diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 3174 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 6642 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 200 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8022 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 21149 |
5 files changed, 19605 insertions, 19582 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 2580538e..35b97233 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(1965557 . 3580468866) +(1966230 . 3580478883) (-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 shallowly mutable 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 @@ -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}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}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}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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},{}...,{}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},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . 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}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-3995 . T) (-3993 . T) (-3992 . T) ((-4000 "*") . T) (-3991 . T) (-3996 . T) (-3990 . T)) +((-3998 . T) (-3996 . T) (-3995 . T) ((-4003 "*") . T) (-3994 . T) (-3999 . T) (-3993 . T)) NIL (-30) ((|refine| (($ $ (|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."))) @@ -56,10 +56,10 @@ 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 `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3095) +(-32 R -3098) ((|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| (QUOTE (-952 (-486))))) +((|HasCategory| |#1| (QUOTE (-954 (-488))))) (-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)}\"")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\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 @@ -82,20 +82,20 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . 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 \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -3095 UP UPUP -2617) +(-40 -3098 UP UPUP -2620) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-3991 |has| (-350 |#2|) (-312)) (-3996 |has| (-350 |#2|) (-312)) (-3990 |has| (-350 |#2|) (-312)) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1092))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1092)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1092))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-813 (-1092)))))) (|HasCategory| (-350 |#2|) (QUOTE (-582 (-486)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-952 (-350 (-486)))))) (|HasCategory| (-350 |#2|) (QUOTE (-952 (-350 (-486))))) (|HasCategory| (-350 |#2|) (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-813 (-1092))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1092)))))) -(-41 R -3095) +((-3994 |has| (-352 |#2|) (-314)) (-3999 |has| (-352 |#2|) (-314)) (-3993 |has| (-352 |#2|) (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-352 |#2|) (QUOTE (-118))) (|HasCategory| (-352 |#2|) (QUOTE (-120))) (|HasCategory| (-352 |#2|) (QUOTE (-301))) (OR (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-322))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-191))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-301))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094)))))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-815 (-1094)))))) (|HasCategory| (-352 |#2|) (QUOTE (-584 (-488)))) (OR (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-352 (-488)))))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-322))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-191))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-815 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094)))))) +(-41 R -3098) ((|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}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'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 (-393))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#2| (|%list| (QUOTE -364) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (|%list| (QUOTE -366) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -103,34 +103,34 @@ NIL (-43 R A) ((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note: right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note: left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,a) = 0} and \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,x,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,b,x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,a,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis. Note: if \\spad{A} has a unit,{} then \\spadfunFrom{doubleRank}{AlgebraPackage},{} \\spadfunFrom{weakBiRank}{AlgebraPackage} and \\spadfunFrom{biRank}{AlgebraPackage} coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis."))) NIL -((|HasCategory| |#1| (QUOTE (-258)))) +((|HasCategory| |#1| (QUOTE (-260)))) (-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."))) -((-3995 |has| |#1| (-497)) (-3993 . T) (-3992 . T)) -((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) +((-3998 |has| |#1| (-499)) (-3996 . T) (-3995 . T)) +((|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (-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."))) 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(QUOTE -1039) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-760)))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| $ (|%list| (QUOTE -1039) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|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.")) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL -((|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) +((|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-314)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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.")) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (QUOTE (-952 (-486))))) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| $ (QUOTE (-965))) (|HasCategory| $ (QUOTE (-954 (-488))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|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}."))) -((-3995 . T)) +((-3998 . T)) NIL (-51) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3095) +(-54 |Base| R -3098) ((|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},{}...,{}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},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -171,15 +171,15 @@ NIL (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) (-61 R L) ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) NIL -((|HasCategory| |#1| (QUOTE (-312)))) +((|HasCategory| |#1| (QUOTE (-314)))) (-62 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}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) (-63 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -202,11 +202,11 @@ NIL NIL (-68) ((|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.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4000 "*") . T) (-3995 . T) (-3993 . T) (-3992 . T) (-3991 . T) (-3996 . T) (-3990 . T) (-3989 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3994 . T) (-3997 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3985 . T)) +(((-4003 "*") . T) (-3998 . T) (-3996 . T) (-3995 . T) (-3994 . T) (-3999 . T) (-3993 . T) (-3992 . T) (-3991 . T) (-3990 . T) (-3989 . T) (-3997 . T) (-4000 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3988 . T)) NIL (-69 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}."))) -((-3995 . T)) +((-3998 . T)) NIL (-70 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}."))) @@ -223,11 +223,11 @@ NIL (-73 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 pl and 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{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 ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) (-74 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 (-4000 "*")))) +((|HasAttribute| |#1| (QUOTE (-4003 "*")))) (-75 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}."))) NIL @@ -238,8 +238,8 @@ NIL NIL (-77) ((|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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-486) (QUOTE (-823))) (|HasCategory| (-486) (QUOTE (-952 (-1092)))) (|HasCategory| (-486) (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-120))) (|HasCategory| (-486) (QUOTE (-555 (-475)))) (|HasCategory| (-486) (QUOTE (-935))) (|HasCategory| (-486) (QUOTE (-742))) (|HasCategory| (-486) (QUOTE (-758))) (OR (|HasCategory| (-486) (QUOTE (-742))) (|HasCategory| (-486) (QUOTE (-758)))) (|HasCategory| (-486) (QUOTE (-952 (-486)))) (|HasCategory| (-486) (QUOTE (-1068))) (|HasCategory| (-486) (QUOTE (-798 (-330)))) (|HasCategory| (-486) (QUOTE (-798 (-486)))) (|HasCategory| (-486) (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-486) (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-486) (QUOTE (-189))) (|HasCategory| (-486) (QUOTE (-813 (-1092)))) (|HasCategory| (-486) (QUOTE (-190))) (|HasCategory| (-486) (QUOTE (-811 (-1092)))) (|HasCategory| (-486) (QUOTE (-457 (-1092) (-486)))) (|HasCategory| (-486) (QUOTE (-260 (-486)))) (|HasCategory| (-486) (QUOTE (-241 (-486) (-486)))) (|HasCategory| (-486) (QUOTE (-258))) (|HasCategory| (-486) (QUOTE (-485))) (|HasCategory| (-486) (QUOTE (-582 (-486)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-823)))) (|HasCategory| (-486) (QUOTE (-118))))) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-488) (QUOTE (-825))) (|HasCategory| (-488) (QUOTE (-954 (-1094)))) (|HasCategory| (-488) (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-120))) (|HasCategory| (-488) (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-937))) (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760))) (OR (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760)))) (|HasCategory| (-488) (QUOTE (-954 (-488)))) (|HasCategory| (-488) (QUOTE (-1070))) (|HasCategory| (-488) (QUOTE (-800 (-332)))) (|HasCategory| (-488) (QUOTE (-800 (-488)))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-488) (QUOTE (-191))) (|HasCategory| (-488) (QUOTE (-815 (-1094)))) (|HasCategory| (-488) (QUOTE (-192))) (|HasCategory| (-488) (QUOTE (-813 (-1094)))) (|HasCategory| (-488) (QUOTE (-459 (-1094) (-488)))) (|HasCategory| (-488) (QUOTE (-262 (-488)))) (|HasCategory| (-488) (QUOTE (-243 (-488) (-488)))) (|HasCategory| (-488) (QUOTE (-260))) (|HasCategory| (-488) (QUOTE (-487))) (|HasCategory| (-488) (QUOTE (-584 (-488)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (|HasCategory| (-488) (QUOTE (-118))))) (-78) ((|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 `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -255,10 +255,10 @@ NIL (-81) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) NIL -((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1015)))) (|HasCategory| (-85) (QUOTE (-555 (-475)))) (|HasCategory| (-85) (QUOTE (-758))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-554 (-774)))) (|HasCategory| (-85) (QUOTE (-1015))) (-12 (|HasCategory| $ (QUOTE (-1037 (-85)))) (|HasCategory| (-85) (QUOTE (-758)))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1037 (-85))))) +((-12 (|HasCategory| (-85) (QUOTE (-262 (-85)))) (|HasCategory| (-85) (QUOTE (-1017)))) (|HasCategory| (-85) (QUOTE (-557 (-477)))) (|HasCategory| (-85) (QUOTE (-760))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-556 (-776)))) (|HasCategory| (-85) (QUOTE (-1017))) (-12 (|HasCategory| $ (QUOTE (-1039 (-85)))) (|HasCategory| (-85) (QUOTE (-760)))) (|HasCategory| $ (QUOTE (-320 (-85)))) (-12 (|HasCategory| $ (QUOTE (-320 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1039 (-85))))) (-82 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}"))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL (-83 S) ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) @@ -280,22 +280,22 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-88 -3095 UP) +(-88 -3098 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 (-89 |p|) ((|constructor| (NIL "Stream-based implementation of 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}."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL (-90 |p|) ((|constructor| (NIL "Stream-based implementation of 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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-89 |#1|) (QUOTE (-823))) (|HasCategory| (-89 |#1|) (QUOTE (-952 (-1092)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-475)))) (|HasCategory| (-89 |#1|) (QUOTE (-935))) (|HasCategory| (-89 |#1|) (QUOTE (-742))) (|HasCategory| (-89 |#1|) (QUOTE (-758))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-742))) (|HasCategory| (-89 |#1|) (QUOTE (-758)))) (|HasCategory| (-89 |#1|) (QUOTE (-952 (-486)))) (|HasCategory| (-89 |#1|) (QUOTE (-1068))) (|HasCategory| (-89 |#1|) (QUOTE (-798 (-330)))) (|HasCategory| (-89 |#1|) (QUOTE (-798 (-486)))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-89 |#1|) (QUOTE (-582 (-486)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-813 (-1092)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1092)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -457) (QUOTE (-1092)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-485))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-823)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-89 |#1|) (QUOTE (-825))) (|HasCategory| (-89 |#1|) (QUOTE (-954 (-1094)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-557 (-477)))) (|HasCategory| (-89 |#1|) (QUOTE (-937))) (|HasCategory| (-89 |#1|) (QUOTE (-744))) (|HasCategory| (-89 |#1|) (QUOTE (-760))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-744))) (|HasCategory| (-89 |#1|) (QUOTE (-760)))) (|HasCategory| (-89 |#1|) (QUOTE (-954 (-488)))) (|HasCategory| (-89 |#1|) (QUOTE (-1070))) (|HasCategory| (-89 |#1|) (QUOTE (-800 (-332)))) (|HasCategory| (-89 |#1|) (QUOTE (-800 (-488)))) (|HasCategory| (-89 |#1|) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-89 |#1|) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-89 |#1|) (QUOTE (-584 (-488)))) (|HasCategory| (-89 |#1|) (QUOTE (-191))) (|HasCategory| (-89 |#1|) (QUOTE (-815 (-1094)))) (|HasCategory| (-89 |#1|) (QUOTE (-192))) (|HasCategory| (-89 |#1|) (QUOTE (-813 (-1094)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -459) (QUOTE (-1094)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -262) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -243) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-260))) (|HasCategory| (-89 |#1|) (QUOTE (-487))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-825)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) (-91 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -1037) (|devaluate| |#2|)))) +((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|)))) (-92 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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 @@ -307,7 +307,7 @@ NIL (-94 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"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) (-95 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -327,11 +327,11 @@ NIL (-99 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) (-100 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."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) (-101) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL @@ -339,7 +339,7 @@ NIL (-102) ((|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 `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `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."))) NIL -((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-758)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1015))))) (|HasCategory| (-101) (QUOTE (-554 (-774)))) (|HasCategory| (-101) (QUOTE (-555 (-475)))) (OR (|HasCategory| (-101) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-1015)))) (|HasCategory| (-101) (QUOTE (-758))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1015))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1015)))) (-12 (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| (-101) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| $ (QUOTE (-1037 (-101)))) (-12 (|HasCategory| $ (QUOTE (-1037 (-101)))) (|HasCategory| (-101) (QUOTE (-758))))) +((OR (-12 (|HasCategory| (-101) (QUOTE (-262 (-101)))) (|HasCategory| (-101) (QUOTE (-760)))) (-12 (|HasCategory| (-101) (QUOTE (-262 (-101)))) (|HasCategory| (-101) (QUOTE (-1017))))) (|HasCategory| (-101) (QUOTE (-556 (-776)))) (|HasCategory| (-101) (QUOTE (-557 (-477)))) (OR (|HasCategory| (-101) (QUOTE (-760))) (|HasCategory| (-101) (QUOTE (-1017)))) (|HasCategory| (-101) (QUOTE (-760))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-760))) (|HasCategory| (-101) (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1017))) (-12 (|HasCategory| (-101) (QUOTE (-262 (-101)))) (|HasCategory| (-101) (QUOTE (-1017)))) (-12 (|HasCategory| $ (QUOTE (-320 (-101)))) (|HasCategory| (-101) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-320 (-101)))) (|HasCategory| $ (QUOTE (-1039 (-101)))) (-12 (|HasCategory| $ (QUOTE (-1039 (-101)))) (|HasCategory| (-101) (QUOTE (-760))))) (-103) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -358,13 +358,13 @@ NIL NIL (-107) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4000 "*") . T)) +(((-4003 "*") . T)) NIL -(-108 |minix| -2624 R) +(-108 |minix| -2627 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) NIL NIL -(-109 |minix| -2624 S T$) +(-109 |minix| -2627 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL @@ -386,8 +386,8 @@ NIL NIL (-114) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}."))) -((-3988 . T)) -((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015))))) (|HasCategory| (-117) (QUOTE (-555 (-475)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-554 (-774)))) (|HasCategory| (-117) (QUOTE (-1015))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72))))) +((-3991 . T)) +((OR (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-322)))) (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-1017))))) (|HasCategory| (-117) (QUOTE (-557 (-477)))) (|HasCategory| (-117) (QUOTE (-322))) (|HasCategory| (-117) (QUOTE (-760))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-556 (-776)))) (|HasCategory| (-117) (QUOTE (-1017))) (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-1017)))) (|HasCategory| $ (QUOTE (-320 (-117)))) (-12 (|HasCategory| $ (QUOTE (-320 (-117)))) (|HasCategory| (-117) (QUOTE (-72))))) (-115 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}'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}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -402,7 +402,7 @@ NIL NIL (-118) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-3995 . T)) +((-3998 . T)) NIL (-119 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 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) @@ -410,9 +410,9 @@ NIL NIL (-120) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-3995 . T)) +((-3998 . T)) NIL -(-121 -3095 UP UPUP) +(-121 -3098 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 @@ -423,14 +423,14 @@ NIL (-123 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|construct| (($ (|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| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#2|)))) +((|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -320) (|devaluate| |#2|)))) (-124 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|construct| (($ (|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 (-125 |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."))) -((-3993 . T) (-3992 . T) (-3995 . T)) +((-3996 . T) (-3995 . T) (-3998 . T)) NIL (-126) ((|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."))) @@ -452,7 +452,7 @@ 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 -(-131 R -3095) +(-131 R -3098) ((|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})/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.} 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.} 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.} n!/(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 @@ -480,4301 +480,4309 @@ NIL ((|constructor| (NIL "A package for swapping the order of two variables in a tower of two UnivariatePolynomialCategory extensions.")) (|swap| ((|#3| |#3|) "\\spad{swap(p(x,y))} returns \\spad{p}(\\spad{y},{}\\spad{x})."))) NIL NIL -(-138 S R) +(-138 T$) +((|constructor| (NIL "This domain implements commutative operations.")) (|commutativeOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{commutativeOperation f} constructs a commutative operation over \\spad{T},{} thus asserting a commutativity property."))) +(((|%Rule| |commutativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|)) (-3062 (|f| |x| |y|) (|f| |y| |x|)))) . T)) +NIL +(-139 T$) +((|constructor| (NIL "This is the category of all domains that implement commutative operations."))) +(((|%Rule| |commutativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|)) (-3062 (|f| |x| |y|) (|f| |y| |x|)))) . T)) +NIL +(-140 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 (-823))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-917))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasAttribute| |#2| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-497)))) -(-139 R) +((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-919))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3997)) (|HasAttribute| |#2| (QUOTE -4000)) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-499)))) +(-141 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})"))) -((-3991 OR (|has| |#1| (-497)) (-12 (|has| |#1| (-258)) (|has| |#1| (-823)))) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3997 |has| |#1| (-6 -3997)) (-1377 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 OR (|has| |#1| (-499)) (-12 (|has| |#1| (-260)) (|has| |#1| (-825)))) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3997 |has| |#1| (-6 -3997)) (-4000 |has| |#1| (-6 -4000)) (-1380 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-140 RR PR) +(-142 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."))) NIL NIL -(-141) +(-143) ((|constructor| (NIL "This package implements a Spad compiler.")) (|elaborate| (((|Maybe| (|Elaboration|)) (|SpadAst|)) "\\spad{elaborate(s)} returns the elaboration of the syntax object \\spad{s} in the empty environement.")) (|macroExpand| (((|SpadAst|) (|SpadAst|) (|Environment|)) "\\spad{macroExpand(s,e)} traverses the syntax object \\spad{s} replacing all (niladic) macro invokations with the corresponding substitution."))) NIL NIL -(-142 R) +(-144 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}."))) -((-3991 OR (|has| |#1| (-497)) (-12 (|has| |#1| (-258)) (|has| |#1| (-823)))) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3997 |has| |#1| (-6 -3997)) (-1377 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . 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T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . 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(|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL NIL -(-144 R S CS) +(-146 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 NIL -(-145) +(-147) ((|constructor| (NIL "This domain implements some global properties of subspaces.")) (|copy| (($ $) "\\spad{copy(x)} \\undocumented")) (|solid| (((|Boolean|) $ (|Boolean|)) "\\spad{solid(x,b)} \\undocumented")) (|close| (((|Boolean|) $ (|Boolean|)) "\\spad{close(x,b)} \\undocumented")) (|solid?| (((|Boolean|) $) "\\spad{solid?(x)} \\undocumented")) (|closed?| (((|Boolean|) $) "\\spad{closed?(x)} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented"))) NIL NIL -(-146) +(-148) ((|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."))) -(((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-147) +(-149) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) NIL NIL -(-148 R) +(-150 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4000 "*") . T) (-3991 . T) (-3996 . T) (-3990 . T) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") . T) (-3994 . T) (-3999 . T) (-3993 . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-149) +(-151) ((|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|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) NIL NIL -(-150 R) +(-152 R) ((|constructor| (NIL "CoordinateSystems provides coordinate transformation functions for plotting. Functions in this package return conversion functions which take points expressed in other coordinate systems and return points with the corresponding Cartesian coordinates.")) (|conical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|) "\\spad{conical(a,b)} transforms from conical coordinates to Cartesian coordinates: \\spad{conical(a,b)} is a function which will map the point \\spad{(lambda,mu,nu)} to \\spad{x = lambda*mu*nu/(a*b)},{} \\spad{y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2))},{} \\spad{z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2))}.")) (|toroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{toroidal(a)} transforms from toroidal coordinates to Cartesian coordinates: \\spad{toroidal(a)} is a function which will map the point \\spad{(u,v,phi)} to \\spad{x = a*sinh(v)*cos(phi)/(cosh(v)-cos(u))},{} \\spad{y = a*sinh(v)*sin(phi)/(cosh(v)-cos(u))},{} \\spad{z = a*sin(u)/(cosh(v)-cos(u))}.")) (|bipolarCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolarCylindrical(a)} transforms from bipolar cylindrical coordinates to Cartesian coordinates: \\spad{bipolarCylindrical(a)} is a function which will map the point \\spad{(u,v,z)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))},{} \\spad{z}.")) (|bipolar| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolar(a)} transforms from bipolar coordinates to Cartesian coordinates: \\spad{bipolar(a)} is a function which will map the point \\spad{(u,v)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))}.")) (|oblateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{oblateSpheroidal(a)} transforms from oblate spheroidal coordinates to Cartesian coordinates: \\spad{oblateSpheroidal(a)} is a function which will map the point \\spad{(xi,eta,phi)} to \\spad{x = a*sinh(xi)*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(xi)*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(xi)*cos(eta)}.")) (|prolateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{prolateSpheroidal(a)} transforms from prolate spheroidal coordinates to Cartesian coordinates: \\spad{prolateSpheroidal(a)} is a function which will map the point \\spad{(xi,eta,phi)} to \\spad{x = a*sinh(xi)*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(xi)*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(xi)*cos(eta)}.")) (|ellipticCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{ellipticCylindrical(a)} transforms from elliptic cylindrical coordinates to Cartesian coordinates: \\spad{ellipticCylindrical(a)} is a function which will map the point \\spad{(u,v,z)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)},{} \\spad{z}.")) (|elliptic| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{elliptic(a)} transforms from elliptic coordinates to Cartesian coordinates: \\spad{elliptic(a)} is a function which will map the point \\spad{(u,v)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)}.")) (|paraboloidal| (((|Point| |#1|) (|Point| |#1|)) "\\spad{paraboloidal(pt)} transforms \\spad{pt} from paraboloidal coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,v,phi)} to \\spad{x = u*v*cos(phi)},{} \\spad{y = u*v*sin(phi)},{} \\spad{z = 1/2 * (u**2 - v**2)}.")) (|parabolicCylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolicCylindrical(pt)} transforms \\spad{pt} from parabolic cylindrical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,v,z)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v},{} \\spad{z}.")) (|parabolic| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolic(pt)} transforms \\spad{pt} from parabolic coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,v)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v}.")) (|spherical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{spherical(pt)} transforms \\spad{pt} from spherical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,theta,phi)} to \\spad{x = r*sin(phi)*cos(theta)},{} \\spad{y = r*sin(phi)*sin(theta)},{} \\spad{z = r*cos(phi)}.")) (|cylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cylindrical(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,theta,z)} to \\spad{x = r * cos(theta)},{} \\spad{y = r * sin(theta)},{} \\spad{z}.")) (|polar| (((|Point| |#1|) (|Point| |#1|)) "\\spad{polar(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,theta)} to \\spad{x = r * cos(theta)} ,{} \\spad{y = r * sin(theta)}.")) (|cartesian| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cartesian(pt)} returns the Cartesian coordinates of point \\spad{pt}."))) NIL NIL -(-151 R |PolR| E) +(-153 R |PolR| E) ((|constructor| (NIL "This package implements characteristicPolynomials for monogenic algebras using resultants")) (|characteristicPolynomial| ((|#2| |#3|) "\\spad{characteristicPolynomial(e)} returns the characteristic polynomial of \\spad{e} using resultants"))) NIL NIL -(-152 R S CS) +(-154 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-859 |#2|) (|%list| (QUOTE -798) (|devaluate| |#1|)))) -(-153 R) +((|HasCategory| (-861 |#2|) (|%list| (QUOTE -800) (|devaluate| |#1|)))) +(-155 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL NIL -(-154) +(-156) ((|constructor| (NIL "This domain represents `coerce' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-155 R UP) +(-157 R UP) ((|constructor| (NIL "\\spadtype{ComplexRootFindingPackage} provides functions to find all roots of a polynomial \\spad{p} over the complex number by using Plesken's idea to calculate in the polynomial ring modulo \\spad{f} and employing the Chinese Remainder Theorem. In this first version,{} the precision (see \\spadfunFrom{digits}{Float}) is not increased when this is necessary to avoid rounding errors. Hence it is the user's responsibility to increase the precision if necessary. Note also,{} if this package is called with \\spadignore{e.g.