430594 "DIRPROD2" 431071 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-239 418901 424907 424960 "DIRPCAT" 425370 NIL DIRPCAT (NIL NIL T) -9 NIL 426210 NIL) (-238 416227 416869 417750 "DIRPCAT-" 418087 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-237 415514 415674 415860 "DIOSP" 416061 T DIOSP (NIL) -7 NIL NIL NIL) (-236 412169 414426 414467 "DIOPS" 414901 NIL DIOPS (NIL T) -9 NIL 415130 NIL) (-235 411718 411832 412023 "DIOPS-" 412028 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-234 410541 411169 411197 "DIFRING" 411384 T DIFRING (NIL) -9 NIL 411494 NIL) (-233 410187 410264 410416 "DIFRING-" 410421 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-232 407923 409195 409236 "DIFEXT" 409599 NIL DIFEXT (NIL T) -9 NIL 409893 NIL) (-231 406208 406636 407302 "DIFEXT-" 407307 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-230 403483 405740 405781 "DIAGG" 405786 NIL DIAGG (NIL T) -9 NIL 405806 NIL) (-229 402867 403024 403276 "DIAGG-" 403281 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-228 398284 401826 402103 "DHMATRIX" 402636 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-227 393896 394805 395815 "DFSFUN" 397294 T DFSFUN (NIL) -7 NIL NIL NIL) (-226 388975 392827 393139 "DFLOAT" 393604 T DFLOAT (NIL) -8 NIL NIL NIL) (-225 387238 387519 387908 "DFINTTLS" 388683 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-224 384267 385259 385659 "DERHAM" 386904 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-223 382068 384042 384131 "DEQUEUE" 384211 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-222 381322 381455 381638 "DEGRED" 381930 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-221 377752 378497 379343 "DEFINTRF" 380550 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-220 375307 375776 376368 "DEFINTEF" 377271 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-219 374657 374927 375042 "DEFAST" 375212 T DEFAST (NIL) -8 NIL NIL NIL) (-218 368661 374252 374401 "DECIMAL" 374528 T DECIMAL (NIL) -8 NIL NIL NIL) (-217 366173 366631 367137 "DDFACT" 368205 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-216 365769 365812 365963 "DBLRESP" 366124 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-215 363641 364002 364362 "DBASE" 365536 NIL DBASE (NIL T) -8 NIL NIL NIL) (-214 362883 363121 363267 "DATAARY" 363540 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-213 361989 362842 362870 "D03FAFA" 362875 T D03FAFA (NIL) -8 NIL NIL NIL) (-212 361096 361948 361976 "D03EEFA" 361981 T D03EEFA (NIL) -8 NIL NIL NIL) (-211 359046 359512 360001 "D03AGNT" 360627 T D03AGNT (NIL) -7 NIL NIL NIL) (-210 358335 359005 359033 "D02EJFA" 359038 T D02EJFA (NIL) -8 NIL NIL NIL) (-209 357624 358294 358322 "D02CJFA" 358327 T D02CJFA (NIL) -8 NIL NIL NIL) (-208 356913 357583 357611 "D02BHFA" 357616 T D02BHFA (NIL) -8 NIL NIL NIL) (-207 356202 356872 356900 "D02BBFA" 356905 T D02BBFA (NIL) -8 NIL NIL NIL) (-206 349399 350988 352594 "D02AGNT" 354616 T D02AGNT (NIL) -7 NIL NIL NIL) (-205 347167 347690 348236 "D01WGTS" 348873 T D01WGTS (NIL) -7 NIL NIL NIL) (-204 346234 347126 347154 "D01TRNS" 347159 T D01TRNS (NIL) -8 NIL NIL NIL) (-203 345302 346193 346221 "D01GBFA" 346226 T D01GBFA (NIL) -8 NIL NIL NIL) (-202 344370 345261 345289 "D01FCFA" 345294 T D01FCFA (NIL) -8 NIL NIL NIL) (-201 343438 344329 344357 "D01ASFA" 344362 T D01ASFA (NIL) -8 NIL NIL NIL) (-200 342506 343397 343425 "D01AQFA" 343430 T D01AQFA (NIL) -8 NIL NIL NIL) (-199 341574 342465 342493 "D01APFA" 342498 T D01APFA (NIL) -8 NIL NIL NIL) (-198 340642 341533 341561 "D01ANFA" 341566 T D01ANFA (NIL) -8 NIL NIL NIL) (-197 339710 340601 340629 "D01AMFA" 340634 T D01AMFA (NIL) -8 NIL NIL NIL) (-196 338778 339669 339697 "D01ALFA" 339702 T D01ALFA (NIL) -8 NIL NIL NIL) (-195 337846 338737 338765 "D01AKFA" 338770 T D01AKFA (NIL) -8 NIL NIL NIL) (-194 336914 337805 337833 "D01AJFA" 337838 T D01AJFA (NIL) -8 NIL NIL NIL) (-193 330209 331762 333323 "D01AGNT" 335373 T D01AGNT (NIL) -7 NIL NIL NIL) (-192 329546 329674 329826 "CYCLOTOM" 330077 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-191 326281 326994 327721 "CYCLES" 328839 T CYCLES (NIL) -7 NIL NIL NIL) (-190 325593 325727 325898 "CVMP" 326142 NIL CVMP (NIL T) -7 NIL NIL NIL) (-189 323434 323692 324061 "CTRIGMNP" 325321 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-188 322870 323228 323301 "CTOR" 323381 T CTOR (NIL) -8 NIL NIL NIL) (-187 322379 322601 322702 "CTORKIND" 322789 T CTORKIND (NIL) -8 NIL NIL NIL) (-186 321670 321986 322014 "CTORCAT" 322196 T CTORCAT (NIL) -9 NIL 322309 NIL) (-185 321268 321379 321538 "CTORCAT-" 321543 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-184 320730 320942 321050 "CTORCALL" 321192 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-183 320104 320203 320356 "CSTTOOLS" 320627 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-182 315903 316560 317318 "CRFP" 319416 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-181 315378 315624 315716 "CRCEAST" 315831 T CRCEAST (NIL) -8 NIL NIL NIL) (-180 314425 314610 314838 "CRAPACK" 315182 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-179 313809 313910 314114 "CPMATCH" 314301 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-178 313534 313562 313668 "CPIMA" 313775 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-177 309882 310554 311273 "COORDSYS" 312869 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-176 309294 309415 309557 "CONTOUR" 309760 T CONTOUR (NIL) -8 NIL NIL NIL) (-175 305185 307297 307789 "CONTFRAC" 308834 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-174 305065 305086 305114 "CONDUIT" 305151 T CONDUIT (NIL) -9 NIL NIL NIL) (-173 304153 304707 304735 "COMRING" 304740 T COMRING (NIL) -9 NIL 304792 NIL) (-172 303207 303511 303695 "COMPPROP" 303989 T COMPPROP (NIL) -8 NIL NIL NIL) (-171 302868 302903 303031 "COMPLPAT" 303166 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-170 293159 302677 302786 "COMPLEX" 302791 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-169 292795 292852 292959 "COMPLEX2" 293096 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-168 292134 292255 292415 "COMPILER" 292655 T COMPILER (NIL) -8 NIL NIL NIL) (-167 291852 291887 291985 "COMPFACT" 292093 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275932 285926 285966 "COMPCAT" 286970 NIL COMPCAT (NIL T) -9 NIL 288318 NIL) (-165 265444 268371 271998 "COMPCAT-" 272354 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265173 265201 265304 "COMMUPC" 265410 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264967 265001 265060 "COMMONOP" 265134 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264523 264718 264805 "COMM" 264900 T COMM (NIL) -8 NIL NIL NIL) (-161 264099 264327 264402 "COMMAAST" 264468 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263348 263542 263570 "COMBOPC" 263908 T COMBOPC (NIL) -9 NIL 264083 NIL) (-159 262244 262454 262696 "COMBINAT" 263138 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258701 259275 259902 "COMBF" 261666 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257459 257817 258052 "COLOR" 258486 T COLOR (NIL) -8 NIL NIL NIL) (-156 256935 257180 257272 "COLONAST" 257387 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256575 256622 256747 "CMPLXRT" 256882 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256023 256275 256374 "CLLCTAST" 256496 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251522 252553 253633 "CLIP" 254963 T CLIP (NIL) -7 NIL NIL NIL) (-152 249868 250628 250867 "CLIF" 251349 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246043 248014 248055 "CLAGG" 248984 NIL CLAGG (NIL T) -9 NIL 249520 NIL) (-150 244465 244922 245505 "CLAGG-" 245510 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244009 244094 244234 "CINTSLPE" 244374 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241510 241981 242529 "CHVAR" 243537 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240684 241238 241266 "CHARZ" 241271 T CHARZ (NIL) -9 NIL 241286 NIL) (-146 240438 240478 240556 "CHARPOL" 240638 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239496 240083 240111 "CHARNZ" 240158 T CHARNZ (NIL) -9 NIL 240214 NIL) (-144 237402 238150 238503 "CHAR" 239163 T CHAR (NIL) -8 NIL NIL NIL) (-143 237128 237189 237217 "CFCAT" 237328 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236373 236484 236666 "CDEN" 237012 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232338 235526 235806 "CCLASS" 236113 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231589 231746 231923 "CATEGORY" 232181 T -10 (NIL) -8 NIL NIL NIL) (-139 231162 231508 231556 "CATCTOR" 231561 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230613 230865 230963 "CATAST" 231084 T CATAST (NIL) -8 NIL NIL NIL) (-137 230089 230334 230426 "CASEAST" 230541 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225098 226118 226871 "CARTEN" 229392 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224206 224354 224575 "CARTEN2" 224945 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222522 223356 223613 "CARD" 223969 T CARD (NIL) -8 NIL NIL NIL) (-133 222098 222326 222401 "CAPSLAST" 222467 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221602 221810 221838 "CACHSET" 221970 T CACHSET (NIL) -9 NIL 222048 NIL) (-131 221072 221394 221422 "CABMON" 221472 T CABMON (NIL) -9 NIL 221528 NIL) (-130 220545 220776 220886 "BYTEORD" 220982 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219527 220079 220221 "BYTE" 220384 T BYTE (NIL) -8 NIL NIL 220506) (-128 214877 219032 219204 "BYTEBUF" 219375 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212386 214569 214676 "BTREE" 214803 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209835 212034 212156 "BTOURN" 212296 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207205 209305 209346 "BTCAT" 209414 NIL BTCAT (NIL T) -9 NIL 209491 NIL) (-124 206872 206952 207101 "BTCAT-" 207106 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202137 206015 206043 "BTAGG" 206265 T BTAGG (NIL) -9 NIL 206426 NIL) (-122 201627 201752 201958 "BTAGG-" 201963 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198622 200905 201120 "BSTREE" 201444 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197760 197886 198070 "BRILL" 198478 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194412 196486 196527 "BRAGG" 197176 NIL BRAGG (NIL T) -9 NIL 197434 NIL) (-118 192941 193347 193902 "BRAGG-" 193907 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186170 192287 192471 "BPADICRT" 192789 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184485 186107 186152 "BPADIC" 186157 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184183 184213 184327 "BOUNDZRO" 184449 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179411 180609 181521 "BOP" 183291 T BOP (NIL) -8 NIL NIL NIL) (-113 177192 177596 178071 "BOP1" 178969 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176017 176766 176915 "BOOLEAN" 177063 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175296 175700 175754 "BMODULE" 175759 NIL BMODULE (NIL T T) -9 NIL 175824 NIL) (-110 171097 175094 175167 "BITS" 175243 T BITS (NIL) -8 NIL NIL NIL) (-109 170518 170637 170777 "BINDING" 170977 T BINDING (NIL) -8 NIL NIL NIL) (-108 164525 170115 170263 "BINARY" 170390 T BINARY (NIL) -8 NIL NIL NIL) (-107 162305 163780 163821 "BGAGG" 164081 NIL BGAGG (NIL T) -9 NIL 164218 NIL) (-106 162136 162168 162259 "BGAGG-" 162264 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161207 161520 161725 "BFUNCT" 161951 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159897 160075 160363 "BEZOUT" 161031 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156366 158749 159079 "BBTREE" 159600 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156100 156153 156181 "BASTYPE" 156300 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155952 155981 156054 "BASTYPE-" 156059 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155386 155462 155614 "BALFACT" 155863 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154242 154801 154987 "AUTOMOR" 155231 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153968 153973 153999 "ATTREG" 154004 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152220 152665 153017 "ATTRBUT" 153634 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151828 152048 152114 "ATTRAST" 152172 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151364 151477 151503 "ATRIG" 151704 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151173 151214 151301 "ATRIG-" 151306 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150818 151004 151030 "ASTCAT" 151035 T ASTCAT (NIL) -9 NIL 151065 NIL) (-92 150545 150604 150723 "ASTCAT-" 150728 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148694 150321 150409 "ASTACK" 150488 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147199 147496 147861 "ASSOCEQ" 148376 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146231 146858 146982 "ASP9" 147106 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145994 146179 146218 "ASP8" 146223 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144862 145599 145741 "ASP80" 145883 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143760 144497 144629 "ASP7" 144761 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142714 143437 143555 "ASP78" 143673 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141683 142394 142511 "ASP77" 142628 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140595 141321 141452 "ASP74" 141583 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139495 140230 140362 "ASP73" 140494 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138599 139321 139421 "ASP6" 139426 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137544 138276 138394 "ASP55" 138512 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136493 137218 137337 "ASP50" 137456 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135581 136194 136304 "ASP4" 136414 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134669 135282 135392 "ASP49" 135502 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133453 134208 134376 "ASP42" 134558 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132229 132986 133156 "ASP41" 133340 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131179 131906 132024 "ASP35" 132142 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130944 131127 131166 "ASP34" 131171 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130681 130748 130824 "ASP33" 130899 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129574 130316 130448 "ASP31" 130580 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129339 129522 129561 "ASP30" 129566 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129074 129143 129219 "ASP29" 129294 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128839 129022 129061 "ASP28" 129066 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128604 128787 128826 "ASP27" 128831 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127688 128302 128413 "ASP24" 128524 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126764 127490 127602 "ASP20" 127607 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125852 126465 126575 "ASP1" 126685 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124794 125526 125645 "ASP19" 125764 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124531 124598 124674 "ASP12" 124749 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123383 124130 124274 "ASP10" 124418 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121234 123227 123318 "ARRAY2" 123323 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116999 120882 120996 "ARRAY1" 121151 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116031 116204 116425 "ARRAY12" 116822 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110343 112261 112336 "ARR2CAT" 114966 NIL ARR2CAT (NIL T T T) -9 NIL 115724 NIL) (-56 107777 108521 109475 "ARR2CAT-" 109480 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107094 107404 107529 "ARITY" 107670 T ARITY (NIL) -8 NIL NIL NIL) (-54 105870 106022 106321 "APPRULE" 106930 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105521 105569 105688 "APPLYORE" 105816 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104875 105114 105234 "ANY" 105419 T ANY (NIL) -8 NIL NIL NIL) (-51 104153 104276 104433 "ANY1" 104749 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101683 102590 102917 "ANTISYM" 103877 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101175 101390 101486 "ANON" 101605 T ANON (NIL) -8 NIL NIL NIL) (-48 95424 99714 100168 "AN" 100739 T AN (NIL) -8 NIL NIL NIL) (-47 91322 92710 92761 "AMR" 93509 NIL AMR (NIL T T) -9 NIL 94109 NIL) (-46 90434 90655 91018 "AMR-" 91023 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74873 90351 90412 "ALIST" 90417 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74467 74636 "ALGSC" 74791 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3226982 3226987 3226992 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3226967 3226972 3226977 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3226952 3226957 3226962 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3226937 3226942 3226947 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1301 3226080 3226812 3226889 "ZMOD" 3226894 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1300 3225190 3225354 3225563 "ZLINDEP" 3225912 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1299 3214490 3216258 3218230 "ZDSOLVE" 3223320 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1298 3213736 3213877 3214066 "YSTREAM" 3214336 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1297 3211510 3213037 3213241 "XRPOLY" 3213579 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3208063 3209381 3209956 "XPR" 3210982 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1295 3205784 3207394 3207598 "XPOLY" 3207894 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1294 3203437 3204805 3204860 "XPOLYC" 3205148 NIL XPOLYC (NIL T T) -9 NIL 3205261 NIL) (-1293 3199813 3201954 3202342 "XPBWPOLY" 3203095 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1292 3195508 3197803 3197845 "XF" 3198466 NIL XF (NIL T) -9 NIL 3198866 NIL) (-1291 3195129 3195217 3195386 "XF-" 3195391 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1290 3190325 3191614 3191669 "XFALG" 3193841 NIL XFALG (NIL T T) -9 NIL 3194630 NIL) (-1289 3189458 3189562 3189767 "XEXPPKG" 3190217 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1288 3187567 3189308 3189404 "XDPOLY" 3189409 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3186374 3186974 3187017 "XALG" 3187022 NIL XALG (NIL T) -9 NIL 3187133 NIL) (-1286 3179816 3184351 3184845 "WUTSET" 3185966 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1285 3178072 3178868 3179191 "WP" 3179627 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1284 3177674 3177894 3177964 "WHILEAST" 3178024 T WHILEAST (NIL) -8 NIL NIL NIL) (-1283 3177146 3177391 3177485 "WHEREAST" 3177602 T WHEREAST (NIL) -8 NIL NIL NIL) (-1282 3176032 3176230 3176525 "WFFINTBS" 3176943 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1281 3173936 3174363 3174825 "WEIER" 3175604 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1280 3172982 3173432 3173474 "VSPACE" 3173610 NIL VSPACE (NIL T) -9 NIL 3173684 NIL) (-1279 3172820 3172847 3172938 "VSPACE-" 3172943 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1278 3172629 3172671 3172739 "VOID" 3172774 T VOID (NIL) -8 NIL NIL NIL) (-1277 3170765 3171124 3171530 "VIEW" 3172245 T VIEW (NIL) -7 NIL NIL NIL) (-1276 3167189 3167828 3168565 "VIEWDEF" 3170050 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1275 3156493 3158737 3160910 "VIEW3D" 3165038 T VIEW3D (NIL) -8 NIL NIL NIL) (-1274 3148744 3150404 3151983 "VIEW2D" 3154936 T VIEW2D (NIL) -8 NIL NIL NIL) (-1273 3144097 3148514 3148606 "VECTOR" 3148687 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1272 3142674 3142933 3143251 "VECTOR2" 3143827 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1271 3136148 3140455 3140498 "VECTCAT" 3141493 NIL VECTCAT (NIL T) -9 NIL 3142080 NIL) (-1270 3135162 3135416 3135806 "VECTCAT-" 3135811 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1269 3134616 3134813 3134933 "VARIABLE" 3135077 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1268 3134549 3134554 3134584 "UTYPE" 3134589 T UTYPE (NIL) -9 NIL NIL NIL) (-1267 3133379 3133533 3133795 "UTSODETL" 3134375 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1266 3130819 3131279 3131803 "UTSODE" 3132920 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1265 3122656 3128445 3128934 "UTS" 3130388 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1264 3113530 3118897 3118940 "UTSCAT" 3120052 NIL UTSCAT (NIL T) -9 NIL 3120810 NIL) (-1263 3110877 3111600 3112589 "UTSCAT-" 3112594 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1262 3110504 3110547 3110680 "UTS2" 3110828 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1261 3104730 3107342 3107385 "URAGG" 3109455 NIL URAGG (NIL T) -9 NIL 3110178 NIL) (-1260 3101669 3102532 3103655 "URAGG-" 3103660 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1259 3097378 3100304 3100769 "UPXSSING" 3101333 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1258 3089444 3096625 3096898 "UPXS" 3097163 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1257 3082517 3089348 3089420 "UPXSCONS" 3089425 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1256 3072262 3079055 3079117 "UPXSCCA" 3079691 NIL UPXSCCA (NIL T T) -9 NIL 3079924 NIL) (-1255 3071900 3071985 3072159 "UPXSCCA-" 3072164 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1254 3061497 3068063 3068106 "UPXSCAT" 3068754 NIL UPXSCAT (NIL T) -9 NIL 3069363 NIL) (-1253 3060927 3061006 3061185 "UPXS2" 3061412 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1252 3059581 3059834 3060185 "UPSQFREE" 3060670 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1251 3053002 3056059 3056114 "UPSCAT" 3057275 NIL UPSCAT (NIL T T) -9 NIL 3058049 NIL) (-1250 3052206 3052413 3052740 "UPSCAT-" 3052745 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 3037861 3045629 3045672 "UPOLYC" 3047773 NIL UPOLYC (NIL T) -9 NIL 3048994 NIL) (-1248 3029189 3031615 3034762 "UPOLYC-" 3034767 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1247 3028816 3028859 3028992 "UPOLYC2" 3029140 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1246 3020627 3028499 3028628 "UP" 3028735 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1245 3019966 3020073 3020237 "UPMP" 3020516 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1244 3019519 3019600 3019739 "UPDIVP" 3019879 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1243 3018087 3018336 3018652 "UPDECOMP" 3019268 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1242 3017322 3017434 3017619 "UPCDEN" 3017971 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1241 3016841 3016910 3017059 "UP2" 3017247 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1240 3015308 3016045 3016322 "UNISEG" 3016599 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1239 3014523 3014650 3014855 "UNISEG2" 3015151 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1238 3013583 3013763 3013989 "UNIFACT" 3014339 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1237 2997515 3012760 3013011 "ULS" 3013390 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1236 2985513 2997419 2997491 "ULSCONS" 2997496 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1235 2967532 2979517 2979579 "ULSCCAT" 2980217 NIL ULSCCAT (NIL T T) -9 NIL 2980505 NIL) (-1234 2966582 2966827 2967215 "ULSCCAT-" 2967220 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1233 2955956 2962436 2962479 "ULSCAT" 2963342 NIL ULSCAT (NIL T) -9 NIL 2964073 NIL) (-1232 2955386 2955465 2955644 "ULS2" 2955871 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1231 2954513 2955023 2955130 "UINT8" 2955241 T UINT8 (NIL) -8 NIL NIL 2955326) (-1230 2953639 2954149 2954256 "UINT64" 2954367 T UINT64 (NIL) -8 NIL NIL 2954452) (-1229 2952765 2953275 2953382 "UINT32" 2953493 T UINT32 (NIL) -8 NIL NIL 2953578) (-1228 2951891 2952401 2952508 "UINT16" 2952619 T UINT16 (NIL) -8 NIL NIL 2952704) (-1227 2950194 2951151 2951181 "UFD" 2951393 T UFD (NIL) -9 NIL 2951507 NIL) (-1226 2949988 2950034 2950129 "UFD-" 2950134 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1225 2949070 2949253 2949469 "UDVO" 2949794 T UDVO (NIL) -7 NIL NIL NIL) (-1224 2946886 2947295 2947766 "UDPO" 2948634 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1223 2946819 2946824 2946854 "TYPE" 2946859 T TYPE (NIL) -9 NIL NIL NIL) (-1222 2946579 2946774 2946805 "TYPEAST" 2946810 T TYPEAST (NIL) -8 NIL NIL NIL) (-1221 2945550 2945752 2945992 "TWOFACT" 2946373 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1220 2944573 2944959 2945194 "TUPLE" 2945350 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1219 2942264 2942783 2943322 "TUBETOOL" 2944056 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1218 2941113 2941318 2941559 "TUBE" 2942057 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1217 2935842 2940085 2940368 "TS" 2940865 NIL TS (NIL T) -8 NIL NIL NIL) (-1216 2924482 2928601 2928698 "TSETCAT" 2933967 NIL TSETCAT (NIL T T T T) -9 NIL 2935498 NIL) (-1215 2919214 2920814 2922705 "TSETCAT-" 2922710 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1214 2913853 2914700 2915629 "TRMANIP" 2918350 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1213 2913294 2913357 2913520 "TRIMAT" 2913785 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1212 2911160 2911397 2911754 "TRIGMNIP" 2913043 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1211 2910680 2910793 2910823 "TRIGCAT" 2911036 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1210 2910349 2910428 2910569 "TRIGCAT-" 2910574 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1209 2907194 2909207 2909488 "TREE" 2910103 NIL TREE (NIL T) -8 NIL NIL NIL) (-1208 2906468 2906996 2907026 "TRANFUN" 2907061 T TRANFUN (NIL) -9 NIL 2907127 NIL) (-1207 2905747 2905938 2906218 "TRANFUN-" 2906223 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1206 2905551 2905583 2905644 "TOPSP" 2905708 T TOPSP (NIL) -7 NIL NIL NIL) (-1205 2904899 2905014 2905168 "TOOLSIGN" 2905432 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1204 2903533 2904076 2904315 "TEXTFILE" 2904682 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1203 2901445 2901986 2902415 "TEX" 2903126 T TEX (NIL) -8 NIL NIL NIL) (-1202 2901226 2901257 2901329 "TEX1" 2901408 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1201 2900874 2900937 2901027 "TEMUTL" 2901158 T TEMUTL (NIL) -7 NIL NIL NIL) (-1200 2899028 2899308 2899633 "TBCMPPK" 2900597 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1199 2890805 2897188 2897244 "TBAGG" 2897644 NIL TBAGG (NIL T T) -9 NIL 2897855 NIL) (-1198 2885875 2887363 2889117 "TBAGG-" 2889122 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1197 2885259 2885366 2885511 "TANEXP" 2885764 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1196 2878649 2885116 2885209 "TABLE" 2885214 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1195 2878061 2878160 2878298 "TABLEAU" 2878546 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1194 2872669 2873889 2875137 "TABLBUMP" 2876847 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1193 2871891 2872038 2872219 "SYSTEM" 2872510 T SYSTEM (NIL) -8 NIL NIL NIL) (-1192 2868350 2869049 2869832 "SYSSOLP" 2871142 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1191 2868148 2868305 2868336 "SYSPTR" 2868341 T SYSPTR (NIL) -8 NIL NIL NIL) (-1190 2867192 2867697 2867816 "SYSNNI" 2868002 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868087) (-1189 2866499 2866958 2867037 "SYSINT" 2867097 NIL SYSINT (NIL NIL) -8 NIL NIL 2867142) (-1188 2862831 2863777 2864487 "SYNTAX" 2865811 T SYNTAX (NIL) -8 NIL NIL NIL) (-1187 2859989 2860591 2861223 "SYMTAB" 2862221 T SYMTAB (NIL) -8 NIL NIL NIL) (-1186 2855238 2856140 2857123 "SYMS" 2859028 T SYMS (NIL) -8 NIL NIL NIL) (-1185 2852473 2854696 2854926 "SYMPOLY" 2855043 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1184 2851990 2852065 2852188 "SYMFUNC" 2852385 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1183 2848010 2849302 2850115 "SYMBOL" 2851199 T SYMBOL (NIL) -8 NIL NIL NIL) (-1182 2841549 2843238 2844958 "SWITCH" 2846312 T SWITCH (NIL) -8 NIL NIL NIL) (-1181 2834783 2840370 2840673 "SUTS" 2841304 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1180 2826849 2834030 2834303 "SUPXS" 2834568 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1179 2818608 2826467 2826593 "SUP" 2826758 NIL SUP (NIL T) -8 NIL NIL NIL) (-1178 2817767 2817894 2818111 "SUPFRACF" 2818476 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1177 2817388 2817447 2817560 "SUP2" 2817702 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1176 2815836 2816110 2816466 "SUMRF" 2817087 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1175 2815171 2815237 2815429 "SUMFS" 2815757 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1174 2799138 2814348 2814599 "SULS" 2814978 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1173 2798740 2798960 2799030 "SUCHTAST" 2799090 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1172 2798035 2798265 2798405 "SUCH" 2798648 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1171 2791901 2792941 2793900 "SUBSPACE" 2797123 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1170 2791331 2791421 2791585 "SUBRESP" 2791789 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1169 2784697 2785996 2787307 "STTF" 2790067 NIL STTF (NIL T) -7 NIL NIL NIL) (-1168 2778870 2779990 2781137 "STTFNC" 2783597 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1167 2770181 2772052 2773846 "STTAYLOR" 2777111 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1166 2763311 2770045 2770128 "STRTBL" 2770133 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1165 2758675 2763266 2763297 "STRING" 2763302 T STRING (NIL) -8 NIL NIL NIL) (-1164 2753536 2758048 2758078 "STRICAT" 2758137 T STRICAT (NIL) -9 NIL 2758199 NIL) (-1163 2746289 2751155 2751766 "STREAM" 2752960 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1162 2745799 2745876 2746020 "STREAM3" 2746206 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1161 2744781 2744964 2745199 "STREAM2" 2745612 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1160 2744469 2744521 2744614 "STREAM1" 2744723 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1159 2743485 2743666 2743897 "STINPROD" 2744285 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1158 2743037 2743247 2743277 "STEP" 2743357 T STEP (NIL) -9 NIL 2743435 NIL) (-1157 2742224 2742526 2742674 "STEPAST" 2742911 T STEPAST (NIL) -8 NIL NIL NIL) (-1156 2735656 2742123 2742200 "STBL" 2742205 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1155 2730782 2734877 2734920 "STAGG" 2735073 NIL STAGG (NIL T) -9 NIL 2735162 NIL) (-1154 2728484 2729086 2729958 "STAGG-" 2729963 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1153 2726631 2728254 2728346 "STACK" 2728427 NIL STACK (NIL T) -8 NIL NIL NIL) (-1152 2719326 2724772 2725228 "SREGSET" 2726261 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1151 2711751 2713120 2714633 "SRDCMPK" 2717932 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1150 2704668 2709191 2709221 "SRAGG" 2710524 T SRAGG (NIL) -9 NIL 2711132 NIL) (-1149 2703685 2703940 2704319 "SRAGG-" 2704324 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1148 2698145 2702632 2703053 "SQMATRIX" 2703311 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1147 2691830 2694863 2695590 "SPLTREE" 2697490 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1146 2687793 2688486 2689132 "SPLNODE" 2691256 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1145 2686840 2687073 2687103 "SPFCAT" 2687547 T SPFCAT (NIL) -9 NIL NIL NIL) (-1144 2685577 2685787 2686051 "SPECOUT" 2686598 T SPECOUT (NIL) -7 NIL NIL NIL) (-1143 2676687 2678559 2678589 "SPADXPT" 2683265 T SPADXPT (NIL) -9 NIL 2685429 NIL) (-1142 2676448 2676488 2676557 "SPADPRSR" 2676640 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1141 2674497 2676403 2676434 "SPADAST" 2676439 T SPADAST (NIL) -8 NIL NIL NIL) (-1140 2666442 2668215 2668258 "SPACEC" 2672631 NIL SPACEC (NIL T) -9 NIL 2674447 NIL) (-1139 2664572 2666374 2666423 "SPACE3" 2666428 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1138 2663324 2663495 2663786 "SORTPAK" 2664377 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1137 2661416 2661719 2662131 "SOLVETRA" 2662988 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1136 2660466 2660688 2660949 "SOLVESER" 2661189 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1135 2655770 2656658 2657653 "SOLVERAD" 2659518 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1134 2651585 2652194 2652923 "SOLVEFOR" 2655137 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1133 2645855 2650934 2651031 "SNTSCAT" 2651036 NIL SNTSCAT (NIL T T T T) -9 NIL 2651106 NIL) (-1132 2639961 2644178 2644569 "SMTS" 2645545 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1131 2634646 2639849 2639926 "SMP" 2639931 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1130 2632805 2633106 2633504 "SMITH" 2634343 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1129 2625518 2629714 2629817 "SMATCAT" 2631168 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631718 NIL) (-1128 2622458 2623281 2624459 "SMATCAT-" 2624464 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1127 2620124 2621694 2621737 "SKAGG" 2621998 NIL SKAGG (NIL T) -9 NIL 2622133 NIL) (-1126 2616435 2619540 2619735 "SINT" 2619922 T SINT (NIL) -8 NIL NIL 2620095) (-1125 2616207 2616245 2616311 "SIMPAN" 2616391 T SIMPAN (NIL) -7 NIL NIL NIL) (-1124 2615486 2615742 2615882 "SIG" 2616089 T SIG (NIL) -8 NIL NIL NIL) (-1123 2614324 2614545 2614820 "SIGNRF" 2615245 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1122 2613157 2613308 2613592 "SIGNEF" 2614153 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1121 2612463 2612740 2612864 "SIGAST" 2613055 T SIGAST (NIL) -8 NIL NIL NIL) (-1120 2610153 2610607 2611113 "SHP" 2612004 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1119 2604005 2610054 2610130 "SHDP" 2610135 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1118 2603578 2603770 2603800 "SGROUP" 2603893 T SGROUP (NIL) -9 NIL 2603955 NIL) (-1117 2603436 2603462 2603535 "SGROUP-" 2603540 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1116 2600271 2600969 2601692 "SGCF" 2602735 T SGCF (NIL) -7 NIL NIL NIL) (-1115 2594639 2599718 2599815 "SFRTCAT" 2599820 NIL SFRTCAT (NIL T T T T) -9 NIL 2599859 NIL) (-1114 2588060 2589078 2590214 "SFRGCD" 2593622 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1113 2581186 2582259 2583445 "SFQCMPK" 2586993 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1112 2580806 2580895 2581006 "SFORT" 2581127 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1111 2579924 2580646 2580767 "SEXOF" 2580772 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1110 2579031 2579805 2579873 "SEX" 2579878 T SEX (NIL) -8 NIL NIL NIL) (-1109 2574544 2575259 2575354 "SEXCAT" 2578291 NIL SEXCAT (NIL T T T T T) -9 NIL 2578869 NIL) (-1108 2571697 2574478 2574526 "SET" 2574531 NIL SET (NIL T) -8 NIL NIL NIL) (-1107 2569921 2570410 2570715 "SETMN" 2571438 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1106 2569417 2569569 2569599 "SETCAT" 2569775 T SETCAT (NIL) -9 NIL 2569885 NIL) (-1105 2569109 2569187 2569317 "SETCAT-" 2569322 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1104 2565470 2567570 2567613 "SETAGG" 2568483 NIL SETAGG (NIL T) -9 NIL 2568823 NIL) (-1103 2564928 2565044 2565281 "SETAGG-" 2565286 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1102 2564371 2564624 2564725 "SEQAST" 2564849 T SEQAST (NIL) -8 NIL NIL NIL) (-1101 2563570 2563864 2563925 "SEGXCAT" 2564211 NIL SEGXCAT (NIL T T) -9 NIL 2564331 NIL) (-1100 2562576 2563236 2563418 "SEG" 2563423 NIL SEG (NIL T) -8 NIL NIL NIL) (-1099 2561555 2561769 2561812 "SEGCAT" 2562334 NIL SEGCAT (NIL T) -9 NIL 2562555 NIL) (-1098 2560487 2560918 2561126 "SEGBIND" 2561382 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1097 2560108 2560167 2560280 "SEGBIND2" 2560422 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1096 2559681 2559909 2559986 "SEGAST" 2560053 T SEGAST (NIL) -8 NIL NIL NIL) (-1095 2558900 2559026 2559230 "SEG2" 2559525 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1094 2558310 2558835 2558882 "SDVAR" 2558887 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1093 2550837 2558080 2558210 "SDPOL" 2558215 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1092 2549430 2549696 2550015 "SCPKG" 2550552 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1091 2548594 2548766 2548958 "SCOPE" 2549260 T SCOPE (NIL) -8 NIL NIL NIL) (-1090 2547814 2547948 2548127 "SCACHE" 2548449 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1089 2547460 2547646 2547676 "SASTCAT" 2547681 T SASTCAT (NIL) -9 NIL 2547694 NIL) (-1088 2546947 2547295 2547371 "SAOS" 2547406 T SAOS (NIL) -8 NIL NIL NIL) (-1087 2546512 2546547 2546720 "SAERFFC" 2546906 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1086 2540451 2546409 2546489 "SAE" 2546494 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1085 2540044 2540079 2540238 "SAEFACT" 2540410 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1084 2538365 2538679 2539080 "RURPK" 2539710 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1083 2537002 2537308 2537613 "RULESET" 2538199 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1082 2534225 2534755 2535213 "RULE" 2536683 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1081 2533837 2534019 2534102 "RULECOLD" 2534177 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1080 2533627 2533655 2533726 "RTVALUE" 2533788 T RTVALUE (NIL) -8 NIL NIL NIL) (-1079 2533098 2533344 2533438 "RSTRCAST" 2533555 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1078 2527946 2528741 2529661 "RSETGCD" 2532297 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1077 2517176 2522255 2522352 "RSETCAT" 2526471 NIL RSETCAT (NIL T T T T) -9 NIL 2527568 NIL) (-1076 2515103 2515642 2516466 "RSETCAT-" 2516471 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1075 2507489 2508865 2510385 "RSDCMPK" 2513702 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1074 2505468 2505935 2506009 "RRCC" 2507095 NIL RRCC (NIL T T) -9 NIL 2507439 NIL) (-1073 2504819 2504993 2505272 "RRCC-" 2505277 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1072 2504262 2504515 2504616 "RPTAST" 2504740 T RPTAST (NIL) -8 NIL NIL NIL) (-1071 2478113 2487470 2487537 "RPOLCAT" 2498201 NIL RPOLCAT (NIL T T T) -9 NIL 2501360 NIL) (-1070 2469611 2471951 2475073 "RPOLCAT-" 2475078 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1069 2460542 2467822 2468304 "ROUTINE" 2469151 T ROUTINE (NIL) -8 NIL NIL NIL) (-1068 2457340 2460168 2460308 "ROMAN" 2460424 T ROMAN (NIL) -8 NIL NIL NIL) (-1067 2455584 2456200 2456460 "ROIRC" 2457145 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1066 2451816 2454100 2454130 "RNS" 2454434 T RNS (NIL) -9 NIL 2454708 NIL) (-1065 2450325 2450708 2451242 "RNS-" 2451317 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1064 2449728 2450136 2450166 "RNG" 2450171 T RNG (NIL) -9 NIL 2450192 NIL) (-1063 2448731 2449093 2449295 "RNGBIND" 2449579 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1062 2448130 2448518 2448561 "RMODULE" 2448566 NIL RMODULE (NIL T) -9 NIL 2448593 NIL) (-1061 2446966 2447060 2447396 "RMCAT2" 2448031 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1060 2443816 2446312 2446609 "RMATRIX" 2446728 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1059 2436643 2438903 2439018 "RMATCAT" 2442377 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443359 NIL) (-1058 2436018 2436165 2436472 "RMATCAT-" 2436477 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1057 2435419 2435640 2435683 "RLINSET" 2435877 NIL RLINSET (NIL T) -9 NIL 2435968 NIL) (-1056 2434986 2435061 2435189 "RINTERP" 2435338 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1055 2434044 2434598 2434628 "RING" 2434684 T RING (NIL) -9 NIL 2434776 NIL) (-1054 2433836 2433880 2433977 "RING-" 2433982 NIL RING- (NIL T) -8 NIL NIL NIL) (-1053 2432677 2432914 2433172 "RIDIST" 2433600 T RIDIST (NIL) -7 NIL NIL NIL) (-1052 2423966 2432145 2432351 "RGCHAIN" 2432525 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1051 2423316 2423722 2423763 "RGBCSPC" 2423821 NIL RGBCSPC (NIL T) -9 NIL 2423873 NIL) (-1050 2422474 2422855 2422896 "RGBCMDL" 2423128 NIL RGBCMDL (NIL T) -9 NIL 2423242 NIL) (-1049 2419468 2420082 2420752 "RF" 2421838 NIL RF (NIL T) -7 NIL NIL NIL) (-1048 2419114 2419177 2419280 "RFFACTOR" 2419399 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1047 2418839 2418874 2418971 "RFFACT" 2419073 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1046 2416956 2417320 2417702 "RFDIST" 2418479 T RFDIST (NIL) -7 NIL NIL NIL) (-1045 2416409 2416501 2416664 "RETSOL" 2416858 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1044 2416045 2416125 2416168 "RETRACT" 2416301 NIL RETRACT (NIL T) -9 NIL 2416388 NIL) (-1043 2415894 2415919 2416006 "RETRACT-" 2416011 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1042 2415496 2415716 2415786 "RETAST" 2415846 T RETAST (NIL) -8 NIL NIL NIL) (-1041 2408234 2415149 2415276 "RESULT" 2415391 T RESULT (NIL) -8 NIL NIL NIL) (-1040 2406825 2407503 2407702 "RESRING" 2408137 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1039 2406461 2406510 2406608 "RESLATC" 2406762 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1038 2406166 2406201 2406308 "REPSQ" 2406420 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1037 2403588 2404168 2404770 "REP" 2405586 T REP (NIL) -7 NIL NIL NIL) (-1036 2403285 2403320 2403431 "REPDB" 2403547 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1035 2397185 2398574 2399797 "REP2" 2402097 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1034 2393562 2394243 2395051 "REP1" 2396412 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1033 2386258 2391703 2392159 "REGSET" 2393192 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1032 2385023 2385406 2385656 "REF" 2386043 NIL REF (NIL T) -8 NIL NIL NIL) (-1031 2384400 2384503 2384670 "REDORDER" 2384907 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1030 2380368 2383613 2383840 "RECLOS" 2384228 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1029 2379420 2379601 2379816 "REALSOLV" 2380175 T REALSOLV (NIL) -7 NIL NIL NIL) (-1028 2379266 2379307 2379337 "REAL" 2379342 T REAL (NIL) -9 NIL 2379377 NIL) (-1027 2375749 2376551 2377435 "REAL0Q" 2378431 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1026 2371350 2372338 2373399 "REAL0" 2374730 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1025 2370821 2371067 2371161 "RDUCEAST" 2371278 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1024 2370226 2370298 2370505 "RDIV" 2370743 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1023 2369294 2369468 2369681 "RDIST" 2370048 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1022 2367891 2368178 2368550 "RDETRS" 2369002 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1021 2365703 2366157 2366695 "RDETR" 2367433 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1020 2364328 2364606 2365003 "RDEEFS" 2365419 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1019 2362837 2363143 2363568 "RDEEF" 2364016 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1018 2356898 2359818 2359848 "RCFIELD" 2361143 T RCFIELD (NIL) -9 NIL 2361874 NIL) (-1017 2354962 2355466 2356162 "RCFIELD-" 2356237 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1016 2351231 2353063 2353106 "RCAGG" 2354190 NIL RCAGG (NIL T) -9 NIL 2354655 NIL) (-1015 2350859 2350953 2351116 "RCAGG-" 2351121 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1014 2350194 2350306 2350471 "RATRET" 2350743 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1013 2349747 2349814 2349935 "RATFACT" 2350122 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1012 2349055 2349175 2349327 "RANDSRC" 2349617 T RANDSRC (NIL) -7 NIL NIL NIL) (-1011 2348789 2348833 2348906 "RADUTIL" 2349004 T RADUTIL (NIL) -7 NIL NIL NIL) (-1010 2341905 2347622 2347932 "RADIX" 2348513 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1009 2333524 2341747 2341877 "RADFF" 2341882 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1008 2333171 2333246 2333276 "RADCAT" 2333436 T RADCAT (NIL) -9 NIL NIL NIL) (-1007 2332953 2333001 2333101 "RADCAT-" 2333106 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1006 2331051 2332723 2332815 "QUEUE" 2332896 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1005 2327588 2330984 2331032 "QUAT" 2331037 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1004 2327219 2327262 2327393 "QUATCT2" 2327539 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1003 2320668 2324013 2324055 "QUATCAT" 2324846 NIL QUATCAT (NIL T) -9 NIL 2325612 NIL) (-1002 2316807 2317844 2319234 "QUATCAT-" 2319330 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1001 2314272 2315883 2315926 "QUAGG" 2316307 NIL QUAGG (NIL T) -9 NIL 2316482 NIL) (-1000 2313874 2314094 2314164 "QQUTAST" 2314224 T QQUTAST (NIL) -8 NIL NIL NIL) (-999 2312772 2313272 2313444 "QFORM" 2313746 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-998 2303777 2309016 2309056 "QFCAT" 2309714 NIL QFCAT (NIL T) -9 NIL 2310715 NIL) (-997 2299349 2300550 2302141 "QFCAT-" 2302235 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-996 2298987 2299030 2299157 "QFCAT2" 2299300 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-995 2298447 2298557 2298687 "QEQUAT" 2298877 T QEQUAT (NIL) -8 NIL NIL NIL) (-994 2291593 2292666 2293850 "QCMPACK" 2297380 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-993 2289142 2289590 2290018 "QALGSET" 2291248 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-992 2288387 2288561 2288793 "QALGSET2" 2288962 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-991 2287077 2287301 2287618 "PWFFINTB" 2288160 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-990 2285259 2285427 2285781 "PUSHVAR" 2286891 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-989 2281177 2282231 2282272 "PTRANFN" 2284156 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-988 2279579 2279870 2280192 "PTPACK" 2280888 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-987 2279211 2279268 2279377 "PTFUNC2" 2279516 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-986 2273688 2278083 2278124 "PTCAT" 2278420 NIL PTCAT (NIL T) -9 NIL 2278573 NIL) (-985 2273346 2273381 2273505 "PSQFR" 2273647 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-984 2271941 2272239 2272573 "PSEUDLIN" 2273044 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-983 2258704 2261075 2263399 "PSETPK" 2269701 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-982 2251722 2254462 2254558 "PSETCAT" 2257579 NIL PSETCAT (NIL T T T T) -9 NIL 2258393 NIL) (-981 2249558 2250192 2251013 "PSETCAT-" 2251018 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-980 2248907 2249072 2249100 "PSCURVE" 2249368 T PSCURVE (NIL) -9 NIL 2249535 NIL) (-979 2244905 2246421 2246486 "PSCAT" 2247330 NIL PSCAT (NIL T T T) -9 NIL 2247570 NIL) (-978 2243968 2244184 2244584 "PSCAT-" 2244589 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2242673 2243333 2243538 "PRTITION" 2243783 T PRTITION (NIL) -8 NIL NIL NIL) (-976 2242148 2242394 2242486 "PRTDAST" 2242601 T PRTDAST (NIL) -8 NIL NIL NIL) (-975 2231238 2233452 2235640 "PRS" 2240010 NIL PRS (NIL T T) -7 NIL NIL NIL) (-974 2229049 2230588 2230628 "PRQAGG" 2230811 NIL PRQAGG (NIL T) -9 NIL 2230913 NIL) (-973 2228253 2228558 2228586 "PROPLOG" 2228833 T PROPLOG (NIL) -9 NIL 2228999 NIL) (-972 2226434 2227000 2227297 "PROPFRML" 2227989 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-971 2225903 2226010 2226138 "PROPERTY" 2226326 T PROPERTY (NIL) -8 NIL NIL NIL) (-970 2219961 2224069 2224889 "PRODUCT" 2225129 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-969 2217239 2219419 2219653 "PR" 2219772 NIL PR (NIL T T) -8 NIL NIL NIL) (-968 2217035 2217067 2217126 "PRINT" 2217200 T PRINT (NIL) -7 NIL NIL NIL) (-967 2216375 2216492 2216644 "PRIMES" 2216915 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-966 2214440 2214841 2215307 "PRIMELT" 2215954 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-965 2214169 2214218 2214246 "PRIMCAT" 2214370 T PRIMCAT (NIL) -9 NIL NIL NIL) (-964 2210284 2214107 2214152 "PRIMARR" 2214157 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-963 2209291 2209469 2209697 "PRIMARR2" 2210102 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-962 2208934 2208990 2209101 "PREASSOC" 2209229 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-961 2208409 2208542 2208570 "PPCURVE" 2208775 T PPCURVE (NIL) -9 NIL 2208911 NIL) (-960 2208004 2208204 2208287 "PORTNUM" 2208346 T PORTNUM (NIL) -8 NIL NIL NIL) (-959 2205363 2205762 2206354 "POLYROOT" 2207585 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-958 2199545 2204967 2205127 "POLY" 2205236 NIL POLY (NIL T) -8 NIL NIL NIL) (-957 2198928 2198986 2199220 "POLYLIFT" 2199481 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-956 2195203 2195652 2196281 "POLYCATQ" 2198473 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-955 2181915 2187043 2187108 "POLYCAT" 2190622 NIL POLYCAT (NIL T T T) -9 NIL 2192500 NIL) (-954 2175364 2177226 2179610 "POLYCAT-" 2179615 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-953 2174951 2175019 2175139 "POLY2UP" 2175290 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-952 2174583 2174640 2174749 "POLY2" 2174888 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-951 2173268 2173507 2173783 "POLUTIL" 2174357 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-950 2171623 2171900 2172231 "POLTOPOL" 2172990 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-949 2167088 2171559 2171605 "POINT" 2171610 NIL POINT (NIL T) -8 NIL NIL NIL) (-948 2165275 2165632 2166007 "PNTHEORY" 2166733 T PNTHEORY (NIL) -7 NIL NIL NIL) (-947 2163733 2164030 2164429 "PMTOOLS" 2164973 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-946 2163326 2163404 2163521 "PMSYM" 2163649 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-945 2162836 2162905 2163079 "PMQFCAT" 2163251 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-944 2162191 2162301 2162457 "PMPRED" 2162713 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-943 2161584 2161670 2161832 "PMPREDFS" 2162092 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-942 2160248 2160456 2160834 "PMPLCAT" 2161346 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-941 2159780 2159859 2160011 "PMLSAGG" 2160163 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-940 2159253 2159329 2159511 "PMKERNEL" 2159698 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-939 2158870 2158945 2159058 "PMINS" 2159172 NIL PMINS (NIL T) -7 NIL NIL NIL) (-938 2158312 2158381 2158590 "PMFS" 2158795 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-937 2157540 2157658 2157863 "PMDOWN" 2158189 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-936 2156707 2156865 2157046 "PMASS" 2157379 T PMASS (NIL) -7 NIL NIL NIL) (-935 2155980 2156090 2156253 "PMASSFS" 2156594 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-934 2155635 2155703 2155797 "PLOTTOOL" 2155906 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-933 2150242 2151446 2152594 "PLOT" 2154507 T PLOT (NIL) -8 NIL NIL NIL) (-932 2146046 2147090 2148011 "PLOT3D" 2149341 T PLOT3D (NIL) -8 NIL NIL NIL) (-931 2144958 2145135 2145370 "PLOT1" 2145850 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-930 2120347 2125024 2129875 "PLEQN" 2140224 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-929 2119665 2119787 2119967 "PINTERP" 2120212 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-928 2119358 2119405 2119508 "PINTERPA" 2119612 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-927 2118579 2119127 2119214 "PI" 2119254 T PI (NIL) -8 NIL NIL 2119321) (-926 2116876 2117851 2117879 "PID" 2118061 T PID (NIL) -9 NIL 2118195 NIL) (-925 2116627 2116664 2116739 "PICOERCE" 2116833 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-924 2115947 2116086 2116262 "PGROEB" 2116483 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-923 2111534 2112348 2113253 "PGE" 2115062 T PGE (NIL) -7 NIL NIL NIL) (-922 2109657 2109904 2110270 "PGCD" 2111251 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-921 2108995 2109098 2109259 "PFRPAC" 2109541 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-920 2105635 2107543 2107896 "PFR" 2108674 NIL PFR (NIL T) -8 NIL NIL NIL) (-919 2104024 2104268 2104593 "PFOTOOLS" 2105382 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-918 2102557 2102796 2103147 "PFOQ" 2103781 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-917 2101058 2101270 2101626 "PFO" 2102341 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-916 2097611 2100947 2101016 "PF" 2101021 NIL PF (NIL NIL) -8 NIL NIL NIL) (-915 2094945 2096216 2096244 "PFECAT" 2096829 T PFECAT (NIL) -9 NIL 2097213 NIL) (-914 2094390 2094544 2094758 "PFECAT-" 2094763 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-913 2092993 2093245 2093546 "PFBRU" 2094139 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-912 2090859 2091211 2091643 "PFBR" 2092644 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-911 2086741 2088235 2088911 "PERM" 2090216 NIL PERM (NIL T) -8 NIL NIL NIL) (-910 2081975 2082948 2083818 "PERMGRP" 2085904 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-909 2080081 2081038 2081079 "PERMCAT" 2081525 NIL PERMCAT (NIL T) -9 NIL 2081830 NIL) (-908 2079734 2079775 2079899 "PERMAN" 2080034 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-907 2077222 2079399 2079521 "PENDTREE" 2079645 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-906 2075246 2076014 2076055 "PDRING" 2076712 NIL PDRING (NIL T) -9 NIL 2076998 NIL) (-905 2074349 2074567 2074929 "PDRING-" 2074934 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-904 2071564 2072342 2073010 "PDEPROB" 2073701 T PDEPROB (NIL) -8 NIL NIL NIL) (-903 2069109 2069613 2070168 "PDEPACK" 2071029 T PDEPACK (NIL) -7 NIL NIL NIL) (-902 2068021 2068211 2068462 "PDECOMP" 2068908 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-901 2065600 2066443 2066471 "PDECAT" 2067258 T PDECAT (NIL) -9 NIL 2067971 NIL) (-900 2065351 2065384 2065474 "PCOMP" 2065561 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-899 