} \\spadtype{Fraction Integer},{} the precise calculations could require a lot of time. Also note that evaluating the zeros is not necessarily a good check whether the result is correct: already evaluation can cause rounding errors.")) (|startPolynomial| (((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|) "\\spad{startPolynomial(p)} uses the ideas of Schoenhage's variant of Graeffe's method to construct circles which separate roots to get a good start polynomial,{} \\spadignore{i.e.} one whose image under the Chinese Remainder Isomorphism has both entries of norm smaller and greater or equal to 1. In case the roots are found during internal calculations. The corresponding factors are in {\\em factors} which are otherwise 1.")) (|setErrorBound| ((|#1| |#1|) "\\spad{setErrorBound(eps)} changes the internal error bound,{} by default being {\\em 10 ** (-3)} to \\spad{eps},{} if \\spad{R} is a member in the category \\spadtype{QuotientFieldCategory Integer}. The internal {\\em globalDigits} is set to {\\em ceiling(1/r)**2*10} being {\\em 10**7} by default.")) (|schwerpunkt| (((|Complex| |#1|) |#2|) "\\spad{schwerpunkt(p)} determines the 'Schwerpunkt' of the roots of the polynomial \\spad{p} of degree \\spad{n},{} \\spadignore{i.e.} the center of gravity,{} which is {\\em coeffient of \\spad{x**(n-1)}} divided by {\\em n times coefficient of \\spad{x**n}}.")) (|rootRadius| ((|#1| |#2|) "\\spad{rootRadius(p)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em 1+globalEps},{} where {\\em globalEps} is the internal error bound,{} which can be set by {\\em setErrorBound}.") ((|#1| |#2| |#1|) "\\spad{rootRadius(p,errQuot)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em errQuot}.")) (|reciprocalPolynomial| ((|#2| |#2|) "\\spad{reciprocalPolynomial(p)} calulates a polynomial which has exactly the inverses of the non-zero roots of \\spad{p} as roots,{} and the same number of 0-roots.")) (|pleskenSplit| (((|Factored| |#2|) |#2| |#1|) "\\spad{pleskenSplit(poly, eps)} determines a start polynomial {\\em start}\\\\ by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} -1\". Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{pleskenSplit(poly,eps,info)} determines a start polynomial {\\em start} by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} -1\". Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough. If {\\em info} is {\\em true},{} then information messages are issued.")) (|norm| ((|#1| |#2|) "\\spad{norm(p)} determines sum of absolute values of coefficients Note: this function depends on \\spadfunFrom{abs}{Complex}.")) (|graeffe| ((|#2| |#2|) "\\spad{graeffe p} determines \\spad{q} such that \\spad{q(-z**2) = p(z)*p(-z)}. Note that the roots of \\spad{q} are the squares of the roots of \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} tries to factor \\spad{p} into linear factors with error atmost {\\em globalEps},{} the internal error bound,{} which can be set by {\\em setErrorBound}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1|) "\\spad{factor(p, eps)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{factor(p, eps, info)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization. If {\\em info} is {\\em true},{} then information messages are given.")) (|divisorCascade| (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|) "\\spad{divisorCascade(p,tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions is calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial.") (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|)) "\\spad{divisorCascade(p,tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions are calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial. If {\\em info} is {\\em true},{} then information messages are issued.")) (|complexZeros| (((|List| (|Complex| |#1|)) |#2| |#1|) "\\spad{complexZeros(p, eps)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by {\\em eps}.") (((|List| (|Complex| |#1|)) |#2|) "\\spad{complexZeros(p)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by the package constant {\\em globalEps} which you may change by {\\em setErrorBound}."))) NIL NIL -(-156 S ST) +(-158 S ST) ((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic"))) NIL NIL -(-157) +(-159) ((|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 -(-158 C) +(-160 C) ((|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments(t)} returns the list of syntax objects for the arguments used to invoke the constructor.")) (|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain") ((|#1| $) "\\spad{constructor(t)} returns the name of the constructor used to make the call."))) NIL NIL -(-159 S) +(-161 S) ((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(\\spad{i+1}) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) NIL NIL -(-160) +(-162) ((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(\\spad{i+1}) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) NIL NIL -(-161) +(-163) ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-162 R -3095) +(-164 R -3098) ((|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 -(-163 R) +(-165 R) ((|constructor| (NIL "CoerceVectorMatrixPackage: an unexposed,{} technical package for data conversions")) (|coerce| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))) "\\spad{coerce(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Fraction Polynomial R}")) (|coerceP| (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|))) "\\spad{coerceP(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Polynomial R}"))) NIL NIL -(-164) +(-166) ((|constructor| (NIL "Enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{SFunction(li)} is the \\spad{S}-function of the partition \\spad{li} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}"))) NIL NIL -(-165) +(-167) ((|constructor| (NIL "This package \\undocumented{}")) (|cyclotomicFactorization| (((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicFactorization(n)} \\undocumented{}")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} \\undocumented{}")) (|cyclotomicDecomposition| (((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicDecomposition(n)} \\undocumented{}"))) NIL NIL -(-166 N T$) +(-168 N T$) ((|constructor| (NIL "This domain provides for a fixed-sized homogeneous data buffer.")) (|qsetelt| ((|#2| $ (|NonNegativeInteger|) |#2|) "setelt(\\spad{b},{}\\spad{i},{}\\spad{x}) sets the \\spad{i}th entry of data buffer `b' to `x'. Indexing is 0-based.")) (|qelt| ((|#2| $ (|NonNegativeInteger|)) "elt(\\spad{b},{}\\spad{i}) returns the \\spad{i}th element in buffer `b'. Indexing is 0-based.")) (|new| (($) "\\spad{new()} returns a fresly allocated data buffer or length \\spad{N}."))) NIL NIL -(-167 S) +(-169 S) ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-168 |vars|) +(-170 |vars|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-169 -3095 UP UPUP R) +(-171 -3098 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 -(-170 -3095 FP) +(-172 -3098 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 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 -(-171) +(-173) ((|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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-486) (QUOTE (-823))) (|HasCategory| (-486) (QUOTE (-952 (-1092)))) (|HasCategory| (-486) (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-120))) (|HasCategory| (-486) (QUOTE (-555 (-475)))) (|HasCategory| (-486) (QUOTE (-935))) (|HasCategory| (-486) (QUOTE (-742))) (|HasCategory| (-486) (QUOTE (-758))) (OR (|HasCategory| (-486) (QUOTE (-742))) (|HasCategory| (-486) (QUOTE (-758)))) (|HasCategory| (-486) (QUOTE (-952 (-486)))) (|HasCategory| (-486) (QUOTE (-1068))) (|HasCategory| (-486) (QUOTE (-798 (-330)))) (|HasCategory| (-486) (QUOTE (-798 (-486)))) (|HasCategory| (-486) (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-486) (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-486) (QUOTE (-189))) (|HasCategory| (-486) (QUOTE (-813 (-1092)))) (|HasCategory| (-486) (QUOTE (-190))) (|HasCategory| (-486) (QUOTE (-811 (-1092)))) (|HasCategory| (-486) (QUOTE (-457 (-1092) (-486)))) (|HasCategory| (-486) (QUOTE (-260 (-486)))) (|HasCategory| (-486) (QUOTE (-241 (-486) (-486)))) (|HasCategory| (-486) (QUOTE (-258))) (|HasCategory| (-486) (QUOTE (-485))) (|HasCategory| (-486) (QUOTE (-582 (-486)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-823)))) (|HasCategory| (-486) (QUOTE (-118))))) -(-172) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-488) (QUOTE (-825))) (|HasCategory| (-488) (QUOTE (-954 (-1094)))) (|HasCategory| (-488) (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-120))) (|HasCategory| (-488) (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-937))) (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760))) (OR (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760)))) (|HasCategory| (-488) (QUOTE (-954 (-488)))) (|HasCategory| (-488) (QUOTE (-1070))) (|HasCategory| (-488) (QUOTE (-800 (-332)))) (|HasCategory| (-488) (QUOTE (-800 (-488)))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-488) (QUOTE (-191))) (|HasCategory| (-488) (QUOTE (-815 (-1094)))) (|HasCategory| (-488) (QUOTE (-192))) (|HasCategory| (-488) (QUOTE (-813 (-1094)))) (|HasCategory| (-488) (QUOTE (-459 (-1094) (-488)))) (|HasCategory| (-488) (QUOTE (-262 (-488)))) (|HasCategory| (-488) (QUOTE (-243 (-488) (-488)))) (|HasCategory| (-488) (QUOTE (-260))) (|HasCategory| (-488) (QUOTE (-487))) (|HasCategory| (-488) (QUOTE (-584 (-488)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (|HasCategory| (-488) (QUOTE (-118))))) +(-174) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `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 `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 -(-173 R -3095) +(-175 R -3098) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL -(-174 R) +(-176 R) ((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\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}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\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 -(-175 R1 R2) +(-177 R1 R2) ((|constructor| (NIL "This package \\undocumented{}")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}"))) NIL NIL -(-176 S) +(-178 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}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-177 |CoefRing| |listIndVar|) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-179 |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}.")) (|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}."))) -((-3995 . T)) +((-3998 . T)) NIL -(-178 R -3095) +(-180 R -3098) ((|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 -(-179) +(-181) ((|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.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|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}."))) -((-3773 . T) (-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3776 . T) (-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-180) +(-182) ((|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)}.}"))) NIL NIL -(-181 R) +(-183 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}"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-497))) (|HasAttribute| |#1| (QUOTE (-4000 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) -(-182 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-499))) (|HasAttribute| |#1| (QUOTE (-4003 "*"))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-72)))) +(-184 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 -(-183 S) +(-185 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 -(-184 R) +(-186 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-3995 . T)) +((-3998 . T)) NIL -(-185 S T$) +(-187 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) NIL NIL -(-186 T$) +(-188 T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#1| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#1| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) NIL NIL -(-187 R) +(-189 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-188 S) +(-190 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) NIL NIL -(-189) +(-191) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) NIL NIL -(-190) +(-192) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-3995 . T)) +((-3998 . T)) NIL -(-191) +(-193) ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) NIL NIL -(-192 A S) +(-194 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 -((|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#2|)))) -(-193 S) +((|HasCategory| |#1| (|%list| (QUOTE -320) (|devaluate| |#2|)))) +(-195 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}."))) NIL NIL -(-194) +(-196) ((|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 -(-195 S -2624 R) +(-197 S -2627 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) NIL -((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-719))) (|HasCategory| |#3| (QUOTE (-758))) (|HasAttribute| |#3| (QUOTE -3995)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-665))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-963))) (|HasCategory| |#3| (QUOTE (-1015)))) -(-196 -2624 R) +((|HasCategory| |#3| (QUOTE (-314))) (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (QUOTE (-760))) (|HasAttribute| |#3| (QUOTE -3998)) (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#3| (QUOTE (-667))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-965))) (|HasCategory| |#3| (QUOTE (-1017)))) +(-198 -2627 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) -((-3992 |has| |#2| (-963)) (-3993 |has| |#2| (-963)) (-3995 |has| |#2| (-6 -3995))) +((-3995 |has| |#2| (-965)) (-3996 |has| |#2| (-965)) (-3998 |has| |#2| (-6 -3998))) NIL -(-197 -2624 R) +(-199 -2627 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-3992 |has| |#2| (-963)) (-3993 |has| |#2| (-963)) (-3995 |has| |#2| (-6 -3995))) -((OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) 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(((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL NIL -(-200 S) +(-202 S) ((|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}."))) NIL NIL -(-201) +(-203) ((|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}."))) -((-3991 . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-202 S) +(-204 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."))) NIL NIL -(-203 S) +(-205 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}"))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) -(-204 M) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) +(-206 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'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 -(-205 R) +(-207 R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-206 |vl| R) +(-208 |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"))) -(((-4000 "*") |has| |#2| (-146)) (-3991 |has| |#2| (-497)) (-3996 |has| |#2| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . 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T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-825))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-209) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) 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(|HasCategory| |#3| (QUOTE (-813 (-1094))))) (|HasCategory| |#3| (QUOTE (-1017))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-192))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-314))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-667))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-760))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-813 (-1094)))) (|HasCategory| |#3| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#3| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#3| 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(|HasCategory| (-488) (QUOTE (-760))) (-12 (|HasCategory| |#3| (QUOTE (-584 (-488)))) (|HasCategory| |#3| (QUOTE (-965)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-813 (-1094)))) (|HasCategory| |#3| (QUOTE (-965)))) (-12 (|HasCategory| |#3| (QUOTE (-815 (-1094)))) (|HasCategory| |#3| (QUOTE (-965))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-192))) (|HasCategory| |#3| (QUOTE (-965)))) (-12 (|HasCategory| |#3| (QUOTE (-191))) (|HasCategory| |#3| (QUOTE (-965))))) (-12 (|HasCategory| |#3| (QUOTE (-954 (-488)))) (|HasCategory| |#3| (QUOTE (-1017)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-954 (-488)))) (|HasCategory| |#3| (QUOTE (-1017)))) (|HasCategory| |#3| (QUOTE (-965)))) (-12 (|HasCategory| |#3| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#3| (QUOTE (-1017)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-813 (-1094)))) (|HasCategory| |#3| (QUOTE (-965)))) (|HasAttribute| |#3| (QUOTE -3998)) (-12 (|HasCategory| |#3| (QUOTE (-192))) (|HasCategory| |#3| (QUOTE (-965))))) (-12 (|HasCategory| |#3| (QUOTE (-191))) (|HasCategory| |#3| (QUOTE (-965)))) (-12 (|HasCategory| |#3| (QUOTE (-815 (-1094)))) (|HasCategory| |#3| (QUOTE (-965)))) (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-556 (-776)))) (-12 (|HasCategory| |#3| (QUOTE (-1017))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#3|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#3|)))) +(-214 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} := 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 (-190)))) -(-213 R S V E) +((|HasCategory| |#2| (QUOTE (-192)))) +(-215 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} := 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."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) NIL -(-214 S) +(-216 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}."))) NIL NIL -(-215 |Ex|) +(-217 |Ex|) ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL NIL -(-216) +(-218) ((|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."))) NIL NIL -(-217 R |Ex|) +(-219 R |Ex|) ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,y) = g(x,y),x,y,l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) NIL NIL -(-218) +(-220) ((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,rRange,iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f, -2..2, -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,rRange,iRange,arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f, 0.3..3, 0..2*\\%pi, false)}} Parameter descriptions: \\indented{2}{f:\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) NIL NIL -(-219 R) +(-221 R) ((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) NIL NIL -(-220) +(-222) ((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,lz,l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly,lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) NIL NIL -(-221) +(-223) ((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,y,z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,y,z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) NIL NIL -(-222) +(-224) ((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn't exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) NIL NIL -(-223 S) +(-225 S) ((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) NIL NIL -(-224 S R) +(-226 S R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL -((|HasCategory| |#2| (QUOTE (-813 (-1092)))) (|HasCategory| |#2| (QUOTE (-189)))) -(-225 R) +((|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-191)))) +(-227 R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL NIL -(-226 R S V) +(-228 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"))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-330)))) (|HasCategory| |#3| (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| |#3| (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-330))))) (|HasCategory| |#3| (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#3| (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#3| (QUOTE (-555 (-475))))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1092)))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#1| (QUOTE (-393))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-227 A S) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| |#3| (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#3| (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#3| (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#3| (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#3| (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-229 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.")) (|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 NIL -(-228 S) +(-230 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.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL NIL -(-229) +(-231) ((|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|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1'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 -(-230 R -3095) +(-232 R -3098) ((|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 -(-231 R -3095) +(-233 R -3098) ((|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 -(-232 |Coef| UTS ULS) +(-234 |Coef| UTS ULS) ((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}"))) NIL -((|HasCategory| |#1| (QUOTE (-312)))) -(-233 |Coef| ULS UPXS EFULS) +((|HasCategory| |#1| (QUOTE (-314)))) +(-235 |Coef| ULS UPXS EFULS) ((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}"))) NIL -((|HasCategory| |#1| (QUOTE (-312)))) -(-234) +((|HasCategory| |#1| (QUOTE (-314)))) +(-236) ((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Identifier|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Identifier|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|Syntax|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter."))) NIL NIL -(-235) +(-237) ((|environment| (((|Environment|) $) "\\spad{environment(x)} returns the environment of the elaboration \\spad{x}.")) (|typeForm| (((|InternalTypeForm|) $) "\\spad{typeForm(x)} returns the type form of the elaboration \\spad{x}.")) (|irForm| (((|InternalRepresentationForm|) $) "\\spad{irForm(x)} returns the internal representation form of the elaboration \\spad{x}.")) (|elaboration| (($ (|InternalRepresentationForm|) (|InternalTypeForm|) (|Environment|)) "\\spad{elaboration(ir,ty,env)} construct an elaboration object for for the internal representation form \\spad{ir},{} with type \\spad{ty},{} and environment \\spad{env}."))) NIL NIL -(-236 A S) +(-238 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-72)))) -(-237 S) +((|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72)))) +(-239 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}."))) NIL NIL -(-238 S) +(-240 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) NIL NIL -(-239) +(-241) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) NIL NIL -(-240 |Coef| UTS) +(-242 |Coef| UTS) ((|constructor| (NIL "The elliptic functions sn,{} sc and dn are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,k)} expands the elliptic function dn as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,k)} expands the elliptic function cn as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,k)} expands the elliptic function sn as a Taylor \\indented{1}{series.}"))) NIL NIL -(-241 S T$) +(-243 S T$) ((|constructor| (NIL "An eltable over domains \\spad{S} and \\spad{T} is a structure which can be viewed as a function from \\spad{S} to \\spad{T}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures,{} \\spadignore{e.g.} \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,s)} (also written: \\spad{u.s}) returns the value of \\spad{u} at \\spad{s}. Error: if \\spad{u} is not defined at \\spad{s}."))) NIL NIL -(-242 S |Dom| |Im|) +(-244 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 -((|HasCategory| |#1| (|%list| (QUOTE -1037) (|devaluate| |#3|)))) -(-243 |Dom| |Im|) +((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#3|)))) +(-245 |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 -(-244 S R |Mod| -2039 -3521 |exactQuo|) +(-246 S R |Mod| -2042 -3524 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-245 S) +(-247 S) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) NIL NIL -(-246) +(-248) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-3991 . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-247) +(-249) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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"))) NIL NIL -(-248 R) +(-250 R) ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,m,k,g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) NIL NIL -(-249 S) +(-251 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| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{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}.")) (|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."))) -((-3995 OR (|has| |#1| (-963)) (|has| |#1| (-414))) (-3992 |has| |#1| (-963)) (-3993 |has| |#1| (-963))) -((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (OR (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-414))) (|HasCategory| |#1| (QUOTE (-665)))) (|HasCategory| |#1| (QUOTE (-414))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-414))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1015)))) (OR (|HasCategory| |#1| (QUOTE (-414))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (|%list| (QUOTE -457) (QUOTE (-1092)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-414)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-665)))) (OR (|HasCategory| |#1| (QUOTE (-414))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-665)))) -(-250 S R) +((-3998 OR (|has| |#1| (-965)) (|has| |#1| (-416))) (-3995 |has| |#1| (-965)) (-3996 |has| |#1| (-965))) +((|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (OR (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-667)))) (|HasCategory| |#1| (QUOTE (-416))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-1017)))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#1| (QUOTE (-1029)))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-256))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-416)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-667)))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-667)))) +(-252 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL -(-251 |Key| |Entry|) +(-253 |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."))) NIL -((-12 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-475)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#2|)))) -(-252) +((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) +(-254) ((|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 -(-253 S) +(-255 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-963)))) -(-254) +((|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-965)))) +(-256) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-255 -3095 S) +(-257 -3098 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 -(-256 E -3095) +(-258 E -3098) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\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 -(-257 S) +(-259 S) ((|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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\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}."))) NIL NIL -(-258) +(-260) ((|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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-259 S R) +(-261 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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}."))) NIL NIL -(-260 R) +(-262 R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' 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 -(-261 -3095) +(-263 -3098) ((|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 -(-262) +(-264) ((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) NIL NIL -(-263) +(-265) ((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) NIL NIL -(-264 R FE |var| |cen|) +(-266 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|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))}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-823))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-952 (-1092)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-555 (-475)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-935))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-742))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-758))) (OR (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-742))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-758)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-952 (-486)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-1068))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-798 (-330)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-798 (-486)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-582 (-486)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-813 (-1092)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1092)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -457) (QUOTE (-1092)) (|%list| (QUOTE -1168) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1168) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1168) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1168) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-485))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-823)))) (|HasCategory| (-1168 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) -(-265 R) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . 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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 NIL -(-267 R FE) +(-269 R FE) ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-268 R -3095) +(-270 R -3098) ((|constructor| (NIL "Taylor series solutions of explicit ODE'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 -(-269) +(-271) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}."))) NIL NIL -(-270 FE |var| |cen|) +(-272 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."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-486)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486)))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-29 (-486)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -585) (QUOTE (-1092))) (|devaluate| |#1|))))))) -(-271 M) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|)))) (|HasCategory| (-352 (-488)) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) +(-273 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},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL NIL -(-272 E OV R P) +(-274 E OV R P) ((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between -k and \\spad{k} as a member of \\spad{R}.")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R}. An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of \\spad{upoly}.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly, lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly, lvar, lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R}."))) NIL NIL -(-273 S) +(-275 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}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) -((-3993 . T) (-3992 . T)) -((|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| (-486) (QUOTE (-718)))) -(-274 S E) +((-3996 . T) (-3995 . T)) +((|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-488) (QUOTE (-720)))) +(-276 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}'s are in \\spad{S},{} and the \\spad{ni}'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}'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|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL NIL -(-275 S) +(-277 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-696) (QUOTE (-718)))) -(-276 S R E) +((|HasCategory| (-698) (QUOTE (-720)))) +(-278 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-146)))) -(-277 R E) +((|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148)))) +(-279 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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 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."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-278 S) +(-280 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."))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))))) -(-279 S -3095) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) +(-281 S -3098) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL -((|HasCategory| |#2| (QUOTE (-320)))) -(-280 -3095) +((|HasCategory| |#2| (QUOTE (-322)))) +(-282 -3098) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-281 E) +(-283 E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) NIL NIL -(-282) +(-284) ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-283 -3095 UP UPUP R) +(-285 -3098 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}'s are integers and the \\spad{P}'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 -(-284 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +(-286 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|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 -(-285 S -3095 UP UPUP R) +(-287 S -3098 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}'s are integers and the \\spad{P}'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 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 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 -(-286 -3095 UP UPUP R) +(-288 -3098 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}'s are integers and the \\spad{P}'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 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 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 -(-287 S R) +(-289 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -457) (QUOTE (-1092)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) -(-288 R) +((|HasCategory| |#2| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -243) (|devaluate| |#2|) (|devaluate| |#2|)))) +(-290 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides."))) NIL NIL -(-289 |p| |n|) +(-291 |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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-320)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-320))) (|HasCategory| (-819 |#1|) (QUOTE (-118)))) -(-290 S -3095 UP UPUP) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| (-821 |#1|) (QUOTE (-118))) (|HasCategory| (-821 |#1|) (QUOTE (-322)))) (|HasCategory| (-821 |#1|) (QUOTE (-120))) (|HasCategory| (-821 |#1|) (QUOTE (-322))) (|HasCategory| (-821 |#1|) (QUOTE (-118)))) +(-292 S -3098 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 \\spad{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 (-320))) (|HasCategory| |#2| (QUOTE (-312)))) -(-291 -3095 UP UPUP) +((|HasCategory| |#2| (QUOTE (-322))) (|HasCategory| |#2| (QUOTE (-314)))) +(-293 -3098 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 \\spad{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."))) -((-3991 |has| (-350 |#2|) (-312)) (-3996 |has| (-350 |#2|) (-312)) (-3990 |has| (-350 |#2|) (-312)) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 |has| (-352 |#2|) (-314)) (-3999 |has| (-352 |#2|) (-314)) (-3993 |has| (-352 |#2|) (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-292 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +(-294 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 -(-293 |p| |extdeg|) +(-295 |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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-320)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-320))) (|HasCategory| (-819 |#1|) (QUOTE (-118)))) -(-294 GF |defpol|) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| (-821 |#1|) (QUOTE (-118))) (|HasCategory| (-821 |#1|) (QUOTE (-322)))) (|HasCategory| (-821 |#1|) (QUOTE (-120))) (|HasCategory| (-821 |#1|) (QUOTE (-322))) (|HasCategory| (-821 |#1|) (QUOTE (-118)))) +(-296 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) -(-295 GF |extdeg|) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) +(-297 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) -(-296 GF) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) +(-298 GF) ((|constructor| (NIL "FiniteFieldFunctions(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 NIL -(-297 F1 GF F2) +(-299 F1 GF F2) ((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}GF,{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn't divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn't divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) NIL NIL -(-298 S) +(-300 S) ((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) NIL NIL -(-299) +(-301) ((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-300 R UP -3095) +(-302 R UP -3098) ((|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 -(-301 |p| |extdeg|) +(-303 |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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-320)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-320))) (|HasCategory| (-819 |#1|) (QUOTE (-118)))) -(-302 GF |uni|) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| (-821 |#1|) (QUOTE (-118))) (|HasCategory| (-821 |#1|) (QUOTE (-322)))) (|HasCategory| (-821 |#1|) (QUOTE (-120))) (|HasCategory| (-821 |#1|) (QUOTE (-322))) (|HasCategory| (-821 |#1|) (QUOTE (-118)))) +(-304 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) -(-303 GF |extdeg|) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) +(-305 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) -(-304 GF |defpol|) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) +(-306 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) -(-305 GF) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) +(-307 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(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(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(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(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(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(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 -(-306 -3095 GF) +(-308 -3098 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}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 -(-307 -3095 FP FPP) +(-309 -3098 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}'s exists."))) NIL NIL -(-308 GF |n|) +(-310 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) -(-309 R |ls|) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) +(-311 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{ls}."))) NIL NIL -(-310 S) +(-312 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}'s are in \\spad{S},{} and the \\spad{ni}'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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-3995 . T)) +((-3998 . T)) NIL -(-311 S) +(-313 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) NIL NIL -(-312) +(-314) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-313 S) +(-315 S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL -(-314 |Name| S) +(-316 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer'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."))) NIL NIL -(-315 S R) +(-317 S R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn'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'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'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(\"*\")} 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'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'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'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't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-497)))) -(-316 R) +((|HasCategory| |#2| (QUOTE (-499)))) +(-318 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'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'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'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(\"*\")} 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'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'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'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'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."))) -((-3995 |has| |#1| (-497)) (-3993 . T) (-3992 . T)) +((-3998 |has| |#1| (-499)) (-3996 . T) (-3995 . T)) NIL -(-317 A S) +(-319 A S) ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|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})}.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\spad{p(x)} is \\spad{true},{} and \\spad{\"failed\"} otherwise.")) (|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 \\spad{reduce(f,u,x)},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\spad{reduce(f,u,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 starting value,{} usually the identity operation of \\spad{f}. Same as \\spad{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\spad{f(x,y)} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\spad{reduce(+,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 \\spad{[x,y,...,z]} then \\spad{reduce(f,u)} returns \\spad{f(..f(f(x,y),...),z)}. Note: if \\spad{u} has one element \\spad{x},{} \\spad{reduce(f,u)} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{members([\\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} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. 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}) holds 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 \\spad{p(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})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) NIL ((|HasCategory| |#2| (QUOTE (-72)))) -(-318 S) +(-320 S) ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|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})}.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\spad{p(x)} is \\spad{true},{} and \\spad{\"failed\"} otherwise.")) (|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 \\spad{reduce(f,u,x)},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\spad{reduce(f,u,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 starting value,{} usually the identity operation of \\spad{f}. Same as \\spad{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\spad{f(x,y)} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\spad{reduce(+,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 \\spad{[x,y,...,z]} then \\spad{reduce(f,u)} returns \\spad{f(..f(f(x,y),...),z)}. Note: if \\spad{u} has one element \\spad{x},{} \\spad{reduce(f,u)} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{members([\\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} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. 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}) holds 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 \\spad{p(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})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) NIL NIL -(-319 S) +(-321 S) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) NIL NIL -(-320) +(-322) ((|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."))) NIL NIL -(-321 S R UP) +(-323 S 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| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'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| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|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."))) NIL -((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-312)))) -(-322 R UP) +((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-314)))) +(-324 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 ( Tr(\\spad{vi} * 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}'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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-323 A S) +(-325 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -1037) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-72)))) -(-324 S) +((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72)))) +(-326 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL NIL -(-325 S A R B) +(-327 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) NIL NIL -(-326 |VarSet| R) +(-328 |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.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#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) (-3993 . T) (-3992 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3996 . T) (-3995 . T)) NIL -(-327 S V) +(-329 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."))) NIL NIL -(-328 S R) +(-330 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (QUOTE (-582 (-486))))) -(-329 R) +((|HasCategory| |#2| (QUOTE (-584 (-488))))) +(-331 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL NIL -(-330) +(-332) ((|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}."))) -((-3981 . T) (-3989 . T) (-3773 . T) (-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3984 . T) (-3992 . T) (-3776 . T) (-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-331 |Par|) +(-333 |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 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}."))) NIL NIL -(-332 |Par|) +(-334 |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 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}."))) NIL NIL -(-333 R S) +(-335 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."))) -((-3993 . T) (-3992 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) -(-334 R S) +((-3996 . T) (-3995 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) +(-336 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.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-3993 . T) (-3992 . T)) -((|HasCategory| |#1| (QUOTE (-146)))) -(-335 R |Basis|) +((-3996 . T) (-3995 . T)) +((|HasCategory| |#1| (QUOTE (-148)))) +(-337 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.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}.}")) (|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}."))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-336 S) +(-338 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}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL NIL -(-337 S) +(-339 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) NIL -((|HasCategory| |#1| (QUOTE (-758)))) -(-338) +((|HasCategory| |#1| (QUOTE (-760)))) +(-340) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) NIL NIL -(-339) +(-341) ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,pref,e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,n,e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used."))) NIL NIL -(-340 |n| |class| R) +(-342 |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|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-341 -3095 UP UPUP R) +(-343 -3098 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL -(-342 -3095 UP) +(-344 -3098 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL -(-343 R) +(-345 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) NIL NIL -(-344 S) +(-346 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) NIL NIL -(-345) +(-347) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-346 S) +(-348 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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'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'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 -3981)) (|HasAttribute| |#1| (QUOTE -3989))) -(-347) +((|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#1| (QUOTE -3992))) +(-349) ((|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(\"+\") 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'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'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\"."))) -((-3773 . T) (-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3776 . T) (-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-348 R) +(-350 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 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|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-457 (-1092) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-1136))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-1136)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (|%list| (QUOTE -457) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1092)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-393)))) -(-349 R S) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-459 (-1094) $))) (|HasCategory| |#1| (QUOTE (-262 $))) (|HasCategory| |#1| (QUOTE (-243 $ $))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-1138))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-1138)))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -243) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-395)))) +(-351 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL -(-350 S) +(-352 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 gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-3985 -12 (|has| |#1| (-6 -3996)) (|has| |#1| (-393)) (|has| |#1| (-6 -3985))) (-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-952 (-1092)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-758)))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-798 (-330)))) (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-330))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1092)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (|%list| (QUOTE -457) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-485))) (-12 (|HasAttribute| |#1| (QUOTE -3985)) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#1| (QUOTE (-393)))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-351 A B) +((-3988 -12 (|has| |#1| (-6 -3999)) (|has| |#1| (-395)) (|has| |#1| (-6 -3988))) (-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-954 (-1094)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-744))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-744))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -243) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-487))) (-12 (|HasAttribute| |#1| (QUOTE -3988)) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395)))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-353 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL NIL -(-352 S R UP) +(-354 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} 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},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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 -(-353 R UP) +(-355 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} 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},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-354 A S) +(-356 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-486))))) -(-355 S) +((|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488))))) +(-357 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-356 R -3095 UP A) +(-358 R -3098 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-3995 . T)) +((-3998 . T)) NIL -(-357 R1 F1 U1 A1 R2 F2 U2 A2) +(-359 R1 F1 U1 A1 R2 F2 U2 A2) ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-358 R -3095 UP A |ibasis|) +(-360 R -3098 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (|%list| (QUOTE -952) (|devaluate| |#2|)))) -(-359 AR R AS S) +((|HasCategory| |#4| (|%list| (QUOTE -954) (|devaluate| |#2|)))) +(-361 AR R AS S) ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL NIL -(-360 S R) +(-362 S R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\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't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\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| |#2|))) "\\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| |#2|) $) "\\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| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\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| |#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 \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\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| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|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| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-312)))) -(-361 R) +((|HasCategory| |#2| (QUOTE (-314)))) +(-363 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-3995 |has| |#1| (-497)) (-3993 . T) (-3992 . T)) +((-3998 |has| |#1| (-499)) (-3996 . T) (-3995 . T)) NIL -(-362 R) +(-364 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 NIL -(-363 S R) +(-365 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|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}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (QUOTE (-952 (-486)))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-414))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-555 (-475))))) -(-364 R) +((|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-416))) (|HasCategory| |#2| (QUOTE (-1029))) (|HasCategory| |#2| (QUOTE (-557 (-477))))) +(-366 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|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}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo'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}."))) -((-3995 OR (|has| |#1| (-963)) (|has| |#1| (-414))) (-3993 |has| |#1| (-146)) (-3992 |has| |#1| (-146)) ((-4000 "*") |has| |#1| (-497)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-497)) (-3990 |has| |#1| (-497))) +((-3998 OR (|has| |#1| (-965)) (|has| |#1| (-416))) (-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) ((-4003 "*") |has| |#1| (-499)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-499)) (-3993 |has| |#1| (-499))) NIL -(-365 R A S B) +(-367 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) NIL NIL -(-366 R FE |x| |cen|) +(-368 R FE |x| |cen|) ((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) NIL NIL -(-367 R FE |Expon| UPS TRAN |x|) +(-369 R FE |Expon| UPS TRAN |x|) ((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) NIL NIL -(-368 A S) +(-370 A S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) NIL -((|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-320)))) -(-369 S) +((|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-322)))) +(-371 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-3988 . T)) +((-3991 . T)) NIL -(-370 S A R B) +(-372 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-371 R -3095) +(-373 R -3098) ((|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 -(-372 R E) +(-374 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"))) -((-3985 -12 (|has| |#1| (-6 -3985)) (|has| |#2| (-6 -3985))) (-3992 . T) (-3993 . T) (-3995 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -3985)) (|HasAttribute| |#2| (QUOTE -3985)))) -(-373 R -3095) +((-3988 -12 (|has| |#1| (-6 -3988)) (|has| |#2| (-6 -3988))) (-3995 . T) (-3996 . T) (-3998 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -3988)) (|HasAttribute| |#2| (QUOTE -3988)))) +(-375 R -3098) ((|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 -(-374 R -3095) +(-376 R -3098) ((|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 -(-375 R -3095) +(-377 R -3098) ((|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 \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{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)))) -(-376 R -3095) +(-378 R -3098) ((|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 -(-377) +(-379) ((|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 -(-378 R -3095 UP) +(-380 R -3098 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| (QUOTE (-952 (-48))))) -(-379) +((|HasCategory| |#2| (QUOTE (-954 (-48))))) +(-381) ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) NIL NIL -(-380 |f|) +(-382 |f|) ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-381 S) +(-383 S) ((|constructor| (NIL "This category describes the class of structural objects that behave functorially in distinguished class of components.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,x)} returns an object with similar shape and structure as \\spad{x},{} where all \\spad{S}-items \\spad{s} in \\spad{x} have been replacement elementwise by \\spad{f s}."))) NIL NIL -(-382) +(-384) ((|constructor| (NIL "This is the datatype for exported function descriptor. A function descriptor consists of: (1) a signature; (2) a predicate; and (3) a slot into the scope object.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}."))) NIL NIL -(-383 UP) +(-385 UP) ((|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's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein'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'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 -(-384 R UP -3095) +(-386 R UP -3098) ((|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 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'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'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's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri'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 -(-385 R UP) +(-387 R UP) ((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored} (July 1994).")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1)."))) NIL NIL -(-386 R) +(-388 R) ((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,r)} returns the binomial coefficient \\spad{C(n,r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation."))) NIL -((|HasCategory| |#1| (QUOTE (-347)))) -(-387) +((|HasCategory| |#1| (QUOTE (-349)))) +(-389) ((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(zi)} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p},{} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(zi)} produces the complete factorization of the complex integer \\spad{zi}."))) NIL NIL -(-388 |Dom| |Expon| |VarSet| |Dpol|) +(-390 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp, infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) NIL -((|HasCategory| |#1| (QUOTE (-312)))) -(-389 |Dom| |Expon| |VarSet| |Dpol|) +((|HasCategory| |#1| (QUOTE (-314)))) +(-391 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp, infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) NIL NIL -(-390 |Dom| |Expon| |VarSet| |Dpol|) +(-392 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions, info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) NIL NIL -(-391 |Dom| |Expon| |VarSet| |Dpol|) +(-393 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) NIL NIL -(-392 S) +(-394 S) ((|constructor| (NIL "This category describes domains where \\spadfun{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| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) NIL NIL -(-393) +(-395) ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|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| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-394 R |n| |ls| |gamma|) +(-396 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"))) -((-3995 |has| (-350 (-859 |#1|)) (-497)) (-3993 . T) (-3992 . T)) -((|HasCategory| (-350 (-859 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| (-350 (-859 |#1|)) (QUOTE (-497)))) -(-395 |vl| R E) +((-3998 |has| (-352 (-861 |#1|)) (-499)) (-3996 . T) (-3995 . T)) +((|HasCategory| (-352 (-861 |#1|)) (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| (-352 (-861 |#1|)) (QUOTE (-499)))) +(-397 |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"))) -(((-4000 "*") |has| |#2| (-146)) (-3991 |has| |#2| (-497)) (-3996 |has| |#2| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-823))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-497)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-330)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-486)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-475))))) (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-393))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-396 R BP) +(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-825))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-398 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's conditional."))) NIL NIL -(-397 OV E S R P) +(-399 OV E S 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| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|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 -(-398 E OV R P) +(-400 E OV R P) ((|constructor| (NIL "This package provides operations for GCD computations on polynomials")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,q)} returns the GCD of \\spad{p} and \\spad{q}"))) NIL NIL -(-399 R) +(-401 R) ((|constructor| (NIL "\\indented{1}{Description} This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}"))) NIL NIL -(-400 R FE) +(-402 R FE) ((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),n,x = a,n0..)