2063529 2064152 2064449 "PBWLB" 2065080 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-898 2056002 2057602 2058940 "PATTERN" 2062212 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-897 2055634 2055691 2055800 "PATTERN2" 2055939 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-896 2053391 2053779 2054236 "PATTERN1" 2055223 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-895 2050759 2051340 2051821 "PATRES" 2052956 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-894 2050323 2050390 2050522 "PATRES2" 2050686 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-893 2048206 2048611 2049018 "PATMATCH" 2049990 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-892 2047716 2047925 2047966 "PATMAB" 2048073 NIL PATMAB (NIL T) -9 NIL 2048156 NIL) (-891 2046234 2046570 2046828 "PATLRES" 2047521 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-890 2045780 2045903 2045944 "PATAB" 2045949 NIL PATAB (NIL T) -9 NIL 2046121 NIL) (-889 2043261 2043793 2044366 "PARTPERM" 2045227 T PARTPERM (NIL) -7 NIL NIL NIL) (-888 2042882 2042945 2043047 "PARSURF" 2043192 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-887 2042514 2042571 2042680 "PARSU2" 2042819 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-886 2042278 2042318 2042385 "PARSER" 2042467 T PARSER (NIL) -7 NIL NIL NIL) (-885 2041899 2041962 2042064 "PARSCURV" 2042209 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-884 2041531 2041588 2041697 "PARSC2" 2041836 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-883 2041170 2041228 2041325 "PARPCURV" 2041467 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-882 2040802 2040859 2040968 "PARPC2" 2041107 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-881 2039863 2040175 2040357 "PARAMAST" 2040640 T PARAMAST (NIL) -8 NIL NIL NIL) (-880 2039383 2039469 2039588 "PAN2EXPR" 2039764 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-879 2038160 2038504 2038732 "PALETTE" 2039175 T PALETTE (NIL) -8 NIL NIL NIL) (-878 2036553 2037165 2037525 "PAIR" 2037846 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-877 2030423 2035812 2036006 "PADICRC" 2036408 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-876 2023652 2029769 2029953 "PADICRAT" 2030271 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-875 2021967 2023589 2023634 "PADIC" 2023639 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-874 2019077 2020641 2020681 "PADICCT" 2021262 NIL PADICCT (NIL NIL) -9 NIL 2021544 NIL) (-873 2018034 2018234 2018502 "PADEPAC" 2018864 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-872 2017246 2017379 2017585 "PADE" 2017896 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-871 2015633 2016454 2016734 "OWP" 2017050 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-870 2015126 2015339 2015436 "OVERSET" 2015556 T OVERSET (NIL) -8 NIL NIL NIL) (-869 2014172 2014731 2014903 "OVAR" 2014994 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-868 2013436 2013557 2013718 "OUT" 2014031 T OUT (NIL) -7 NIL NIL NIL) (-867 2002308 2004545 2006745 "OUTFORM" 2011256 T OUTFORM (NIL) -8 NIL NIL NIL) (-866 2001644 2001905 2002032 "OUTBFILE" 2002201 T OUTBFILE (NIL) -8 NIL NIL NIL) (-865 2000951 2001116 2001144 "OUTBCON" 2001462 T OUTBCON (NIL) -9 NIL 2001628 NIL) (-864 2000552 2000664 2000821 "OUTBCON-" 2000826 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-863 1999932 2000281 2000370 "OSI" 2000483 T OSI (NIL) -8 NIL NIL NIL) (-862 1999462 1999800 1999828 "OSGROUP" 1999833 T OSGROUP (NIL) -9 NIL 1999855 NIL) (-861 1998207 1998434 1998719 "ORTHPOL" 1999209 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-860 1995758 1998042 1998163 "OREUP" 1998168 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-859 1993161 1995449 1995576 "ORESUP" 1995700 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-858 1990689 1991189 1991750 "OREPCTO" 1992650 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-857 1984375 1986576 1986617 "OREPCAT" 1988965 NIL OREPCAT (NIL T) -9 NIL 1990069 NIL) (-856 1981522 1982304 1983362 "OREPCAT-" 1983367 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-855 1980673 1980971 1980999 "ORDSET" 1981308 T ORDSET (NIL) -9 NIL 1981472 NIL) (-854 1980104 1980252 1980476 "ORDSET-" 1980481 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-853 1978669 1979460 1979488 "ORDRING" 1979690 T ORDRING (NIL) -9 NIL 1979815 NIL) (-852 1978314 1978408 1978552 "ORDRING-" 1978557 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-851 1977694 1978157 1978185 "ORDMON" 1978190 T ORDMON (NIL) -9 NIL 1978211 NIL) (-850 1976856 1977003 1977198 "ORDFUNS" 1977543 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-849 1976194 1976613 1976641 "ORDFIN" 1976706 T ORDFIN (NIL) -9 NIL 1976780 NIL) (-848 1972753 1974780 1975189 "ORDCOMP" 1975818 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-847 1972019 1972146 1972332 "ORDCOMP2" 1972613 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-846 1968600 1969510 1970324 "OPTPROB" 1971225 T OPTPROB (NIL) -8 NIL NIL NIL) (-845 1965402 1966041 1966745 "OPTPACK" 1967916 T OPTPACK (NIL) -7 NIL NIL NIL) (-844 1963089 1963855 1963883 "OPTCAT" 1964702 T OPTCAT (NIL) -9 NIL 1965352 NIL) (-843 1962473 1962766 1962871 "OPSIG" 1963004 T OPSIG (NIL) -8 NIL NIL NIL) (-842 1962241 1962280 1962346 "OPQUERY" 1962427 T OPQUERY (NIL) -7 NIL NIL NIL) (-841 1959372 1960552 1961056 "OP" 1961770 NIL OP (NIL T) -8 NIL NIL NIL) (-840 1958746 1958972 1959013 "OPERCAT" 1959225 NIL OPERCAT (NIL T) -9 NIL 1959322 NIL) (-839 1958501 1958557 1958674 "OPERCAT-" 1958679 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-838 1955314 1957298 1957667 "ONECOMP" 1958165 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-837 1954619 1954734 1954908 "ONECOMP2" 1955186 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-836 1954038 1954144 1954274 "OMSERVER" 1954509 T OMSERVER (NIL) -7 NIL NIL NIL) (-835 1950900 1953478 1953518 "OMSAGG" 1953579 NIL OMSAGG (NIL T) -9 NIL 1953643 NIL) (-834 1949523 1949786 1950068 "OMPKG" 1950638 T OMPKG (NIL) -7 NIL NIL NIL) (-833 1948953 1949056 1949084 "OM" 1949383 T OM (NIL) -9 NIL NIL NIL) (-832 1947500 1948502 1948671 "OMLO" 1948834 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-831 1946460 1946607 1946827 "OMEXPR" 1947326 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-830 1945751 1946006 1946142 "OMERR" 1946344 T OMERR (NIL) -8 NIL NIL NIL) (-829 1944902 1945172 1945332 "OMERRK" 1945611 T OMERRK (NIL) -8 NIL NIL NIL) (-828 1944353 1944579 1944687 "OMENC" 1944814 T OMENC (NIL) -8 NIL NIL NIL) (-827 1938248 1939433 1940604 "OMDEV" 1943202 T OMDEV (NIL) -8 NIL NIL NIL) (-826 1937317 1937488 1937682 "OMCONN" 1938074 T OMCONN (NIL) -8 NIL NIL NIL) (-825 1935838 1936814 1936842 "OINTDOM" 1936847 T OINTDOM (NIL) -9 NIL 1936868 NIL) (-824 1933176 1934526 1934863 "OFMONOID" 1935533 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-823 1932587 1933113 1933158 "ODVAR" 1933163 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-822 1930010 1932332 1932487 "ODR" 1932492 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-821 1922591 1929786 1929912 "ODPOL" 1929917 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-820 1916413 1922463 1922568 "ODP" 1922573 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-819 1915179 1915394 1915669 "ODETOOLS" 1916187 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-818 1912146 1912804 1913520 "ODESYS" 1914512 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-817 1907028 1907936 1908961 "ODERTRIC" 1911221 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-816 1906454 1906536 1906730 "ODERED" 1906940 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-815 1903342 1903890 1904567 "ODERAT" 1905877 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-814 1900299 1900766 1901363 "ODEPRRIC" 1902871 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-813 1898242 1898838 1899324 "ODEPROB" 1899833 T ODEPROB (NIL) -8 NIL NIL NIL) (-812 1894762 1895247 1895894 "ODEPRIM" 1897721 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-811 1894011 1894113 1894373 "ODEPAL" 1894654 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-810 1890173 1890964 1891828 "ODEPACK" 1893167 T ODEPACK (NIL) -7 NIL NIL NIL) (-809 1889234 1889341 1889563 "ODEINT" 1890062 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-808 1883335 1884760 1886207 "ODEIFTBL" 1887807 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-807 1878733 1879519 1880471 "ODEEF" 1882494 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-806 1878082 1878171 1878394 "ODECONST" 1878638 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-805 1876207 1876868 1876896 "ODECAT" 1877501 T ODECAT (NIL) -9 NIL 1878032 NIL) (-804 1873062 1875912 1876034 "OCT" 1876117 NIL OCT (NIL T) -8 NIL NIL NIL) (-803 1872700 1872743 1872870 "OCTCT2" 1873013 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-802 1867349 1869784 1869824 "OC" 1870921 NIL OC (NIL T) -9 NIL 1871779 NIL) (-801 1864576 1865324 1866314 "OC-" 1866408 NIL OC- (NIL T T) -8 NIL NIL NIL) (-800 1863928 1864396 1864424 "OCAMON" 1864429 T OCAMON (NIL) -9 NIL 1864450 NIL) (-799 1863459 1863800 1863828 "OASGP" 1863833 T OASGP (NIL) -9 NIL 1863853 NIL) (-798 1862720 1863209 1863237 "OAMONS" 1863277 T OAMONS (NIL) -9 NIL 1863320 NIL) (-797 1862134 1862567 1862595 "OAMON" 1862600 T OAMON (NIL) -9 NIL 1862620 NIL) (-796 1861392 1861910 1861938 "OAGROUP" 1861943 T OAGROUP (NIL) -9 NIL 1861963 NIL) (-795 1861082 1861132 1861220 "NUMTUBE" 1861336 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-794 1854655 1856173 1857709 "NUMQUAD" 1859566 T NUMQUAD (NIL) -7 NIL NIL NIL) (-793 1850411 1851399 1852424 "NUMODE" 1853650 T NUMODE (NIL) -7 NIL NIL NIL) (-792 1847766 1848646 1848674 "NUMINT" 1849597 T NUMINT (NIL) -9 NIL 1850361 NIL) (-791 1846714 1846911 1847129 "NUMFMT" 1847568 T NUMFMT (NIL) -7 NIL NIL NIL) (-790 1833073 1836018 1838550 "NUMERIC" 1844221 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-789 1827443 1832522 1832617 "NTSCAT" 1832622 NIL NTSCAT (NIL T T T T) -9 NIL 1832661 NIL) (-788 1826637 1826802 1826995 "NTPOLFN" 1827282 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-787 1814714 1823462 1824274 "NSUP" 1825858 NIL NSUP (NIL T) -8 NIL NIL NIL) (-786 1814346 1814403 1814512 "NSUP2" 1814651 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-785 1804574 1814120 1814253 "NSMP" 1814258 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-784 1803006 1803307 1803664 "NREP" 1804262 NIL NREP (NIL T) -7 NIL NIL NIL) (-783 1801597 1801849 1802207 "NPCOEF" 1802749 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-782 1800663 1800778 1800994 "NORMRETR" 1801478 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-781 1798704 1798994 1799403 "NORMPK" 1800371 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-780 1798389 1798417 1798541 "NORMMA" 1798670 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-779 1798189 1798346 1798375 "NONE" 1798380 T NONE (NIL) -8 NIL NIL NIL) (-778 1797978 1798007 1798076 "NONE1" 1798153 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-777 1797475 1797537 1797716 "NODE1" 1797910 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-776 1795760 1796611 1796866 "NNI" 1797213 T NNI (NIL) -8 NIL NIL 1797448) (-775 1794180 1794493 1794857 "NLINSOL" 1795428 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-774 1790421 1791416 1792315 "NIPROB" 1793301 T NIPROB (NIL) -8 NIL NIL NIL) (-773 1789178 1789412 1789714 "NFINTBAS" 1790183 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-772 1788352 1788828 1788869 "NETCLT" 1789041 NIL NETCLT (NIL T) -9 NIL 1789123 NIL) (-771 1787060 1787291 1787572 "NCODIV" 1788120 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-770 1786822 1786859 1786934 "NCNTFRAC" 1787017 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-769 1785002 1785366 1785786 "NCEP" 1786447 NIL NCEP (NIL T) -7 NIL NIL NIL) (-768 1783853 1784626 1784654 "NASRING" 1784764 T NASRING (NIL) -9 NIL 1784844 NIL) (-767 1783648 1783692 1783786 "NASRING-" 1783791 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-766 1782755 1783280 1783308 "NARNG" 1783425 T NARNG (NIL) -9 NIL 1783516 NIL) (-765 1782447 1782514 1782648 "NARNG-" 1782653 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-764 1781326 1781533 1781768 "NAGSP" 1782232 T NAGSP (NIL) -7 NIL NIL NIL) (-763 1772598 1774282 1775955 "NAGS" 1779673 T NAGS (NIL) -7 NIL NIL NIL) (-762 1771146 1771454 1771785 "NAGF07" 1772287 T NAGF07 (NIL) -7 NIL NIL NIL) (-761 1765684 1766975 1768282 "NAGF04" 1769859 T NAGF04 (NIL) -7 NIL NIL NIL) (-760 1758652 1760266 1761899 "NAGF02" 1764071 T NAGF02 (NIL) -7 NIL NIL NIL) (-759 1753876 1754976 1756093 "NAGF01" 1757555 T NAGF01 (NIL) -7 NIL NIL NIL) (-758 1747504 1749070 1750655 "NAGE04" 1752311 T NAGE04 (NIL) -7 NIL NIL NIL) (-757 1738673 1740794 1742924 "NAGE02" 1745394 T NAGE02 (NIL) -7 NIL NIL NIL) (-756 1734626 1735573 1736537 "NAGE01" 1737729 T NAGE01 (NIL) -7 NIL NIL NIL) (-755 1732421 1732955 1733513 "NAGD03" 1734088 T NAGD03 (NIL) -7 NIL NIL NIL) (-754 1724171 1726099 1728053 "NAGD02" 1730487 T NAGD02 (NIL) -7 NIL NIL NIL) (-753 1717982 1719407 1720847 "NAGD01" 1722751 T NAGD01 (NIL) -7 NIL NIL NIL) (-752 1714191 1715013 1715850 "NAGC06" 1717165 T NAGC06 (NIL) -7 NIL NIL NIL) (-751 1712656 1712988 1713344 "NAGC05" 1713855 T NAGC05 (NIL) -7 NIL NIL NIL) (-750 1712032 1712151 1712295 "NAGC02" 1712532 T NAGC02 (NIL) -7 NIL NIL NIL) (-749 1710991 1711574 1711614 "NAALG" 1711693 NIL NAALG (NIL T) -9 NIL 1711754 NIL) (-748 1710826 1710855 1710945 "NAALG-" 1710950 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-747 1704776 1705884 1707071 "MULTSQFR" 1709722 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-746 1704095 1704170 1704354 "MULTFACT" 1704688 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-745 1696819 1700732 1700785 "MTSCAT" 1701855 NIL MTSCAT (NIL T T) -9 NIL 1702370 NIL) (-744 1696531 1696585 1696677 "MTHING" 1696759 NIL MTHING (NIL T) -7 NIL NIL NIL) (-743 1696323 1696356 1696416 "MSYSCMD" 1696491 T MSYSCMD (NIL) -7 NIL NIL NIL) (-742 1692405 1695078 1695398 "MSET" 1696036 NIL MSET (NIL T) -8 NIL NIL NIL) (-741 1689474 1691966 1692007 "MSETAGG" 1692012 NIL MSETAGG (NIL T) -9 NIL 1692046 NIL) (-740 1685315 1686853 1687598 "MRING" 1688774 NIL MRING (NIL T T) -8 NIL NIL NIL) (-739 1684881 1684948 1685079 "MRF2" 1685242 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-738 1684499 1684534 1684678 "MRATFAC" 1684840 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-737 1682111 1682406 1682837 "MPRFF" 1684204 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-736 1676408 1681965 1682062 "MPOLY" 1682067 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-735 1675898 1675933 1676141 "MPCPF" 1676367 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-734 1675412 1675455 1675639 "MPC3" 1675849 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1674607 1674688 1674909 "MPC2" 1675327 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-732 1672908 1673245 1673635 "MONOTOOL" 1674267 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-731 1672133 1672450 1672478 "MONOID" 1672697 T MONOID (NIL) -9 NIL 1672844 NIL) (-730 1671679 1671798 1671979 "MONOID-" 1671984 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-729 1662154 1668105 1668164 "MONOGEN" 1668838 NIL MONOGEN (NIL T T) -9 NIL 1669294 NIL) (-728 1659372 1660107 1661107 "MONOGEN-" 1661226 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-727 1658205 1658651 1658679 "MONADWU" 1659071 T MONADWU (NIL) -9 NIL 1659309 NIL) (-726 1657577 1657736 1657984 "MONADWU-" 1657989 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-725 1656936 1657180 1657208 "MONAD" 1657415 T MONAD (NIL) -9 NIL 1657527 NIL) (-724 1656621 1656699 1656831 "MONAD-" 1656836 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-723 1654910 1655534 1655813 "MOEBIUS" 1656374 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-722 1654188 1654592 1654632 "MODULE" 1654637 NIL MODULE (NIL T) -9 NIL 1654676 NIL) (-721 1653756 1653852 1654042 "MODULE-" 1654047 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-720 1651436 1652120 1652447 "MODRING" 1653580 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-719 1648380 1649541 1650062 "MODOP" 1650965 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-718 1646968 1647447 1647724 "MODMONOM" 1648243 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-717 1637010 1645259 1645673 "MODMON" 1646605 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-716 1634166 1635854 1636130 "MODFIELD" 1636885 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1633143 1633447 1633637 "MMLFORM" 1633996 T MMLFORM (NIL) -8 NIL NIL NIL) (-714 1632669 1632712 1632891 "MMAP" 1633094 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-713 1630748 1631515 1631556 "MLO" 1631979 NIL MLO (NIL T) -9 NIL 1632221 NIL) (-712 1628114 1628630 1629232 "MLIFT" 1630229 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-711 1627505 1627589 1627743 "MKUCFUNC" 1628025 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-710 1627104 1627174 1627297 "MKRECORD" 1627428 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-709 1626151 1626313 1626541 "MKFUNC" 1626915 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-708 1625539 1625643 1625799 "MKFLCFN" 1626034 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-707 1624816 1624918 1625103 "MKBCFUNC" 1625432 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-706 1621523 1624370 1624506 "MINT" 1624700 T MINT (NIL) -8 NIL NIL NIL) (-705 1620335 1620578 1620855 "MHROWRED" 1621278 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-704 1615715 1618870 1619275 "MFLOAT" 1619950 T MFLOAT (NIL) -8 NIL NIL NIL) (-703 1615072 1615148 1615319 "MFINFACT" 1615627 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-702 1611387 1612235 1613119 "MESH" 1614208 T MESH (NIL) -7 NIL NIL NIL) (-701 1609777 1610089 1610442 "MDDFACT" 1611074 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-700 1606572 1608936 1608977 "MDAGG" 1609232 NIL MDAGG (NIL T) -9 NIL 1609375 NIL) (-699 1596312 1605865 1606072 "MCMPLX" 1606385 T MCMPLX (NIL) -8 NIL NIL NIL) (-698 1595453 1595599 1595799 "MCDEN" 1596161 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-697 1593343 1593613 1593993 "MCALCFN" 1595183 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-696 1592268 1592508 1592741 "MAYBE" 1593149 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-695 1589880 1590403 1590965 "MATSTOR" 1591739 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-694 1585837 1589252 1589500 "MATRIX" 1589665 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-693 1581601 1582310 1583046 "MATLIN" 1585194 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-692 1571707 1574893 1574970 "MATCAT" 1579850 NIL MATCAT (NIL T T T) -9 NIL 1581267 NIL) (-691 1568063 1569084 1570440 "MATCAT-" 1570445 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-690 1566657 1566810 1567143 "MATCAT2" 1567898 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-689 1564769 1565093 1565477 "MAPPKG3" 1566332 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-688 1563750 1563923 1564145 "MAPPKG2" 1564593 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-687 1562249 1562533 1562860 "MAPPKG1" 1563456 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-686 1561328 1561655 1561832 "MAPPAST" 1562092 T MAPPAST (NIL) -8 NIL NIL NIL) (-685 1560939 1560997 1561120 "MAPHACK3" 1561264 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-684 1560531 1560592 1560706 "MAPHACK2" 1560871 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-683 1559968 1560072 1560214 "MAPHACK1" 1560422 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-682 1558047 1558668 1558972 "MAGMA" 1559696 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-681 1557526 1557771 1557862 "MACROAST" 1557976 T MACROAST (NIL) -8 NIL NIL NIL) (-680 1553944 1555765 1556226 "M3D" 1557098 NIL M3D (NIL T) -8 NIL NIL NIL) (-679 1548050 1552313 1552354 "LZSTAGG" 1553136 NIL LZSTAGG (NIL T) -9 NIL 1553431 NIL) (-678 1544007 1545181 1546638 "LZSTAGG-" 1546643 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-677 1541094 1541898 1542385 "LWORD" 1543552 NIL LWORD (NIL T) -8 NIL NIL NIL) (-676 1540670 1540898 1540973 "LSTAST" 1541039 T LSTAST (NIL) -8 NIL NIL NIL) (-675 1533836 1540441 1540575 "LSQM" 1540580 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-674 1533060 1533199 1533427 "LSPP" 1533691 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-673 1530872 1531173 1531629 "LSMP" 1532749 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-672 1527651 1528325 1529055 "LSMP1" 1530174 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-671 1521528 1526818 1526859 "LSAGG" 1526921 NIL LSAGG (NIL T) -9 NIL 1526999 NIL) (-670 1518223 1519147 1520360 "LSAGG-" 1520365 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-669 1515822 1517367 1517616 "LPOLY" 1518018 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-668 1515404 1515489 1515612 "LPEFRAC" 1515731 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-667 1513725 1514498 1514751 "LO" 1515236 NIL LO (NIL T T T) -8 NIL NIL NIL) (-666 1513377 1513489 1513517 "LOGIC" 1513628 T LOGIC (NIL) -9 NIL 1513709 NIL) (-665 1513239 1513262 1513333 "LOGIC-" 1513338 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-664 1512432 1512572 1512765 "LODOOPS" 1513095 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-663 1509855 1512348 1512414 "LODO" 1512419 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-662 1508393 1508628 1508981 "LODOF" 1509602 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-661 1504611 1507042 1507083 "LODOCAT" 1507521 NIL LODOCAT (NIL T) -9 NIL 1507732 NIL) (-660 1504344 1504402 1504529 "LODOCAT-" 1504534 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-659 1501664 1504185 1504303 "LODO2" 1504308 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-658 1499099 1501601 1501646 "LODO1" 1501651 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-657 1497980 1498145 1498450 "LODEEF" 1498922 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-656 1493219 1496110 1496151 "LNAGG" 1497098 NIL LNAGG (NIL T) -9 NIL 1497542 NIL) (-655 1492366 1492580 1492922 "LNAGG-" 1492927 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-654 1488502 1489291 1489930 "LMOPS" 1491781 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-653 1487905 1488293 1488334 "LMODULE" 1488339 NIL LMODULE (NIL T) -9 NIL 1488365 NIL) (-652 1485103 1487550 1487673 "LMDICT" 1487815 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-651 1484509 1484730 1484771 "LLINSET" 1484962 NIL LLINSET (NIL T) -9 NIL 1485053 NIL) (-650 1484208 1484417 1484477 "LITERAL" 1484482 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-649 1477371 1483142 1483446 "LIST" 1483937 NIL LIST (NIL T) -8 NIL NIL NIL) (-648 1476896 1476970 1477109 "LIST3" 1477291 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-647 1475903 1476081 1476309 "LIST2" 1476714 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-646 1474037 1474349 1474748 "LIST2MAP" 1475550 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-645 1473633 1473870 1473911 "LINSET" 1473916 NIL LINSET (NIL T) -9 NIL 1473950 NIL) (-644 1472294 1472964 1473005 "LINEXP" 1473260 NIL LINEXP (NIL T) -9 NIL 1473409 NIL) (-643 1470941 1471201 1471498 "LINDEP" 1472046 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-642 1467708 1468427 1469204 "LIMITRF" 1470196 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-641 1466011 1466307 1466716 "LIMITPS" 1467403 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-640 1460439 1465522 1465750 "LIE" 1465832 NIL LIE (NIL T T) -8 NIL NIL NIL) (-639 1459387 1459856 1459896 "LIECAT" 1460036 NIL LIECAT (NIL T) -9 NIL 1460187 NIL) (-638 1459228 1459255 1459343 "LIECAT-" 1459348 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-637 1451724 1458677 1458842 "LIB" 1459083 T LIB (NIL) -8 NIL NIL NIL) (-636 1447359 1448242 1449177 "LGROBP" 1450841 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-635 1445357 1445631 1445981 "LF" 1447080 NIL LF (NIL T T) -7 NIL NIL NIL) (-634 1444197 1444889 1444917 "LFCAT" 1445124 T LFCAT (NIL) -9 NIL 1445263 NIL) (-633 1441099 1441729 1442417 "LEXTRIPK" 1443561 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-632 1437843 1438669 1439172 "LEXP" 1440679 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-631 1437319 1437564 1437656 "LETAST" 1437771 T LETAST (NIL) -8 NIL NIL NIL) (-630 1435717 1436030 1436431 "LEADCDET" 1437001 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-629 1434907 1434981 1435210 "LAZM3PK" 1435638 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-628 1429824 1432984 1433522 "LAUPOL" 1434419 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-627 1429403 1429447 1429608 "LAPLACE" 1429774 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-626 1427342 1428504 1428755 "LA" 1429236 NIL LA (NIL T T T) -8 NIL NIL NIL) (-625 1426336 1426920 1426961 "LALG" 1427023 NIL LALG (NIL T) -9 NIL 1427082 NIL) (-624 1426050 1426109 1426245 "LALG-" 1426250 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-623 1425885 1425909 1425950 "KVTFROM" 1426012 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-622 1424808 1425252 1425437 "KTVLOGIC" 1425720 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-621 1424643 1424667 1424708 "KRCFROM" 1424770 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-620 1423547 1423734 1424033 "KOVACIC" 1424443 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-619 1423382 1423406 1423447 "KONVERT" 1423509 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-618 1423217 1423241 1423282 "KOERCE" 1423344 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-617 1421047 1421810 1422187 "KERNEL" 1422873 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-616 1420543 1420624 1420756 "KERNEL2" 1420961 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-615 1414313 1419082 1419136 "KDAGG" 1419513 NIL KDAGG (NIL T T) -9 NIL 1419719 NIL) (-614 1413842 1413966 1414171 "KDAGG-" 1414176 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1406990 1413503 1413658 "KAFILE" 1413720 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-612 1401418 1406501 1406729 "JORDAN" 1406811 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-611 1400797 1401067 1401188 "JOINAST" 1401317 T JOINAST (NIL) -8 NIL NIL NIL) (-610 1400643 1400702 1400757 "JAVACODE" 1400762 T JAVACODE (NIL) -8 NIL NIL NIL) (-609 1396895 1398848 1398902 "IXAGG" 1399831 NIL IXAGG (NIL T T) -9 NIL 1400290 NIL) (-608 1395814 1396120 1396539 "IXAGG-" 1396544 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-607 1391344 1395736 1395795 "IVECTOR" 1395800 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-606 1390110 1390347 1390613 "ITUPLE" 1391111 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-605 1388612 1388789 1389084 "ITRIGMNP" 1389932 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-604 1387357 1387561 1387844 "ITFUN3" 1388388 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-603 1386989 1387046 1387155 "ITFUN2" 1387294 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-602 1386148 1386469 1386643 "ITFORM" 1386835 T ITFORM (NIL) -8 NIL NIL NIL) (-601 1384109 1385168 1385446 "ITAYLOR" 1385903 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-600 1373054 1378246 1379409 "ISUPS" 1382979 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-599 1372158 1372298 1372534 "ISUMP" 1372901 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-598 1367533 1372103 1372144 "ISTRING" 1372149 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-597 1367009 1367254 1367346 "ISAST" 1367461 T ISAST (NIL) -8 NIL NIL NIL) (-596 1366218 1366300 1366516 "IRURPK" 1366923 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-595 1365154 1365355 1365595 "IRSN" 1365998 T IRSN (NIL) -7 NIL NIL NIL) (-594 1363225 1363580 1364009 "IRRF2F" 1364792 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-593 1362972 1363010 1363086 "IRREDFFX" 1363181 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-592 1361587 1361846 1362145 "IROOT" 1362705 NIL IROOT (NIL T) -7 NIL NIL NIL) (-591 1358191 1359271 1359963 "IR" 1360927 NIL IR (NIL T) -8 NIL NIL NIL) (-590 1357396 1357684 1357835 "IRFORM" 1358060 T IRFORM (NIL) -8 NIL NIL NIL) (-589 1355009 1355504 1356070 "IR2" 1356874 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-588 1354109 1354222 1354436 "IR2F" 1354892 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-587 1353900 1353934 1353994 "IPRNTPK" 1354069 T IPRNTPK (NIL) -7 NIL NIL NIL) (-586 1350481 1353789 1353858 "IPF" 1353863 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-585 1348808 1350406 1350463 "IPADIC" 1350468 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-584 1348120 1348368 1348498 "IP4ADDR" 1348698 T IP4ADDR (NIL) -8 NIL NIL NIL) (-583 1347494 1347749 1347881 "IOMODE" 1348008 T IOMODE (NIL) -8 NIL NIL NIL) (-582 1346567 1347091 1347218 "IOBFILE" 1347387 T IOBFILE (NIL) -8 NIL NIL NIL) (-581 1346055 1346471 1346499 "IOBCON" 1346504 T IOBCON (NIL) -9 NIL 1346525 NIL) (-580 1345566 1345624 1345807 "INVLAPLA" 1345991 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-579 1335214 1337568 1339954 "INTTR" 1343230 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-578 1331549 1332291 1333156 "INTTOOLS" 1334399 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-577 1331135 1331226 1331343 "INTSLPE" 1331452 T INTSLPE (NIL) -7 NIL NIL NIL) (-576 1329088 1331058 1331117 "INTRVL" 1331122 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-575 1326690 1327202 1327777 "INTRF" 1328573 NIL INTRF (NIL T) -7 NIL NIL NIL) (-574 1326101 1326198 1326340 "INTRET" 1326588 NIL INTRET (NIL T) -7 NIL NIL NIL) (-573 1324098 1324487 1324957 "INTRAT" 1325709 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-572 1321361 1321944 1322563 "INTPM" 1323583 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-571 1318106 1318705 1319443 "INTPAF" 1320747 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-570 1313285 1314247 1315298 "INTPACK" 1317075 T INTPACK (NIL) -7 NIL NIL NIL) (-569 1310233 1313082 1313191 "INT" 1313196 T INT (NIL) -8 NIL NIL NIL) (-568 1309485 1309637 1309845 "INTHERTR" 1310075 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-567 1308924 1309004 1309192 "INTHERAL" 1309399 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-566 1306770 1307213 1307670 "INTHEORY" 1308487 T INTHEORY (NIL) -7 NIL NIL NIL) (-565 1298176 1299797 1301569 "INTG0" 1305122 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-564 1278749 1283539 1288349 "INTFTBL" 1293386 T INTFTBL (NIL) -8 NIL NIL NIL) (-563 1277998 1278136 1278309 "INTFACT" 1278608 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-562 1275425 1275871 1276428 "INTEF" 1277552 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-561 1273792 1274531 1274559 "INTDOM" 1274860 T INTDOM (NIL) -9 NIL 1275067 NIL) (-560 1273161 1273335 1273577 "INTDOM-" 1273582 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-559 1269549 1271477 1271531 "INTCAT" 1272330 NIL INTCAT (NIL T) -9 NIL 1272651 NIL) (-558 1269021 1269124 1269252 "INTBIT" 1269441 T INTBIT (NIL) -7 NIL NIL NIL) (-557 1267720 1267874 1268181 "INTALG" 1268866 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-556 1267203 1267293 1267450 "INTAF" 1267624 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-555 1260546 1267013 1267153 "INTABL" 1267158 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-554 1259887 1260353 1260418 "INT8" 1260452 T INT8 (NIL) -8 NIL NIL 1260497) (-553 1259227 1259693 1259758 "INT64" 1259792 T INT64 (NIL) -8 NIL NIL 1259837) (-552 1258567 1259033 1259098 "INT32" 1259132 T INT32 (NIL) -8 NIL NIL 1259177) (-551 1257907 1258373 1258438 "INT16" 1258472 T INT16 (NIL) -8 NIL NIL 1258517) (-550 1252817 1255530 1255558 "INS" 1256492 T INS (NIL) -9 NIL 1257157 NIL) (-549 1250057 1250828 1251802 "INS-" 1251875 NIL INS- (NIL T) -8 NIL NIL NIL) (-548 1248832 1249059 1249357 "INPSIGN" 1249810 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-547 1247950 1248067 1248264 "INPRODPF" 1248712 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-546 1246844 1246961 1247198 "INPRODFF" 1247830 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-545 1245844 1245996 1246256 "INNMFACT" 1246680 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-544 1245041 1245138 1245326 "INMODGCD" 1245743 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-543 1243549 1243794 1244118 "INFSP" 1244786 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-542 1242733 1242850 1243033 "INFPROD0" 1243429 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-541 1239588 1240798 1241313 "INFORM" 1242226 T INFORM (NIL) -8 NIL NIL NIL) (-540 1239198 1239258 1239356 "INFORM1" 1239523 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-539 1238721 1238810 1238924 "INFINITY" 1239104 T INFINITY (NIL) -7 NIL NIL NIL) (-538 1237897 1238441 1238542 "INETCLTS" 1238640 T INETCLTS (NIL) -8 NIL NIL NIL) (-537 1236513 1236763 1237084 "INEP" 1237645 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-536 1235762 1236410 1236475 "INDE" 1236480 NIL INDE (NIL T) -8 NIL NIL NIL) (-535 1235326 1235394 1235511 "INCRMAPS" 1235689 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-534 1234144 1234595 1234801 "INBFILE" 1235140 T INBFILE (NIL) -8 NIL NIL NIL) (-533 1229444 1230380 1231324 "INBFF" 1233232 NIL INBFF (NIL T) -7 NIL NIL NIL) (-532 1228352 1228621 1228649 "INBCON" 1229162 T INBCON (NIL) -9 NIL 1229428 NIL) (-531 1227604 1227827 1228103 "INBCON-" 1228108 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-530 1227083 1227328 1227419 "INAST" 1227533 T INAST (NIL) -8 NIL NIL NIL) (-529 1226510 1226762 1226868 "IMPTAST" 1226997 T IMPTAST (NIL) -8 NIL NIL NIL) (-528 1222956 1226354 1226458 "IMATRIX" 1226463 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-527 1221668 1221791 1222106 "IMATQF" 1222812 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-526 1219888 1220115 1220452 "IMATLIN" 1221424 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-525 1214466 1219812 1219870 "ILIST" 1219875 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-524 1212371 1214326 1214439 "IIARRAY2" 1214444 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-523 1207769 1212282 1212346 "IFF" 1212351 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-522 1207116 1207386 1207502 "IFAST" 1207673 T IFAST (NIL) -8 NIL NIL NIL) (-521 1202111 1206408 1206596 "IFARRAY" 1206973 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-520 1201291 1202015 1202088 "IFAMON" 1202093 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-519 1200875 1200940 1200994 "IEVALAB" 1201201 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-518 1200550 1200618 1200778 "IEVALAB-" 1200783 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-517 1200181 1200464 1200527 "IDPO" 1200532 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-516 1199431 1200070 1200145 "IDPOAMS" 1200150 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-515 1198738 1199320 1199395 "IDPOAM" 1199400 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-514 1197797 1198073 1198126 "IDPC" 1198539 NIL IDPC (NIL T T) -9 NIL 1198688 NIL) (-513 1197266 1197689 1197762 "IDPAM" 1197767 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-512 1196642 1197158 1197231 "IDPAG" 1197236 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-511 1196287 1196478 1196553 "IDENT" 1196587 T IDENT (NIL) -8 NIL NIL NIL) (-510 1192542 1193390 1194285 "IDECOMP" 1195444 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-509 1185380 1186465 1187512 "IDEAL" 1191578 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-508 1184544 1184656 1184855 "ICDEN" 1185264 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-507 1183615 1184024 1184171 "ICARD" 1184417 T ICARD (NIL) -8 NIL NIL NIL) (-506 1181675 1181988 1182393 "IBPTOOLS" 1183292 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-505 1177282 1181295 1181408 "IBITS" 1181594 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-504 1174005 1174581 1175276 "IBATOOL" 1176699 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-503 1171784 1172246 1172779 "IBACHIN" 1173540 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-502 1169613 1171630 1171733 "IARRAY2" 1171738 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-501 1165719 1169539 1169596 "IARRAY1" 1169601 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-500 1159828 1164131 1164612 "IAN" 1165258 T IAN (NIL) -8 NIL NIL NIL) (-499 1159339 1159396 1159569 "IALGFACT" 1159765 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-498 1158867 1158980 1159008 "HYPCAT" 1159215 T HYPCAT (NIL) -9 NIL NIL NIL) (-497 1158405 1158522 1158708 "HYPCAT-" 1158713 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-496 1158000 1158200 1158283 "HOSTNAME" 1158342 T HOSTNAME (NIL) -8 NIL NIL NIL) (-495 1157845 1157882 1157923 "HOMOTOP" 1157928 NIL HOMOTOP (NIL T) -9 NIL 1157961 NIL) (-494 1154477 1155855 1155896 "HOAGG" 1156877 NIL HOAGG (NIL T) -9 NIL 1157556 NIL) (-493 1153071 1153470 1153996 "HOAGG-" 1154001 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-492 1147075 1152666 1152815 "HEXADEC" 1152942 T HEXADEC (NIL) -8 NIL NIL NIL) (-491 1145823 1146045 1146308 "HEUGCD" 1146852 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-490 1144899 1145660 1145790 "HELLFDIV" 1145795 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-489 1143078 1144676 1144764 "HEAP" 1144843 NIL HEAP (NIL T) -8 NIL NIL NIL) (-488 1142341 1142630 1142764 "HEADAST" 1142964 T HEADAST (NIL) -8 NIL NIL NIL) (-487 1136207 1142256 1142318 "HDP" 1142323 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-486 1130195 1135842 1135994 "HDMP" 1136108 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-485 1129519 1129659 1129823 "HB" 1130051 T HB (NIL) -7 NIL NIL NIL) (-484 1122905 1129365 1129469 "HASHTBL" 1129474 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-483 1122381 1122626 1122718 "HASAST" 1122833 T HASAST (NIL) -8 NIL NIL NIL) (-482 1120159 1122003 1122185 "HACKPI" 1122219 T HACKPI (NIL) -8 NIL NIL NIL) (-481 1115827 1120012 1120125 "GTSET" 1120130 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-480 1109242 1115705 1115803 "GSTBL" 1115808 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-479 1101520 1108273 1108538 "GSERIES" 1109033 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-478 1100661 1101078 1101106 "GROUP" 1101309 T GROUP (NIL) -9 NIL 1101443 NIL) (-477 1100027 1100186 1100437 "GROUP-" 1100442 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-476 1098394 1098715 1099102 "GROEBSOL" 1099704 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-475 1097308 1097596 1097647 "GRMOD" 1098176 NIL GRMOD (NIL T T) -9 NIL 1098344 NIL) (-474 1097076 1097112 1097240 "GRMOD-" 1097245 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-473 1092366 1093430 1094430 "GRIMAGE" 1096096 T GRIMAGE (NIL) -8 NIL NIL NIL) (-472 1090832 1091093 1091417 "GRDEF" 1092062 T GRDEF (NIL) -7 NIL NIL NIL) (-471 1090276 1090392 1090533 "GRAY" 1090711 T GRAY (NIL) -7 NIL NIL NIL) (-470 1089463 1089869 1089920 "GRALG" 1090073 NIL GRALG (NIL T T) -9 NIL 1090166 NIL) (-469 1089124 1089197 1089360 "GRALG-" 1089365 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-468 1085901 1088709 1088887 "GPOLSET" 1089031 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-467 1085255 1085312 1085570 "GOSPER" 1085838 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-466 1080987 1081693 1082219 "GMODPOL" 1084954 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-465 1079992 1080176 1080414 "GHENSEL" 1080799 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-464 1074148 1074991 1076011 "GENUPS" 1079076 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-463 1073845 1073896 1073985 "GENUFACT" 1074091 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-462 1073257 1073334 1073499 "GENPGCD" 1073763 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-461 1072731 1072766 1072979 "GENMFACT" 1073216 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-460 1071297 1071554 1071861 "GENEEZ" 1072474 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-459 1065443 1070908 1071070 "GDMP" 1071220 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-458 1054785 1059214 1060320 "GCNAALG" 1064426 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-457 1053112 1053974 1054002 "GCDDOM" 1054257 T GCDDOM (NIL) -9 NIL 1054414 NIL) (-456 1052582 1052709 1052924 "GCDDOM-" 1052929 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-455 1051254 1051439 1051743 "GB" 1052361 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-454 1039870 1042200 1044592 "GBINTERN" 1048945 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-453 1037707 1037999 1038420 "GBF" 1039545 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-452 1036488 1036653 1036920 "GBEUCLID" 1037523 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-451 1035837 1035962 1036111 "GAUSSFAC" 1036359 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-450 1034204 1034506 1034820 "GALUTIL" 1035556 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-449 1032512 1032786 1033110 "GALPOLYU" 1033931 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-448 1029877 1030167 1030574 "GALFACTU" 1032209 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-447 1021682 1023182 1024790 "GALFACT" 1028309 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-446 1019070 1019728 1019756 "FVFUN" 1020912 T FVFUN (NIL) -9 NIL 1021632 NIL) (-445 1018336 1018518 1018546 "FVC" 1018837 T FVC (NIL) -9 NIL 1019020 NIL) (-444 1017979 1018161 1018229 "FUNDESC" 1018288 T FUNDESC (NIL) -8 NIL NIL NIL) (-443 1017594 1017776 1017857 "FUNCTION" 1017931 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-442 1015338 1015916 1016382 "FT" 1017148 T FT (NIL) -8 NIL NIL NIL) (-441 1014129 1014639 1014842 "FTEM" 1015155 T FTEM (NIL) -8 NIL NIL NIL) (-440 1012420 1012709 1013106 "FSUPFACT" 1013820 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-439 1010817 1011106 1011438 "FST" 1012108 T FST (NIL) -8 NIL NIL NIL) (-438 1010016 1010122 1010310 "FSRED" 1010699 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-437 1008715 1008971 1009318 "FSPRMELT" 1009731 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-436 1006021 1006459 1006945 "FSPECF" 1008278 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-435 987659 995990 996031 "FS" 999915 NIL FS (NIL T) -9 NIL 1002204 NIL) (-434 976302 979295 983352 "FS-" 983652 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 975830 975884 976054 "FSINT" 976243 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-432 974122 974823 975126 "FSERIES" 975609 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-431 973164 973280 973504 "FSCINT" 974002 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-430 969372 972108 972149 "FSAGG" 972519 NIL FSAGG (NIL T) -9 NIL 972778 NIL) (-429 967134 967735 968531 "FSAGG-" 968626 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-428 966176 966319 966546 "FSAGG2" 966987 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-427 963858 964138 964685 "FS2UPS" 965894 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-426 963492 963535 963664 "FS2" 963809 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-425 962370 962541 962843 "FS2EXPXP" 963317 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-424 961796 961911 962063 "FRUTIL" 962250 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-423 953209 957291 958649 "FR" 960470 NIL FR (NIL T) -8 NIL NIL NIL) (-422 948178 950852 950892 "FRNAALG" 952288 NIL FRNAALG (NIL T) -9 NIL 952895 NIL) (-421 943851 944927 946202 "FRNAALG-" 946952 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-420 943489 943532 943659 "FRNAAF2" 943802 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-419 941869 942343 942638 "FRMOD" 943301 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-418 939620 940252 940569 "FRIDEAL" 941660 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-417 938815 938902 939191 "FRIDEAL2" 939527 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-416 937948 938362 938403 "FRETRCT" 938408 NIL FRETRCT (NIL T) -9 NIL 938584 NIL) (-415 937060 937291 937642 "FRETRCT-" 937647 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-414 934148 935358 935417 "FRAMALG" 936299 NIL FRAMALG (NIL T T) -9 NIL 936591 NIL) (-413 932282 932737 933367 "FRAMALG-" 933590 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-412 926203 931757 932033 "FRAC" 932038 NIL FRAC (NIL T) -8 NIL NIL NIL) (-411 925839 925896 926003 "FRAC2" 926140 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-410 925475 925532 925639 "FR2" 925776 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-409 919988 922881 922909 "FPS" 924028 T FPS (NIL) -9 NIL 924585 NIL) (-408 919437 919546 919710 "FPS-" 919856 NIL FPS- (NIL T) -8 NIL NIL NIL) (-407 916739 918408 918436 "FPC" 918661 T FPC (NIL) -9 NIL 918803 NIL) (-406 916532 916572 916669 "FPC-" 916674 NIL FPC- (NIL T) -8 NIL NIL NIL) (-405 915322 916020 916061 "FPATMAB" 916066 NIL FPATMAB (NIL T) -9 NIL 916218 NIL) (-404 912995 913498 913924 "FPARFRAC" 914959 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-403 908389 908887 909569 "FORTRAN" 912427 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-402 906105 906605 907144 "FORT" 907870 T FORT (NIL) -7 NIL NIL NIL) (-401 903781 904343 904371 "FORTFN" 905431 T FORTFN (NIL) -9 NIL 906055 NIL) (-400 903545 903595 903623 "FORTCAT" 903682 T FORTCAT (NIL) -9 NIL 903744 NIL) (-399 901651 902161 902551 "FORMULA" 903175 T FORMULA (NIL) -8 NIL NIL NIL) (-398 901439 901469 901538 "FORMULA1" 901615 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-397 900962 901014 901187 "FORDER" 901381 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-396 900058 900222 900415 "FOP" 900789 T FOP (NIL) -7 NIL NIL NIL) (-395 898639 899338 899512 "FNLA" 899940 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-394 897368 897783 897811 "FNCAT" 898271 T FNCAT (NIL) -9 NIL 898531 NIL) (-393 896907 897327 897355 "FNAME" 897360 T FNAME (NIL) -8 NIL NIL NIL) (-392 895470 896433 896461 "FMTC" 896466 T FMTC (NIL) -9 NIL 896502 NIL) (-391 894216 895406 895452 "FMONOID" 895457 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-390 891044 892212 892253 "FMONCAT" 893470 NIL FMONCAT (NIL T) -9 NIL 894075 NIL) (-389 890236 890786 890935 "FM" 890940 NIL FM (NIL T T) -8 NIL NIL NIL) (-388 887660 888306 888334 "FMFUN" 889478 T FMFUN (NIL) -9 NIL 890186 NIL) (-387 886929 887110 887138 "FMC" 887428 T FMC (NIL) -9 NIL 887610 NIL) (-386 884008 884868 884922 "FMCAT" 886117 NIL FMCAT (NIL T T) -9 NIL 886612 NIL) (-385 882874 883774 883874 "FM1" 883953 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-384 880648 881064 881558 "FLOATRP" 882425 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-383 874222 878377 878998 "FLOAT" 880047 T FLOAT (NIL) -8 NIL NIL NIL) (-382 871660 872160 872738 "FLOATCP" 873689 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-381 870400 871238 871279 "FLINEXP" 871284 NIL FLINEXP (NIL T) -9 NIL 871377 NIL) (-380 869554 869789 870117 "FLINEXP-" 870122 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-379 868630 868774 868998 "FLASORT" 869406 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-378 865746 866614 866666 "FLALG" 867893 NIL FLALG (NIL T T) -9 NIL 868360 NIL) (-377 859482 863232 863273 "FLAGG" 864535 NIL FLAGG (NIL T) -9 NIL 865187 NIL) (-376 858208 858547 859037 "FLAGG-" 859042 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-375 857250 857393 857620 "FLAGG2" 858061 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-374 854101 855109 855168 "FINRALG" 856296 NIL FINRALG (NIL T T) -9 NIL 856804 NIL) (-373 853261 853490 853829 "FINRALG-" 853834 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-372 852641 852880 852908 "FINITE" 853104 T FINITE (NIL) -9 NIL 853211 NIL) (-371 844998 847185 847225 "FINAALG" 850892 NIL FINAALG (NIL T) -9 NIL 852345 NIL) (-370 840330 841380 842524 "FINAALG-" 843903 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-369 839698 840085 840188 "FILE" 840260 NIL FILE (NIL T) -8 NIL NIL NIL) (-368 838356 838694 838748 "FILECAT" 839432 NIL FILECAT (NIL T T) -9 NIL 839648 NIL) (-367 836072 837600 837628 "FIELD" 837668 T FIELD (NIL) -9 NIL 837748 NIL) (-366 834692 835077 835588 "FIELD-" 835593 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-365 832542 833327 833674 "FGROUP" 834378 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-364 831632 831796 832016 "FGLMICPK" 832374 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-363 827464 831557 831614 "FFX" 831619 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-362 827065 827126 827261 "FFSLPE" 827397 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-361 823055 823837 824633 "FFPOLY" 826301 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-360 822559 822595 822804 "FFPOLY2" 823013 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-359 818403 822478 822541 "FFP" 822546 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-358 813801 818314 818378 "FF" 818383 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-357 808927 813144 813334 "FFNBX" 813655 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-356 803855 808062 808320 "FFNBP" 808781 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-355 798488 803139 803350 "FFNB" 803688 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-354 797320 797518 797833 "FFINTBAS" 798285 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-353 793389 795609 795637 "FFIELDC" 796257 T FFIELDC (NIL) -9 NIL 796633 NIL) (-352 792051 792422 792919 "FFIELDC-" 792924 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-351 791620 791666 791790 "FFHOM" 791993 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-350 789315 789802 790319 "FFF" 791135 NIL FFF (NIL T) -7 NIL NIL NIL) (-349 784933 789057 789158 "FFCGX" 789258 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-348 780555 784665 784772 "FFCGP" 784876 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-347 775738 780282 780390 "FFCG" 780491 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-346 757134 766215 766301 "FFCAT" 771466 NIL FFCAT (NIL T T T) -9 NIL 772917 NIL) (-345 752331 753379 754693 "FFCAT-" 755923 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-344 751742 751785 752020 "FFCAT2" 752282 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 741065 744714 745934 "FEXPR" 750594 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-342 740065 740500 740541 "FEVALAB" 740625 NIL FEVALAB (NIL T) -9 NIL 740886 NIL) (-341 739224 739434 739772 "FEVALAB-" 739777 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-340 737790 738607 738810 "FDIV" 739123 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-339 734810 735551 735666 "FDIVCAT" 737234 NIL FDIVCAT (NIL T T T T) -9 NIL 737671 NIL) (-338 734572 734599 734769 "FDIVCAT-" 734774 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-337 733792 733879 734156 "FDIV2" 734479 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-336 732766 733087 733289 "FCTRDATA" 733610 T FCTRDATA (NIL) -8 NIL NIL NIL) (-335 731452 731711 732000 "FCPAK1" 732497 T FCPAK1 (NIL) -7 NIL NIL NIL) (-334 730551 730952 731093 "FCOMP" 731343 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-333 714256 717701 721239 "FC" 727033 T FC (NIL) -8 NIL NIL NIL) (-332 706619 710647 710687 "FAXF" 712489 NIL FAXF (NIL T) -9 NIL 713181 NIL) (-331 703895 704553 705378 "FAXF-" 705843 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-330 698947 703271 703447 "FARRAY" 703752 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-329 693841 695908 695961 "FAMR" 696984 NIL FAMR (NIL T T) -9 NIL 697444 NIL) (-328 692731 693033 693468 "FAMR-" 693473 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-327 691900 692653 692706 "FAMONOID" 692711 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-326 689686 690396 690449 "FAMONC" 691390 NIL FAMONC (NIL T T) -9 NIL 691776 NIL) (-325 688350 689440 689577 "FAGROUP" 689582 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-324 686145 686464 686867 "FACUTIL" 688031 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-323 685244 685429 685651 "FACTFUNC" 685955 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-322 677666 684547 684746 "EXPUPXS" 685100 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-321 675149 675689 676275 "EXPRTUBE" 677100 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-320 671420 672012 672742 "EXPRODE" 674488 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-319 656905 670069 670498 "EXPR" 671024 NIL EXPR (NIL T) -8 NIL NIL NIL) (-318 651459 652046 652852 "EXPR2UPS" 656203 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-317 651091 651148 651257 "EXPR2" 651396 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-316 642481 650244 650534 "EXPEXPAN" 650928 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-315 642281 642438 642467 "EXIT" 642472 T EXIT (NIL) -8 NIL NIL NIL) (-314 641761 642005 642096 "EXITAST" 642210 T EXITAST (NIL) -8 NIL NIL NIL) (-313 641388 641450 641563 "EVALCYC" 641693 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-312 640929 641047 641088 "EVALAB" 641258 NIL EVALAB (NIL T) -9 NIL 641362 NIL) (-311 640410 640532 640753 "EVALAB-" 640758 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-310 637778 639080 639108 "EUCDOM" 639663 T EUCDOM (NIL) -9 NIL 640013 NIL) (-309 636183 636625 637215 "EUCDOM-" 637220 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-308 623721 626481 629231 "ESTOOLS" 633453 T ESTOOLS (NIL) -7 NIL NIL NIL) (-307 623353 623410 623519 "ESTOOLS2" 623658 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-306 623104 623146 623226 "ESTOOLS1" 623305 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-305 617141 618749 618777 "ES" 621545 T ES (NIL) -9 NIL 622955 NIL) (-304 612088 613375 615192 "ES-" 615356 NIL ES- (NIL T) -8 NIL NIL NIL) (-303 608462 609223 610003 "ESCONT" 611328 T ESCONT (NIL) -7 NIL NIL NIL) (-302 608207 608239 608321 "ESCONT1" 608424 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-301 607882 607932 608032 "ES2" 608151 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-300 607512 607570 607679 "ES1" 607818 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-299 606728 606857 