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}; \\spad{taylor(a(n),n,x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n +-> a(n),x = a,n0..)} returns \\spad{sum(n=n0..,a(n)*(x-a)**n)}; \\spad{taylor(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}."))) NIL NIL -(-401 RP TP) +(-403 RP TP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni} General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,lfact,prime,bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,lfacts,prime,bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done ."))) NIL NIL -(-402 |vl| R IS E |ff| P) +(-404 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-403 E V R P Q) +(-405 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) NIL NIL -(-404 R E |VarSet| P) +(-406 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) NIL -((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-475)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-1015))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) -(-405 S R E) +((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) +(-407 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) NIL NIL -(-406 R E) +(-408 R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) NIL NIL -(-407) +(-409) ((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector {\\em ww} to start a loop using {\\em nextSubsetGray(ww,n)}")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,n)} returns a vector {\\em vv} whose components have the following meanings:\\begin{items} \\item {\\em vv.1}: a vector of length \\spad{n} whose entries are 0 or 1. This \\indented{3}{can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n};} \\indented{3}{{\\em vv.1} differs from {\\em ww.1} by exactly one entry;} \\item {\\em vv.2.1} is the number of the entry of {\\em vv.1} which \\indented{3}{will be changed next time;} \\item {\\em vv.2.1 = n+1} means that {\\em vv.1} is the last subset; \\indented{3}{trying to compute nextSubsetGray(vv) if {\\em vv.2.1 = n+1}} \\indented{3}{will produce an error!} \\end{items} The other components of {\\em vv.2} are needed to compute nextSubsetGray efficiently. Note: this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case {\\em r1 = r2 = ... = rn = 2}; Note: nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} {\\em nextSubsetGray(vv)} and {\\em vv := nextSubsetGray(vv)} will have the same effect."))) NIL NIL -(-408) +(-410) ((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n}.") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n}.")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is \\spad{false}.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is \\spad{true}.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done."))) NIL NIL -(-409) +(-411) ((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(gi)} returns the indicated graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}pt) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(gi,pt,pal)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{gi},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(gi,pt)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,lp,pal1,pal2,p)} sets the components of the graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{gi} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp,lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it's data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it's elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) NIL NIL -(-410 S R E) +(-412 S R E) ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\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.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-411 R E) +(-413 R E) ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-412 |lv| -3095 R) +(-414 |lv| -3098 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL -(-413 S) +(-415 S) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) NIL NIL -(-414) +(-416) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|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}."))) -((-3995 . T)) +((-3998 . T)) NIL -(-415 |Coef| |var| |cen|) +(-417 |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)}.")) 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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)}"))) NIL -((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-475)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-1015))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) -(-418) +((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) +(-420) ((|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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-419) +(-421) ((|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'."))) NIL NIL -(-420 |Key| |Entry| |hashfn|) +(-422 |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."))) NIL -((-12 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-475)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#2|)))) -(-421) +((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) +(-423) ((|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's book Lie Groups -- 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{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 -(-422 |vl| R) +(-424 |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"))) -(((-4000 "*") |has| |#2| (-146)) (-3991 |has| |#2| (-497)) (-3996 |has| |#2| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-823))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-497)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-330)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-486)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-475))))) (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-393))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-423 -2624 S) +(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-825))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-425 -2627 S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. 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(QUOTE (-954 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-667))) (|HasCategory| |#2| (QUOTE (-954 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-965))))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-488) (QUOTE (-760))) (-12 (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-965)))) (-12 (|HasCategory| |#2| (QUOTE (-191))) (|HasCategory| |#2| (QUOTE (-965)))) (-12 (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-965)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-1017)))) (|HasCategory| |#2| (QUOTE (-965)))) (-12 (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-1017)))) (-12 (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-1017)))) (|HasAttribute| |#2| (QUOTE -3998)) (-12 (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-965)))) (-12 (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-965)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) +(-426) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `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 -(-425 S) +(-427 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}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-426 -3095 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-428 -3098 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}'s are integers and the \\spad{P}'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 -(-427 BP) +(-429 BP) ((|constructor| (NIL "This package provides the functions for the heuristic integer gcd. Geddes's algorithm,{}for univariate polynomials with integer coefficients")) (|lintgcd| (((|Integer|) (|List| (|Integer|))) "\\spad{lintgcd([a1,..,ak])} = gcd of a list of integers")) (|content| (((|List| (|Integer|)) (|List| |#1|)) "\\spad{content([f1,..,fk])} = content of a list of univariate polynonials")) (|gcdcofactprim| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofactprim([f1,..fk])} = gcd and cofactors of \\spad{k} primitive polynomials.")) (|gcdcofact| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofact([f1,..fk])} = gcd and cofactors of \\spad{k} univariate polynomials.")) (|gcdprim| ((|#1| (|List| |#1|)) "\\spad{gcdprim([f1,..,fk])} = gcd of \\spad{k} PRIMITIVE univariate polynomials")) (|gcd| ((|#1| (|List| |#1|)) "\\spad{gcd([f1,..,fk])} = gcd of the polynomials \\spad{fi}."))) NIL NIL -(-428) +(-430) ((|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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-486) (QUOTE (-823))) (|HasCategory| (-486) (QUOTE (-952 (-1092)))) (|HasCategory| (-486) (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-120))) (|HasCategory| (-486) (QUOTE (-555 (-475)))) (|HasCategory| (-486) (QUOTE (-935))) (|HasCategory| (-486) (QUOTE (-742))) (|HasCategory| (-486) (QUOTE (-758))) (OR (|HasCategory| (-486) (QUOTE (-742))) (|HasCategory| (-486) (QUOTE (-758)))) (|HasCategory| (-486) (QUOTE (-952 (-486)))) (|HasCategory| (-486) (QUOTE (-1068))) (|HasCategory| (-486) (QUOTE (-798 (-330)))) (|HasCategory| (-486) (QUOTE (-798 (-486)))) (|HasCategory| (-486) (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-486) (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-486) (QUOTE (-189))) (|HasCategory| (-486) (QUOTE (-813 (-1092)))) (|HasCategory| (-486) (QUOTE (-190))) (|HasCategory| (-486) (QUOTE (-811 (-1092)))) (|HasCategory| (-486) (QUOTE (-457 (-1092) (-486)))) (|HasCategory| (-486) (QUOTE (-260 (-486)))) (|HasCategory| (-486) (QUOTE (-241 (-486) (-486)))) (|HasCategory| (-486) (QUOTE (-258))) (|HasCategory| (-486) (QUOTE (-485))) (|HasCategory| (-486) (QUOTE (-582 (-486)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-823)))) (|HasCategory| (-486) (QUOTE (-118))))) -(-429 A S) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-488) (QUOTE (-825))) (|HasCategory| (-488) (QUOTE (-954 (-1094)))) (|HasCategory| (-488) (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-120))) (|HasCategory| (-488) (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-937))) (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760))) (OR (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760)))) (|HasCategory| (-488) (QUOTE (-954 (-488)))) (|HasCategory| (-488) (QUOTE (-1070))) (|HasCategory| (-488) (QUOTE (-800 (-332)))) (|HasCategory| (-488) (QUOTE (-800 (-488)))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-488) (QUOTE (-191))) (|HasCategory| (-488) (QUOTE (-815 (-1094)))) (|HasCategory| (-488) (QUOTE (-192))) (|HasCategory| (-488) (QUOTE (-813 (-1094)))) (|HasCategory| (-488) (QUOTE (-459 (-1094) (-488)))) (|HasCategory| (-488) (QUOTE (-262 (-488)))) (|HasCategory| (-488) (QUOTE (-243 (-488) (-488)))) (|HasCategory| (-488) (QUOTE (-260))) (|HasCategory| (-488) (QUOTE (-487))) (|HasCategory| (-488) (QUOTE (-584 (-488)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (|HasCategory| (-488) (QUOTE (-118))))) +(-431 A S) ((|constructor| (NIL "\\indented{2}{A homogeneous aggregate is an aggregate of elements all of the} \\indented{2}{same type,{} and is functorial in stored elements..} In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) -(-430 S) +((|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) +(-432 S) ((|constructor| (NIL "\\indented{2}{A homogeneous aggregate is an aggregate of elements all of the} \\indented{2}{same type,{} and is functorial in stored elements..} In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates."))) NIL NIL -(-431 S) +(-433 S) ((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A."))) NIL NIL -(-432) +(-434) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name `n'."))) NIL NIL -(-433 S) +(-435 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-434) +(-436) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-435 -3095 UP |AlExt| |AlPol|) +(-437 -3098 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL -(-436) +(-438) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (QUOTE (-952 (-486))))) -(-437 S |mn|) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| $ (QUOTE (-965))) (|HasCategory| $ (QUOTE (-954 (-488))))) +(-439 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))))) -(-438 R |Row| |Col|) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) +(-440 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-439 K R UP) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-441 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 -(-440 R UP -3095) +(-442 R UP -3098) ((|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 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 -(-441 |mn|) +(-443 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) NIL -((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1015)))) (|HasCategory| (-85) (QUOTE (-555 (-475)))) (|HasCategory| (-85) (QUOTE (-758))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-554 (-774)))) (|HasCategory| (-85) (QUOTE (-1015))) (-12 (|HasCategory| $ (QUOTE (-1037 (-85)))) (|HasCategory| (-85) (QUOTE (-758)))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1037 (-85))))) -(-442 K R UP L) +((-12 (|HasCategory| (-85) (QUOTE (-262 (-85)))) (|HasCategory| (-85) (QUOTE (-1017)))) (|HasCategory| (-85) (QUOTE (-557 (-477)))) (|HasCategory| (-85) (QUOTE (-760))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-556 (-776)))) (|HasCategory| (-85) (QUOTE (-1017))) (-12 (|HasCategory| $ (QUOTE (-1039 (-85)))) (|HasCategory| (-85) (QUOTE (-760)))) (|HasCategory| $ (QUOTE (-320 (-85)))) (-12 (|HasCategory| $ (QUOTE (-320 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1039 (-85))))) +(-444 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL NIL -(-443) +(-445) ((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}."))) NIL NIL -(-444 R Q A B) +(-446 R Q A B) ((|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}'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}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-445 -3095 |Expon| |VarSet| |DPoly|) +(-447 -3098 |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| (QUOTE (-555 (-1092))))) -(-446 |vl| |nv|) +((|HasCategory| |#3| (QUOTE (-557 (-1094))))) +(-448 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL NIL -(-447 T$) +(-449 T$) ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) -(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3059 (|f| |x| |x|) |x|))) . T)) +(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3062 (|f| |x| |x|) |x|))) . T)) NIL -(-448) +(-450) ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) NIL NIL -(-449 A S) +(-451 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) -(-450 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) +(-452 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) -(-451 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) +(-453 A S) ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}"))) NIL NIL -(-452 A S) +(-454 A S) ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{combineWithIf(u,v,f,p)} returns the result of combining index-wise,{} coefficients of \\spad{u} and \\spad{u} if when satisfy the predicate \\spad{p}. Those pairs of coefficients which fail\\spad{p} are implicitly ignored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) -(-453 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) +(-455 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) -(-454 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) +(-456 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) -(-455 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) +(-457 A S) ((|constructor| (NIL "An indexed product term is a utility domain used in the representation of indexed direct product objects.")) (|coefficient| ((|#1| $) "\\spad{coefficient t} returns the coefficient of the tern \\spad{t}.")) (|index| ((|#2| $) "\\spad{index t} returns the index of the term \\spad{t}.")) (|term| (($ |#2| |#1|) "\\spad{term(s,a)} constructs a term with index \\spad{s} and coefficient \\spad{a}."))) NIL NIL -(-456 S A B) +(-458 S A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-457 A B) +(-459 A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-458 S E |un|) +(-460 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) NIL -((|HasCategory| |#2| (QUOTE (-718)))) -(-459 S |mn|) +((|HasCategory| |#2| (QUOTE (-720)))) +(-461 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{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}"))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))))) -(-460) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) +(-462) ((|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 -(-461 |p| |n|) +(-463 |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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((OR (|HasCategory| (-519 |#1|) (QUOTE (-118))) (|HasCategory| (-519 |#1|) (QUOTE (-320)))) (|HasCategory| (-519 |#1|) (QUOTE (-120))) (|HasCategory| (-519 |#1|) (QUOTE (-320))) (|HasCategory| (-519 |#1|) (QUOTE (-118)))) -(-462 R |Row| |Col| M) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((OR (|HasCategory| (-521 |#1|) (QUOTE (-118))) (|HasCategory| (-521 |#1|) (QUOTE (-322)))) (|HasCategory| (-521 |#1|) (QUOTE (-120))) (|HasCategory| (-521 |#1|) (QUOTE (-322))) (|HasCategory| (-521 |#1|) (QUOTE (-118)))) +(-464 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,{} m*h and 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 -((|HasCategory| |#3| (|%list| (QUOTE -1037) (|devaluate| |#1|)))) -(-463 R |Row| |Col| M QF |Row2| |Col2| M2) +((|HasCategory| |#3| (|%list| (QUOTE -1039) (|devaluate| |#1|)))) +(-465 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 -((|HasCategory| |#7| (|%list| (QUOTE -1037) (|devaluate| |#5|)))) -(-464) +((|HasCategory| |#7| (|%list| (QUOTE -1039) (|devaluate| |#5|)))) +(-466) ((|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 NIL -(-465) +(-467) ((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) NIL NIL -(-466 S) +(-468 S) ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) NIL NIL -(-467) +(-469) ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) NIL NIL -(-468 GF) +(-470 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(GF) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{**}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,e,d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases\",{} Information and Computation 78,{} pp.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,n,k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in GF(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} pp.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,...,vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field GF."))) NIL NIL -(-469) +(-471) ((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file `f'.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file."))) NIL NIL -(-470 R) +(-472 R) ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} := increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} := increment()} then \\spad{f x} is \\spad{x+1}."))) NIL NIL -(-471 |Varset|) +(-473 |Varset|) ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-696) (QUOTE (-1015))))) -(-472 K -3095 |Par|) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| (-698) (QUOTE (-1017))))) +(-474 K -3098 |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 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 -(-473) +(-475) NIL NIL NIL -(-474) +(-476) ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) NIL NIL -(-475) +(-477) ((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}'s are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) (|One| (($) "\\spad{1} returns the input form corresponding to 1.")) (|Zero| (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], f)} returns the input form corresponding to \\spad{f(x1,...,xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op, [a1,...,an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) NIL NIL -(-476 R) +(-478 R) ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) NIL NIL -(-477 |Coef| UTS) +(-479 |Coef| UTS) ((|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 -(-478 K -3095 |Par|) +(-480 K -3098 |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 -(-479 R BP |pMod| |nextMod|) +(-481 R BP |pMod| |nextMod|) ((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the gcd of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the gcd of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) NIL NIL -(-480 OV E R P) +(-482 OV E R P) ((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) NIL NIL -(-481 K UP |Coef| UTS) +(-483 K UP |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|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| ((|#4| |#4|) "\\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| ((|#4| |#4|) "\\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| ((|#4| |#4|) "\\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 -(-482 |Coef| UTS) +(-484 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|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 -(-483 R UP) +(-485 R UP) ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) NIL NIL -(-484 S) +(-486 S) ((|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|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) NIL NIL -(-485) +(-487) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) -((-3996 . T) (-3997 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3999 . T) (-4000 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-486) +(-488) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-3986 . T) (-3990 . T) (-3985 . T) (-3996 . T) (-3997 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3989 . T) (-3993 . T) (-3988 . T) (-3999 . T) (-4000 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-487) +(-489) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) NIL NIL -(-488) +(-490) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) NIL NIL -(-489) +(-491) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) NIL NIL -(-490) +(-492) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) NIL NIL -(-491 |Key| |Entry| |addDom|) +(-493 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) NIL -((-12 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-475)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#2|)))) -(-492 R -3095) +((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) +(-494 R -3098) ((|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 -(-493 R0 -3095 UP UPUP R) +(-495 R0 -3098 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 -(-494) +(-496) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) NIL NIL -(-495 R) +(-497 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{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3773 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3776 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-496 S) +(-498 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) NIL NIL -(-497) +(-499) ((|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."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-498 R -3095) +(-500 R -3098) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'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}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL -(-499 I) +(-501 I) ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-500 R -3095 L) +(-502 R -3098 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL -((|HasCategory| |#3| (|%list| (QUOTE -602) (|devaluate| |#2|)))) -(-501) +((|HasCategory| |#3| (|%list| (QUOTE -604) (|devaluate| |#2|)))) +(-503) ((|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 -(-502 -3095 UP UPUP R) +(-504 -3098 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 -(-503 -3095 UP) +(-505 -3098 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 -(-504 R -3095 L) +(-506 R -3098 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'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 -602) (|devaluate| |#2|)))) -(-505 R -3095) +((|HasCategory| |#3| (|%list| (QUOTE -604) (|devaluate| |#2|)))) +(-507 R -3098) ((|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| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| |#2| (QUOTE (-571))))) -(-506 -3095 UP) +((-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-1057)))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-573))))) +(-508 -3098 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}'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 -(-507 S) +(-509 S) ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-508 -3095) +(-510 -3098) ((|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}'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 -(-509 R) +(-511 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."))) -((-3773 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3776 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-510) +(-512) ((|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}'s exists."))) NIL NIL -(-511 R -3095) +(-513 R -3098) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-952 (-1092))))) (-12 (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-497)))) -(-512 -3095 UP) +((-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-241))) (|HasCategory| |#2| (QUOTE (-573))) (|HasCategory| |#2| (QUOTE (-954 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-241)))) (|HasCategory| |#1| (QUOTE (-499)))) +(-514 -3098 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-513 R -3095) +(-515 R -3098) ((|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 -(-514) +(-516) ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) NIL NIL -(-515) +(-517) ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if `f' is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by `f' as a binary file."))) NIL NIL -(-516) +(-518) ((|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 -(-517) +(-519) ((|constructor| (NIL "This domain provides representation for ARPA Internet \\spad{IP4} addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the \\spad{IP4} address of host `h'.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address `x'.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) NIL NIL -(-518 |p| |unBalanced?|) +(-520 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-519 |p|) +(-521 |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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) -(-520) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-322)))) +(-522) ((|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 -(-521 -3095) +(-523 -3098) ((|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 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}."))) -((-3993 . T) (-3992 . T)) -((|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-952 (-1092))))) -(-522 E -3095) +((-3996 . T) (-3995 . T)) +((|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-954 (-1094))))) +(-524 E -3098) ((|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 -(-523 R -3095) +(-525 R -3098) ((|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},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL -(-524) +(-526) ((|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 -(-525 I) +(-527 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL NIL -(-526 GF) +(-528 GF) ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) NIL NIL -(-527 R) +(-529 R) ((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL ((|HasCategory| |#1| (QUOTE (-120)))) -(-528) +(-530) ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young's natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young's natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young's natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) NIL NIL -(-529 R E V P TS) +(-531 R E V P TS) ((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) NIL NIL -(-530) +(-532) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) NIL NIL -(-531 E V R P) +(-533 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL -(-532 |Coef|) +(-534 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-497))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-486)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-486)) (|devaluate| |#1|)))) (|HasCategory| (-486) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-486))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-486)))))) -(-533 |Coef|) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-488)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-488)) (|devaluate| |#1|)))) (|HasCategory| (-488) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-488)))))) +(-535 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4000 "*") |has| |#1| (-497)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-497)))) -(-534) +(((-4003 "*") |has| |#1| (-499)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-499)))) +(-536) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) NIL NIL -(-535 A B) +(-537 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-536 A B C) +(-538 A B C) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-537 R -3095 FG) +(-539 R -3098 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and 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 -(-538 S) +(-540 S) ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}."))) NIL NIL -(-539 S |Index| |Entry|) +(-541 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 -((|HasCategory| |#1| (|%list| (QUOTE -1037) (|devaluate| |#3|))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-72)))) -(-540 |Index| |Entry|) +((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#3|))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -320) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-72)))) +(-542 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL NIL -(-541) +(-543) ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) NIL NIL -(-542 R A) +(-544 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)."))) -((-3995 OR (-2565 (|has| |#2| (-316 |#1|)) (|has| |#1| (-497))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-497)))) (-3993 . T) (-3992 . T)) -((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) -(-543) +((-3998 OR (-2568 (|has| |#2| (-318 |#1|)) (|has| |#1| (-499))) (-12 (|has| |#2| (-363 |#1|)) (|has| |#1| (-499)))) (-3996 . T) (-3995 . T)) +((OR (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|)))) +(-545) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL NIL -(-544) +(-546) ((|constructor| (NIL "JVM class file access bitmask and values.")) (|jvmAbstract| (($) "The class was declared abstract; therefore object of this class may not be created.")) (|jvmInterface| (($) "The class file represents an interface,{} not a class.")) (|jvmSuper| (($) "Instruct the JVM to treat base clss method invokation specially.")) (|jvmFinal| (($) "The class was declared final; therefore no derived class allowed.")) (|jvmPublic| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) NIL NIL -(-545) +(-547) ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "The correspondong constant pool entry represents the name and type of a field or method info.")) (|jvmInterfaceMethodConstantTag| (($) "The correspondong constant pool entry represents an interface method info.")) (|jvmMethodrefConstantTag| (($) "The correspondong constant pool entry represents a class method info.")) (|jvmFieldrefConstantTag| (($) "The corresponding constant pool entry represents a class field info.")) (|jvmStringConstantTag| (($) "The corresponding constant pool entry is a string constant info.")) (|jvmClassConstantTag| (($) "The corresponding constant pool entry represents a class or and interface.")) (|jvmDoubleConstantTag| (($) "The corresponding constant pool entry is a double constant info.")) (|jvmLongConstantTag| (($) "The corresponding constant pool entry is a long constant info.")) (|jvmFloatConstantTag| (($) "The corresponding constant pool entry is a float constant info.")) (|jvmIntegerConstantTag| (($) "The corresponding constant pool entry is an integer constant info.")) (|jvmUTF8ConstantTag| (($) "The corresponding constant pool entry is sequence of bytes representing Java \\spad{UTF8} string constant."))) NIL NIL -(-546) +(-548) ((|constructor| (NIL "JVM class field access bitmask and values.")) (|jvmTransient| (($) "The field was declared transient.")) (|jvmVolatile| (($) "The field was declared volatile.")) (|jvmFinal| (($) "The field was declared final; therefore may not be modified after initialization.")) (|jvmStatic| (($) "The field was declared static.")) (|jvmProtected| (($) "The field was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The field was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The field was declared public; therefore mey accessed from outside its package."))) NIL NIL -(-547) +(-549) ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "The method was declared fpstrict; therefore floating-point mode is FP-strict.")) (|jvmAbstract| (($) "The method was declared abstract; therefore no implementation is provided.")) (|jvmNative| (($) "The method was declared native; therefore implemented in a language other than Java.")) (|jvmSynchronized| (($) "The method was declared synchronized.")) (|jvmFinal| (($) "The method was declared final; therefore may not be overriden. in derived classes.")) (|jvmStatic| (($) "The method was declared static.")) (|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package."))) NIL NIL -(-548) +(-550) ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) NIL NIL -(-549 |Entry|) +(-551 |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."))) NIL -((-12 (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1075))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-555 (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1075) (QUOTE (-758))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1075))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1075))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-72))))) -(-550 S |Key| |Entry|) +((-12 (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-1017)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1077) (QUOTE (-760))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-72))))) +(-552 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 -(-551 |Key| |Entry|) +(-553 |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}."))) NIL NIL -(-552 S) +(-554 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) NIL -((|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-330))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-486)))))) -(-553 R S) +((|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-488)))))) +(-555 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) NIL NIL -(-554 S) +(-556 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-555 S) +(-557 S) ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-556 -3095 UP) +(-558 -3098 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -(-557 S) +(-559 S) ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-558) +(-560) ((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'"))) NIL NIL -(-559 S) +(-561 S) ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-560 A R S) +(-562 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}."))) -((-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-757)))) -(-561 S R) +((-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-759)))) +(-563 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-562 R) +(-564 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."))) -((-3995 . T)) +((-3998 . T)) NIL -(-563 R -3095) +(-565 R -3098) ((|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 -(-564 R UP) +(-566 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"))) -((-3993 . T) (-3992 . T) ((-4000 "*") . T) (-3991 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-811 (-1092)))) (|HasCategory| |#2| (QUOTE (-813 (-1092)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486))))) -(-565 R E V P TS ST) +((-3996 . T) (-3995 . T) ((-4003 "*") . T) (-3994 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) +(-567 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(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) NIL NIL -(-566 OV E Z P) +(-568 OV E Z P) ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) NIL NIL -(-567) +(-569) ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) NIL NIL -(-568 |VarSet| R |Order|) +(-570 |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.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(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}}."))) -((-3995 . T)) +((-3998 . T)) NIL -(-569 R |ls|) +(-571 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(lp,{} norm?)} decomposes the variety associated with \\axiom{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{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(lp,{} norm?)} decomposes the variety associated with \\axiom{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{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(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{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(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-570 R -3095) +(-572 R -3098) ((|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 -(-571) +(-573) ((|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 -(-572 |lv| -3095) +(-574 |lv| -3098) ((|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 -(-573) +(-575) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) NIL -((-12 (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3864 (-1075)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-1015)))) (OR (|HasCategory| (-51) (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-1015)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-554 (-774)))) (|HasCategory| (-51) (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-555 (-475)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1015)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-1075) (QUOTE (-758))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1015))) (|HasCategory| (-51) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-1015))) (-12 (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3864 (-1075)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3864 (-1075)) (|:| |entry| (-51)))))) (-12 (|HasCategory| $ (QUOTE (-318 (-51)))) (|HasCategory| (-51) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1037 (-51))))) -(-574 R A) +((-12 (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-262 (-2 (|:| -3867 (-1077)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-1017)))) (OR (|HasCategory| (-51) (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-1017)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-556 (-776)))) (|HasCategory| (-51) (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-557 (-477)))) (-12 (|HasCategory| (-51) (QUOTE (-262 (-51)))) (|HasCategory| (-51) (QUOTE (-1017)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-1077) (QUOTE (-760))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1017))) (|HasCategory| (-51) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-1017))) (-12 (|HasCategory| $ (QUOTE (-320 (-2 (|:| -3867 (-1077)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-320 (-2 (|:| -3867 (-1077)) (|:| |entry| (-51)))))) (-12 (|HasCategory| $ (QUOTE (-320 (-51)))) (|HasCategory| (-51) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1039 (-51))))) +(-576 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)."))) -((-3995 OR (-2565 (|has| |#2| (-316 |#1|)) (|has| |#1| (-497))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-497)))) (-3993 . T) (-3992 . T)) -((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) -(-575 S R) +((-3998 OR (-2568 (|has| |#2| (-318 |#1|)) (|has| |#1| (-499))) (-12 (|has| |#2| (-363 |#1|)) (|has| |#1| (-499)))) (-3996 . T) (-3995 . T)) +((OR (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|)))) +(-577 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{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL -((|HasCategory| |#2| (QUOTE (-312)))) -(-576 R) +((|HasCategory| |#2| (QUOTE (-314)))) +(-578 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{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) (-3993 . T) (-3992 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3996 . T) (-3995 . T)) NIL -(-577 R FE) +(-579 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL NIL -(-578 R) +(-580 R) ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL -(-579 |vars|) +(-581 |vars|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) NIL NIL -(-580 S R) +(-582 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}'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}'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}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2563 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) -(-581 K B) +((-2566 (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-314)))) +(-583 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) -((-3993 . T) (-3992 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-579 |#2|) (QUOTE (-1015))))) -(-582 R) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| (-581 |#2|) (QUOTE (-1017))))) +(-584 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL NIL -(-583 K B) +(-585 K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-584 S) +(-586 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) NIL NIL -(-585 S) +(-587 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. 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."))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) -(-586 A B) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) +(-588 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL NIL -(-587 A B) +(-589 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and lb of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index lb. Error: if \\spad{la} and lb are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL NIL -(-588 A B C) +(-590 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL -(-589 T$) +(-591 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL -(-590 S) +(-592 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-591 S) +(-593 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) -(-592 R) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) +(-594 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL NIL -(-593 S E |un|) +(-595 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) NIL NIL -(-594 A S) +(-596 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{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{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}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -1037) (|devaluate| |#2|)))) -(-595 S) +((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|)))) +(-597 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{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{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}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-596 M R S) +(-598 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}."))) -((-3993 . T) (-3992 . T)) -((|HasCategory| |#1| (QUOTE (-716)))) -(-597 R -3095 L) +((-3996 . T) (-3995 . T)) +((|HasCategory| |#1| (QUOTE (-718)))) +(-599 R -3098 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 -(-598 A -2495) +(-600 A -2498) ((|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}}"))) -((-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-312)))) -(-599 A) +((-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-314)))) +(-601 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}}"))) -((-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-312)))) -(-600 A M) +((-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-314)))) +(-602 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-312)))) -(-601 S A) +((-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-314)))) +(-603 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL -((|HasCategory| |#2| (QUOTE (-312)))) -(-602 A) +((|HasCategory| |#2| (QUOTE (-314)))) +(-604 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}."))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-603 -3095 UP) +(-605 -3098 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)))) -(-604 A L) +(-606 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-605 S) +(-607 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spad{x\\/y} returns the logical `join',{} \\spadignore{e.g.} disjunction,{} or \\spad{x} and \\spad{y}.")) (|/\\| (($ $ $) "\\spad {x/\\y} returns the logical `meet',{} \\spadignore{e.g.} conjunction,{} of \\spad{x} and \\spad{y}.")) (~ (($ $) "\\spad{~x} returns the logical complement of \\spad{x}."))) NIL NIL -(-606) +(-608) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spad{x\\/y} returns the logical `join',{} \\spadignore{e.g.} disjunction,{} or \\spad{x} and \\spad{y}.")) (|/\\| (($ $ $) "\\spad {x/\\y} returns the logical `meet',{} \\spadignore{e.g.} conjunction,{} of \\spad{x} and \\spad{y}.")) (~ (($ $) "\\spad{~x} returns the logical complement of \\spad{x}."))) NIL NIL -(-607 R) +(-609 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-608 |VarSet| R) +(-610 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|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) (-3993 . T) (-3992 . T)) -((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146)))) -(-609 A S) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3996 . T) (-3995 . T)) +((|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-148)))) +(-611 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) NIL NIL -(-610 S) +(-612 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}."))) NIL NIL -(-611 -3095 |Row| |Col| M) +(-613 -3098 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-612 -3095) +(-614 -3098) ((|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's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-613 R E OV P) +(-615 R E OV P) ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) NIL NIL -(-614 |n| R) +(-616 |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."))) -((-3995 . T) (-3992 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-811 (-1092)))) (|HasCategory| |#2| (QUOTE (-813 (-1092)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-4000 #1="*"))) (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-811 (-1092)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-497))) (OR (|HasAttribute| |#2| (QUOTE (-4000 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-811 (-1092))))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) -(-615) +((-3998 . T) (-3995 . T) (-3996 . T)) +((|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-191))) (|HasAttribute| |#2| (QUOTE (-4003 #1="*"))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-499))) (OR (|HasAttribute| |#2| (QUOTE (-4003 #1#))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-813 (-1094))))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-148)))) +(-617) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL NIL -(-616 |VarSet|) +(-618 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL -(-617 A S) +(-619 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-618 S) +(-620 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-619) +(-621) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL NIL -(-620 |VarSet|) +(-622 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL NIL -(-621 A) +(-623 A) ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) NIL NIL -(-622 A C) +(-624 A C) ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) NIL NIL -(-623 A B C) +(-625 A B C) ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) NIL NIL -(-624) +(-626) ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) NIL NIL -(-625 A) +(-627 A) ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) NIL NIL -(-626 A C) +(-628 A C) ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) NIL NIL -(-627 A B C) +(-629 A B C) ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) NIL NIL -(-628 S R |Row| |Col|) +(-630 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise."))) NIL -((|HasAttribute| |#2| (QUOTE (-4000 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-497)))) -(-629 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-4003 "*"))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-499)))) +(-631 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise."))) NIL NIL -(-630 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-632 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-631 R |Row| |Col| M) +(-633 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 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} ~=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} ~=j)")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) NIL -((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-497)))) -(-632 R) +((|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-499)))) +(-634 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."))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-497))) (|HasAttribute| |#1| (QUOTE (-4000 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-633 R) +((OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-499))) (|HasAttribute| |#1| (QUOTE (-4003 "*"))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) +(-635 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{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL NIL -(-634 T$) +(-636 T$) ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `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 `x' into \\%."))) NIL NIL -(-635 R Q) +(-637 R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) NIL NIL -(-636 S) +(-638 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}."))) NIL NIL -(-637 U) +(-639 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 gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) NIL NIL -(-638) +(-640) ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-639 OV E -3095 PG) +(-641 OV E -3098 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 -(-640 R) +(-642 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) NIL NIL -(-641 S D1 D2 I) +(-643 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) NIL NIL -(-642 S) +(-644 S) ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) NIL NIL -(-643 S) +(-645 S) ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}."))) NIL NIL -(-644 S T$) +(-646 S T$) ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-645 S -2672 I) +(-647 S -2675 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 -(-646 E OV R P) +(-648 E OV R P) ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) NIL NIL -(-647 R) +(-649 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)}.}"))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-648 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-650 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) NIL NIL -(-649) +(-651) ((|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 -(-650 R |Mod| -2039 -3521 |exactQuo|) +(-652 R |Mod| -2042 -3524 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-651 R P) +(-653 R P) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3994 |has| |#1| (-312)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-330)))) (|HasCategory| (-996) (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| (-996) (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| (-996) (QUOTE (-555 (-475))))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-813 (-1092)))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#1| (QUOTE (-393))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-652 IS E |ff|) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3997 |has| |#1| (-314)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| (-998) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| (-998) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-998) (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-192))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-654 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL -(-653 R M) +(-655 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-3993 |has| |#1| (-146)) (-3992 |has| |#1| (-146)) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-654 R |Mod| -2039 -3521 |exactQuo|) +((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) +(-656 R |Mod| -2042 -3524 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-3995 . T)) +((-3998 . T)) NIL -(-655 S R) +(-657 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL NIL -(-656 R) +(-658 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-657 -3095) +(-659 -3098) ((|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]]}."))) -((-3995 . T)) +((-3998 . T)) NIL -(-658 S) +(-660 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-659) +(-661) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-660 S) +(-662 S) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-661) +(-663) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-662 S R UP) +(-664 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL -((|HasCategory| |#2| (QUOTE (-299))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320)))) -(-663 R UP) +((|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-322)))) +(-665 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."))) -((-3991 |has| |#1| (-312)) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 |has| |#1| (-314)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-664 S) +(-666 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) NIL NIL -(-665) +(-667) ((|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| (($) "1 is the multiplicative identity."))) NIL NIL -(-666 T$) +(-668 T$) ((|constructor| (NIL "This domain implements monoid operations.")) (|monoidOperation| (($ (|Mapping| |#1| |#1| |#1|) |#1|) "\\spad{monoidOperation(f,e)} constructs a operation from the binary mapping \\spad{f} with neutral value \\spad{e}."))) -(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3059 (|f| |x| (-2414 |f|)) |x|) (|exit| 1 (-3059 (|f| (-2414 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3059 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3062 (|f| |x| (-2417 |f|)) |x|) (|exit| 1 (-3062 (|f| (-2417 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3062 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-667 T$) +(-669 T$) ((|constructor| (NIL "This is the category of all domains that implement monoid operations")) (|neutralValue| ((|#1| $) "\\spad{neutralValue f} returns the neutral value of the monoid operation \\spad{f}."))) -(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3059 (|f| |x| (-2414 |f|)) |x|) (|exit| 1 (-3059 (|f| (-2414 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3059 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3062 (|f| |x| (-2417 |f|)) |x|) (|exit| 1 (-3062 (|f| (-2417 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3062 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-668 -3095 UP) +(-670 -3098 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 -(-669 |VarSet| E1 E2 R S PR PS) +(-671 |VarSet| E1 E2 R S PR PS) ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-670 |Vars1| |Vars2| E1 E2 R PR1 PR2) +(-672 |Vars1| |Vars2| E1 E2 R PR1 PR2) ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-671 E OV R PPR) +(-673 E OV R PPR) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-672 |vl| R) +(-674 |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."))) -(((-4000 "*") |has| |#2| (-146)) (-3991 |has| |#2| (-497)) (-3996 |has| |#2| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-823))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-497)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-330)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-486)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-475))))) (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-393))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-673 E OV R PRF) +(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-825))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-675 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-674 E OV R P) +(-676 E OV R P) ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) NIL NIL -(-675 R S M) +(-677 R S M) ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) NIL NIL -(-676 R M) +(-678 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.")) (|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}."))) -((-3993 |has| |#1| (-146)) (-3992 |has| |#1| (-146)) (-3995 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-758)))) -(-677 S) +((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#2| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-760)))) +(-679 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.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{members}.")) (|multiset| (($ (|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}."))) -((-3988 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) -(-678 S) +((-3991 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) +(-680 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-3988 . T)) +((-3991 . T)) NIL -(-679) +(-681) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL NIL -(-680 S) +(-682 S) ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) NIL NIL -(-681 |Coef| |Var|) +(-683 |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}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3993 . T) (-3992 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3996 . T) (-3995 . T) (-3998 . T)) NIL -(-682 OV E R P) +(-684 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) NIL NIL -(-683 E OV R P) +(-685 E OV R P) ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) NIL NIL -(-684 S R) +(-686 S R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) NIL NIL -(-685 R) +(-687 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(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}."))