607033 "ERROR" 607356 T ERROR (NIL) -7 NIL NIL NIL) (-298 600120 606587 606678 "EQTBL" 606683 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-297 592623 595434 596883 "EQ" 598704 NIL -2087 (NIL T) -8 NIL NIL NIL) (-296 592255 592312 592421 "EQ2" 592560 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-295 587545 588593 589686 "EP" 591194 NIL EP (NIL T) -7 NIL NIL NIL) (-294 586145 586436 586742 "ENV" 587259 T ENV (NIL) -8 NIL NIL NIL) (-293 585239 585793 585821 "ENTIRER" 585826 T ENTIRER (NIL) -9 NIL 585872 NIL) (-292 581706 583194 583564 "EMR" 585038 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-291 580850 581035 581089 "ELTAGG" 581469 NIL ELTAGG (NIL T T) -9 NIL 581680 NIL) (-290 580569 580631 580772 "ELTAGG-" 580777 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-289 580358 580387 580441 "ELTAB" 580525 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-288 579484 579630 579829 "ELFUTS" 580209 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-287 579226 579282 579310 "ELEMFUN" 579415 T ELEMFUN (NIL) -9 NIL NIL NIL) (-286 579096 579117 579185 "ELEMFUN-" 579190 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-285 573940 577196 577237 "ELAGG" 578177 NIL ELAGG (NIL T) -9 NIL 578640 NIL) (-284 572225 572659 573322 "ELAGG-" 573327 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-283 571537 571674 571830 "ELABOR" 572089 T ELABOR (NIL) -8 NIL NIL NIL) (-282 570198 570477 570771 "ELABEXPR" 571263 T ELABEXPR (NIL) -8 NIL NIL NIL) (-281 563062 564865 565692 "EFUPXS" 569474 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-280 556512 558313 559123 "EFULS" 562338 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-279 553997 554355 554827 "EFSTRUC" 556144 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-278 543788 545354 546902 "EF" 552512 NIL EF (NIL T T) -7 NIL NIL NIL) (-277 542862 543273 543422 "EAB" 543659 T EAB (NIL) -8 NIL NIL NIL) (-276 542044 542821 542849 "E04UCFA" 542854 T E04UCFA (NIL) -8 NIL NIL NIL) (-275 541226 542003 542031 "E04NAFA" 542036 T E04NAFA (NIL) -8 NIL NIL NIL) (-274 540408 541185 541213 "E04MBFA" 541218 T E04MBFA (NIL) -8 NIL NIL NIL) (-273 539590 540367 540395 "E04JAFA" 540400 T E04JAFA (NIL) -8 NIL NIL NIL) (-272 538774 539549 539577 "E04GCFA" 539582 T E04GCFA (NIL) -8 NIL NIL NIL) (-271 537958 538733 538761 "E04FDFA" 538766 T E04FDFA (NIL) -8 NIL NIL NIL) (-270 537140 537917 537945 "E04DGFA" 537950 T E04DGFA (NIL) -8 NIL NIL NIL) (-269 531313 532665 534029 "E04AGNT" 535796 T E04AGNT (NIL) -7 NIL NIL NIL) (-268 529993 530499 530539 "DVARCAT" 531014 NIL DVARCAT (NIL T) -9 NIL 531213 NIL) (-267 529197 529409 529723 "DVARCAT-" 529728 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-266 522334 528996 529125 "DSMP" 529130 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-265 517115 518279 519347 "DROPT" 521286 T DROPT (NIL) -8 NIL NIL NIL) (-264 516780 516839 516937 "DROPT1" 517050 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-263 511895 513021 514158 "DROPT0" 515663 T DROPT0 (NIL) -7 NIL NIL NIL) (-262 510240 510565 510951 "DRAWPT" 511529 T DRAWPT (NIL) -7 NIL NIL NIL) (-261 504827 505750 506829 "DRAW" 509214 NIL DRAW (NIL T) -7 NIL NIL NIL) (-260 504460 504513 504631 "DRAWHACK" 504768 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-259 503191 503460 503751 "DRAWCX" 504189 T DRAWCX (NIL) -7 NIL NIL NIL) (-258 502706 502775 502926 "DRAWCURV" 503117 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-257 493174 495136 497251 "DRAWCFUN" 500611 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-256 489938 491867 491908 "DQAGG" 492537 NIL DQAGG (NIL T) -9 NIL 492811 NIL) (-255 478062 484531 484614 "DPOLCAT" 486466 NIL DPOLCAT (NIL T T T T) -9 NIL 487011 NIL) (-254 472898 474247 476205 "DPOLCAT-" 476210 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-253 466020 472759 472857 "DPMO" 472862 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-252 459045 465800 465967 "DPMM" 465972 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-251 458523 458737 458835 "DOMTMPLT" 458967 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-250 457956 458325 458405 "DOMCTOR" 458463 T DOMCTOR (NIL) -8 NIL NIL NIL) (-249 457168 457436 457587 "DOMAIN" 457825 T DOMAIN (NIL) -8 NIL NIL NIL) (-248 451156 456803 456955 "DMP" 457069 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-247 450756 450812 450956 "DLP" 451094 NIL DLP (NIL T) -7 NIL NIL NIL) (-246 444578 450083 450273 "DLIST" 450598 NIL DLIST (NIL T) -8 NIL NIL NIL) (-245 441375 443431 443472 "DLAGG" 444022 NIL DLAGG (NIL T) -9 NIL 444252 NIL) (-244 440051 440715 440743 "DIVRING" 440835 T DIVRING (NIL) -9 NIL 440918 NIL) (-243 439288 439478 439778 "DIVRING-" 439783 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-242 437390 437747 438153 "DISPLAY" 438902 T DISPLAY (NIL) -7 NIL NIL NIL) (-241 431278 437304 437367 "DIRPROD" 437372 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-240 430126 430329 430594 "DIRPROD2" 431071 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-239 418901 424907 424960 "DIRPCAT" 425370 NIL DIRPCAT (NIL NIL T) -9 NIL 426210 NIL) (-238 416227 416869 417750 "DIRPCAT-" 418087 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-237 415514 415674 415860 "DIOSP" 416061 T DIOSP (NIL) -7 NIL NIL NIL) (-236 412169 414426 414467 "DIOPS" 414901 NIL DIOPS (NIL T) -9 NIL 415130 NIL) (-235 411718 411832 412023 "DIOPS-" 412028 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-234 410541 411169 411197 "DIFRING" 411384 T DIFRING (NIL) -9 NIL 411494 NIL) (-233 410187 410264 410416 "DIFRING-" 410421 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-232 407923 409195 409236 "DIFEXT" 409599 NIL DIFEXT (NIL T) -9 NIL 409893 NIL) (-231 406208 406636 407302 "DIFEXT-" 407307 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-230 403483 405740 405781 "DIAGG" 405786 NIL DIAGG (NIL T) -9 NIL 405806 NIL) (-229 402867 403024 403276 "DIAGG-" 403281 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-228 398284 401826 402103 "DHMATRIX" 402636 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-227 393896 394805 395815 "DFSFUN" 397294 T DFSFUN (NIL) -7 NIL NIL NIL) (-226 388975 392827 393139 "DFLOAT" 393604 T DFLOAT (NIL) -8 NIL NIL NIL) (-225 387238 387519 387908 "DFINTTLS" 388683 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-224 384267 385259 385659 "DERHAM" 386904 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-223 382068 384042 384131 "DEQUEUE" 384211 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-222 381322 381455 381638 "DEGRED" 381930 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-221 377752 378497 379343 "DEFINTRF" 380550 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-220 375307 375776 376368 "DEFINTEF" 377271 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-219 374657 374927 375042 "DEFAST" 375212 T DEFAST (NIL) -8 NIL NIL NIL) (-218 368661 374252 374401 "DECIMAL" 374528 T DECIMAL (NIL) -8 NIL NIL NIL) (-217 366173 366631 367137 "DDFACT" 368205 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-216 365769 365812 365963 "DBLRESP" 366124 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-215 363641 364002 364362 "DBASE" 365536 NIL DBASE (NIL T) -8 NIL NIL NIL) (-214 362883 363121 363267 "DATAARY" 363540 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-213 361989 362842 362870 "D03FAFA" 362875 T D03FAFA (NIL) -8 NIL NIL NIL) (-212 361096 361948 361976 "D03EEFA" 361981 T D03EEFA (NIL) -8 NIL NIL NIL) (-211 359046 359512 360001 "D03AGNT" 360627 T D03AGNT (NIL) -7 NIL NIL NIL) (-210 358335 359005 359033 "D02EJFA" 359038 T D02EJFA (NIL) -8 NIL NIL NIL) (-209 357624 358294 358322 "D02CJFA" 358327 T D02CJFA (NIL) -8 NIL NIL NIL) (-208 356913 357583 357611 "D02BHFA" 357616 T D02BHFA (NIL) -8 NIL NIL NIL) (-207 356202 356872 356900 "D02BBFA" 356905 T D02BBFA (NIL) -8 NIL NIL NIL) (-206 349399 350988 352594 "D02AGNT" 354616 T D02AGNT (NIL) -7 NIL NIL NIL) (-205 347167 347690 348236 "D01WGTS" 348873 T D01WGTS (NIL) -7 NIL NIL NIL) (-204 346234 347126 347154 "D01TRNS" 347159 T D01TRNS (NIL) -8 NIL NIL NIL) (-203 345302 346193 346221 "D01GBFA" 346226 T D01GBFA (NIL) -8 NIL NIL NIL) (-202 344370 345261 345289 "D01FCFA" 345294 T D01FCFA (NIL) -8 NIL NIL NIL) (-201 343438 344329 344357 "D01ASFA" 344362 T D01ASFA (NIL) -8 NIL NIL NIL) (-200 342506 343397 343425 "D01AQFA" 343430 T D01AQFA (NIL) -8 NIL NIL NIL) (-199 341574 342465 342493 "D01APFA" 342498 T D01APFA (NIL) -8 NIL NIL NIL) (-198 340642 341533 341561 "D01ANFA" 341566 T D01ANFA (NIL) -8 NIL NIL NIL) (-197 339710 340601 340629 "D01AMFA" 340634 T D01AMFA (NIL) -8 NIL NIL NIL) (-196 338778 339669 339697 "D01ALFA" 339702 T D01ALFA (NIL) -8 NIL NIL NIL) (-195 337846 338737 338765 "D01AKFA" 338770 T D01AKFA (NIL) -8 NIL NIL NIL) (-194 336914 337805 337833 "D01AJFA" 337838 T D01AJFA (NIL) -8 NIL NIL NIL) (-193 330209 331762 333323 "D01AGNT" 335373 T D01AGNT (NIL) -7 NIL NIL NIL) (-192 329546 329674 329826 "CYCLOTOM" 330077 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-191 326281 326994 327721 "CYCLES" 328839 T CYCLES (NIL) -7 NIL NIL NIL) (-190 325593 325727 325898 "CVMP" 326142 NIL CVMP (NIL T) -7 NIL NIL NIL) (-189 323434 323692 324061 "CTRIGMNP" 325321 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-188 322870 323228 323301 "CTOR" 323381 T CTOR (NIL) -8 NIL NIL NIL) (-187 322379 322601 322702 "CTORKIND" 322789 T CTORKIND (NIL) -8 NIL NIL NIL) (-186 321670 321986 322014 "CTORCAT" 322196 T CTORCAT (NIL) -9 NIL 322309 NIL) (-185 321268 321379 321538 "CTORCAT-" 321543 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-184 320730 320942 321050 "CTORCALL" 321192 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-183 320104 320203 320356 "CSTTOOLS" 320627 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-182 315903 316560 317318 "CRFP" 319416 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-181 315378 315624 315716 "CRCEAST" 315831 T CRCEAST (NIL) -8 NIL NIL NIL) (-180 314425 314610 314838 "CRAPACK" 315182 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-179 313809 313910 314114 "CPMATCH" 314301 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-178 313534 313562 313668 "CPIMA" 313775 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-177 309882 310554 311273 "COORDSYS" 312869 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-176 309294 309415 309557 "CONTOUR" 309760 T CONTOUR (NIL) -8 NIL NIL NIL) (-175 305185 307297 307789 "CONTFRAC" 308834 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-174 305065 305086 305114 "CONDUIT" 305151 T CONDUIT (NIL) -9 NIL NIL NIL) (-173 304153 304707 304735 "COMRING" 304740 T COMRING (NIL) -9 NIL 304792 NIL) (-172 303207 303511 303695 "COMPPROP" 303989 T COMPPROP (NIL) -8 NIL NIL NIL) (-171 302868 302903 303031 "COMPLPAT" 303166 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-170 293159 302677 302786 "COMPLEX" 302791 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-169 292795 292852 292959 "COMPLEX2" 293096 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-168 292134 292255 292415 "COMPILER" 292655 T COMPILER (NIL) -8 NIL NIL NIL) (-167 291852 291887 291985 "COMPFACT" 292093 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275932 285926 285966 "COMPCAT" 286970 NIL COMPCAT (NIL T) -9 NIL 288318 NIL) (-165 265444 268371 271998 "COMPCAT-" 272354 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265173 265201 265304 "COMMUPC" 265410 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264967 265001 265060 "COMMONOP" 265134 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264523 264718 264805 "COMM" 264900 T COMM (NIL) -8 NIL NIL NIL) (-161 264099 264327 264402 "COMMAAST" 264468 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263348 263542 263570 "COMBOPC" 263908 T COMBOPC (NIL) -9 NIL 264083 NIL) (-159 262244 262454 262696 "COMBINAT" 263138 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258701 259275 259902 "COMBF" 261666 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257459 257817 258052 "COLOR" 258486 T COLOR (NIL) -8 NIL NIL NIL) (-156 256935 257180 257272 "COLONAST" 257387 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256575 256622 256747 "CMPLXRT" 256882 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256023 256275 256374 "CLLCTAST" 256496 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251522 252553 253633 "CLIP" 254963 T CLIP (NIL) -7 NIL NIL NIL) (-152 249868 250628 250867 "CLIF" 251349 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246043 248014 248055 "CLAGG" 248984 NIL CLAGG (NIL T) -9 NIL 249520 NIL) (-150 244465 244922 245505 "CLAGG-" 245510 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244009 244094 244234 "CINTSLPE" 244374 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241510 241981 242529 "CHVAR" 243537 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240684 241238 241266 "CHARZ" 241271 T CHARZ (NIL) -9 NIL 241286 NIL) (-146 240438 240478 240556 "CHARPOL" 240638 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239496 240083 240111 "CHARNZ" 240158 T CHARNZ (NIL) -9 NIL 240214 NIL) (-144 237402 238150 238503 "CHAR" 239163 T CHAR (NIL) -8 NIL NIL NIL) (-143 237128 237189 237217 "CFCAT" 237328 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236373 236484 236666 "CDEN" 237012 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232338 235526 235806 "CCLASS" 236113 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231589 231746 231923 "CATEGORY" 232181 T -10 (NIL) -8 NIL NIL NIL) (-139 231162 231508 231556 "CATCTOR" 231561 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230613 230865 230963 "CATAST" 231084 T CATAST (NIL) -8 NIL NIL NIL) (-137 230089 230334 230426 "CASEAST" 230541 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225098 226118 226871 "CARTEN" 229392 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224206 224354 224575 "CARTEN2" 224945 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222522 223356 223613 "CARD" 223969 T CARD (NIL) -8 NIL NIL NIL) (-133 222098 222326 222401 "CAPSLAST" 222467 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221602 221810 221838 "CACHSET" 221970 T CACHSET (NIL) -9 NIL 222048 NIL) (-131 221072 221394 221422 "CABMON" 221472 T CABMON (NIL) -9 NIL 221528 NIL) (-130 220545 220776 220886 "BYTEORD" 220982 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219527 220079 220221 "BYTE" 220384 T BYTE (NIL) -8 NIL NIL 220506) (-128 214877 219032 219204 "BYTEBUF" 219375 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212386 214569 214676 "BTREE" 214803 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209835 212034 212156 "BTOURN" 212296 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207205 209305 209346 "BTCAT" 209414 NIL BTCAT (NIL T) -9 NIL 209491 NIL) (-124 206872 206952 207101 "BTCAT-" 207106 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202137 206015 206043 "BTAGG" 206265 T BTAGG (NIL) -9 NIL 206426 NIL) (-122 201627 201752 201958 "BTAGG-" 201963 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198622 200905 201120 "BSTREE" 201444 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197760 197886 198070 "BRILL" 198478 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194412 196486 196527 "BRAGG" 197176 NIL BRAGG (NIL T) -9 NIL 197434 NIL) (-118 192941 193347 193902 "BRAGG-" 193907 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186170 192287 192471 "BPADICRT" 192789 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184485 186107 186152 "BPADIC" 186157 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184183 184213 184327 "BOUNDZRO" 184449 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179411 180609 181521 "BOP" 183291 T BOP (NIL) -8 NIL NIL NIL) (-113 177192 177596 178071 "BOP1" 178969 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176017 176766 176915 "BOOLEAN" 177063 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175296 175700 175754 "BMODULE" 175759 NIL BMODULE (NIL T T) -9 NIL 175824 NIL) (-110 171097 175094 175167 "BITS" 175243 T BITS (NIL) -8 NIL NIL NIL) (-109 170518 170637 170777 "BINDING" 170977 T BINDING (NIL) -8 NIL NIL NIL) (-108 164525 170115 170263 "BINARY" 170390 T BINARY (NIL) -8 NIL NIL NIL) (-107 162305 163780 163821 "BGAGG" 164081 NIL BGAGG (NIL T) -9 NIL 164218 NIL) (-106 162136 162168 162259 "BGAGG-" 162264 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161207 161520 161725 "BFUNCT" 161951 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159897 160075 160363 "BEZOUT" 161031 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156366 158749 159079 "BBTREE" 159600 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156100 156153 156181 "BASTYPE" 156300 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155952 155981 156054 "BASTYPE-" 156059 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155386 155462 155614 "BALFACT" 155863 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154242 154801 154987 "AUTOMOR" 155231 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153968 153973 153999 "ATTREG" 154004 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152220 152665 153017 "ATTRBUT" 153634 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151828 152048 152114 "ATTRAST" 152172 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151364 151477 151503 "ATRIG" 151704 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151173 151214 151301 "ATRIG-" 151306 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150818 151004 151030 "ASTCAT" 151035 T ASTCAT (NIL) -9 NIL 151065 NIL) (-92 150545 150604 150723 "ASTCAT-" 150728 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148694 150321 150409 "ASTACK" 150488 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147199 147496 147861 "ASSOCEQ" 148376 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146231 146858 146982 "ASP9" 147106 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145994 146179 146218 "ASP8" 146223 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144862 145599 145741 "ASP80" 145883 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143760 144497 144629 "ASP7" 144761 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142714 143437 143555 "ASP78" 143673 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141683 142394 142511 "ASP77" 142628 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140595 141321 141452 "ASP74" 141583 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139495 140230 140362 "ASP73" 140494 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138599 139321 139421 "ASP6" 139426 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137544 138276 138394 "ASP55" 138512 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136493 137218 137337 "ASP50" 137456 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135581 136194 136304 "ASP4" 136414 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134669 135282 135392 "ASP49" 135502 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133453 134208 134376 "ASP42" 134558 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132229 132986 133156 "ASP41" 133340 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131179 131906 132024 "ASP35" 132142 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130944 131127 131166 "ASP34" 131171 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130681 130748 130824 "ASP33" 130899 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129574 130316 130448 "ASP31" 130580 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129339 129522 129561 "ASP30" 129566 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129074 129143 129219 "ASP29" 129294 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128839 129022 129061 "ASP28" 129066 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128604 128787 128826 "ASP27" 128831 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127688 128302 128413 "ASP24" 128524 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126764 127490 127602 "ASP20" 127607 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125852 126465 126575 "ASP1" 126685 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124794 125526 125645 "ASP19" 125764 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124531 124598 124674 "ASP12" 124749 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123383 124130 124274 "ASP10" 124418 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121234 123227 123318 "ARRAY2" 123323 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116999 120882 120996 "ARRAY1" 121151 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116031 116204 116425 "ARRAY12" 116822 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110343 112261 112336 "ARR2CAT" 114966 NIL ARR2CAT (NIL T T T) -9 NIL 115724 NIL) (-56 107777 108521 109475 "ARR2CAT-" 109480 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107094 107404 107529 "ARITY" 107670 T ARITY (NIL) -8 NIL NIL NIL) (-54 105870 106022 106321 "APPRULE" 106930 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105521 105569 105688 "APPLYORE" 105816 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104875 105114 105234 "ANY" 105419 T ANY (NIL) -8 NIL NIL NIL) (-51 104153 104276 104433 "ANY1" 104749 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101683 102590 102917 "ANTISYM" 103877 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101175 101390 101486 "ANON" 101605 T ANON (NIL) -8 NIL NIL NIL) (-48 95424 99714 100168 "AN" 100739 T AN (NIL) -8 NIL NIL NIL) (-47 91322 92710 92761 "AMR" 93509 NIL AMR (NIL T T) -9 NIL 94109 NIL) (-46 90434 90655 91018 "AMR-" 91023 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74873 90351 90412 "ALIST" 90417 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74467 74636 "ALGSC" 74791 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 5bd5381b..8e2b47b0 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,109 +1,83 @@ -(733159 . 3477887509) -(((*1 *2 *1 *2) - (-12 (|has| *1 (-6 -4444)) (-4 *1 (-1261 *2)) (-4 *2 (-1223))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) -(((*1 *1 *1) - (-12 (-5 *1 (-600 *2)) (-4 *2 (-38 (-412 (-569)))) (-4 *2 (-1055))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-310)) (-5 *2 (-112))))) -(((*1 *2) (-12 (-5 *2 (-838 (-569))) (-5 *1 (-539)))) - ((*1 *1) (-12 (-5 *1 (-838 *2)) (-4 *2 (-1106))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) - (-4 *3 (-1071 *5 *6 *7)) (-5 *2 (-649 *4)) - (-5 *1 (-1114 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) - (-12 (-5 *3 (-569)) (-5 *5 (-694 (-226))) (-5 *4 (-226)) - (-5 *2 (-1041)) (-5 *1 (-757))))) -(((*1 *1 *2) (-12 (-5 *2 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((*1 *1 *1 *2) + (-12 (|has| *1 (-6 -4445)) (-4 *1 (-609 *3 *2)) (-4 *3 (-1106)) + (-4 *2 (-1223))))) (((*1 *1 *1 *1) (-4 *1 (-666)))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-649 *7)) (-5 *3 (-569)) (-4 *7 (-955 *4 *5 *6)) - (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) - (-5 *1 (-454 *4 *5 *6 *7))))) -(((*1 *2 *3) - (-12 (-5 *3 (-649 *2)) (-4 *2 (-435 *4)) (-5 *1 (-158 *4 *2)) - (-4 *4 (-561))))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-13 (-1044 (-569)) (-644 (-569)) (-457))) - (-5 *2 (-848 *4)) (-5 *1 (-316 *3 *4 *5 *6)) - (-4 *4 (-13 (-27) (-1208) (-435 *3))) (-14 *5 (-1183)) - (-14 *6 *4))) - ((*1 *2 *1) - (|partial| -12 (-4 *3 (-13 (-1044 (-569)) (-644 (-569)) (-457))) - (-5 *2 (-848 *4)) (-5 *1 (-1259 *3 *4 *5 *6)) - (-4 *4 (-13 (-27) (-1208) (-435 *3))) (-14 *5 (-1183)) - (-14 *6 *4)))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) -(((*1 *1 *1) - (-12 (-5 *1 (-600 *2)) (-4 *2 (-38 (-412 (-569)))) (-4 *2 (-1055))))) -(((*1 *2 *1 *1 *1) - (|partial| -12 (-5 *2 (-2 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*5 *3)) (-5 *1 (-893 *5 *3 *4)) + (-1745 (-4 *3 (-1044 (-1183)))) (-1745 (-4 *3 (-1055))) + (-4 *3 (-892 *5)) (-4 *4 (-619 (-898 *5)))))) +(((*1 *1) (-5 *1 (-130)))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-776)) (-4 *4 (-353)) (-5 *1 (-217 *4 *2)) + (-4 *2 (-1249 *4))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-649 *3)) (-4 *3 (-955 *4 *6 *5)) (-4 *4 (-457)) + (-4 *5 (-855)) (-4 *6 (-798)) (-5 *1 (-993 *4 *5 *6 *3))))) (((*1 *2 *2 *3) - (-12 (-5 *3 (-649 *2)) (-4 *2 (-955 *4 *5 *6)) (-4 *4 (-457)) - (-4 *5 (-798)) (-4 *6 (-855)) (-5 *1 (-454 *4 *5 *6 *2))))) + (-12 (-5 *3 (-1183)) + (-4 *4 (-13 (-310) (-147) (-1044 (-569)) (-644 (-569)))) + (-5 *1 (-431 *4 *2)) (-4 *2 (-13 (-1208) (-29 *4))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-412 (-958 *5))) (-5 *4 (-1183)) (-4 *5 (-147)) + (-4 *5 (-13 (-457) (-1044 (-569)) (-644 (-569)))) (-5 *2 (-319 *5)) + (-5 *1 (-594 *5))))) (((*1 *2 *3) - (-12 (-5 *3 (-649 *2)) (-4 *2 (-435 *4)) (-5 *1 (-158 *4 *2)) - (-4 *4 (-561))))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-13 (-1044 (-569)) (-644 (-569)) (-457))) - (-5 *2 - (-2 - (|:| |%term| - (-2 (|:| |%coef| (-1258 *4 *5 *6)) - (|:| |%expon| (-322 *4 *5 *6)) - (|:| |%expTerms| - (-649 (-2 (|:| |k| (-412 (-569))) (|:| |c| *4)))))) - (|:| |%type| (-1165)))) - (-5 *1 (-1259 *3 *4 *5 *6)) (-4 *4 (-13 (-27) (-1208) (-435 *3))) - (-14 *5 (-1183)) (-14 *6 *4)))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) -(((*1 *1 *1) - (-12 (-5 *1 (-600 *2)) (-4 *2 (-38 (-412 (-569)))) (-4 *2 (-1055))))) -(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-649 *1)) (-4 *1 (-310))))) + (-12 (-5 *3 (-933)) + (-5 *2 + (-2 (|:| |brans| (-649 (-649 (-949 (-226))))) + (|:| |xValues| (-1100 (-226))) (|:| |yValues| (-1100 (-226))))) + (-5 *1 (-153)))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-933)) (-5 *4 (-412 (-569))) + (-5 *2 + (-2 (|:| |brans| (-649 (-649 (-949 (-226))))) + (|:| |xValues| (-1100 (-226))) (|:| |yValues| (-1100 (-226))))) + (-5 *1 (-153)))) + ((*1 *2 *3) + (-12 + (-5 *2 + (-2 (|:| |brans| (-649 (-649 (-949 (-226))))) + (|:| |xValues| (-1100 (-226))) (|:| |yValues| (-1100 (-226))))) + (-5 *1 (-153)) (-5 *3 (-649 (-949 (-226)))))) + ((*1 *2 *3) + (-12 + (-5 *2 + (-2 (|:| |brans| (-649 (-649 (-949 (-226))))) + (|:| |xValues| (-1100 (-226))) (|:| |yValues| (-1100 (-226))))) + (-5 *1 (-153)) (-5 *3 (-649 (-649 (-949 (-226))))))) + ((*1 *1 *2) (-12 (-5 *2 (-649 (-1100 (-383)))) (-5 *1 (-265)))) + ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-265))))) +(((*1 *2 *1) (-12 (-5 *2 (-964 (-776))) (-5 *1 (-336))))) (((*1 *2 *1) (-12 (-5 *2 (-1131 (-569) (-617 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-998 *2)) (-4 *4 (-1249 *3)) (-4 *2 (-310)) @@ -120,27 +94,6 @@ (-5 *1 (-667 *3 *4 *2)) (-4 *3 (-722 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-998 *2)) (-4 *2 (-561))))) (((*1 *2 *3) (-12 (-5 *3 (-649 (-52))) (-5 *2 (-1278)) (-5 *1 (-868))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-112)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) - (-4 *3 (-1071 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-649 *4)) - (|:| |todo| (-649 (-2 (|:| |val| (-649 *3)) (|:| -3550 *4)))))) - (-5 *1 (-1075 *6 *7 *8 *3 *4)) (-4 *4 (-1077 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) - (-4 *3 (-1071 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-649 *4)) - (|:| |todo| (-649 (-2 (|:| |val| (-649 *3)) (|:| -3550 *4)))))) - (-5 *1 (-1151 *5 *6 *7 *3 *4)) (-4 *4 (-1115 *5 *6 *7 