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-686 S) +(-688 S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-687) +(-689) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-688 S) +(-690 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-689) +(-691) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-690 |Par|) +(-692 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-691 -3095) +(-693 -3098) ((|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 -(-692 P -3095) +(-694 P -3098) ((|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''."))) NIL NIL -(-693 T$) +(-695 T$) NIL NIL NIL -(-694 UP -3095) +(-696 UP -3098) ((|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 -(-695 R) +(-697 R) ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-696) +(-698) ((|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."))) -(((-4000 "*") . T)) +(((-4003 "*") . T)) NIL -(-697 R -3095) +(-699 R -3098) ((|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 -(-698) +(-700) ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-699 S) +(-701 S) ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-700 R |PolR| E |PolE|) +(-702 R |PolR| E |PolE|) ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) NIL NIL -(-701 R E V P TS) +(-703 R E V P TS) ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}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},{}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 -(-702 -3095 |ExtF| |SUEx| |ExtP| |n|) +(-704 -3098 |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 -(-703 BP E OV R P) +(-705 BP E OV R P) ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) NIL NIL -(-704 |Par|) +(-706 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable."))) NIL NIL -(-705 R |VarSet|) +(-707 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-330)))) (|HasCategory| |#2| (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| |#2| (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-330))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-555 (-475))))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (-12 (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#2| (QUOTE (-555 (-1092))))) (|HasCategory| |#2| (QUOTE (-555 (-1092)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-555 (-1092))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-486)))) (|HasCategory| |#2| (QUOTE (-555 (-1092)))) (-2563 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-555 (-1092)))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-555 (-1092)))) (-2563 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486)))))) (-2563 (|HasCategory| |#1| (QUOTE (-38 (-486)))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-486)))) (|HasCategory| |#2| (QUOTE (-555 (-1092)))) (-2563 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486)))))) (-2563 (|HasCategory| |#1| (QUOTE (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-555 (-1092)))) (-2563 (|HasCategory| |#1| (QUOTE (-906 (-486))))))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#1| (QUOTE (-393))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-706 R) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| |#2| (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-557 (-1094))))) (|HasCategory| |#2| (QUOTE (-557 (-1094)))) (|HasCategory| |#1| (QUOTE (-314))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-557 (-1094))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-488)))) (|HasCategory| |#2| (QUOTE (-557 (-1094)))) (-2566 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-557 (-1094)))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-557 (-1094)))) (-2566 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) (-2566 (|HasCategory| |#1| (QUOTE (-38 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-488)))) (|HasCategory| |#2| (QUOTE (-557 (-1094)))) (-2566 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) (-2566 (|HasCategory| |#1| (QUOTE (-487))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-557 (-1094)))) (-2566 (|HasCategory| |#1| (QUOTE (-908 (-488))))))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-708 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3994 |has| |#1| (-312)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . 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T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| (-998) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| (-998) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-998) (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-192))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-709 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-708 R) +(-710 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486)))))) -(-709 R E V P) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) +(-711 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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.}"))) NIL NIL -(-710 S) +(-712 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-758)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-146)))) -(-711) +((-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-148)))) +(-713) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL NIL -(-712) +(-714) ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,n,x1,x2,ns,derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try , did , next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation's right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) NIL NIL -(-713) +(-715) ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) NIL NIL -(-714 |Curve|) +(-716 |Curve|) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) NIL NIL -(-715 S) +(-717 S) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-716) +(-718) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-717 S) +(-719 S) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-718) +(-720) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-719) +(-721) ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-720) +(-722) ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-721 S R) +(-723 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-320)))) -(-722 R) +((|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-322)))) +(-724 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-723) +(-725) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-724 R) +(-726 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -457) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-350 (-486)))))) (OR (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-486))))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-350 (-486))))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486))))) -(-725 OR R OS S) +((-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -243) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-913 |#1|) (QUOTE (-954 (-352 (-488)))))) (OR (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| (-913 |#1|) (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-913 |#1|) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-913 |#1|) (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) +(-727 OR R OS S) ((|constructor| (NIL "\\spad{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 -(-726 R -3095 L) +(-728 R -3098 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}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-727 R -3095) +(-729 R -3098) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL -(-728 R -3095) +(-730 R -3098) ((|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 -(-729 -3095 UP UPUP R) +(-731 -3098 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 -(-730 -3095 UP L LQ) +(-732 -3098 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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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 -(-731 -3095 UP L LQ) +(-733 -3098 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}'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)}'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}'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}'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 mj for some \\spad{j},{} and its leading coefficient is then a zero of 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 {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-732 -3095 UP) +(-734 -3098 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-733 -3095 L UP A LO) +(-735 -3098 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 -(-734 -3095 UP) +(-736 -3098 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}'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 ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'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)))) -(-735 -3095 LO) +(-737 -3098 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 -(-736 -3095 LODO) +(-738 -3098 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) (-3995 . T) (-3998 . 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T) (-3993 . T) (-3992 . T)) -((|HasCategory| |#2| (QUOTE (-312)))) -(-740 S) +(((-4003 "*") |has| |#2| (-314)) (-3994 |has| |#2| (-314)) (-3999 |has| |#2| (-314)) (-3993 |has| |#2| (-314)) (-3998 . T) (-3996 . T) (-3995 . T)) +((|HasCategory| |#2| (QUOTE (-314)))) +(-742 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) NIL NIL -(-741 S) +(-743 S) ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-758)))) -(-742) +((|HasCategory| |#1| (QUOTE (-760)))) +(-744) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-743 P R) +(-745 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) -((-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) -(-744 S) +((-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-192)))) +(-746 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-3988 . T)) +((-3991 . T)) NIL -(-745 R) +(-747 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."))) -((-3995 |has| |#1| (-757))) -((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-952 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-485)))) -(-746 R S) +((-3998 |has| |#1| (-759))) +((|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-759)))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-487)))) +(-748 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-747 R) +(-749 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-3993 |has| |#1| (-146)) (-3992 |has| |#1| (-146)) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-748 A S) +((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) +(-750 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 NIL -(-749 S) +(-751 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|) $ |#1|) "\\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| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-750) +(-752) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) NIL NIL -(-751) +(-753) ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) NIL NIL -(-752 R) +(-754 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-3995 |has| |#1| (-757))) -((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-952 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-485)))) -(-753 R S) +((-3998 |has| |#1| (-759))) +((|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-759)))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-487)))) +(-755 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-754) +(-756) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-755 -2624 S) +(-757 -2627 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-756) +(-758) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-757) +(-759) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((-3995 . T)) +((-3998 . T)) NIL -(-758) +(-760) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) NIL NIL -(-759 T$ |f|) +(-761 T$ |f|) ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) NIL -((|HasCategory| |#1| (QUOTE (-554 (-774))))) -(-760 S) +((|HasCategory| |#1| (QUOTE (-556 (-776))))) +(-762 S) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-761) +(-763) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-762 S R) +(-764 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the 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''.")) (|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''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-146)))) -(-763 R) +((|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148)))) +(-765 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\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 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''.")) (|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''.")) (|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)}.}"))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-764 R C) +(-766 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{\\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{\\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{\\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{\\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 (-312))) (|HasCategory| |#1| (QUOTE (-497)))) -(-765 R |sigma| -3247) +((|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) +(-767 R |sigma| -3250) ((|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."))) -((-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-312)))) -(-766 |x| R |sigma| -3247) +((-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-314)))) +(-768 |x| R |sigma| -3250) ((|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}."))) -((-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-312)))) -(-767 R) +((-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-314)))) +(-769 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) NIL -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486)))))) -(-768) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) +(-770) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-769) +(-771) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-770) +(-772) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-771 S) +(-773 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-772) +(-774) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-773) +(-775) ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) NIL NIL -(-774) +(-776) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-775 |VariableList|) +(-777 |VariableList|) ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) NIL NIL -(-776) +(-778) ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) NIL NIL -(-777 R |vl| |wl| |wtlevel|) +(-779 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: 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)"))) -((-3993 |has| |#1| (-146)) (-3992 |has| |#1| (-146)) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) -(-778 R PS UP) +((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314)))) +(-780 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-779 R |x| |pt|) +(-781 R |x| |pt|) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-780 |p|) +(-782 |p|) ((|constructor| (NIL "Stream-based implementation of 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)."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-781 |p|) +(-783 |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}."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-782 |p|) +(-784 |p|) ((|constructor| (NIL "Stream-based implementation of 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)."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-780 |#1|) (QUOTE (-823))) (|HasCategory| (-780 |#1|) (QUOTE (-952 (-1092)))) (|HasCategory| (-780 |#1|) (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-120))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-475)))) (|HasCategory| (-780 |#1|) (QUOTE (-935))) (|HasCategory| (-780 |#1|) (QUOTE (-742))) (|HasCategory| (-780 |#1|) (QUOTE (-758))) (OR (|HasCategory| (-780 |#1|) (QUOTE (-742))) (|HasCategory| (-780 |#1|) (QUOTE (-758)))) (|HasCategory| (-780 |#1|) (QUOTE (-952 (-486)))) (|HasCategory| (-780 |#1|) (QUOTE (-1068))) (|HasCategory| (-780 |#1|) (QUOTE (-798 (-330)))) (|HasCategory| (-780 |#1|) (QUOTE (-798 (-486)))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-780 |#1|) (QUOTE (-582 (-486)))) (|HasCategory| (-780 |#1|) (QUOTE (-189))) (|HasCategory| (-780 |#1|) (QUOTE (-813 (-1092)))) (|HasCategory| (-780 |#1|) (QUOTE (-190))) (|HasCategory| (-780 |#1|) (QUOTE (-811 (-1092)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -457) (QUOTE (-1092)) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -780) (|devaluate| |#1|)) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (QUOTE (-258))) (|HasCategory| (-780 |#1|) (QUOTE (-485))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-823)))) (|HasCategory| (-780 |#1|) (QUOTE (-118))))) -(-783 |p| PADIC) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-782 |#1|) (QUOTE (-825))) (|HasCategory| (-782 |#1|) (QUOTE (-954 (-1094)))) (|HasCategory| (-782 |#1|) (QUOTE (-118))) (|HasCategory| (-782 |#1|) (QUOTE (-120))) (|HasCategory| (-782 |#1|) (QUOTE (-557 (-477)))) (|HasCategory| (-782 |#1|) (QUOTE (-937))) (|HasCategory| (-782 |#1|) (QUOTE (-744))) (|HasCategory| (-782 |#1|) (QUOTE (-760))) (OR (|HasCategory| (-782 |#1|) (QUOTE (-744))) (|HasCategory| (-782 |#1|) (QUOTE (-760)))) (|HasCategory| (-782 |#1|) (QUOTE (-954 (-488)))) (|HasCategory| (-782 |#1|) (QUOTE (-1070))) (|HasCategory| (-782 |#1|) (QUOTE (-800 (-332)))) (|HasCategory| (-782 |#1|) (QUOTE (-800 (-488)))) (|HasCategory| (-782 |#1|) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-782 |#1|) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-782 |#1|) (QUOTE (-584 (-488)))) (|HasCategory| (-782 |#1|) (QUOTE (-191))) (|HasCategory| (-782 |#1|) (QUOTE (-815 (-1094)))) (|HasCategory| (-782 |#1|) (QUOTE (-192))) (|HasCategory| (-782 |#1|) (QUOTE (-813 (-1094)))) (|HasCategory| (-782 |#1|) (|%list| (QUOTE -459) (QUOTE (-1094)) (|%list| (QUOTE -782) (|devaluate| |#1|)))) (|HasCategory| (-782 |#1|) (|%list| (QUOTE -262) (|%list| (QUOTE -782) (|devaluate| |#1|)))) (|HasCategory| (-782 |#1|) (|%list| (QUOTE -243) (|%list| (QUOTE -782) (|devaluate| |#1|)) (|%list| (QUOTE -782) (|devaluate| |#1|)))) (|HasCategory| (-782 |#1|) (QUOTE (-260))) (|HasCategory| (-782 |#1|) (QUOTE (-487))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-782 |#1|) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-782 |#1|) (QUOTE (-825)))) (|HasCategory| (-782 |#1|) (QUOTE (-118))))) +(-785 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of 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)}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-952 (-1092)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758))) (OR (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758)))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-798 (-330)))) (|HasCategory| |#2| (QUOTE (-798 (-486)))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-330))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-813 (-1092)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-811 (-1092)))) (|HasCategory| |#2| (|%list| (QUOTE -457) (QUOTE (-1092)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-485))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-784 S T$) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-954 (-1094)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-744))) (|HasCategory| |#2| (QUOTE (-760))) (OR (|HasCategory| |#2| (QUOTE (-744))) (|HasCategory| |#2| (QUOTE (-760)))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-191))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -243) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-487))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-786 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 `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#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 `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774)))))) -(-785) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) (-12 (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776)))))) +(-787) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|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'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's lowest value."))) NIL NIL -(-786) +(-788) ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-787) +(-789) ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) NIL NIL -(-788 CF1 CF2) +(-790 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-789 |ComponentFunction|) +(-791 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-790 CF1 CF2) +(-792 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-791 |ComponentFunction|) +(-793 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-792) +(-794) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) NIL NIL -(-793 CF1 CF2) +(-795 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-794 |ComponentFunction|) +(-796 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-795) +(-797) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) NIL NIL -(-796 R) +(-798 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-797 R S L) +(-799 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-798 S) +(-800 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-799 |Base| |Subject| |Pat|) +(-801 |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 (-2563 (|HasCategory| |#2| (QUOTE (-952 (-1092))))) (-2563 (|HasCategory| |#2| (QUOTE (-963))))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (-2563 (|HasCategory| |#2| (QUOTE (-952 (-1092)))))) (|HasCategory| |#2| (QUOTE (-952 (-1092))))) -(-800 R S) +((-12 (-2566 (|HasCategory| |#2| (QUOTE (-954 (-1094))))) (-2566 (|HasCategory| |#2| (QUOTE (-965))))) (-12 (|HasCategory| |#2| (QUOTE (-965))) (-2566 (|HasCategory| |#2| (QUOTE (-954 (-1094)))))) (|HasCategory| |#2| (QUOTE (-954 (-1094))))) +(-802 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don'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},{}\\spad{e1}),{}...,{}(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 -(-801 R A B) +(-803 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}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) NIL NIL -(-802 R) +(-804 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) (|One| (($) "1")) (|Zero| (($) "0"))) NIL NIL -(-803 R -2672) +(-805 R -2675) ((|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 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 -(-804 R S) +(-806 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-805 |VarSet|) +(-807 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) (|One| (($) "\\spad{1} returns the empty list."))) NIL NIL -(-806 UP R) +(-808 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-807 A T$ S) +(-809 A T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-808 T$ S) +(-810 T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-809 UP -3095) +(-811 UP -3098) ((|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 -(-810 R S) +(-812 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-811 S) +(-813 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-3995 . T)) +((-3998 . T)) NIL -(-812 A S) +(-814 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-813 S) +(-815 S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|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}\\spad{-}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)}."))) NIL NIL -(-814 S) +(-816 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})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) -(-815 S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) +(-817 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-3995 . T)) -((OR (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-758)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-758)))) -(-816 |n| R) +((-3998 . T)) +((OR (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-760)))) +(-818 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 -(-817 S) +(-819 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-3995 . T)) +((-3998 . T)) NIL -(-818 S) +(-820 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-819 |p|) +(-821 |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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) -(-820 R E |VarSet| S) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-322)))) +(-822 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 NIL -(-821 R S) +(-823 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-822 S) +(-824 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} 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}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-118)))) -(-823) +(-825) ((|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| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} 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}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} 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}."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-824 R0 -3095 UP UPUP R) +(-826 R0 -3098 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 -(-825 UP UPUP R) +(-827 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-826 UP UPUP) +(-828 UP UPUP) ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-827 R) +(-829 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'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' 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} ``p-adically'' 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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-828 R) +(-830 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) NIL NIL -(-829 E OV R P) +(-831 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-830) +(-832) ((|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'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's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik'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's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\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 -(-831 -3095) +(-833 -3098) ((|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 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 -(-832) +(-834) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4000 "*") . T)) +(((-4003 "*") . T)) NIL -(-833 R) +(-835 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-834) +(-836) ((|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| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} 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)}"))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-835 |xx| -3095) +(-837 |xx| -3098) ((|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 -(-836 -3095 P) +(-838 -3098 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-837 R |Var| |Expon| GR) +(-839 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank >= \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} ~= 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-838) +(-840) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) NIL NIL -(-839 S) +(-841 S) ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> SF are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-840) +(-842) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-841) +(-843) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-842) +(-844) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-843 R -3095) +(-845 R -3098) ((|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 '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 -(-844 S A B) +(-846 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-845 S R -3095) +(-847 S R -3098) ((|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 -(-846 I) +(-848 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-847 S E) +(-849 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-848 S R L) +(-850 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-849 S E V R P) +(-851 S E V R P) ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL -((|HasCategory| |#3| (|%list| (QUOTE -798) (|devaluate| |#1|)))) -(-850 -2672) +((|HasCategory| |#3| (|%list| (QUOTE -800) (|devaluate| |#1|)))) +(-852 -2675) ((|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 fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-851 R -3095 -2672) +(-853 R -3098 -2675) ((|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 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 -(-852 S R Q) +(-854 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-853 S) +(-855 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-854 S R P) +(-856 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-855) +(-857) ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = n E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = n B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) NIL NIL -(-856 R) +(-858 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))))) -(-857 |lv| R) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#1| (QUOTE (-965))) (-12 (|HasCategory| |#1| (QUOTE (-919))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) +(-859 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL NIL -(-858 |TheField| |ThePols|) +(-860 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@sn,{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}p')}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL -((|HasCategory| |#1| (QUOTE (-757)))) -(-859 R) +((|HasCategory| |#1| (QUOTE (-759)))) +(-861 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}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-330)))) (|HasCategory| (-1092) (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| (-1092) (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-1092) (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-1092) (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| (-1092) (QUOTE (-555 (-475))))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#1| (QUOTE (-393))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-860 R S) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| (-1094) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| (-1094) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-1094) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-1094) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-1094) (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-862 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-861 |x| R) +(-863 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-862 S R E |VarSet|) +(-864 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 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 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 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 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 (-823))) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-798 (-330)))) (|HasCategory| |#2| (QUOTE (-798 (-330)))) (|HasCategory| |#4| (QUOTE (-798 (-486)))) (|HasCategory| |#2| (QUOTE (-798 (-486)))) (|HasCategory| |#4| (QUOTE (-555 (-802 (-330))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-330))))) (|HasCategory| |#4| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#4| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-555 (-475))))) -(-863 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-825))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#4| (QUOTE (-800 (-332)))) (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| |#4| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| |#4| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#4| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-557 (-477))))) +(-865 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 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 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 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 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}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) NIL -(-864 E V R P -3095) +(-866 E V R P -3098) ((|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},{}...,{}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 -(-865 E |Vars| R P S) +(-867 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-866 E V R P -3095) +(-868 E V R P -3098) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL -((|HasCategory| |#3| (QUOTE (-393)))) -(-867) +((|HasCategory| |#3| (QUOTE (-395)))) +(-869) ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) NIL NIL -(-868) +(-870) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-869 R E) +(-871 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-497))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-393))) (-12 (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3996))) -(-870 R L) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3999))) +(-872 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL -(-871 S) +(-873 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))))) -(-872 A B) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) +(-874 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL -(-873) +(-875) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-874 -3095) +(-876 -3098) ((|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}'s are the defining polynomials for the \\spad{ai}'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}'s are the defining polynomials for the \\spad{ai}'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}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL -(-875 I) +(-877 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-876) +(-878) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-877 A B) +(-879 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) -((-3995 -12 (|has| |#2| (-414)) (|has| |#1| (-414)))) -((OR (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-758))))) (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-414))) (|HasCategory| |#2| (QUOTE (-414)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-414))) (|HasCategory| |#2| (QUOTE (-414)))) (-12 (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-665))))) (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-414))) (|HasCategory| |#2| (QUOTE (-414)))) (-12 (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-665))))) (-12 (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-665)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-758))))) -(-878) +((-3998 -12 (|has| |#2| (-416)) (|has| |#1| (-416)))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-760))))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#2| (QUOTE (-416)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#2| (QUOTE (-416)))) (-12 (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#2| (QUOTE (-667))))) (-12 (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#2| (QUOTE (-322)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#2| (QUOTE (-416)))) (-12 (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#2| (QUOTE (-667))))) (-12 (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#2| (QUOTE (-667)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-760))))) +(-880) ((|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 `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-879 T$) +(-881 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-880 T$) +(-882 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-881 S T$) +(-883 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-882) +(-884) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-883 S) +(-885 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) NIL NIL -(-884 R |polR|) +(-886 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{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{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.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{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\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{gcd(\\spad{P},{} \\spad{Q})} returns the 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} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{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{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- 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{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- 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}) >= 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 = +/- 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 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}) >= 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}) >= 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}) >= 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{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL -((|HasCategory| |#1| (QUOTE (-393)))) -(-885) +((|HasCategory| |#1| (QUOTE (-395)))) +(-887) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-886) +(-888) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-887 S |Coef| |Expon| |Var|) +(-889 S |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) NIL NIL -(-888 |Coef| |Expon| |Var|) +(-890 |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}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-889) +(-891) ((|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 x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-890 S R E |VarSet| P) +(-892 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}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{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}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{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{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?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL -((|HasCategory| |#2| (QUOTE (-497)))) -(-891 R E |VarSet| P) +((|HasCategory| |#2| (QUOTE (-499)))) +(-893 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?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}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,{}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{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}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{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{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?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL NIL -(-892 R E V P) +(-894 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(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*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 gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*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(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(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(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{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(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{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(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{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},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}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(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{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(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in 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(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(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{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?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{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 gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{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(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-393)))) -(-893 K) +((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-260)))) (|HasCategory| |#1| (QUOTE (-395)))) +(-895 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-894 |VarSet| E RC P) +(-896 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-895 R) +(-897 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}."))) NIL NIL -(-896 R1 R2) +(-898 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-897 R) +(-899 R) ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-898 K) +(-900 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-899 R E OV PPR) +(-901 R E OV PPR) ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-900 K R UP -3095) +(-902 K R UP -3098) ((|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 -(-901 R |Var| |Expon| |Dpoly|) +(-903 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258))))) -(-902 |vl| |nv|) +((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-260))))) +(-904 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL -(-903 R E V P TS) +(-905 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-904) +(-906) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) NIL NIL -(-905 A S) +(-907 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-952 (-1092)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (|HasCategory| |#2| (QUOTE (-1068)))) -(-906 S) +((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-954 (-1094)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-744))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-1070)))) +(-908 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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-907 A B R S) +(-909 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL NIL -(-908 |n| K) +(-910 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-909) +(-911) ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) NIL NIL -(-910 S) +(-912 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|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\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."))) NIL NIL -(-911 R) +(-913 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.}"))) -((-3991 |has| |#1| (-246)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (|HasCategory| |#1| (|%list| (QUOTE -457) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1092)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-485)))) -(-912 S R) +((-3994 |has| |#1| (-248)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-248))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-248))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -243) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (QUOTE (-487)))) +(-914 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-246)))) -(-913 R) +((|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-248)))) +(-915 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-3991 |has| |#1| (-246)) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 |has| |#1| (-248)) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-914 QR R QS S) +(-916 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-915 S) +(-917 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-916 S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-918 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-917) +(-919) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-918 -3095 UP UPUP |radicnd| |n|) +(-920 -3098 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-3991 |has| (-350 |#2|) (-312)) (-3996 |has| (-350 |#2|) (-312)) (-3990 |has| (-350 |#2|) (-312)) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1092))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1092)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1092))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-813 (-1092)))))) (|HasCategory| (-350 |#2|) (QUOTE (-582 (-486)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-952 (-350 (-486)))))) (|HasCategory| (-350 |#2|) (QUOTE (-952 (-350 (-486))))) (|HasCategory| (-350 |#2|) (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-813 (-1092))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1092)))))) -(-919 |bb|) +((-3994 |has| (-352 |#2|) (-314)) (-3999 |has| (-352 |#2|) (-314)) (-3993 |has| (-352 |#2|) (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-352 |#2|) (QUOTE (-118))) (|HasCategory| (-352 |#2|) (QUOTE (-120))) (|HasCategory| (-352 |#2|) (QUOTE (-301))) (OR (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-322))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-191))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-301))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094)))))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-815 (-1094)))))) (|HasCategory| (-352 |#2|) (QUOTE (-584 (-488)))) (OR (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-352 (-488)))))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-322))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-191))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-815 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094)))))) +(-921 |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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-486) (QUOTE (-823))) (|HasCategory| (-486) (QUOTE (-952 (-1092)))) (|HasCategory| (-486) (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-120))) (|HasCategory| (-486) (QUOTE (-555 (-475)))) (|HasCategory| (-486) (QUOTE (-935))) (|HasCategory| (-486) (QUOTE (-742))) (|HasCategory| (-486) (QUOTE (-758))) (OR (|HasCategory| (-486) (QUOTE (-742))) (|HasCategory| (-486) (QUOTE (-758)))) (|HasCategory| (-486) (QUOTE (-952 (-486)))) (|HasCategory| (-486) (QUOTE (-1068))) (|HasCategory| (-486) (QUOTE (-798 (-330)))) (|HasCategory| (-486) (QUOTE (-798 (-486)))) (|HasCategory| (-486) (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-486) (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-486) (QUOTE (-189))) (|HasCategory| (-486) (QUOTE (-813 (-1092)))) (|HasCategory| (-486) (QUOTE (-190))) (|HasCategory| (-486) (QUOTE (-811 (-1092)))) (|HasCategory| (-486) (QUOTE (-457 (-1092) (-486)))) (|HasCategory| (-486) (QUOTE (-260 (-486)))) (|HasCategory| (-486) (QUOTE (-241 (-486) (-486)))) (|HasCategory| (-486) (QUOTE (-258))) (|HasCategory| (-486) (QUOTE (-485))) (|HasCategory| (-486) (QUOTE (-582 (-486)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-486) (QUOTE (-823)))) (|HasCategory| (-486) (QUOTE (-118))))) -(-920) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-488) (QUOTE (-825))) (|HasCategory| (-488) (QUOTE (-954 (-1094)))) (|HasCategory| (-488) (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-120))) (|HasCategory| (-488) (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-937))) (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760))) (OR (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760)))) (|HasCategory| (-488) (QUOTE (-954 (-488)))) (|HasCategory| (-488) (QUOTE (-1070))) (|HasCategory| (-488) (QUOTE (-800 (-332)))) (|HasCategory| (-488) (QUOTE (-800 (-488)))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-488) (QUOTE (-191))) (|HasCategory| (-488) (QUOTE (-815 (-1094)))) (|HasCategory| (-488) (QUOTE (-192))) (|HasCategory| (-488) (QUOTE (-813 (-1094)))) (|HasCategory| (-488) (QUOTE (-459 (-1094) (-488)))) (|HasCategory| (-488) (QUOTE (-262 (-488)))) (|HasCategory| (-488) (QUOTE (-243 (-488) (-488)))) (|HasCategory| (-488) (QUOTE (-260))) (|HasCategory| (-488) (QUOTE (-487))) (|HasCategory| (-488) (QUOTE (-584 (-488)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (|HasCategory| (-488) (QUOTE (-118))))) +(-922) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL NIL -(-921) +(-923) ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-922 RP) +(-924 RP) ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-923 S) +(-925 S) ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-924 A S) +(-926 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{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 -((|HasCategory| |#1| (|%list| (QUOTE -1037) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-72)))) -(-925 S) +((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-72)))) +(-927 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{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-926 S) +(-928 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-927) +(-929) ((|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} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (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}}"))) -((-3991 . T) (-3996 . T) (-3990 . T) (-3993 . T) (-3992 . T) ((-4000 "*") . T) (-3995 . T)) +((-3994 . T) (-3999 . T) (-3993 . T) (-3996 . T) (-3995 . T) ((-4003 "*") . T) (-3998 . T)) NIL -(-928 R -3095) +(-930 R -3098) ((|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 -(-929 R -3095) +(-931 R -3098) ((|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 -(-930 -3095 UP) +(-932 -3098 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 -(-931 -3095 UP) +(-933 -3098 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 -(-932 S) +(-934 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-933 F1 UP UPUP R F2) +(-935 F1 UP UPUP R F2) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) NIL NIL -(-934) +(-936) ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-935) +(-937) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-936 |Pol|) +(-938 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-937 |Pol|) +(-939 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-938) +(-940) ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL NIL -(-939 |TheField|) +(-941 |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"))) -((-3991 . T) (-3996 . T) (-3990 . T) (-3993 . T) (-3992 . T) ((-4000 "*") . T) (-3995 . T)) -((OR (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| (-350 (-486)) (QUOTE (-952 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| (-350 (-486)) (QUOTE (-952 (-350 (-486))))) (|HasCategory| (-350 (-486)) (QUOTE (-952 (-486))))) -(-940 -3095 L) +((-3994 . T) (-3999 . T) (-3993 . T) (-3996 . T) (-3995 . T) ((-4003 "*") . T) (-3998 . T)) +((OR (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| (-352 (-488)) (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| (-352 (-488)) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-352 (-488)) (QUOTE (-954 (-488))))) +(-942 -3098 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 -(-941 S) +(-943 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(r,s)} reset the reference \\spad{r} to refer to \\spad{s}")) (|deref| ((|#1| $) "\\spad{deref(r)} returns the object referenced by \\spad{r}")) (|ref| (($ |#1|) "\\spad{ref(s)} creates a reference to the object \\spad{s}."))) NIL NIL -(-942 R E V P) +(-944 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(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(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(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(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},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) NIL -((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-475)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-1015))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) -(-943) +((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) +(-945) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-944 R) +(-946 R) ((|constructor| (NIL "\\spad{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{i} <= \\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{i} <= \\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 (-4000 "*")))) -(-945 R) +((|HasAttribute| |#1| (QUOTE (-4003 "*")))) +(-947 R) ((|constructor| (NIL "\\spad{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'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's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker'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'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'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'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'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's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258)))) -(-946 S) +((-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-260)))) +(-948 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-947 S) +(-949 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-948 S) +(-950 S) ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-949 -3095 |Expon| |VarSet| |FPol| |LFPol|) +(-951 -3098 |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"))) -(((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-950) +(-952) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-951 A S) +(-953 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-952 S) +(-954 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-953 Q R) +(-955 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-954 R) +(-956 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-955) +(-957) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-956 UP) +(-958 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-957 R) +(-959 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL -(-958 T$) +(-960 T$) ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) NIL NIL -(-959 T$) +(-961 T$) ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-960 R |ls|) +(-962 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a 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}."))) NIL -((-12 (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-1015))) (|HasCategory| (-705 |#1| (-775 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -705) (|devaluate| |#1|) (|%list| (QUOTE -775) (|devaluate| |#2|)))))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-555 (-475)))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| (-775 |#2|) (QUOTE (-320))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-1015))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -705) (|devaluate| |#1|) (|%list| (QUOTE -775) (|devaluate| |#2|))))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -705) (|devaluate| |#1|) (|%list| (QUOTE -775) (|devaluate| |#2|)))))) -(-961) +((-12 (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-1017))) (|HasCategory| (-707 |#1| (-777 |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -707) (|devaluate| |#1|) (|%list| (QUOTE -777) (|devaluate| |#2|)))))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-557 (-477)))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| (-777 |#2|) (QUOTE (-322))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -707) (|devaluate| |#1|) (|%list| (QUOTE -777) (|devaluate| |#2|))))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -707) (|devaluate| |#1|) (|%list| (QUOTE -777) (|devaluate| |#2|)))))) +(-963) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-962 S) +(-964 S) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL NIL -(-963) +(-965) ((|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."))) -((-3995 . T)) +((-3998 . T)) NIL -(-964 |xx| -3095) +(-966 |xx| -3098) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-965 S) +(-967 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-966 S |m| |n| R |Row| |Col|) +(-968 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix."))) NIL -((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-497))) (|HasCategory| |#4| (QUOTE (-146)))) -(-967 |m| |n| R |Row| |Col|) +((|HasCategory| |#4| (QUOTE (-260))) (|HasCategory| |#4| (QUOTE (-314))) (|HasCategory| |#4| (QUOTE (-499))) (|HasCategory| |#4| (QUOTE (-148)))) +(-969 |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}.")) (|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."))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-968 |m| |n| R) +(-970 |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}."))) -((-3993 . T) (-3992 . T)) -((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-497))) (-12 (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-554 (-774))))) -(-969 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-3996 . T) (-3995 . T)) +((|HasCategory| |#3| (QUOTE (-148))) (OR (-12 (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-314))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1017))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (QUOTE (-314)))) (|HasCategory| |#3| (QUOTE (-314))) (|HasCategory| |#3| (QUOTE (-260))) (|HasCategory| |#3| (QUOTE (-499))) (-12 (|HasCategory| |#3| (QUOTE (-1017))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1017))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-556 (-776))))) +(-971 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-970 R) +(-972 R) ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) NIL NIL -(-971 S) +(-973 S) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) NIL NIL -(-972) +(-974) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) NIL NIL -(-973 S T$) +(-975 S T$) ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1015)))) -(-974 S) +((|HasCategory| |#1| (QUOTE (-1017)))) +(-976 S) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-975) +(-977) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-976 |TheField| |ThePolDom|) +(-978 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-977) +(-979) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-3986 . T) (-3990 . T) (-3985 . T) (-3996 . T) (-3997 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3989 . T) (-3993 . T) (-3988 . T) (-3999 . T) (-4000 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-978 S R E V) +(-980 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| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-38 (-486)))) (|HasCategory| |#2| (QUOTE (-906 (-486)))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#4| (QUOTE (-555 (-1092))))) -(-979 R E V) +((|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-38 (-488)))) (|HasCategory| |#2| (QUOTE (-908 (-488)))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#4| (QUOTE (-557 (-1094))))) +(-981 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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}}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) NIL -(-980) +(-982) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) NIL NIL -(-981 S |TheField| |ThePols|) +(-983 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-982 |TheField| |ThePols|) +(-984 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-983 R E V P TS) +(-985 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-984 S R E V P) +(-986 S R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,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}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic 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 gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-985 R E V P) +(-987 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}{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 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 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 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}."))) NIL NIL -(-986 R E V P TS) +(-988 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}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},{}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},{}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},{}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},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-987) +(-989) ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-988) +(-990) ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-989 |Base| R -3095) +(-991 |Base| R -3098) ((|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},{}...,{}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 -(-990 |f|) +(-992 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-991 |Base| R -3095) +(-993 |Base| R -3098) ((|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 -(-992 R |ls|) +(-994 R |ls|) ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-993 R UP M) +(-995 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."))) -((-3991 |has| |#1| (-312)) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1092))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1092))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-813 (-1092)))))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-813 (-1092))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))))) -(-994 UP SAE UPA) +((-3994 |has| |#1| (-314)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-301))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-301)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-322))) (OR (-12 (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-301)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-314)))) (-12 (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-301)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-301)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-815 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-314)))) (-12 (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-314)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))))) +(-996 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-995 UP SAE UPA) +(-997 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-996) +(-998) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-997) +(-999) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-998 S) +(-1000 S) ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-999) +(-1001) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1000 R) +(-1002 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-1001 R) +(-1003 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"))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-330)))) (|HasCategory| (-1002 (-1092)) (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| (-1002 (-1092)) (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-1002 (-1092)) (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-1002 (-1092)) (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| (-1002 (-1092)) (QUOTE (-555 (-475))))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1092)))) (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#1| (QUOTE (-393))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1002 S) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| (-1004 (-1094)) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| (-1004 (-1094)) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-1004 (-1094)) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-1004 (-1094)) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-1004 (-1094)) (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-1004 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1003 S) +(-1005 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1015)))) -(-1004 R S) +((|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-1017)))) +(-1006 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL -((|HasCategory| |#1| (QUOTE (-757)))) -(-1005) +((|HasCategory| |#1| (QUOTE (-759)))) +(-1007) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1006 S) +(-1008 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1003 |#1|) (QUOTE (-1015)))) -(-1007 R S) +((|HasCategory| (-1005 |#1|) (QUOTE (-1017)))) +(-1009 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1008 S) +(-1010 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL -(-1009 S L) +(-1011 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) NIL NIL -(-1010) +(-1012) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1011 S) +(-1013 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 members 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)}}"))) -((-3988 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) -(-1012 A S) +((-3991 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) +(-1014 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1013 S) +(-1015 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-3988 . T)) +((-3991 . T)) NIL -(-1014 S) +(-1016 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1015) +(-1017) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1016 |m| |n|) +(-1018 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1017) +(-1019) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1018 |Str| |Sym| |Int| |Flt| |Expr|) +(-1020 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{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 Flt; Error: if \\spad{s} is not an atom that also belongs to 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 Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to 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 Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL NIL -(-1019 |Str| |Sym| |Int| |Flt| |Expr|) +(-1021 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1020 R E V P TS) +(-1022 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1021 R E V P TS) +(-1023 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1022 R E V P) +(-1024 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 gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(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.