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-694 (-170 (-412 (-569))))) - (-5 *2 - (-649 - (-2 (|:| |outval| (-170 *4)) (|:| |outmult| (-569)) - (|:| |outvect| (-649 (-694 (-170 *4))))))) - (-5 *1 (-769 *4)) (-4 *4 (-13 (-367) (-853)))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1223)))) ((*1 *1 *1) (-12 (-5 *1 (-677 *2)) (-4 *2 (-855)))) ((*1 *1 *1) (-12 (-5 *1 (-682 *2)) (-4 *2 (-855)))) @@ -149,22 +102,39 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-853) (-367))) (-5 *1 (-1067 *2 *3)) (-4 *3 (-1249 *2))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-1183)) + (-5 *2 (-3 (|:| |fst| (-439)) (|:| -2577 "void"))) (-5 *1 (-1186))))) +(((*1 *2 *3 *3 *3 *4 *5) + (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1249 *6)) + (-4 *6 (-13 (-367) (-147) (-1044 *4))) (-5 *4 (-569)) + (-5 *2 + (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-112)))) + (|:| -4309 + (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) + (|:| |beta| *3))))) + (-5 *1 (-1021 *6 *3))))) +(((*1 *1 *1 *1) (-4 *1 (-666)))) +(((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-522))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| |preimage| (-649 *3)) (|:| |image| (-649 *3)))) - (-5 *1 (-911 *3)) (-4 *3 (-1106))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-649 *2)) (-4 *2 (-955 *4 *5 *6)) (-4 *4 (-457)) - (-4 *5 (-798)) (-4 *6 (-855)) (-5 *1 (-454 *4 *5 *6 *2))))) -(((*1 *2 *3) - (-12 (-5 *3 (-649 *2)) (-4 *2 (-435 *4)) (-5 *1 (-158 *4 *2)) - (-4 *4 (-561))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1256 *3 *4)) (-4 *3 (-1055)) (-4 *4 (-1233 *3)) - (-5 *2 (-412 (-569)))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -2577 "void"))) + (-5 *1 (-442))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1249 *2)) (-4 *2 (-1055))))) (((*1 *1 *1) (-12 (-5 *1 (-600 *2)) (-4 *2 (-38 (-412 (-569)))) (-4 *2 (-1055))))) -(((*1 *2 *2) (-12 (-5 *2 (-649 *3)) (-4 *3 (-853)) (-5 *1 (-306 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-649 *5)) (-5 *4 (-649 (-1 *6 (-649 *6)))) + (-4 *5 (-38 (-412 (-569)))) (-4 *6 (-1264 *5)) (-5 *2 (-649 *6)) + (-5 *1 (-1266 *5 *6))))) +(((*1 *2 *3) (-12 (-5 *3 (-383)) (-5 *2 (-1165)) (-5 *1 (-308))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-457) (-1044 (-569)))) (-4 *3 (-561)) + (-5 *1 (-41 *3 *2)) (-4 *2 (-435 *3)) + (-4 *2 + (-13 (-367) (-305) + (-10 -8 (-15 -4396 ((-1131 *3 (-617 $)) $)) + (-15 -4409 ((-1131 *3 (-617 $)) $)) + (-15 -3793 ($ (-1131 *3 (-617 $)))))))))) (((*1 *2 *1) (-12 (-5 *2 (-1131 (-569) (-617 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-310)) (-4 *4 (-998 *3)) (-4 *5 (-1249 *4)) @@ -181,17 +151,6 @@ (-12 (-4 *3 (-173)) (-4 *2 (-722 *3)) (-5 *1 (-667 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-731) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-998 *2)) (-4 *2 (-561))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-649 *8)) (-5 *4 (-649 *9)) (-4 *8 (-1071 *5 *6 *7)) - (-4 *9 (-1077 *5 *6 *7 *8)) (-4 *5 (-457)) (-4 *6 (-798)) - (-4 *7 (-855)) (-5 *2 (-776)) (-5 *1 (-1075 *5 *6 *7 *8 *9)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-649 *8)) (-5 *4 (-649 *9)) (-4 *8 (-1071 *5 *6 *7)) - (-4 *9 (-1115 *5 *6 *7 *8)) (-4 *5 (-457)) (-4 *6 (-798)) - (-4 *7 (-855)) (-5 *2 (-776)) (-5 *1 (-1151 *5 *6 *7 *8 *9))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-694 (-170 (-412 (-569))))) (-5 *2 (-649 (-170 *4))) - (-5 *1 (-769 *4)) (-4 *4 (-13 (-367) (-853)))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1223)))) ((*1 *1 *1) (-12 (-5 *1 (-677 *2)) (-4 *2 (-855)))) ((*1 *1 *1) (-12 (-5 *1 (-682 *2)) (-4 *2 (-855)))) @@ -200,35 +159,48 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-853) (-367))) (-5 *1 (-1067 *2 *3)) (-4 *3 (-1249 *2))))) -(((*1 *1 *2) - (-12 (-5 *2 (-649 (-649 *3))) (-4 *3 (-1106)) (-5 *1 (-911 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-310) (-147))) (-4 *5 (-798)) (-4 *6 (-855)) - (-4 *7 (-955 *4 *5 *6)) (-5 *2 (-649 (-649 *7))) - (-5 *1 (-453 *4 *5 *6 *7)) (-5 *3 (-649 *7)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-310) (-147))) (-4 *6 (-798)) - (-4 *7 (-855)) (-4 *8 (-955 *5 *6 *7)) (-5 *2 (-649 (-649 *8))) - (-5 *1 (-453 *5 *6 *7 *8)) (-5 *3 (-649 *8)))) +(((*1 *2) + (-12 (-5 *2 (-1278)) (-5 *1 (-1200 *3 *4)) (-4 *3 (-1106)) + (-4 *4 (-1106))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4445)) (-4 *1 (-245 *2)) (-4 *2 (-1223))))) +(((*1 *2 *1) (-12 (-5 *2 (-649 (-1165))) (-5 *1 (-1203))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1041))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1179 *7)) (-5 *3 (-569)) (-4 *7 (-955 *6 *4 *5)) + (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1055)) + (-5 *1 (-324 *4 *5 *6 *7))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *4 (-649 *10)) (-5 *5 (-112)) (-4 *10 (-1077 *6 *7 *8 *9)) + (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) + (-4 *9 (-1071 *6 *7 *8)) + (-5 *2 + (-649 + (-2 (|:| -4309 (-649 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(-367)) (-5 *2 (-1273 *4)) + (-5 *1 (-819 *4 *3)) (-4 *3 (-661 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-696 (-1141))) (-5 *1 (-1157))))) +(((*1 *2) + (-12 (-5 *2 (-927)) (-5 *1 (-447 *3)) (-4 *3 (-1249 (-569))))) + ((*1 *2 *2) + (-12 (-5 *2 (-927)) (-5 *1 (-447 *3)) (-4 *3 (-1249 (-569)))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1055)) (-4 *3 (-797)))) ((*1 *1 *2 *3) @@ -2964,10 +2697,10 @@ (-4 *2 (-367)) (-14 *5 (-999 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-718 *5 *6 *7)) (-4 *5 (-855)) - (-4 *6 (-239 (-2394 *4) (-776))) + (-4 *6 (-239 (-2426 *4) (-776))) (-14 *7 - (-1 (-112) (-2 (|:| -2114 *5) (|:| -2777 *6)) - (-2 (|:| -2114 *5) (|:| -2777 *6)))) + (-1 (-112) (-2 (|:| -2150 *5) (|:| -4320 *6)) + (-2 (|:| -2150 *5) (|:| -4320 *6)))) (-14 *4 (-649 (-1183))) (-4 *2 (-173)) (-5 *1 (-466 *4 *2 *5 *6 *7 *8)) (-4 *8 (-955 *2 *6 (-869 *4))))) ((*1 *1 *2 *3) @@ -2997,26 +2730,28 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-979 *4 *3 *2)) (-4 *4 (-1055)) (-4 *3 (-797)) (-4 *2 (-855))))) -(((*1 *2 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*2))))) +(((*1 *1 *2 *3) + (-12 (-5 *1 (-970 *2 *3)) (-4 *2 (-1106)) (-4 *3 (-1106))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-367)) (-4 *3 (-1055)) + (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2330 *1))) + (-4 *1 (-857 *3))))) +(((*1 *2 *2 *2 *2 *2) + (-12 (-4 *2 (-13 (-367) (-10 -8 (-15 ** ($ $ (-412 (-569))))))) + (-5 *1 (-1134 *3 *2)) (-4 *3 (-1249 *2))))) +(((*1 *2 *2) + (-12 (-4 *3 (-457)) (-5 *1 (-1214 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1208)))))) +(((*1 *2 *2) (-12 (-5 *1 (-159 *2)) (-4 *2 (-550)))) + ((*1 *1 *2) (-12 (-5 *2 (-649 (-569))) (-5 *1 (-977))))) (((*1 *2 *1 *3) (-12 (-4 *1 (-346 *4 *3 *5)) (-4 *4 (-1227)) (-4 *3 (-1249 *4)) (-4 *5 (-1249 (-412 *3))) (-5 *2 (-112)))) @@ -3026,6 +2761,33 @@ ((*1 *2 *1) (-12 (-4 *1 (-346 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-1249 *3)) (-4 *5 (-1249 (-412 *4))) (-5 *2 (-112))))) +(((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-52)) (-5 *1 (-1201))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-694 (-412 (-569)))) (-5 *2 (-649 *4)) (-5 *1 (-784 *4)) + 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*3 + (-1 (-2 (|:| |ans| *4) (|:| -4407 *4) (|:| |sol?| (-112))) + (-569) *4)) + (-4 *4 (-367)) (-4 *5 (-1249 *4)) (-5 *1 (-579 *4 *5))))) +(((*1 *1 *1) + (-12 (-5 *1 (-600 *2)) (-4 *2 (-38 (-412 (-569)))) (-4 *2 (-1055))))) +(((*1 *2 *1) (-12 (-4 *1 (-532)) (-5 *2 (-696 (-552)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-649 (-694 *5))) (-5 *4 (-569)) (-4 *5 (-367)) + (-4 *5 (-1055)) (-5 *2 (-112)) (-5 *1 (-1035 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-649 (-694 *4))) (-4 *4 (-367)) (-4 *4 (-1055)) + (-5 *2 (-112)) (-5 *1 (-1035 *4))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-986 *2)) (-4 *2 (-1055)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-949 (-226))) (-5 *1 (-1219)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1271 *2)) (-4 *2 (-1223)) (-4 *2 (-1055))))) +(((*1 *2 *3 *3) + (-12 (|has| *2 (-6 (-4446 "*"))) (-4 *5 (-377 *2)) (-4 *6 (-377 *2)) + (-4 *2 (-1055)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1249 *2)) + (-4 *4 (-692 *2 *5 *6))))) +(((*1 *1 *2 *3 *4) + (-12 (-14 *5 (-649 (-1183))) (-4 *2 (-173)) + (-4 *4 (-239 (-2426 *5) (-776))) + (-14 *6 + (-1 (-112) (-2 (|:| -2150 *3) (|:| -4320 *4)) + (-2 (|:| -2150 *3) (|:| -4320 *4)))) + (-5 *1 (-466 *5 *2 *3 *4 *6 *7)) (-4 *3 (-855)) + (-4 *7 (-955 *2 *4 (-869 *5)))))) +(((*1 *2 *2) (-12 (-5 *2 (-383)) (-5 *1 (-1275)))) + ((*1 *2) (-12 (-5 *2 (-383)) (-5 *1 (-1275))))) (((*1 *2 *3 *4 *5 *6 *7) (-12 (-5 *3 (-694 *11)) (-5 *4 (-649 (-412 (-958 *8)))) (-5 *5 (-776)) (-5 *6 (-1165)) (-4 *8 (-13 (-310) (-147))) @@ -3050,485 +2883,233 @@ (|:| |wcond| (-649 (-958 *8))) (|:| |bsoln| (-2 (|:| |partsol| (-1273 (-412 (-958 *8)))) - (|:| -3371 (-649 (-1273 (-412 (-958 *8)))))))))) + (|:| -1903 (-649 (-1273 (-412 (-958 *8)))))))))) (|:| |rgsz| (-569)))) (-5 *1 (-930 *8 *9 *10 *11)) (-5 *7 (-569))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-649 (-869 *5))) (-14 *5 (-649 (-1183))) (-4 *6 (-457)) - (-5 *2 (-649 (-649 (-248 *5 *6)))) (-5 *1 (-476 *5 *6 *7)) - (-5 *3 (-649 (-248 *5 *6))) (-4 *7 (-457))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1185 (-412 (-569)))) (-5 *1 (-191)) (-5 *3 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(-4 *3 (-1249 *2))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-649 (-867))) (-5 *1 (-867)))) ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| -2738 (-649 (-867))) (|:| -3576 (-649 (-867))) - (|:| |presup| (-649 (-867))) (|:| -2728 (-649 (-867))) + (-2 (|:| -3955 (-649 (-867))) (|:| -3217 (-649 (-867))) + (|:| |presup| (-649 (-867))) (|:| -3859 (-649 (-867))) (|:| |args| (-649 (-867))))) (-5 *1 (-1183))))) -(((*1 *2 *3 *3 *3 *4 *5) - (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1249 *6)) - (-4 *6 (-13 (-367) (-147) (-1044 *4))) (-5 *4 (-569)) - (-5 *2 - (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-112)))) - (|:| -4289 - (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) - (|:| |beta| *3))))) - (-5 *1 (-1021 *6 *3))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1 (-649 *7) *7 (-1179 *7))) (-5 *5 (-1 (-423 *7) *7)) - (-4 *7 (-1249 *6)) (-4 *6 (-13 (-367) (-147) (-1044 (-412 (-569))))) - (-5 *2 (-649 (-2 (|:| |frac| (-412 *7)) (|:| -4289 *3)))) - (-5 *1 (-814 *6 *7 *3 *8)) (-4 *3 (-661 *7)) - (-4 *8 (-661 (-412 *7))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-423 *6) *6)) (-4 *6 (-1249 *5)) - (-4 *5 (-13 (-367) (-147) (-1044 (-569)) (-1044 (-412 (-569))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-838 *3)) (-4 *3 (-1106)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-848 *3)) (-4 *3 (-1106))))) +(((*1 *2 *3 *4 *4 *4 *3 *3 *5 *5 *3) + (-12 (-5 *3 (-569)) (-5 *4 (-694 (-226))) (-5 *5 (-226)) + (-5 *2 (-1041)) (-5 *1 (-756))))) +(((*1 *2 *1) + (-12 (-5 *2 - (-649 (-2 (|:| |frac| (-412 *6)) (|:| -4289 (-659 *6 (-412 *6)))))) - (-5 *1 (-817 *5 *6)) (-5 *3 (-659 *6 (-412 *6)))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-649 (-297 *4))) (-5 *1 (-632 *3 *4 *5)) (-4 *3 (-855)) - (-4 *4 (-13 (-173) (-722 (-412 (-569))))) (-14 *5 (-927))))) + (-649 + (-2 + (|:| -2003 + (-2 (|:| |var| (-1183)) (|:| |fn| (-319 (-226))) + (|:| -2080 (-1100 (-848 (-226)))) (|:| |abserr| (-226)) + (|:| |relerr| (-226)))) + (|:| -2214 + (-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| (-1163 (-226))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2080 + (-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 (-564)))) + ((*1 *2 *1) + (-12 (-4 *1 (-609 *3 *4)) (-4 *3 (-1106)) (-4 *4 (-1223)) + (-5 *2 (-649 *4))))) (((*1 *2) - (-12 (-4 *1 (-346 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-1249 *3)) - (-4 *5 (-1249 (-412 *4))) (-5 *2 (-694 (-412 *4)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1140 *3)) (-4 *3 (-1055)) (-5 *2 (-649 (-649 (-172))))))) -(((*1 *2 *3 *3 *4 *3 *5 *3 *5 *4 *5 *5 *4 *4 *5 *3) - (-12 (-5 *4 (-694 (-226))) (-5 *5 (-694 (-569))) (-5 *3 (-569)) - (-5 *2 (-1041)) (-5 *1 (-761))))) -(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-649 *1)) (-4 *1 (-926))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-949 (-226))) (-5 *2 (-1278)) (-5 *1 (-473))))) + (-12 + (-5 *2 (-2 (|:| -1950 (-649 (-1183))) (|:| -2035 (-649 (-1183))))) + (-5 *1 (-1225))))) +(((*1 *2) + (-12 (-4 *3 (-1055)) (-5 *2 (-964 (-717 *3 *4))) (-5 *1 (-717 *3 *4)) + (-4 *4 (-1249 *3))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-569)) (-5 *4 (-694 (-226))) (-5 *2 (-1041)) + (-5 *1 (-752))))) +(((*1 *1 *2) + (-12 (-5 *2 (-776)) (-5 *1 (-680 *3)) (-4 *3 (-1055)) + (-4 *3 (-1106))))) +(((*1 *2 *3 *4 *4 *3 *4 *5 *4 *4 *3 *3 *3 *3 *6 *3 *7) + (-12 (-5 *3 (-569)) (-5 *5 (-112)) (-5 *6 (-694 (-226))) + (-5 *7 (-3 (|:| |fn| (-393)) (|:| |fp| (-77 OBJFUN)))) + (-5 *4 (-226)) (-5 *2 (-1041)) (-5 *1 (-758))))) (((*1 *1 *2) (-12 (-5 *2 (-1273 *4)) (-4 *4 (-1223)) (-4 *1 (-239 *3 *4))))) -(((*1 *2 *3) (-12 (-5 *3 (-511)) (-5 *2 (-696 (-188))) (-5 *1 (-188))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-1275))))) -(((*1 *1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-128))))) +(((*1 *1 *1) (-12 (-4 *1 (-661 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) +(((*1 *2 *1 *3 *3 *2) + (-12 (-5 *3 (-569)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1223)) + (-4 *4 (-377 *2)) (-4 *5 (-377 *2)))) + ((*1 *2 *1 *3 *2) + (-12 (|has| *1 (-6 -4445)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1106)) + (-4 *2 (-1223))))) (((*1 *2 *3) (-12 (-4 *4 (-1055)) (-4 *2 (-13 (-409) (-1044 *4) (-367) (-1208) (-287))) @@ -3543,34 +3124,34 @@ ((*1 *2 *1) (-12 (-4 *1 (-1271 *2)) (-4 *2 (-1223)) (-4 *2 (-1008)) (-4 *2 (-1055))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-569)))) (-4 *5 (-1249 *4)) - (-5 *2 (-2 (|:| |ans| (-412 *5)) (|:| |nosol| (-112)))) - (-5 *1 (-1021 *4 *5)) (-5 *3 (-412 *5))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *7 (-1249 *5)) (-4 *4 (-729 *5 *7)) - (-5 *2 (-2 (|:| -4368 (-694 *6)) (|:| |vec| (-1273 *5)))) - (-5 *1 (-816 *5 *6 *7 *4 *3)) (-4 *6 (-661 *5)) (-4 *3 (-661 *4))))) -(((*1 *2 *3 *4 *5 *6 *7 *6) - (|partial| -12 - (-5 *5 - (-2 (|:| |contp| *3) - (|:| -2671 (-649 (-2 (|:| |irr| *10) (|:| -2727 (-569))))))) - (-5 *6 (-649 *3)) (-5 *7 (-649 *8)) (-4 *8 (-855)) (-4 *3 (-310)) - (-4 *10 (-955 *3 *9 *8)) (-4 *9 (-798)) - (-5 *2 - (-2 (|:| |polfac| (-649 *10)) (|:| |correct| *3) - (|:| |corrfact| (-649 (-1179 *3))))) - (-5 *1 (-630 *8 *9 *3 *10)) (-5 *4 (-649 (-1179 *3)))))) -(((*1 *2) - (-12 (-4 *1 (-346 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-1249 *3)) - (-4 *5 (-1249 (-412 *4))) (-5 *2 (-694 (-412 *4)))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-649 (-958 *4))) (-5 *3 (-649 (-1183))) (-4 *4 (-457)) - (-5 *1 (-924 *4))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-649 (-649 (-949 (-226))))) (-5 *3 (-649 (-879))) - (-5 *1 (-473))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) +(((*1 *1 *1) (-5 *1 (-226))) ((*1 *1 *1) (-5 *1 (-383))) + ((*1 *1) (-5 *1 (-383)))) +(((*1 *1 *2 *3 *3 *3 *4) + (-12 (-4 *4 (-367)) (-4 *3 (-1249 *4)) (-4 *5 (-1249 (-412 *3))) + (-4 *1 (-339 *4 *3 *5 *2)) (-4 *2 (-346 *4 *3 *5)))) + ((*1 *1 *2 *2 *3) + (-12 (-5 *3 (-569)) (-4 *2 (-367)) (-4 *4 (-1249 *2)) + (-4 *5 (-1249 (-412 *4))) (-4 *1 (-339 *2 *4 *5 *6)) + (-4 *6 (-346 *2 *4 *5)))) + ((*1 *1 *2 *2) + (-12 (-4 *2 (-367)) (-4 *3 (-1249 *2)) (-4 *4 (-1249 (-412 *3))) + (-4 *1 (-339 *2 *3 *4 *5)) (-4 *5 (-346 *2 *3 *4)))) + ((*1 *1 *2) + (-12 (-4 *3 (-367)) (-4 *4 (-1249 *3)) (-4 *5 (-1249 (-412 *4))) + (-4 *1 (-339 *3 *4 *5 *2)) (-4 *2 (-346 *3 *4 *5)))) + ((*1 *1 *2) + (-12 (-5 *2 (-418 *4 (-412 *4) *5 *6)) (-4 *4 (-1249 *3)) + (-4 *5 (-1249 (-412 *4))) (-4 *6 (-346 *3 *4 *5)) (-4 *3 (-367)) + (-4 *1 (-339 *3 *4 *5 *6))))) +(((*1 *1 *1) + (-12 (-4 *2 (-310)) (-4 *3 (-998 *2)) (-4 *4 (-1249 *3)) + (-5 *1 (-418 *2 *3 *4 *5)) (-4 *5 (-13 (-414 *3 *4) (-1044 *3)))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-134))))) +(((*1 *2 *2) + (|partial| -12 (-5 *2 (-649 (-898 *3))) (-5 *1 (-898 *3)) + (-4 *3 (-1106))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-829))))) (((*1 *2 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-173)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-561) (-1044 (-569)))) (-5 *2 (-319 *4)) @@ -3578,45 +3159,40 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-569)) (-644 (-569)))) (-5 *1 (-1212 *3 *2)) (-4 *2 (-13 (-27) (-1208) (-435 *3)))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-1223)) (-5 *1 (-183 *3 *2)) (-4 *2 (-679 *3))))) -(((*1 *2 *1 *3 *3 *3) - (-12 (-5 *3 (-383)) (-5 *2 (-1278)) (-5 *1 (-1275))))) -(((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-128))))) -(((*1 *2 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1249 *5)) - (-4 *5 (-13 (-367) (-147) (-1044 (-569)))) - (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-412 *6)) (|:| |c| (-412 *6)) - (|:| -3566 *6))) - (-5 *1 (-1021 *5 *6)) (-5 *3 (-412 *6))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-776)) (-5 *5 (-649 *3)) (-4 *3 (-310)) (-4 *6 (-855)) - (-4 *7 (-798)) (-5 *2 (-112)) (-5 *1 (-630 *6 *7 *3 *8)) - (-4 *8 (-955 *3 *7 *6))))) +(((*1 *2 *3 *4 *4 *2 *2 *2 *2) + (-12 (-5 *2 (-569)) + (-5 *3 + (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-776)) (|:| |poli| *4) + (|:| |polj| *4))) + (-4 *6 (-798)) (-4 *4 (-955 *5 *6 *7)) (-4 *5 (-457)) (-4 *7 (-855)) + (-5 *1 (-454 *5 *6 *7 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-827))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1223)) + (-4 *4 (-377 *3)) (-4 *5 (-377 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4445)) (-4 *1 (-494 *3)) + (-4 *3 (-1223))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1163 *3)) (-4 *3 (-367)) (-4 *3 (-1055)) + (-5 *1 (-1167 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-394)) (-5 *2 (-112))))) (((*1 *2 *3) - (-12 (-5 *3 (-658 (-412 *2))) (-4 *2 (-1249 *4)) (-5 *1 (-815 *4 *2)) - (-4 *4 (-13 (-367) (-147) (-1044 (-569)) (-1044 (-412 (-569))))))) - ((*1 *2 *3) - (-12 (-5 *3 (-659 *2 (-412 *2))) (-4 *2 (-1249 *4)) - (-5 *1 (-815 *4 *2)) - (-4 *4 (-13 (-367) (-147) (-1044 (-569)) (-1044 (-412 (-569)))))))) + (-12 (-4 *4 (-561)) (-5 *2 (-776)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-422 *4))))) (((*1 *2 *1) - (-12 (-4 *1 (-346 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-1249 *3)) - (-4 *5 (-1249 (-412 *4))) - (-5 *2 (-2 (|:| |num| (-1273 *4)) (|:| |den| *4)))))) -(((*1 *1 *1) - (-12 (-5 *1 (-1171 *2 *3)) (-14 *2 (-927)) (-4 *3 (-1055))))) + (-12 (-4 *3 (-457)) (-4 *4 (-855)) (-4 *5 (-798)) (-5 *2 (-649 *6)) + (-5 *1 (-993 *3 *4 *5 *6)) (-4 *6 (-955 *3 *5 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186))))) (((*1 *2 *3) - (-12 (-5 *3 (-1183)) - (-4 *4 (-13 (-310) (-1044 (-569)) (-644 (-569)) (-147))) - (-5 *2 (-1 *5 *5)) (-5 *1 (-809 *4 *5)) - (-4 *5 (-13 (-29 *4) (-1208) (-965)))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-649 (-958 *4))) (-5 *3 (-649 (-1183))) (-4 *4 (-457)) - (-5 *1 (-924 *4))))) + (-12 (-5 *3 (-2 (|:| -4395 (-412 (-569))) (|:| -4407 (-412 (-569))))) + (-5 *2 (-412 (-569))) (-5 *1 (-1026 *4)) (-4 *4 (-1249 (-569)))))) (((*1 *2 *1) (-12 (-5 *2 (-649 (-511))) (-5 *1 (-49)))) ((*1 *2 *1) (-12 (-5 *2 (-649 (-881))) (-5 *1 (-488))))) +(((*1 *2) + (-12 (-5 *2 (-927)) (-5 *1 (-447 *3)) (-4 *3 (-1249 (-569))))) + ((*1 *2 *2) + (-12 (-5 *2 (-927)) (-5 *1 (-447 *3)) (-4 *3 (-1249 (-569)))))) (((*1 *2 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-173)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-561) (-1044 (-569)))) (-5 *2 (-319 *4)) @@ -3626,81 +3202,98 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-569)) (-644 (-569)))) (-5 *1 (-1212 *3 *2)) (-4 *2 (-13 (-27) (-1208) (-435 *3)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-649 (-649 (-949 (-226))))) (-5 *2 (-649 (-226))) - (-5 *1 (-473))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-383)) (-5 *2 (-1278)) (-5 *1 (-1275))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1223)) (-5 *2 (-776)) (-5 *1 (-183 *4 *3)) - (-4 *3 (-679 *4))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-128))))) -(((*1 *2 *3 *4 *4 *4 *5 *6 *7) - (|partial| -12 (-5 *5 (-1183)) - (-5 *6 - (-1 - (-3 - (-2 (|:| |mainpart| *4) - (|:| 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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 (-564)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-776)) (-4 *1 (-700 *2)) (-4 *2 (-1106)))) ((*1 *1 *2) - (-12 (-5 *2 (-649 (-1171 *3 *4))) (-5 *1 (-1171 *3 *4)) - (-14 *3 (-927)) (-4 *4 (-1055)))) - ((*1 *1 *1 *1) - (-12 (-5 *1 (-1171 *2 *3)) (-14 *2 (-927)) (-4 *3 (-1055))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1183)) - (-4 *4 (-13 (-310) (-1044 (-569)) (-644 (-569)) (-147))) - (-5 *1 (-809 *4 *2)) (-4 *2 (-13 (-29 *4) (-1208) (-965)))))) + (-12 + (-5 *2 + (-2 + (|:| -2003 + (-2 (|:| |xinit| (-226)) (|:| |xend| (-226)) + (|:| |fn| (-1273 (-319 (-226)))) (|:| |yinit| (-649 (-226))) + (|:| |intvals| (-649 (-226))) (|:| |g| (-319 (-226))) + (|:| |abserr| (-226)) (|:| |relerr| (-226)))) + (|:| -2214 + (-2 (|:| |stiffness| (-383)) (|:| |stability| (-383)) + (|:| |expense| (-383)) (|:| |accuracy| (-383)) + (|:| |intermediateResults| (-383)))))) + (-5 *1 (-808)))) + ((*1 *2 *3 *4) + (-12 (-5 *2 (-1278)) (-5 *1 (-1200 *3 *4)) (-4 *3 (-1106)) + (-4 *4 (-1106))))) +(((*1 *1 *1) (|partial| -4 *1 (-1158)))) +(((*1 *2 *2) + (-12 (-4 *3 (-457)) (-5 *1 (-1214 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1208)))))) (((*1 *2 *1) (-12 (-5 *2 (-649 (-1222))) (-5 *1 (-686)))) ((*1 *2 *1) (-12 (-5 *2 (-649 (-1188))) (-5 *1 (-1124))))) -(((*1 *2 *3) - (-12 (-5 *3 (-649 (-569))) (-5 *2 (-910 (-569))) (-5 *1 (-923)))) - ((*1 *2 *3) (-12 (-5 *3 (-977)) (-5 *2 (-910 (-569))) (-5 *1 (-923))))) -(((*1 *2 *1) (-12 (-5 *2 (-649 (-1165))) (-5 *1 (-1203))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1147 *2 *3)) (-4 *2 (-13 (-1106) (-34))) + (-4 *3 (-13 (-1106) (-34)))))) +(((*1 *2 *1) (-12 (-4 *1 (-961)) (-5 *2 (-1100 (-226))))) + ((*1 *2 *1) (-12 (-4 *1 (-980)) (-5 *2 (-1100 (-226)))))) (((*1 *1 *1) (-12 (-5 *1 (-343 *2 *3 *4)) (-14 *2 (-649 (-1183))) (-14 *3 (-649 (-1183))) (-4 *4 (-392)))) @@ -3710,28 +3303,16 @@ ((*1 *1 *2) (-12 (-5 *2 (-412 (-569))) (-4 *1 (-1018)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1018)) (-5 *2 (-927)))) ((*1 *1 *1) (-4 *1 (-1018)))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-157)) (-5 *2 (-1278)) (-5 *1 (-1275))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *3 (-649 (-265))) (-5 *1 (-263)))) - ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-265)))) - ((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-472)))) - ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-472))))) -(((*1 *2 *2) - (|partial| -12 (-4 *3 (-1223)) (-5 *1 (-183 *3 *2)) - (-4 *2 (-679 *3))))) -(((*1 *1 *1 *2 *1) (-12 (-5 *1 (-127 *2)) (-4 *2 (-1106)))) - ((*1 *1 *2) (-12 (-5 *1 (-127 *2)) (-4 *2 (-1106))))) (((*1 *1 *2) (-12 (-5 *2 (-649 *3)) (-4 *3 (-1223)) (-4 *1 (-151 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-649 (-2 (|:| -2777 (-776)) (|:| -2132 *4) (|:| |num| *4)))) + (-5 *2 (-649 (-2 (|:| -4320 (-776)) (|:| -2167 *4) (|:| |num| *4)))) (-4 *4 (-1249 *3)) (-4 *3 (-13 (-367) (-147))) (-5 *1 (-404 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -2513 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -2577 "void"))) (-5 *3 (-649 (-958 (-569)))) (-5 *4 (-112)) (-5 *1 (-442)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -2513 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -2577 "void"))) (-5 *3 (-649 (-1183))) (-5 *4 (-112)) (-5 *1 (-442)))) ((*1 *2 *1) (-12 (-5 *2 (-1163 *3)) (-5 *1 (-606 *3)) (-4 *3 (-1223)))) @@ -3751,24 +3332,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-718 *2 *3 *4)) (-4 *2 (-855)) (-4 *3 (-1106)) (-14 *4 - (-1 (-112) (-2 (|:| -2114 *2) (|:| -2777 *3)) - (-2 (|:| -2114 *2) (|:| -2777 *3)))))) + (-1 (-112) (-2 (|:| -2150 *2) (|:| -4320 *3)) + (-2 (|:| -2150 *2) (|:| -4320 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-511)) (-5 *3 (-1124)) (-5 *1 (-843)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-878 *2 *3)) (-4 *2 (-1223)) (-4 *3 (-1223)))) ((*1 *1 *2) - (-12 (-5 *2 (-649 (-2 (|:| -1963 (-1183)) (|:| -2179 *4)))) + (-12 (-5 *2 (-649 (-2 (|:| -2003 (-1183)) (|:| -2214 *4)))) (-4 *4 (-1106)) (-5 *1 (-895 *3 *4)) (-4 *3 (-1106)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-649 *5)) (-4 *5 (-13 (-1106) (-34))) (-5 *2 (-649 (-1146 *3 *5))) (-5 *1 (-1146 *3 *5)) (-4 *3 (-13 (-1106) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-649 (-2 (|:| |val| *4) (|:| -3550 *5)))) + (-12 (-5 *3 (-649 (-2 (|:| |val| *4) (|:| -3660 *5)))) (-4 *4 (-13 (-1106) (-34))) (-4 *5 (-13 (-1106) (-34))) (-5 *2 (-649 (-1146 *4 *5))) (-5 *1 (-1146 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3550 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3660 *4))) (-4 *3 (-13 (-1106) (-34))) (-4 *4 (-13 (-1106) (-34))) (-5 *1 (-1146 *3 *4)))) ((*1 *1 *2 *3) @@ -3791,35 +3372,12 @@ (-4 *4 (-13 (-1106) (-34))) (-5 *1 (-1147 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1172 *2 *3)) (-4 *2 (-1106)) (-4 *3 (-1106))))) -(((*1 *2 *3 *4 *4 *5 *6 *7) - (-12 (-5 *5 (-1183)) - (-5 *6 - (-1 - (-3 - (-2 (|:| |mainpart| *4) - (|:| |limitedlogs| - (-649 (-2 (|:| |coeff| *4) (|:| |logand| *4))))) - "failed") - *4 (-649 *4))) - (-5 *7 - (-1 (-3 (-2 (|:| -2209 *4) (|:| |coeff| *4)) "failed") *4 *4)) - (-4 *4 (-13 (-1208) (-27) (-435 *8))) - (-4 *8 (-13 (-457) (-147) (-1044 *3) (-644 *3))) (-5 *3 (-569)) - (-5 *2 (-2 (|:| |ans| *4) (|:| -4386 *4) (|:| |sol?| (-112)))) - (-5 *1 (-1019 *8 *4))))) -(((*1 *2 *2 *3) - (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-569))))) - (-4 *3 (-1249 *4)) (-5 *1 (-814 *4 *3 *2 *5)) (-4 *2 (-661 *3)) - (-4 *5 (-661 (-412 *3))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-412 *5)) - (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-569))))) (-4 *5 (-1249 *4)) - (-5 *1 (-814 *4 *5 *2 *6)) (-4 *2 (-661 *5)) (-4 *6 (-661 *3))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) (((*1 *2 *1) - (-12 (-4 *2 (-561)) (-5 *1 (-628 *2 *3)) (-4 *3 (-1249 *2))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1273 *3)) (-4 *3 (-1249 *4)) (-4 *4 (-1227)) - (-4 *1 (-346 *4 *3 *5)) (-4 *5 (-1249 (-412 *3)))))) + (-12 (-4 *2 (-1106)) (-5 *1 (-970 *2 *3)) (-4 *3 (-1106))))) +(((*1 *2 *3 *3 *4 *4 *3 *3 *5 *3) + (-12 (-5 *3 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(-383)) (|:| |accuracy| (-383)) - (|:| |intermediateResults| (-383)))) - (-5 *1 (-808))))) -(((*1 *2) (-12 (-5 *2 (-910 (-569))) (-5 *1 (-923))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-472)))) - ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-472))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-112)) (-4 *6 (-13 (-457) (-1044 (-569)) (-644 (-569)))) + (-4 *3 (-13 (-27) (-1208) (-435 *6) (-10 -8 (-15 -3793 ($ *7))))) + (-4 *7 (-853)) + (-4 *8 + (-13 (-1251 *3 *7) (-367) (-1208) + (-10 -8 (-15 -3514 ($ $)) (-15 -2488 ($ $))))) + (-5 *2 + (-3 (|:| |%series| *8) + (|:| |%problem| (-2 (|:| |func| (-1165)) (|:| |prob| (-1165)))))) + (-5 *1 (-427 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1165)) (-4 *9 (-989 *8)) + (-14 *10 (-1183))))) +(((*1 *1) (-5 *1 (-141)))) +(((*1 *2 *2) + (-12 (-5 *2 (-649 *6)) (-4 *6 (-1071 *3 *4 *5)) (-4 *3 (-147)) + (-4 *3 (-310)) (-4 *3 (-561)) (-4 *4 (-798)) (-4 *5 (-855)) + (-5 *1 (-983 *3 *4 *5 *6))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-694 *2)) (-4 *2 (-173)) (-5 *1 (-146 *2)))) + ((*1 *2 *3) + (-12 (-4 *4 (-173)) (-4 *2 (-1249 *4)) (-5 *1 (-178 *4 *2 *3)) + (-4 *3 (-729 *4 *2)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-694 (-412 (-958 *5)))) (-5 *4 (-1183)) + (-5 *2 (-958 *5)) (-5 *1 (-295 *5)) (-4 *5 (-457)))) + ((*1 *2 *3) + (-12 (-5 *3 (-694 (-412 (-958 *4)))) (-5 *2 (-958 *4)) + (-5 *1 (-295 *4)) (-4 *4 (-457)))) + ((*1 *2 *1) + (-12 (-4 *1 (-374 *3 *2)) (-4 *3 (-173)) (-4 *2 (-1249 *3)))) + ((*1 *2 *3) + (-12 (-5 *3 (-694 (-170 (-412 (-569))))) + (-5 *2 (-958 (-170 (-412 (-569))))) (-5 *1 (-769 *4)) + (-4 *4 (-13 (-367) (-853))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-694 (-170 (-412 (-569))))) (-5 *4 (-1183)) + (-5 *2 (-958 (-170 (-412 (-569))))) (-5 *1 (-769 *5)) + (-4 *5 (-13 (-367) (-853))))) + ((*1 *2 *3) + (-12 (-5 *3 (-694 (-412 (-569)))) (-5 *2 (-958 (-412 (-569)))) + (-5 *1 (-784 *4)) (-4 *4 (-13 (-367) (-853))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-694 (-412 (-569)))) (-5 *4 (-1183)) + (-5 *2 (-958 (-412 (-569)))) (-5 *1 (-784 *5)) + (-4 *5 (-13 (-367) (-853)))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1148 *3 *4)) (-14 *3 (-927)) (-4 *4 (-367)) + (-5 *1 (-999 *3 *4))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-649 (-48))) (-5 *2 (-423 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1249 (-48))))) @@ -3900,8 +3482,8 @@ (-12 (-4 *4 (-13 (-855) - (-10 -8 (-15 -1384 ((-1183) $)) - (-15 -2599 ((-3 $ "failed") (-1183)))))) + (-10 -8 (-15 -1408 ((-1183) $)) + (-15 -2671 ((-3 $ "failed") (-1183)))))) (-4 *5 (-798)) (-4 *7 (-561)) (-5 *2 (-423 *3)) (-5 *1 (-461 *4 *5 *6 *7 *3)) (-4 *6 (-561)) (-4 *3 (-955 *7 *5 *4)))) @@ -3950,13 +3532,13 @@ (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) - (-10 -8 (-15 -1384 ((-1183) $)) - (-15 -2599 ((-3 $ "failed") (-1183)))))) + (-10 -8 (-15 -1408 ((-1183) $)) + (-15 -2671 ((-3 $ "failed") (-1183)))))) (-4 *6 (-310)) (-5 *2 (-423 *3)) (-5 *1 (-735 *4 *5 *6 *3)) (-4 *3 (-955 (-958 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-798)) - (-4 *5 (-13 (-855) (-10 -8 (-15 -1384 ((-1183) $))))) (-4 *6 (-561)) + (-4 *5 (-13 (-855) (-10 -8 (-15 -1408 ((-1183) $))))) (-4 *6 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*6) (|:| -3371 (-649 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -1903 (-649 *6))) "failed") *7 *6)) (-4 *6 (-367)) (-4 *7 (-661 *6)) - (-5 *2 (-2 (|:| |particular| (-1273 *6)) (|:| -3371 (-694 *6)))) + (-5 *2 (-2 (|:| |particular| (-1273 *6)) (|:| -1903 (-694 *6)))) (-5 *1 (-818 *6 *7)) (-5 *3 (-694 *6)) (-5 *4 (-1273 *6)))) ((*1 *2 *3) (-12 (-5 *3 (-904)) (-5 *2 (-1041)) (-5 *1 (-903)))) ((*1 *2 *3 *4) @@ -8563,179 +8482,57 @@ ((*1 *2 *3) (-12 (-4 *4 (-561)) (-5 *2 (-649 (-297 (-412 (-958 *4))))) (-5 *1 (-1192 *4)) (-5 *3 (-297 (-412 (-958 *4))))))) -(((*1 *1 *1 *2) - (-12 (-4 *1 (-982 *3 *4 *2 *5)) (-4 *3 (-1055)) (-4 *4 (-798)) - (-4 *2 (-855)) (-4 *5 (-1071 *3 *4 *2))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-617 *3)) (-4 *3 (-13 (-435 *5) (-27) (-1208))) - (-4 *5 (-13 (-457) (-1044 (-569)) (-147) (-644 (-569)))) - (-5 *2 (-591 *3)) (-5 *1 (-571 *5 *3 *6)) (-4 *6 (-1106))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1110)) (-5 *1 (-282))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-649 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(-12 (-4 *1 (-661 *2)) (-4 *2 (-1055)) (-4 *2 (-367)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-367)) (-5 *1 (-664 *4 *2)) + (-4 *2 (-661 *4))))) +(((*1 *2 *3) + (-12 (-4 *4 (-561)) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4304 *4))) + (-5 *1 (-975 *4 *3)) (-4 *3 (-1249 *4))))) (((*1 *2 *1) (-12 (-5 *2 (-649 (-2 (|:| |var| (-1183)) (|:| |fn| (-319 (-226))) - (|:| -3396 (-1100 (-848 (-226)))) (|:| |abserr| (-226)) + (|:| -2080 (-1100 (-848 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226))))) (-5 *1 (-564)))) ((*1 *2 *1) @@ -9526,13 +9200,63 @@ (|:| |intvals| (-649 (-226))) (|:| |g| (-319 (-226))) (|:| |abserr| (-226)) (|:| |relerr| (-226))))) (-5 *1 (-808))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *5 (-776)) (-4 *6 (-1106)) (-4 *7 (-906 *6)) + (-5 *2 (-694 *7)) (-5 *1 (-697 *6 *7 *3 *4)) (-4 *3 (-377 *7)) + (-4 *4 (-13 (-377 *6) (-10 -7 (-6 -4444))))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *3 (-3 (-412 (-958 *6)) (-1172 (-1183) (-958 *6)))) + (-5 *5 (-776)) (-4 *6 (-457)) (-5 *2 (-649 (-694 (-412 (-958 *6))))) + (-5 *1 (-295 *6)) (-5 *4 (-694 (-412 (-958 *6)))))) + ((*1 *2 *3 *4) + (-12 + (-5 *3 + (-2 (|:| |eigval| (-3 (-412 (-958 *5)) (-1172 (-1183) (-958 *5)))) + (|:| |eigmult| (-776)) (|:| |eigvec| (-649 *4)))) + (-4 *5 (-457)) (-5 *2 (-649 (-694 (-412 (-958 *5))))) + (-5 *1 (-295 *5)) (-5 *4 (-694 (-412 (-958 *5))))))) +(((*1 *1 *2) (-12 (-5 *1 (-228 *2)) (-4 *2 (-13 (-367) (-1208)))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-982 *3 *4 *2 *5)) (-4 *3 (-1055)) (-4 *4 (-798)) + (-4 *2 (-855)) (-4 *5 (-1071 *3 *4 *2))))) +(((*1 *1 *2) (-12 (-5 *2 (-412 (-569))) (-5 *1 (-492))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-898 *3)) (-4 *3 (-1106))))) +(((*1 *2 *1) (-12 (-4 *1 (-371 *2)) (-4 *2 (-173))))) (((*1 *2) - (-12 (-4 *3 (-1055)) (-5 *2 (-964 (-717 *3 *4))) (-5 *1 (-717 *3 *4)) - (-4 *4 (-1249 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-776)) (-5 *4 (-1273 *2)) (-4 *5 (-310)) - (-4 *6 (-998 *5)) (-4 *2 (-13 (-414 *6 *7) (-1044 *6))) - (-5 *1 (-418 *5 *6 *7 *2)) (-4 *7 (-1249 *6))))) + (-12 (-4 *4 (-173)) (-5 *2 (-1179 (-958 *4))) (-5 *1 (-421 *3 *4)) + (-4 *3 (-422 *4)))) + ((*1 *2) + (-12 (-4 *1 (-422 *3)) (-4 *3 (-173)) (-4 *3 (-367)) + (-5 *2 (-1179 (-958 *3))))) + ((*1 *2) + (-12 (-5 *2 (-1179 (-412 (-958 *3)))) (-5 *1 (-458 *3 *4 *5 *6)) + (-4 *3 (-561)) (-4 *3 (-173)) (-14 *4 (-927)) + (-14 *5 (-649 (-1183))) (-14 *6 (-1273 (-694 *3)))))) +(((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-827))))) +(((*1 *1 *2 *2) + (-12 + (-5 *2 + (-3 (|:| I (-319 (-569))) (|:| -1666 (-319 (-383))) + (|:| CF (-319 (-170 (-383)))) (|:| |switch| (-1182)))) + (-5 *1 (-1182))))) +(((*1 *1 *2) + (-12 (-5 *2 (-412 (-569))) (-4 *1 (-559 *3)) + (-4 *3 (-13 (-409) (-1208))))) + ((*1 *1 *2) (-12 (-4 *1 (-559 *2)) (-4 *2 (-13 (-409) (-1208))))) + ((*1 *1 *2 *2) (-12 (-4 *1 (-559 *2)) (-4 *2 (-13 (-409) (-1208)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-776)) (-5 *2 (-1278)) (-5 *1 (-871 *4 *5 *6 *7)) + (-4 *4 (-1055)) (-14 *5 (-649 (-1183))) (-14 *6 (-649 *3)) + (-14 *7 *3))) + ((*1 *2 *3) + (-12 (-5 *3 (-776)) (-4 *4 (-1055)) (-4 *5 (-855)) (-4 *6 (-798)) + (-14 *8 (-649 *5)) (-5 *2 (-1278)) + (-5 *1 (-1285 *4 *5 *6 *7 *8 *9 *10)) (-4 *7 (-955 *4 *6 *5)) + (-14 *9 (-649 *3)) (-14 *10 *3)))) +(((*1 *1 *2) (-12 (-5 *2 (-649 *3)) (-4 *3 (-855)) (-5 *1 (-121 *3))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-569)) (-4 *1 (-57 *4 *5 *3)) (-4 *4 (-1223)) + (-4 *5 (-377 *4)) (-4 *3 (-377 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) (-4 *2 (-13 (-435 *3) (-1008))))) @@ -9549,109 +9273,53 @@ ((*1 *2 *2) (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3))))) -(((*1 *2) (-12 (-5 *2 (-1183)) (-5 *1 (-1186))))) -(((*1 *2 *1) (-12 (-5 *2 (-569)) (-5 *1 (-977))))) -(((*1 *1 *2) - (-12 +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1249 *5)) (-4 *5 (-367)) + (-4 *7 (-1249 (-412 *6))) + (-5 *2 (-2 (|:| |answer| *3) (|:| -2438 *3))) + (-5 *1 (-567 *5 *6 *7 *3)) (-4 *3 (-346 *5 *6 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1249 *5)) (-4 *5 (-367)) (-5 *2 - (-649 - (-2 - (|:| -1963 - (-2 (|:| |var| (-1183)) (|:| |fn| (-319 (-226))) - (|:| -3396 (-1100 (-848 (-226)))) (|:| |abserr| (-226)) - (|:| |relerr| (-226)))) - (|:| -2179 - (-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| (-1163 (-226))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3396 - (-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 (-564))))) + (-2 (|:| |answer| (-412 *6)) (|:| -2438 (-412 *6)) + (|:| |specpart| (-412 *6)) (|:| |polypart| *6))) + (-5 *1 (-568 *5 *6)) (-5 *3 (-412 *6))))) +(((*1 *1 *2) + (-12 (-5 *2 (-649 *3)) (-4 *3 (-1223)) (-5 *1 (-1163 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-776)) (-4 *5 (-1055)) (-5 *2 (-569)) + (-5 *1 (-448 *5 *3 *6)) (-4 *3 (-1249 *5)) + (-4 *6 (-13 (-409) (-1044 *5) (-367) (-1208) (-287))))) + ((*1 *2 *3) + (-12 (-4 *4 (-1055)) (-5 *2 (-569)) (-5 *1 (-448 *4 *3 *5)) + (-4 *3 (-1249 *4)) + (-4 *5 (-13 (-409) (-1044 *4) (-367) (-1208) (-287)))))) +(((*1 *2 *3 *3 *2) + (-12 (-5 *2 (-1041)) (-5 *3 (-1183)) (-5 *1 (-193))))) (((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1008)))))) -(((*1 *2 *2) (-12 (-5 *2 (-383)) (-5 *1 (-1275)))) - ((*1 *2) (-12 (-5 *2 (-383)) (-5 *1 (-1275))))) -(((*1 *1 *1) (-5 *1 (-1182))) - ((*1 *1 *2) + (-12 (-5 *2 (-949 *3)) (-4 *3 (-13 (-367) (-1208) (-1008))) + (-5 *1 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(-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-649 (-1183))) (-5 *2 (-1278)) (-5 *1 (-1186)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-649 (-1183))) (-5 *3 (-1183)) (-5 *2 (-1278)) - (-5 *1 (-1186)))) - ((*1 *2 *3 *4 *1) - (-12 (-5 *4 (-649 (-1183))) (-5 *3 (-1183)) (-5 *2 (-1278)) - (-5 *1 (-1186))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-561)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4168 *4))) - (-5 *1 (-975 *4 *3)) (-4 *3 (-1249 *4))))) -(((*1 *1) (-5 *1 (-564)))) -(((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1008)))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1139 (-226))) (-5 *3 (-649 (-265))) (-5 *1 (-1275)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1139 (-226))) (-5 *3 (-1165)) (-5 *1 (-1275)))) - ((*1 *1 *1) (-5 *1 (-1275)))) -(((*1 *1 *1) + (-12 (-4 *4 (-998 *2)) (-4 *2 (-561)) (-5 *1 (-142 *2 *4 *3)) + (-4 *3 (-377 *4)))) + ((*1 *2 *3) + (-12 (-4 *4 (-998 *2)) (-4 *2 (-561)) (-5 *1 (-508 *2 *4 *5 *3)) + (-4 *5 (-377 *2)) (-4 *3 (-377 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-694 *4)) (-4 *4 (-998 *2)) (-4 *2 (-561)) + (-5 *1 (-698 *2 *4)))) + ((*1 *2 *3) + (-12 (-4 *4 (-998 *2)) (-4 *2 (-561)) (-5 *1 (-1242 *2 *4 *3)) + (-4 *3 (-1249 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1165)) (-5 *2 (-569)) (-5 *1 (-1205 *4)) + (-4 *4 (-1055))))) +(((*1 *2 *3) (-12 (-5 *3 (-927)) (-5 *2 (-1165)) (-5 *1 (-791))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) - (-4 *4 (-855))))) -(((*1 *2 *3) (-12 (-5 *3 (-867)) (-5 *2 (-1165)) (-5 *1 (-715))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-867)))) - ((*1 *1 *1) (-5 *1 (-867)))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-569)) (-5 *1 (-423 *2)) (-4 *2 (-561))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-1055)) (-4 *2 (-692 *4 *5 *6)) - (-5 *1 (-104 *4 *3 *2 *5 *6)) (-4 *3 (-1249 *4)) (-4 *5 (-377 *4)) - (-4 *6 (-377 *4))))) + (-4 *4 (-855)))) + ((*1 *2 *2 *1) + (-12 (-4 *1 (-1216 *3 *4 *5 *2)) (-4 *3 (-561)) (-4 *4 (-798)) + (-4 *5 (-855)) (-4 *2 (-1071 *3 *4 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*3))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1249 *4)) (-4 *4 (-1227)) + (-4 *6 (-1249 (-412 *5))) + (-5 *2 + (-2 (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) + (|:| |gd| *5))) + (-4 *1 (-346 *4 *5 *6))))) (((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) (-4 *2 (-13 (-435 *3) (-1008))))) @@ -9722,46 +9414,49 @@ ((*1 *2 *2) (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-3 (|:| |fst| (-439)) (|:| -2513 "void"))) - (-5 *2 (-1278)) (-5 *1 (-1186)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1183)) - (-5 *4 (-3 (|:| |fst| (-439)) (|:| -2513 "void"))) (-5 *2 (-1278)) - (-5 *1 (-1186)))) - ((*1 *2 *3 *4 *1) - (-12 (-5 *3 (-1183)) - (-5 *4 (-3 (|:| |fst| (-439)) (|:| -2513 "void"))) (-5 *2 (-1278)) - (-5 *1 (-1186))))) -(((*1 *2 *3 *3) - (-12 (-4 *2 (-561)) (-5 *1 (-975 *2 *3)) (-4 *3 (-1249 *2))))) -(((*1 *2 *2) (|partial| -12 (-5 *1 (-563 *2)) (-4 *2 (-550))))) -(((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - 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(|:| -4367 (-776))))))) + (|partial| -12 (-5 *2 (-649 (-898 *3))) (-5 *1 (-898 *3)) + (-4 *3 (-1106)))) ((*1 *2 *1) - (-12 (-5 *2 (-649 (-2 (|:| -3699 *3) (|:| -2777 (-569))))) - (-5 *1 (-423 *3)) (-4 *3 (-561))))) + (|partial| -12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) + (-5 *2 (-649 *1)) (-4 *1 (-955 *3 *4 *5)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1055)) + (-4 *7 (-955 *6 *4 *5)) (-5 *2 (-649 *3)) + (-5 *1 (-956 *4 *5 *6 *7 *3)) + (-4 *3 + (-13 (-367) + (-10 -8 (-15 -3793 ($ *7)) (-15 -4396 (*7 $)) + (-15 -4409 (*7 $)))))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-694 (-412 (-958 (-569))))) + (-5 *2 (-694 (-319 (-569)))) (-5 *1 (-1037))))) +(((*1 *1 *2) + (-12 (-5 *2 (-649 (-569))) (-5 *1 (-1010 *3)) (-14 *3 (-569))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-226)) (-5 *4 (-569)) (-5 *2 (-1041)) (-5 *1 (-763))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-649 (-776))) (-5 *3 (-112)) (-5 *1 (-1171 *4 *5)) + (-14 *4 (-927)) (-4 *5 (-1055))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-1071 *3 *4 *2)) (-4 *3 (-1055)) (-4 *4 (-798)) + (-4 *2 (-855)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) + (-4 *4 (-855))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-776)) (-5 *1 (-883 *2)) (-4 *2 (-1223)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-776)) (-5 *1 (-885 *2)) (-4 *2 (-1223)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-776)) (-5 *1 (-888 *2)) (-4 *2 (-1223))))) +(((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-827))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-1055)) (-4 *2 (-692 *4 *5 *6)) - (-5 *1 (-104 *4 *3 *2 *5 *6)) (-4 *3 (-1249 *4)) (-4 *5 (-377 *4)) - (-4 *6 (-377 *4))))) + (-12 (-5 *3 (-649 (-569))) (-5 *2 (-694 (-569))) (-5 *1 (-1116))))) (((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) (-4 *2 (-13 (-435 *3) (-1008))))) @@ -9781,21 +9476,24 @@ ((*1 *2 *2) (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3))))) -(((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-1186)))) - ((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186)))) - ((*1 *2 *3 *1) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186))))) -(((*1 *2 *2 *2 *2 *3) - (-12 (-4 *3 (-561)) (-5 *1 (-975 *3 *2)) (-4 *2 (-1249 *3))))) -(((*1 *2 *3) (-12 (-5 *2 (-423 *3)) (-5 *1 (-563 *3)) (-4 *3 (-550))))) -(((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1008)))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-776)) (-5 *3 (-949 *4)) (-4 *1 (-1140 *4)) - (-4 *4 (-1055)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-776)) (-5 *4 (-949 (-226))) (-5 *2 (-1278)) - (-5 *1 (-1275))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-1077 *4 *5 *6 *3)) (-4 *4 (-457)) (-4 *5 (-798)) + (-4 *6 (-855)) (-4 *3 (-1071 *4 *5 *6)) (-5 *2 (-112))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1 (-949 (-226)) (-949 (-226)))) (-5 *3 (-649 (-265))) + (-5 *1 (-263)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1 (-949 (-226)) (-949 (-226)))) (-5 *1 (-265)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-649 (-486 *5 *6))) (-5 *3 (-486 *5 *6)) + (-14 *5 (-649 (-1183))) (-4 *6 (-457)) (-5 *2 (-1273 *6)) + (-5 *1 (-636 *5 *6))))) +(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-511)) (-5 *3 (-602)) (-5 *1 (-590))))) +(((*1 *1) (-5 *1 (-602)))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1273 *4)) (-5 *3 (-569)) (-4 *4 (-353)) + (-5 *1 (-533 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-569)) (-5 *1 (-932))))) (((*1 *2 *3 *2 *3) (-12 (-5 *2 (-442)) (-5 *3 (-1183)) (-5 *1 (-1186)))) ((*1 *2 *3 *2) (-12 (-5 *2 (-442)) (-5 *3 (-1183)) (-5 *1 (-1186)))) @@ -9808,18 +9506,23 @@ (-12 (-5 *2 (-442)) (-5 *3 (-1183)) (-5 *1 (-1187)))) ((*1 *2 *3 *2 *1) (-12 (-5 *2 (-442)) (-5 *3 (-649 (-1183))) (-5 *1 (-1187))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) - (-4 *4 (-855))))) -(((*1 *1 *1 *1) (-5 *1 (-867)))) -(((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) - (|partial| -12 (-5 *2 (-649 (-1179 *13))) (-5 *3 (-1179 *13)) - (-5 *4 (-649 *12)) (-5 *5 (-649 *10)) (-5 *6 (-649 *13)) - (-5 *7 (-649 (-649 (-2 (|:| -4167 (-776)) (|:| |pcoef| *13))))) - (-5 *8 (-649 (-776))) (-5 *9 (-1273 (-649 (-1179 *10)))) - (-4 *12 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(-1169 *3))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1183)) - (-5 *2 (-3 (|:| |fst| (-439)) (|:| -2513 "void"))) (-5 *1 (-1186))))) -(((*1 *2 *2 *3 *3 *4) - (-12 (-5 *4 (-776)) (-4 *3 (-561)) (-5 *1 (-975 *3 *2)) - (-4 *2 (-1249 *3))))) -(((*1 *2 *3 *4 *5 *6) - (|partial| -12 (-5 *4 (-1183)) (-5 *6 (-649 (-617 *3))) - (-5 *5 (-617 *3)) (-4 *3 (-13 (-27) (-1208) (-435 *7))) - (-4 *7 (-13 (-457) (-147) (-1044 (-569)) (-644 (-569)))) - (-5 *2 (-2 (|:| -2209 *3) (|:| |coeff| *3))) - (-5 *1 (-562 *7 *3))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-828)) (-5 *2 (-1278)) (-5 *1 (-827))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1249 *5)) (-4 *5 (-367)) + (-5 *2 (-2 (|:| -3361 (-423 *3)) (|:| |special| (-423 *3)))) + (-5 *1 (-732 *5 *3))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-649 (-2 (|:| -4395 (-412 (-569))) (|:| -4407 (-412 (-569)))))) + (-5 *2 (-649 (-226))) (-5 *1 (-308))))) +(((*1 *1 *2) (-12 (-5 *2 (-1126)) (-5 *1 (-333))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-1 (-170 (-226)) (-170 (-226)))) (-5 *4 (-1100 (-226))) + (-5 *2 (-1275)) (-5 *1 (-259))))) +(((*1 *1 *1 *2) + (-12 (-4 *3 (-367)) (-4 *4 (-798)) (-4 *5 (-855)) + (-5 *1 (-509 *3 *4 *5 *2)) (-4 *2 (-955 *3 *4 *5)))) + ((*1 *1 *1 *1) + (-12 (-4 *2 (-367)) (-4 *3 (-798)) (-4 *4 (-855)) + (-5 *1 (-509 *2 *3 *4 *5)) (-4 *5 (-955 *2 *3 *4))))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-865)) (-5 *2 (-696 (-129))) (-5 *3 (-129))))) (((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1008)))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-776)) (-5 *2 (-1278)) (-5 *1 (-1274)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-776)) (-5 *2 (-1278)) (-5 *1 (-1275))))) + (-12 (-4 *3 (-13 (-367) (-853))) (-5 *1 (-182 *3 *2)) + (-4 *2 (-1249 (-170 *3)))))) (((*1 *2 *3) - (-12 (-4 *4 (-1055)) (-5 *2 (-112)) (-5 *1 (-449 *4 *3)) - (-4 *3 (-1249 *4)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1071 *3 *4 *5)) (-4 *3 (-1055)) (-4 *4 (-798)) - (-4 *5 (-855)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *5 *6 *7 *8 *9) - (|partial| -12 (-5 *4 (-649 *11)) (-5 *5 (-649 (-1179 *9))) - (-5 *6 (-649 *9)) (-5 *7 (-649 *12)) (-5 *8 (-649 (-776))) - (-4 *11 (-855)) (-4 *9 (-310)) (-4 *12 (-955 *9 *10 *11)) - (-4 *10 (-798)) (-5 *2 (-649 (-1179 *12))) - (-5 *1 (-712 *10 *11 *9 *12)) (-5 *3 (-1179 *12))))) -(((*1 *1 *1 *1 *1) (-5 *1 (-867))) ((*1 *1 *1 *1) (-5 *1 (-867))) - ((*1 *1 *1) (-5 *1 (-867)))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-569)) (-5 *1 (-423 *3)) (-4 *3 (-561))))) + (-12 (-4 *4 (-855)) (-5 *2 (-649 (-649 (-649 *4)))) + (-5 *1 (-1194 *4)) (-5 *3 (-649 (-649 *4)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-649 (-319 (-226)))) (-5 *2 (-112)) (-5 *1 (-269)))) + ((*1 *2 *3) (-12 (-5 *3 (-319 (-226))) (-5 *2 (-112)) (-5 *1 (-269)))) + ((*1 *2 *3) + (-12 (-4 *4 (-561)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-112)) + (-5 *1 (-983 *4 *5 *6 *3)) (-4 *3 (-1071 *4 *5 *6))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) @@ -9886,37 +9589,41 @@ ((*1 *2 *2) (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3))))) -(((*1 *2 *3 *1) - (-12 (-5 *2 (-649 (-1183))) (-5 *1 (-1186)) (-5 *3 (-1183))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-776)) (-4 *2 (-561)) (-5 *1 (-975 *2 *4)) - (-4 *4 (-1249 *2))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1183)) - (-4 *5 (-13 (-457) (-147) (-1044 (-569)) (-644 (-569)))) - (-5 *2 (-591 *3)) (-5 *1 (-562 *5 *3)) - (-4 *3 (-13 (-27) (-1208) (-435 *5)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1008)))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-927)) (-5 *2 (-1278)) (-5 *1 (-1274)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-927)) (-5 *2 (-1278)) (-5 *1 (-1275))))) +(((*1 *2 *1) (-12 (-5 *2 (-569)) (-5 *1 (-867))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-1273 *4)) (-4 *4 (-644 (-569))) + (-5 *2 (-1273 (-569))) (-5 *1 (-1300 *4))))) +(((*1 *1 *1) (-12 (-4 *1 (-1264 *2)) (-4 *2 (-1055))))) +(((*1 *2) + (-12 (-4 *4 (-1227)) (-4 *5 (-1249 *4)) (-4 *6 (-1249 (-412 *5))) + (-5 *2 (-776)) (-5 *1 (-345 *3 *4 *5 *6)) (-4 *3 (-346 *4 *5 *6)))) + ((*1 *2) + (-12 (-4 *1 (-346 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-1249 *3)) + (-4 *5 (-1249 (-412 *4))) (-5 *2 (-776))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-34)) (-5 *3 (-776)) (-5 *2 (-112))))) +(((*1 *2 *3) + (|partial| -12 (-4 *4 (-1227)) (-4 *5 (-1249 *4)) + (-5 *2 (-2 (|:| |radicand| (-412 *5)) (|:| |deg| (-776)))) + (-5 *1 (-148 *4 *5 *3)) (-4 *3 (-1249 (-412 *5)))))) (((*1 *2 *1) - (-12 (-4 *1 (-1071 *3 *4 *5)) (-4 *3 (-1055)) (-4 *4 (-798)) - (-4 *5 (-855)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *5 *6 *2 *7 *8) - (|partial| -12 (-5 *2 (-649 (-1179 *11))) (-5 *3 (-1179 *11)) - (-5 *4 (-649 *10)) (-5 *5 (-649 *8)) (-5 *6 (-649 (-776))) - (-5 *7 (-1273 (-649 (-1179 *8)))) (-4 *10 (-855)) - (-4 *8 (-310)) (-4 *11 (-955 *8 *9 *10)) (-4 *9 (-798)) - (-5 *1 (-712 *9 *10 *8 *11))))) -(((*1 *1 *2) (-12 (-5 *2 (-649 (-867))) (-5 *1 (-867)))) - ((*1 *1 *1) (-5 *1 (-867)))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-569)) (-5 *2 (-3 "nil" "sqfr" "irred" "prime")) - (-5 *1 (-423 *4)) (-4 *4 (-561))))) + (-12 + (-5 *2 + (-1273 + (-2 (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) + (|:| |deltaX| (-226)) (|:| |deltaY| (-226)) (|:| -3538 (-569)) + (|:| -3285 (-569)) (|:| |spline| (-569)) (|:| -1970 (-569)) + (|:| |axesColor| (-879)) (|:| -3154 (-569)) + (|:| |unitsColor| (-879)) (|:| |showing| (-569))))) + (-5 *1 (-1274))))) +(((*1 *2 *3) + (-12 (-5 *3 (-569)) (|has| *1 (-6 -4435)) (-4 *1 (-409)) + (-5 *2 (-927))))) +(((*1 *2 *3) + (-12 (-5 *3 (-649 (-649 (-949 (-226))))) + (-5 *2 (-649 (-1100 (-226)))) (-5 *1 (-934))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-649 (-617 *5))) (-5 *3 (-1183)) (-4 *5 (-435 *4)) + (-4 *4 (-1106)) (-5 *1 (-578 *4 *5))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) @@ -9933,46 +9640,92 @@ ((*1 *2 *2) (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3))))) -(((*1 *2 *3 *1) (-12 (-5 *3 (-1183)) (-5 *2 (-1187)) (-5 *1 (-1186))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -4273 *1) (|:| -2804 *1))) (-4 *1 (-310)))) - ((*1 *2 *1 *1) 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- (-5 *1 (-1168 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) - (-5 *1 (-1169 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-776)) (-4 *4 (-13 (-1055) (-722 (-412 (-569))))) - (-4 *5 (-855)) (-5 *1 (-1289 *4 *5 *2)) (-4 *2 (-1294 *5 *4)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-776)) (-5 *1 (-1293 *3 *4)) - (-4 *4 (-722 (-412 (-569)))) (-4 *3 (-855)) (-4 *4 (-173))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) @@ -10116,46 +9800,37 @@ ((*1 *2 *2) (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-457)) (-4 *4 (-561)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2600 *4))) - (-5 *1 (-975 *4 *3)) (-4 *3 (-1249 *4))))) +(((*1 *2 *1) + (-12 (-4 *1 (-982 *3 *4 *5 *6)) (-4 *3 (-1055)) (-4 *4 (-798)) + (-4 *5 (-855)) (-4 *6 (-1071 *3 *4 *5)) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-898 *3)) (-4 *3 (-1106))))) +(((*1 *2 *3 *3) (-12 (-5 *3 (-1165)) (-5 *2 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+ (-12 (-5 *3 (-511)) (-5 *2 (-696 (-109))) (-5 *1 (-176)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-511)) (-5 *2 (-696 (-109))) (-5 *1 (-1091))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-319 (-569))) (|:| -1649 (-319 (-383))) + (-3 (|:| I (-319 (-569))) (|:| -1666 (-319 (-383))) (|:| CF (-319 (-170 (-383)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1183))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) @@ -10175,9 +9850,10 @@ ((*1 *2 *2) (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *2 (-561)) (-4 *2 (-457)) (-5 *1 (-975 *2 *3)) - (-4 *3 (-1249 *2))))) +(((*1 *2 *2) + (-12 (-5 *2 (-649 (-649 *6))) (-4 *6 (-955 *3 *5 *4)) + (-4 *3 (-13 (-310) (-147))) (-4 *4 (-13 (-855) (-619 (-1183)))) + (-4 *5 (-798)) (-5 *1 (-930 *3 *4 *5 *6))))) (((*1 *2 *1) (-12 (-4 *1 (-268 *2)) (-4 *2 (-855)))) ((*1 *1 *2) (|partial| -12 (-5 *2 (-1183)) (-5 *1 (-869 *3)) (-14 *3 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(-1163 (-226))) - (|:| |singularities| (-1163 (-226))))) - (-5 *1 (-105))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-927)) (-5 *4 (-879)) (-5 *2 (-1278)) (-5 *1 (-1274)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-927)) (-5 *4 (-1165)) (-5 *2 (-1278)) (-5 *1 (-1274)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-1275))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-649 *1)) - (-4 *1 (-1071 *3 *4 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1183)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-707 *4 *5 *6 *7)) - (-4 *4 (-619 (-541))) (-4 *5 (-1223)) (-4 *6 (-1223)) - (-4 *7 (-1223))))) -(((*1 *1 *2) (-12 (-5 *2 (-649 (-867))) (-5 *1 (-867))))) -(((*1 *1 *2) (-12 (-5 *2 (-649 (-383))) (-5 *1 (-265)))) - ((*1 *1) - (|partial| -12 (-4 *1 (-371 *2)) (-4 *2 (-561)) (-4 *2 (-173)))) - ((*1 *2 *1) (-12 (-5 *1 (-423 *2)) (-4 *2 (-561))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-112) *2)) (-4 *2 (-132)) (-5 *1 (-1090 *2)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-569) *2 *2)) (-4 *2 (-132)) (-5 *1 (-1090 *2))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1179 *6)) (-5 *3 (-569)) (-4 *6 (-310)) (-4 *4 (-798)) + (-4 *5 (-855)) (-5 *1 (-747 *4 *5 *6 *7)) (-4 *7 (-955 *6 *4 *5))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-319 (-569))) (|:| -1649 (-319 (-383))) + (-3 (|:| I (-319 (-569))) (|:| -1666 (-319 (-383))) (|:| CF (-319 (-170 (-383)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-649 (-867))) (-5 *1 (-1183))))) (((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) (-4 *2 (-13 (-435 *3) (-1008))))) @@ -10235,38 +9926,92 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-412 (-569)))) (-4 *4 (-1233 *3)) (-5 *1 (-281 *3 *4 *2 *5)) (-4 *2 (-1256 *3 *4)) (-4 *5 (-989 *4)))) + ((*1 *1 *1) (-4 *1 (-287))) + ((*1 *2 *3) + (-12 (-5 *3 (-423 *4)) (-4 *4 (-561)) + (-5 *2 (-649 (-2 (|:| -1433 (-776)) (|:| |logand| *4)))) + (-5 *1 (-323 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-343 *2 *3 *4)) (-14 *2 (-649 (-1183))) + (-14 *3 (-649 (-1183))) (-4 *4 (-392)))) + ((*1 *2 *1) + 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*1) + (|partial| -12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) + (-5 *2 (-649 *1)) (-4 *1 (-955 *3 *4 *5)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1055)) + (-4 *7 (-955 *6 *4 *5)) (-5 *2 (-649 *3)) + (-5 *1 (-956 *4 *5 *6 *7 *3)) + (-4 *3 + (-13 (-367) + (-10 -8 (-15 -3793 ($ *7)) (-15 -4396 (*7 $)) + (-15 -4409 (*7 $)))))))) (((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) (-4 *2 (-13 (-435 *3) (-1008))))) @@ -10323,40 +10147,36 @@ (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3)))) ((*1 *1 *1) (-4 *1 (-1211)))) +(((*1 *1 *2 *2) + (-12 (-5 *2 (-649 (-569))) (-5 *1 (-1010 *3)) (-14 *3 (-569))))) +(((*1 *1 *2 *3 *4) + (-12 + (-5 *3 + (-649 + (-2 (|:| |scalar| (-412 (-569))) (|:| |coeff| (-1179 *2)) + (|:| |logand| (-1179 *2))))) + (-5 *4 (-649 (-2 (|:| |integrand| *2) (|:| |intvar| *2)))) + (-4 *2 (-367)) (-5 *1 (-591 *2))))) +(((*1 *1 *1) + (|partial| -12 (-5 *1 (-1147 *2 *3)) (-4 *2 (-13 (-1106) (-34))) + (-4 *3 (-13 (-1106) (-34)))))) (((*1 *2 *3) - (-12 (-4 *4 (-561)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4180 *4))) - (-5 *1 (-975 *4 *3)) (-4 *3 (-1249 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-561)) (-5 *2 (-112))))) -(((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1008)))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-1275))))) -(((*1 *1 *1 *1 *2) - (-12 (-4 *1 (-1071 *3 *4 *2)) (-4 *3 (-1055)) (-4 *4 (-798)) - (-4 *2 (-855)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) - (-4 *4 (-855))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-534)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-582)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-866))))) -(((*1 *2 *3) - (-12 (-5 *3 (-569)) (|has| *1 (-6 -4434)) (-4 *1 (-409)) - (-5 *2 (-927))))) -(((*1 *2 *1 *3 *3 *4) - (-12 (-5 *3 (-1 (-867) (-867) (-867))) (-5 *4 (-569)) (-5 *2 (-867)) - (-5 *1 (-654 *5 *6 *7)) (-4 *5 (-1106)) (-4 *6 (-23)) (-14 *7 *6))) - ((*1 *2 *1 *2) - (-12 (-5 *2 (-867)) (-5 *1 (-859 *3 *4 *5)) (-4 *3 (-1055)) - (-14 *4 (-99 *3)) (-14 *5 (-1 *3 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-226)) (-5 *1 (-867)))) - ((*1 *1 *2) (-12 (-5 *2 (-1165)) (-5 *1 (-867)))) - ((*1 *1 *2) (-12 (-5 *2 (-1183)) (-5 *1 (-867)))) - ((*1 *1 *2) (-12 (-5 *2 (-569)) (-5 *1 (-867)))) - ((*1 *2 *1 *2) - (-12 (-5 *2 (-867)) (-5 *1 (-1179 *3)) (-4 *3 (-1055))))) + (-12 (-4 *1 (-805)) + (-5 *3 + (-2 (|:| |xinit| (-226)) (|:| |xend| (-226)) + (|:| |fn| (-1273 (-319 (-226)))) (|:| |yinit| (-649 (-226))) + (|:| |intvals| (-649 (-226))) (|:| |g| (-319 (-226))) + (|:| |abserr| (-226)) (|:| |relerr| (-226)))) + (-5 *2 (-1041))))) +(((*1 *2 *2) (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-649 *2)) (-5 *4 (-1 (-112) *2 *2)) (-5 *1 (-1224 *2)) + (-4 *2 (-1106)))) + ((*1 *2 *3) + (-12 (-5 *3 (-649 *2)) (-4 *2 (-1106)) (-4 *2 (-855)) + (-5 *1 (-1224 *2))))) +(((*1 *2 *1) + (-12 (-4 *1 (-368 *3 *2)) (-4 *3 (-1106)) (-4 *2 (-1106))))) (((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) (-4 *2 (-13 (-435 *3) (-1008))))) @@ -10376,42 +10196,44 @@ (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3)))) ((*1 *1 *1) (-4 *1 (-1211)))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-55)))) + ((*1 *2 *1) + (-12 (-4 *3 (-367)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-112)) + (-5 *1 (-509 *3 *4 *5 *6)) (-4 *6 (-955 *3 *4 *5)))) + ((*1 *2 *1) (-12 (-4 *1 (-727)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-731)) (-5 *2 (-112))))) (((*1 *2 *1) (-12 (-4 *1 (-1109 *3 *4 *5 *6 *2)) (-4 *3 (-1106)) (-4 *4 (-1106)) (-4 *5 (-1106)) (-4 *6 (-1106)) (-4 *2 (-1106))))) -(((*1 *2 *3) - (-12 (-4 *4 (-561)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4180 *4))) - (-5 *1 (-975 *4 *3)) (-4 *3 (-1249 *4))))) -(((*1 *1 *2) - (-12 (-5 *2 (-412 (-569))) (-4 *1 (-559 *3)) - (-4 *3 (-13 (-409) (-1208))))) - ((*1 *1 *2) (-12 (-4 *1 (-559 *2)) (-4 *2 (-13 (-409) (-1208))))) - ((*1 *1 *2 *2) (-12 (-4 *1 (-559 *2)) (-4 *2 (-13 (-409) (-1208)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1008)))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-569)) (-5 *2 (-1278)) (-5 *1 (-1275)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-383)) (-5 *2 (-1278)) (-5 *1 (-1275))))) -(((*1 *1 *1 *1 *2) - (-12 (-4 *1 (-1071 *3 *4 *2)) (-4 *3 (-1055)) (-4 *4 (-798)) - (-4 *2 (-855)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) - (-4 *4 (-855))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-1273 *4)) (-5 *3 (-1126)) (-4 *4 (-353)) + (-5 *1 (-533 *4))))) +(((*1 *1) (-5 *1 (-602)))) +(((*1 *2 *2) (-12 (-5 *2 (-1100 (-848 (-226)))) (-5 *1 (-308))))) +(((*1 *1) (-5 *1 (-141)))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-226)) (-5 *4 (-569)) (-5 *2 (-1041)) (-5 *1 (-763))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1223)) (-4 *2 (-855)))) + ((*1 *1 *2 *1 *1) + (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-285 *3)) (-4 *3 (-1223)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-974 *2)) (-4 *2 (-855))))) (((*1 *2 *1 *3) - (-12 (-4 *1 (-865)) (-5 *2 (-696 (-129))) (-5 *3 (-129))))) + (-12 (-4 *1 (-865)) (-5 *2 (-696 (-554))) (-5 *3 (-554))))) (((*1 *2 *3) - (-12 (-5 *3 (-569)) (|has| *1 (-6 -4434)) (-4 *1 (-409)) - (-5 *2 (-927))))) -(((*1 *2 *1) (-12 (-4 *1 (-1016 *3)) (-4 *3 (-1223)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1171 *3 *4)) (-14 *3 (-927)) - (-4 *4 (-1055))))) + (-12 (-5 *3 (-1195 (-649 *4))) (-4 *4 (-855)) + (-5 *2 (-649 (-649 *4))) (-5 *1 (-1194 *4))))) +(((*1 *2 *3) + (-12 (-4 *4 (-561)) (-4 *5 (-798)) (-4 *6 (-855)) + (-4 *7 (-1071 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-649 *7)) (|:| |badPols| (-649 *7)))) + (-5 *1 (-983 *4 *5 *6 *7)) (-5 *3 (-649 *7))))) +(((*1 *2 *3) + (-12 (-5 *3 (-694 (-412 (-958 (-569))))) (-5 *2 (-649 (-319 (-569)))) + (-5 *1 (-1037))))) +(((*1 *1 *2) (-12 (-5 *2 (-569)) (-5 *1 (-867))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1273 *4)) (-4 *4 (-644 (-569))) (-5 *2 (-112)) + (-5 *1 (-1300 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) (-4 *2 (-13 (-435 *3) (-1008))))) @@ -10432,34 +10254,39 @@ (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 (-412 (-569)))) (-5 *1 (-1169 *3)))) ((*1 *1 *1) (-4 *1 (-1211)))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-561)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -1830 *3))) - (-5 *1 (-975 *4 *3)) (-4 *3 (-1249 *4))))) -(((*1 *1 *2 *2) (-12 (-4 *1 (-559 *2)) (-4 *2 (-13 (-409) (-1208)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1008)))))) -(((*1 *1 *1 *2 *2 *2) (-12 (-5 *2 (-1100 (-226))) (-5 *1 (-932)))) - ((*1 *1 *1 *2 *2) (-12 (-5 *2 (-1100 (-226))) (-5 *1 (-933)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1100 (-226))) (-5 *1 (-933)))) - ((*1 *2 *1 *3 *3 *3) - (-12 (-5 *3 (-383)) (-5 *2 (-1278)) (-5 *1 (-1275)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-383)) (-5 *2 (-1278)) (-5 *1 (-1275))))) -(((*1 *1 *1 *1 *2) - (-12 (-4 *1 (-1071 *3 *4 *2)) (-4 *3 (-1055)) (-4 *4 (-798)) - (-4 *2 (-855)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) - (-4 *4 (-855))))) -(((*1 *2 *2) (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-865)) (-5 *2 (-696 (-554))) (-5 *3 (-554))))) +(((*1 *1 *2) (-12 (-5 *2 (-319 (-170 (-383)))) (-5 *1 (-333)))) + ((*1 *1 *2) (-12 (-5 *2 (-319 (-569))) (-5 *1 (-333)))) + ((*1 *1 *2) (-12 (-5 *2 (-319 (-383))) (-5 *1 (-333)))) + ((*1 *1 *2) (-12 (-5 *2 (-319 (-699))) (-5 *1 (-333)))) + ((*1 *1 *2) (-12 (-5 *2 (-319 (-706))) (-5 *1 (-333)))) + ((*1 *1 *2) (-12 (-5 *2 (-319 (-704))) (-5 *1 (-333)))) + ((*1 *1) (-5 *1 (-333)))) +(((*1 *2 *3 *4 *4 *5) + (-12 (-5 *3 (-1 (-170 (-226)) (-170 (-226)))) (-5 *4 (-1100 (-226))) + (-5 *5 (-112)) (-5 *2 (-1275)) (-5 *1 (-259))))) +(((*1 *2) (-12 (-5 *2 (-569)) (-5 *1 (-932))))) (((*1 *1 *1) (-4 *1 (-550)))) +(((*1 *1 *1 *1 *1) (-4 *1 (-550)))) +(((*1 *1 *2 *3 *3 *3 *3) + (-12 (-5 *2 (-1 (-949 (-226)) (-226))) (-5 *3 (-1100 (-226))) + (-5 *1 (-932)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-949 (-226)) (-226))) (-5 *3 (-1100 (-226))) + (-5 *1 (-932)))) + ((*1 *1 *2 *3 *3 *3) + (-12 (-5 *2 (-1 (-949 (-226)) (-226))) (-5 *3 (-1100 (-226))) + (-5 *1 (-933)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-949 (-226)) (-226))) (-5 *3 (-1100 (-226))) + (-5 *1 (-933))))) +(((*1 *2 *3 *4 *3) + (|partial| -12 (-5 *4 (-1183)) + (-4 *5 (-13 (-561) (-1044 (-569)) (-147))) + (-5 *2 + (-2 (|:| -2530 (-412 (-958 *5))) (|:| |coeff| (-412 (-958 *5))))) + (-5 *1 (-575 *5)) (-5 *3 (-412 (-958 *5)))))) (((*1 *2 *1) (-12 (-4 *1 (-353)) (-5 *2 (-776)))) ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-407)) (-5 *2 (-776))))) -(((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1171 *3 *4)) (-14 *3 (-927)) - (-4 *4 (-1055))))) (((*1 *2 *2) (-12 (-4 *3 (-561)) (-5 *1 (-278 *3 *2)) (-4 *2 (-13 (-435 *3) (-1008))))) @@ -10480,241 +10307,306 @@ (-12 (-5 *2 (-1163 *3)) (-4 *3 (-38 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(-4 *1 (-1264 *3)) (-4 *3 (-1055))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) + (-4 *7 (-1071 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-994 *4 *5 *6 *7 *3)) (-4 *3 (-1077 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) + (-4 *7 (-1071 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1113 *4 *5 *6 *7 *3)) (-4 *3 (-1077 *4 *5 *6 *7))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-112)) (-4 *6 (-13 (-457) (-1044 (-569)) (-644 (-569)))) + (-4 *3 (-13 (-27) (-1208) (-435 *6) (-10 -8 (-15 -3793 ($ *7))))) + (-4 *7 (-853)) + (-4 *8 + (-13 (-1251 *3 *7) (-367) (-1208) + (-10 -8 (-15 -3514 ($ $)) (-15 -2488 ($ $))))) + (-5 *2 + (-3 (|:| |%series| *8) + (|:| |%problem| (-2 (|:| |func| (-1165)) (|:| |prob| (-1165)))))) + (-5 *1 (-427 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1165)) (-4 *9 (-989 *8)) + (-14 *10 (-1183))))) +(((*1 *1 *2 *3 *1) + (-12 (-5 *2 (-511)) (-5 *3 (-649 (-971))) (-5 *1 (-294))))) (((*1 *2 *1 *3) - (-12 (-4 *1 (-865)) (-5 *2 (-696 (-1231))) (-5 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(-1278)) (-5 *1 (-827))))) +(((*1 *1) (-5 *1 (-583))) + ((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-868)))) + ((*1 *2 *3) (-12 (-5 *3 (-867)) (-5 *2 (-1278)) (-5 *1 (-868)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-617 *3)) (-4 *3 (-435 *5)) - (-4 *5 (-13 (-561) (-1044 (-569)))) (-5 *2 (-1179 (-412 (-569)))) - (-5 *1 (-438 *5 *3))))) -(((*1 *2 *3 *3 *3 *4 *5) - (-12 (-5 *5 (-649 (-649 (-226)))) (-5 *4 (-226)) - (-5 *2 (-649 (-949 *4))) (-5 *1 (-1219)) (-5 *3 (-949 *4))))) + (-12 (-5 *3 (-1165)) (-5 *4 (-867)) (-5 *2 (-1278)) (-5 *1 (-868)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-569)) (-5 *2 (-1278)) (-5 *1 (-1163 *4)) + (-4 *4 (-1106)) (-4 *4 (-1223))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-569)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1223)) (-4 *4 (-377 *2)) (-4 *5 (-377 *2)))) @@ -14104,14 +13877,14 @@ (-12 (-5 *3 (-1183)) (-5 *2 (-246 (-1165))) (-5 *1 (-215 *4)) (-4 *4 (-13 (-855) - (-10 -8 (-15 -1852 ((-1165) $ *3)) (-15 -4138 ((-1278) $)) - (-15 -4170 ((-1278) $))))))) + (-10 -8 (-15 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(-14 *3 (-649 (-1183))) (-4 *4 (-173)) - (-4 *5 (-239 (-2394 *3) (-776))) - (-14 *6 - (-1 (-112) (-2 (|:| -2114 *2) (|:| -2777 *5)) - (-2 (|:| -2114 *2) (|:| -2777 *5)))) - (-5 *1 (-466 *3 *4 *2 *5 *6 *7)) (-4 *2 (-855)) - (-4 *7 (-955 *4 *5 (-869 *3))))) - ((*1 *2 *2) (-12 (-5 *2 (-949 (-226))) (-5 *1 (-1219))))) -(((*1 *1) (-5 *1 (-583))) - ((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-868)))) - ((*1 *2 *3) (-12 (-5 *3 (-867)) (-5 *2 (-1278)) (-5 *1 (-868)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1165)) (-5 *4 (-867)) (-5 *2 (-1278)) (-5 *1 (-868)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-569)) (-5 *2 (-1278)) (-5 *1 (-1163 *4)) - (-4 *4 (-1106)) (-4 *4 (-1223))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1018)) (-5 *2 (-867))))) +(((*1 *1 *1) (-5 *1 (-1069)))) (((*1 *1 *2) (-12 (-5 *2 (-649 *1)) (-4 *1 (-457)))) ((*1 *1 *1 *1) (-4 *1 (-457))) ((*1 *2 *3) @@ -14332,43 +14003,37 @@ (((*1 *2 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-649 *1)) (-4 *1 (-955 *3 *4 *5))))) +(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) + (-12 (-5 *3 (-1165)) (-5 *4 (-569)) (-5 *5 (-694 (-170 (-226)))) + (-5 *2 (-1041)) (-5 *1 (-759))))) +(((*1 *2 *3 *4 *4 *4 *5 *4 *6 *6 *3) + (-12 (-5 *4 (-694 (-226))) (-5 *5 (-694 (-569))) (-5 *6 (-226)) + (-5 *3 (-569)) (-5 *2 (-1041)) (-5 *1 (-756))))) +(((*1 *2 *2) + (-12 + (-5 *2 + (-649 + (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-776)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *4 (-798)) (-4 *6 (-955 *3 *4 *5)) (-4 *3 (-457)) (-4 *5 (-855)) + (-5 *1 (-454 *3 *4 *5 *6))))) (((*1 *2 *3) - (-12 (-5 *2 (-617 *4)) (-5 *1 (-616 *3 *4)) (-4 *3 (-1106)) - (-4 *4 (-1106))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1240 (-569))) (-4 *1 (-285 *3)) (-4 *3 (-1223)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-569)) (-4 *1 (-285 *3)) (-4 *3 (-1223))))) -(((*1 *2) - (-12 (-4 *3 (-561)) (-5 *2 (-649 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-422 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-412 (-958 *5))) (-5 *4 (-1183)) - (-4 *5 (-13 (-310) (-147))) (-5 *2 (-649 (-319 *5))) - (-5 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(-4 *4 (-13 (-310) (-147))) + (-4 *5 (-13 (-855) (-619 (-1183)))) (-4 *6 (-798)) + (-5 *2 + (-649 + (-2 (|:| |eqzro| (-649 *7)) (|:| |neqzro| (-649 *7)) + (|:| |wcond| (-649 (-958 *4))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1273 (-412 (-958 *4)))) + (|:| -1903 (-649 (-1273 (-412 (-958 *4)))))))))) + (-5 *1 (-930 *4 *5 *6 *7)) (-4 *7 (-955 *4 *6 *5))))) +(((*1 *1 *1 *1) (-5 *1 (-867)))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-1163 (-649 (-569)))) (-5 *1 (-889)) + (-5 *3 (-649 (-569)))))) +(((*1 *1) + (|partial| -12 (-4 *1 (-371 *2)) (-4 *2 (-561)) (-4 *2 (-173))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-797)) (-4 *2 (-1055)))) ((*1 *2 *1) (-12 (-4 *2 (-1055)) (-5 *1 (-50 *2 *3)) (-14 *3 (-649 (-1183))))) @@ -14378,10 +14043,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-386 *2 *3)) (-4 *3 (-1106)) (-4 *2 (-1055)))) ((*1 *2 *1) - (-12 (-14 *3 (-649 (-1183))) (-4 *5 (-239 (-2394 *3) (-776))) + (-12 (-14 *3 (-649 (-1183))) (-4 *5 (-239 (-2426 *3) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2114 *4) (|:| 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(-4 *3 (-550)) (-4 *3 (-1106)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1003 *3)) (-4 *3 (-173)) (-4 *3 (-550)) (-5 *2 (-112)))) + ((*1 *2 *3) + (-12 (-5 *2 (-112)) (-5 *1 (-1014 *3)) (-4 *3 (-1044 (-412 (-569))))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1297 *4 *2)) (-4 *1 (-378 *4 *2)) (-4 *4 (-855)) (-4 *2 (-173)))) @@ -16550,26 +16336,34 @@ (-4 *2 (-1055)))) ((*1 *2 *1 *3) (-12 (-4 *2 (-1055)) (-5 *1 (-1296 *2 *3)) (-4 *3 (-851))))) +(((*1 *2 *1) + (|partial| -12 (-4 *3 (-13 (-1044 (-569)) (-644 (-569)) (-457))) + (-5 *2 + (-2 + (|:| |%term| + (-2 (|:| |%coef| (-1258 *4 *5 *6)) + (|:| |%expon| (-322 *4 *5 *6)) + (|:| |%expTerms| + (-649 (-2 (|:| |k| (-412 (-569))) (|:| |c| *4)))))) + (|:| |%type| (-1165)))) + (-5 *1 (-1259 *3 *4 *5 *6)) (-4 *4 (-13 (-27) (-1208) (-435 *3))) + (-14 *5 (-1183)) (-14 *6 *4)))) (((*1 *2 *3) (-12 (-5 *2 (-569)) (-5 *1 (-574 *3)) (-4 *3 (-1044 *2)))) ((*1 *2 *1) (-12 (-4 *1 (-1109 *3 *4 *2 *5 *6)) (-4 *3 (-1106)) (-4 *4 (-1106)) (-4 *5 (-1106)) (-4 *6 (-1106)) (-4 *2 (-1106))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-649 (-569))) (-5 *3 (-112)) (-5 *1 (-1116))))) +(((*1 *1 *1) (-5 *1 (-867)))) +(((*1 *1 *2 *3 *1 *3) + (-12 (-5 *2 (-898 *4)) (-4 *4 (-1106)) (-5 *1 (-895 *4 *3)) + (-4 *3 (-1106))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-457)) (-4 *6 (-798)) (-4 *7 (-855)) + (-4 *3 (-1071 *5 *6 *7)) + (-5 *2 (-649 (-2 (|:| |val| (-112)) (|:| -3660 *4)))) + (-5 *1 (-781 *5 *6 *7 *3 *4)) (-4 *4 (-1077 *5 *6 *7 *3))))) (((*1 *2 *1) - (-12 (-5 *2 (-649 (-911 *3))) (-5 *1 (-910 *3)) (-4 *3 (-1106))))) -(((*1 *2 *3 *4 *5 *4 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *7 *4) - (-12 (-5 *3 (-1165)) (-5 *5 (-694 (-226))) (-5 *6 (-226)) - (-5 *7 (-694 (-569))) (-5 *4 (-569)) (-5 *2 (-1041)) (-5 *1 (-757))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-776)) (|:| |poli| *2) - (|:| |polj| *2))) - (-4 *5 (-798)) (-4 *2 (-955 *4 *5 *6)) (-5 *1 (-454 *4 *5 *6 *2)) - (-4 *4 (-457)) (-4 *6 (-855))))) -(((*1 *1 *1 *1) (-5 *1 (-162))) - ((*1 *1 *2) (-12 (-5 *2 (-569)) (-5 *1 (-162))))) + (-12 (-5 *2 (-649 (-649 (-776)))) (-5 *1 (-910 *3)) (-4 *3 (-1106))))) +(((*1 *1) (-5 *1 (-130)))) (((*1 *2 *1) (-12 (-4 *1 (-256 *3)) (-4 *3 (-1223)) (-5 *2 (-776)))) ((*1 *2 *1) (-12 (-4 *1 (-305)) (-5 *2 (-776)))) ((*1 *2 *3) @@ -16579,19 +16373,22 @@ ((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-617 *3)) (-4 *3 (-1106)))) ((*1 *2) (-12 (-5 *2 (-569)) (-5 *1 (-867)))) ((*1 *2 *1) (-12 (-5 *2 (-569)) (-5 *1 (-867))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-45 (-1165) (-779))) (-5 *1 (-114))))) -(((*1 *2 *2) - (-12 (-4 *3 (-457)) (-5 *1 (-1214 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1208)))))) -(((*1 *2 *1) - (-12 (-4 *3 (-457)) (-4 *4 (-855)) (-4 *5 (-798)) (-5 *2 (-649 *6)) - (-5 *1 (-993 *3 *4 *5 *6)) (-4 *6 (-955 *3 *5 *4))))) -(((*1 *1 *1) - (-12 (-5 *1 (-600 *2)) (-4 *2 (-38 (-412 (-569)))) (-4 *2 (-1055))))) +(((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-144))))) (((*1 *2 *3) - (-12 (-5 *3 (-1179 *7)) (-4 *7 (-955 *6 *4 *5)) (-4 *4 (-798)) - (-4 *5 (-855)) (-4 *6 (-1055)) (-5 *2 (-1179 *6)) - (-5 *1 (-324 *4 *5 *6 *7))))) + (-12 (-5 *2 (-112)) (-5 *1 (-120 *3)) (-4 *3 (-1249 (-569))))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-120 *3)) (-4 *3 (-1249 (-569)))))) +(((*1 *2 *3 *4 *4 *4 *3 *4 *3) + (-12 (-5 *3 (-569)) (-5 *4 (-694 (-226))) (-5 *2 (-1041)) + (-5 *1 (-756))))) +(((*1 *2 *3) + (-12 (-5 *3 (-694 *4)) (-4 *4 (-367)) (-5 *2 (-1179 *4)) + (-5 *1 (-537 *4 *5 *6)) (-4 *5 (-367)) (-4 *6 (-13 (-367) (-853)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-609 *2 *3)) (-4 *3 (-1223)) (-4 *2 (-1106)) + (-4 *2 (-855))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4445)) (-4 *1 (-119 *2)) (-4 *2 (-1223))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-885 (-1 (-226) (-226)))) (-5 *4 (-1100 (-383))) (-5 *5 (-649 (-265))) (-5 *2 (-1139 (-226))) (-5 *1 (-257)))) @@ -16645,6 +16442,7 @@ (-12 (-5 *3 (-888 *5)) (-5 *4 (-1098 (-383))) (-4 *5 (-13 (-619 (-541)) (-1106))) (-5 *2 (-1139 (-226))) (-5 *1 (-261 *5))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) (((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-181)))) ((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-314)))) ((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-976)))) @@ -16652,7 +16450,7 @@ ((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1042)))) ((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1079))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4443)) (-4 *1 (-151 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4444)) (-4 *1 (-151 *3)) (-4 *3 (-1223)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1223)) (-5 *1 (-606 *3)))) @@ -16663,27 +16461,37 @@ (-4 *5 (-798)) (-4 *3 (-855)) (-4 *2 (-1071 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-776)) (-5 *1 (-1220 *2)) (-4 *2 (-1223))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-569)) (-5 *1 (-566)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1179 (-412 (-569)))) (-5 *1 (-948)) (-5 *3 (-569))))) +(((*1 *2 *3 *3 *3 *4) + (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1249 *5)) + (-4 *5 (-13 (-367) (-147) (-1044 (-569)))) + (-5 *2 + (-2 (|:| |a| *6) (|:| |b| (-412 *6)) (|:| |h| *6) + (|:| |c1| (-412 *6)) (|:| |c2| (-412 *6)) (|:| -3674 *6))) + (-5 *1 (-1022 *5 *6)) (-5 *3 (-412 *6))))) +(((*1 *2 *3 *3 *4 *5 *5 *3) + (-12 (-5 *3 (-569)) (-5 *4 (-1165)) (-5 *5 (-694 (-226))) + (-5 *2 (-1041)) (-5 *1 (-752))))) (((*1 *2 *1) - (-12 (-5 *2 (-649 (-649 (-776)))) (-5 *1 (-910 *3)) (-4 *3 (-1106))))) -(((*1 *2 *3 *3 *2) - (-12 (-5 *2 (-694 (-569))) (-5 *3 (-649 (-569))) (-5 *1 (-1116))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *4 *5 *3 *3 *3 *6 *4 *3) - (-12 (-5 *4 (-694 (-226))) (-5 *5 (-694 (-569))) (-5 *6 (-226)) - (-5 *3 (-569)) (-5 *2 (-1041)) (-5 *1 (-757))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-649 (-2 (|:| |totdeg| (-776)) (|:| -3280 *3)))) - (-5 *4 (-776)) (-4 *3 (-955 *5 *6 *7)) (-4 *5 (-457)) (-4 *6 (-798)) - (-4 *7 (-855)) (-5 *1 (-454 *5 *6 *7 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-561)) (-5 *1 (-158 *3 *2)) (-4 *2 (-435 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1183)) (-4 *4 (-561)) (-5 *1 (-158 *4 *2)) - (-4 *2 (-435 *4)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-160)) (-5 *2 (-1183)))) - ((*1 *1 *1) (-4 *1 (-160)))) + (-12 (-5 *2 (-649 (-2 (|:| |gen| *3) (|:| -4386 (-569))))) + (-5 *1 (-365 *3)) (-4 *3 (-1106)))) + ((*1 *2 *1) + (-12 (-4 *1 (-390 *3)) (-4 *3 (-1106)) + (-5 *2 (-649 (-2 (|:| |gen| *3) (|:| -4386 (-776))))))) + ((*1 *2 *1) + (-12 (-5 *2 (-649 (-2 (|:| -3796 *3) (|:| -4320 (-569))))) + (-5 *1 (-423 *3)) (-4 *3 (-561))))) (((*1 *2 *2) - (-12 (-4 *3 (-457)) (-5 *1 (-1214 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1208)))))) + (-12 + (-5 *2 + (-993 (-412 (-569)) (-869 *3) (-241 *4 (-776)) + (-248 *3 (-412 (-569))))) + (-14 *3 (-649 (-1183))) (-14 *4 (-776)) (-5 *1 (-992 *3 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1273 (-1273 *4))) (-4 *4 (-1055)) (-5 *2 (-694 *4)) + (-5 *1 (-1035 *4))))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-619 *2) (-173))) (-5 *2 (-898 *4)) (-5 *1 (-171 *4 *5 *3)) (-4 *4 (-1106)) (-4 *3 (-166 *5)))) @@ -16716,9 +16524,9 @@ (-12 (-5 *2 (-958 *3)) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *5 (-619 (-1183))) (-4 *4 (-798)) (-4 *5 (-855)))) ((*1 *1 *2) - (-2718 + (-2774 (-12 (-5 *2 (-958 (-569))) (-4 *1 (-1071 *3 *4 *5)) - (-12 (-1728 (-4 *3 (-38 (-412 (-569))))) (-4 *3 (-38 (-569))) + (-12 (-1745 (-4 *3 (-38 (-412 (-569))))) (-4 *3 (-38 (-569))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-958 (-569))) (-4 *1 (-1071 *3 *4 *5)) @@ -16729,12 +16537,12 @@ (-4 *3 (-38 (-412 (-569)))) (-4 *5 (-619 (-1183))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-649 *7)) (|:| -3550 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-649 *7)) (|:| -3660 *8))) (-4 *7 (-1071 *4 *5 *6)) (-4 *8 (-1077 *4 *5 *6 *7)) (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-1165)) (-5 *1 (-1075 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-649 *7)) (|:| -3550 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-649 *7)) (|:| -3660 *8))) (-4 *7 (-1071 *4 *5 *6)) (-4 *8 (-1115 *4 *5 *6 *7)) (-4 *4 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-1165)) (-5 *1 (-1151 *4 *5 *6 *7 *8)))) @@ -16766,15 +16574,17 @@ (-4 *4 (-13 (-853) (-310) (-147) (-1028))) (-14 *6 (-649 (-1183))) (-5 *2 (-649 (-785 *4 (-869 *6)))) (-5 *1 (-1299 *4 *5 *6)) (-14 *5 (-649 (-1183)))))) -(((*1 *2 *1) - (-12 (-4 *2 (-955 *3 *5 *4)) (-5 *1 (-993 *3 *4 *5 *2)) - (-4 *3 (-457)) (-4 *4 (-855)) (-4 *5 (-798))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1055)) (-4 *3 (-1249 *4)) (-4 *2 (-1264 *4)) + (-5 *1 (-1267 *4 *3 *5 *2)) (-4 *5 (-661 *3))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-3 (-112) "failed")) (-4 *3 (-457)) (-4 *4 (-855)) + (-4 *5 (-798)) (-5 *1 (-993 *3 *4 *5 *6)) (-4 *6 (-955 *3 *5 *4))))) +(((*1 *2 *3) + (-12 (-5 *2 (-569)) (-5 *1 (-450 *3)) (-4 *3 (-409)) (-4 *3 (-1055))))) +(((*1 *2 *1) (-12 (-5 *2 (-649 (-878 (-1188) (-776)))) (-5 *1 (-336))))) (((*1 *1 *1) (-12 (-5 *1 (-600 *2)) (-4 *2 (-38 (-412 (-569)))) (-4 *2 (-1055))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1179 *9)) (-5 *4 (-649 *7)) (-5 *5 (-649 *8)) - (-4 *7 (-855)) (-4 *8 (-1055)) (-4 *9 (-955 *8 *6 *7)) - (-4 *6 (-798)) (-5 *2 (-1179 *8)) (-5 *1 (-324 *6 *7 *8 *9))))) (((*1 *2 *1) (-12 (-4 *1 (-1109 *3 *2 *4 *5 *6)) (-4 *3 (-1106)) (-4 *4 (-1106)) (-4 *5 (-1106)) (-4 *6 (-1106)) (-4 *2 (-1106))))) @@ -16782,94 +16592,96 @@ (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1223)) (-5 *1 (-606 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1223)) (-5 *1 (-1163 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-649 (-911 *3))) (-4 *3 (-1106)) (-5 *1 (-910 *3))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-649 (-569))) (-5 *2 (-694 (-569))) (-5 *1 (-1116))))) -(((*1 *2 *3 *4 *5 *5 *5 *6 *4 *4 *4 *5 *4 *5 *7) - (-12 (-5 *3 (-1165)) (-5 *5 (-694 (-226))) (-5 *6 (-226)) - (-5 *7 (-694 (-569))) (-5 *4 (-569)) (-5 *2 (-1041)) (-5 *1 (-757))))) -(((*1 *2 *2) - (-12 (-4 *3 (-457)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *1 (-454 *3 *4 *5 *2)) (-4 *2 (-955 *3 *4 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1183)) (-4 *4 (-561)) (-5 *1 (-158 *4 *2)) - (-4 *2 (-435 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1098 *2)) (-4 *2 (-435 *4)) (-4 *4 (-561)) - (-5 *1 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35150) (-4277 . 35004) + (-4278 . 34922) (-4279 . 34806) (-4280 . 34703) (-4281 . 34480) + (-4282 . 34390) (-4283 . 34291) (-4284 . 34133) (-4285 . 34053) + (-4286 . 33851) (-4287 . 33735) (-4288 . 33558) (-4289 . 33476) + (-4290 . 33380) (-4291 . 33181) (-4292 . 33128) (-4293 . 32849) + (-4294 . 32693) (-4295 . 31923) (-4296 . 31844) (-4297 . 31740) + (-4298 . 31481) (-4299 . 31240) (-4300 . 30955) (-4301 . 30904) + (-4302 . 30846) (-4303 . 30814) (-4304 . 30111) (-4305 . 30041) + (-4306 . 29836) (-4307 . 29670) (-4308 . 29636) (-4309 . 29426) + (-4310 . 29374) (-4311 . 29312) (-4312 . 29180) (-4313 . 29109) + (-4314 . 28829) (-4315 . 28726) (-4316 . 28648) (-4317 . 28401) + (-4318 . 28179) (-4319 . 28078) (-4320 . 27610) (-4321 . 27486) + (-4322 . 27407) (-4323 . 27121) (-4324 . 26894) (-4325 . 26738) + (-4326 . 26474) (-4327 . 26226) (-4328 . 25939) (-4329 . 25889) + (-4330 . 25760) (-4331 . 25530) (-4332 . 25478) (-4333 . 24518) + (-4334 . 23716) (-4335 . 23546) (-4336 . 23458) (-4337 . 22931) + (-4338 . 22798) (-4339 . 22399) (-4340 . 22211) (-4341 . 22123) + (-4342 . 21965) (-4343 . 21430) (-4344 . 20977) (-4345 . 20876) + (-4346 . 20761) (-4347 . 20522) (-4348 . 20346) (-4349 . 20243) + (-4350 . 20135) (-4351 . 19960) (-4352 . 19816) (-4353 . 19788) + (-4354 . 19609) (-4355 . 19485) (-4356 . 19367) (-4357 . 19145) + (-4358 . 19051) (-4359 . 18998) (-4360 . 18752) (-4361 . 18474) + (-4362 . 18241) (-4363 . 18170) (-4364 . 18096) (-4365 . 17964) + (-4366 . 17909) (-4367 . 17325) (-4368 . 17225) (-4369 . 17051) + (-4370 . 16974) (-4371 . 16644) (-4372 . 15826) (-4373 . 15774) + (-4374 . 15610) (-4375 . 15457) (-4376 . 15353) (-4377 . 15243) + (-4378 . 10701) (-4379 . 10510) (-4380 . 10285) (-4381 . 10086) + (-4382 . 9924) (-4383 . 9893) (-4384 . 9660) (-4385 . 9599) + (-4386 . 8399) (-4387 . 7816) (-4388 . 7744) (-4389 . 7111) + (-4390 . 6947) (-4391 . 6894) (-4392 . 6833) (-4393 . 6750) + (-4394 . 6656) (-4395 . 6318) (-4396 . 5616) (-4397 . 5331) + (-4398 . 5263) (-4399 . 5092) (-4400 . 5006) (-4401 . 4946) + (-4402 . 4853) (-4403 . 4800) (-4404 . 4766) (-4405 . 4422) + (-4406 . 4309) (-4407 . 3971) (-4408 . 3897) (-4409 . 3218) + (-4410 . 3159) (-4411 . 2243) (-4412 . 1912) (-4413 . 1768) + (-4414 . 1665) (-4415 . 1637) (-4416 . 927) (-4417 . 850) + (-4418 . 777) (-4419 . 743) (-4420 . 535) (-4421 . 450) (-4422 . 384) + (-4423 . 301) (-4424 . 30))
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