}"))) NIL NIL -(-1023) +(-1025) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1024 T$) +(-1026 T$) ((|constructor| (NIL "This domain implements semigroup operations.")) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{semiGroupOperation f} constructs a semigroup operation out of a binary homogeneous mapping known to be associative."))) -(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3059 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3062 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-1025 T$) +(-1027 T$) ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) -(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3059 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3062 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-1026 S) +(-1028 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1027) +(-1029) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1028 |dimtot| |dim1| S) +(-1030 |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 \\spad{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}."))) -((-3992 |has| |#3| (-963)) (-3993 |has| |#3| (-963)) (-3995 |has| |#3| (-6 -3995))) -((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (|%list| (QUOTE 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(-1094)))) (|HasCategory| |#3| (QUOTE (-965)))) (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1017))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#3|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#3|)))) +(-1031 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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL -((|HasCategory| |#1| (QUOTE (-393)))) -(-1030) +((|HasCategory| |#1| (QUOTE (-395)))) +(-1032) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) NIL NIL -(-1031) +(-1033) ((|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 `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1032 R -3095) +(-1034 R -3098) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1033 R) +(-1035 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1034) +(-1036) ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1035) +(-1037) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-3986 . T) (-3990 . T) (-3985 . T) (-3996 . T) (-3997 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3989 . T) (-3993 . T) (-3988 . T) (-3999 . T) (-4000 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1036 S) +(-1038 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}) = \\#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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) NIL NIL -(-1037 S) +(-1039 S) ((|constructor| (NIL "This category describes the class of homogeneous aggregates that support in place mutation that do not change their general shapes.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\spad{f(x)}"))) NIL NIL -(-1038 S |ndim| R |Row| |Col|) +(-1040 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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}'s on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-4000 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) -(-1039 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-314))) (|HasAttribute| |#3| (QUOTE (-4003 "*"))) (|HasCategory| |#3| (QUOTE (-148)))) +(-1041 |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}'s on the diagonal and zeroes elsewhere."))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1040 R |Row| |Col| M) +(-1042 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) NIL NIL -(-1041 R |VarSet|) +(-1043 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."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-393))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-330)))) (|HasCategory| |#2| (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-486)))) (|HasCategory| |#2| (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-330))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-486))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-555 (-475))))) (|HasCategory| |#1| (QUOTE (-582 (-486)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#1| (QUOTE (-393))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1042 |Coef| |Var| SMP) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| |#2| (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-1044 |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 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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#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}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1043 R E V P) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-314)))) +(-1045 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}"))) NIL NIL -(-1044 UP -3095) +(-1046 UP -3098) ((|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 -(-1045 R) +(-1047 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) NIL NIL -(-1046 R) +(-1048 R) ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1047 R) +(-1049 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1048 S A) +(-1050 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) NIL -((|HasCategory| |#1| (QUOTE (-758)))) -(-1049 R) +((|HasCategory| |#1| (QUOTE (-760)))) +(-1051 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL NIL -(-1050 R) +(-1052 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1051) +(-1053) ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) NIL NIL -(-1052) +(-1054) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) NIL NIL -(-1053) +(-1055) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) NIL NIL -(-1054) +(-1056) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1055) +(-1057) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1056 V C) +(-1058 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1057 V C) +(-1059 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,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in 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},{}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 ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}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 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."))) NIL -((-12 (|HasCategory| (-1056 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1056) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1015)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1015))) (OR (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-1015)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-554 (-774)))) (|HasCategory| (-1056 |#1| |#2|) (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1037) (|%list| (QUOTE -1056) (|devaluate| |#1|) (|devaluate| |#2|))))) -(-1058 |ndim| R) +((-12 (|HasCategory| (-1058 |#1| |#2|) (|%list| (QUOTE -262) (|%list| (QUOTE -1058) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1058 |#1| |#2|) (QUOTE (-1017)))) (|HasCategory| (-1058 |#1| |#2|) (QUOTE (-1017))) (OR (|HasCategory| (-1058 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1058 |#1| |#2|) (QUOTE (-1017)))) (|HasCategory| (-1058 |#1| |#2|) (QUOTE (-556 (-776)))) (|HasCategory| (-1058 |#1| |#2|) (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|%list| (QUOTE -1058) (|devaluate| |#1|) (|devaluate| |#2|))))) +(-1060 |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}."))) -((-3995 . T) (-3987 |has| |#2| (-6 (-4000 "*"))) (-3992 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-811 (-1092)))) (|HasCategory| |#2| (QUOTE (-813 (-1092)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-4000 #1="*"))) (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-811 (-1092)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-4000 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-811 (-1092))))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1059 S) +((-3998 . T) (-3990 |has| |#2| (-6 (-4003 "*"))) (-3995 . T) (-3996 . T)) +((|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-191))) (|HasAttribute| |#2| (QUOTE (-4003 #1="*"))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-314))) (OR (|HasAttribute| |#2| (QUOTE (-4003 #1#))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-813 (-1094))))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-148)))) +(-1061 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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1060) +(-1062) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1061 R E V P TS) +(-1063 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'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{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1062 R E V P) +(-1064 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(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(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(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(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},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) NIL -((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-475)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-1015))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) -(-1063) +((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) +(-1065) ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) NIL NIL -(-1064 S) +(-1066 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}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-1065 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1067 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}.")) (|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.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1066 S) +(-1068 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}.")) (|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.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1067 |Key| |Ent| |dent|) +(-1069 |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."))) NIL -((-12 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-475)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#2|)))) -(-1068) +((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) +(-1070) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1069) +(-1071) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1070 |Coef|) +(-1072 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1071 S) +(-1073 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) -(-1072 S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) +(-1074 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL NIL -(-1073 A B) +(-1075 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-1074 A B C) +(-1076 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) NIL NIL -(-1075) +(-1077) ((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) NIL -((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-758)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015))))) (|HasCategory| (-117) (QUOTE (-554 (-774)))) (|HasCategory| (-117) (QUOTE (-555 (-475)))) (OR (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015)))) (|HasCategory| (-117) (QUOTE (-758))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1015))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| $ (QUOTE (-1037 (-117)))) (-12 (|HasCategory| $ (QUOTE (-1037 (-117)))) (|HasCategory| (-117) (QUOTE (-758))))) -(-1076 |Entry|) +((OR (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-760)))) (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-1017))))) (|HasCategory| (-117) (QUOTE (-556 (-776)))) (|HasCategory| (-117) (QUOTE (-557 (-477)))) (OR (|HasCategory| (-117) (QUOTE (-760))) (|HasCategory| (-117) (QUOTE (-1017)))) (|HasCategory| (-117) (QUOTE (-760))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-760))) (|HasCategory| (-117) (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1017))) (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-1017)))) (-12 (|HasCategory| $ (QUOTE (-320 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-320 (-117)))) (|HasCategory| $ (QUOTE (-1039 (-117)))) (-12 (|HasCategory| $ (QUOTE (-1039 (-117)))) (|HasCategory| (-117) (QUOTE (-760))))) +(-1078 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) NIL -((-12 (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1075))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-555 (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-1075) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-1015))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1075))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3864 (-1075)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1075))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) -(-1077 A) +((-12 (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-1017)))) (OR (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-1017)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-1077) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) +(-1079 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 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 b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL -((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-486)))))) -(-1078 |Coef|) +((|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) +(-1080 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1079 |Coef|) +(-1081 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1080 R UP) +(-1082 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) NIL -((|HasCategory| |#1| (QUOTE (-258)))) -(-1081 |n| R) +((|HasCategory| |#1| (QUOTE (-260)))) +(-1083 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL -(-1086 R) +(-1088 R) ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) NIL NIL -(-1087 R) +(-1089 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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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| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1089 E OV R P) +(-1091 E OV R P) ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) NIL NIL -(-1090 |Coef| |var| |cen|) +(-1092 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-486)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486)))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-29 (-486)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -585) (QUOTE (-1092))) (|devaluate| |#1|))))))) -(-1091 |Coef| |var| |cen|) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|)))) (|HasCategory| (-352 (-488)) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) +(-1093 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-497))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|)))) (|HasCategory| (-696) (QUOTE (-1027))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-29 (-486)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -585) (QUOTE (-1092))) (|devaluate| |#1|))))))) -(-1092) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-698)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-698)) (|devaluate| |#1|)))) (|HasCategory| (-698) (QUOTE (-1029))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-698))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-698))))) (|HasCategory| |#1| (QUOTE (-314))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) +(-1094) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL -(-1093 R) +(-1095 R) ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) NIL NIL -(-1094 R) +(-1096 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-6 -3996)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-497))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#1| (QUOTE (-952 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-952 (-486)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-393))) (-12 (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| (-886) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3996))) -(-1095) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| (-888) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3999))) +(-1097) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL -(-1096) +(-1098) ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) NIL NIL -(-1097) +(-1099) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1098 N) +(-1100 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1099 N) +(-1101 N) ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) NIL NIL -(-1100) +(-1102) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1101 R) +(-1103 R) ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-1102) +(-1104) ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL -(-1103 S) +(-1105 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1104 |Key| |Entry|) +(-1106 |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}"))) NIL -((-12 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-475)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#2|)))) -(-1105 S) +((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) +(-1107 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1106 S) +(-1108 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL NIL -(-1107 R) +(-1109 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1108 S |Key| |Entry|) +(-1110 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}."))) NIL NIL -(-1109 |Key| |Entry|) +(-1111 |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}."))) NIL NIL -(-1110 |Key| |Entry|) +(-1112 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1111) +(-1113) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1112 S) +(-1114 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1113) +(-1115) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1114 R) +(-1116 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1115) +(-1117) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1116 S) +(-1118 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1117) +(-1119) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1118 S) +(-1120 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}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|)))) -(-1119 S) +((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) +(-1121 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1120) +(-1122) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1121 R -3095) +(-1123 R -3098) ((|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 -(-1122 R |Row| |Col| M) +(-1124 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1123 R -3095) +(-1125 R -3098) ((|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 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 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 -555) (|%list| (QUOTE -802) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -798) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -555) (|%list| (QUOTE -802) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -798) (|devaluate| |#1|))))) -(-1124 |Coef|) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -557) (|%list| (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -800) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -557) (|%list| (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -800) (|devaluate| |#1|))))) +(-1126 |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}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1125 S R E V P) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-314)))) +(-1127 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}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|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(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{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(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{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}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{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}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{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}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{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}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{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL -((|HasCategory| |#4| (QUOTE (-320)))) -(-1126 R E V P) +((|HasCategory| |#4| (QUOTE (-322)))) +(-1128 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} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}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|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(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{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(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{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(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{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},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}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{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{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},{}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{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},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}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{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}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{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL NIL -(-1127 |Curve|) +(-1129 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1128) +(-1130) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1129 S) +(-1131 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter'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 (-1015))) (|HasCategory| |#1| (QUOTE (-554 (-774))))) -(-1130 -3095) +((|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-556 (-776))))) +(-1132 -3098) ((|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 -(-1131) +(-1133) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1132) +(-1134) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1133 S) +(-1135 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) NIL -((|HasCategory| |#1| (QUOTE (-758)))) -(-1134) +((|HasCategory| |#1| (QUOTE (-760)))) +(-1136) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1135 S) +(-1137 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) NIL NIL -(-1136) +(-1138) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1137) +(-1139) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1138) +(-1140) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1139) +(-1141) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1140) +(-1142) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1141 |Coef| |var| |cen|) +(-1143 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) 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"\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1143 |Coef|) +(-1145 |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}.") 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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. 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(|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) NIL -((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1015)))) -(-1149 R S) +((|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-1017)))) +(-1151 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") 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T)) -((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-497)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-330)))) (|HasCategory| (-996) (QUOTE (-798 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-486)))) (|HasCategory| (-996) (QUOTE (-798 (-486))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-330))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-486))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-486)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-475)))) (|HasCategory| (-996) (QUOTE (-555 (-475))))) (|HasCategory| |#2| (QUOTE (-582 (-486)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-486)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486)))))) (|HasCategory| |#2| (QUOTE (-952 (-350 (-486))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-813 (-1092)))) (|HasCategory| |#2| (QUOTE (-811 (-1092)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-393))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-1151 |x| R |y| S) +(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3997 |has| |#2| (-314)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-998) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-998) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-998) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-191))) (|HasCategory| |#2| (QUOTE (-192))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-1153 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1152 R Q UP) +(-1154 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1153 R UP) +(-1155 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1154 R UP) +(-1156 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1155 R U) +(-1157 R U) ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) NIL NIL -(-1156 S R) +(-1158 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-393))) (|HasCategory| |#2| (QUOTE (-497))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1068)))) -(-1157 R) +((|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1070)))) +(-1159 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 gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant 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|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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'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}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3994 |has| |#1| (-312)) (-3996 |has| |#1| (-6 -3996)) (-3993 . T) (-3992 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3997 |has| |#1| (-314)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) NIL -(-1158 R PR S PS) +(-1160 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1159 S |Coef| |Expon|) +(-1161 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{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (QUOTE (-811 (-1092)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1027))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#2|) (QUOTE (-1092)))))) -(-1160 |Coef| |Expon|) +((|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1029))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#2|) (QUOTE (-1094)))))) +(-1162 |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{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1161 RC P) +(-1163 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1162 |Coef| |var| |cen|) +(-1164 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-486)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486)))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-29 (-486)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -585) (QUOTE (-1092))) (|devaluate| |#1|))))))) -(-1163 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|)))) (|HasCategory| (-352 (-488)) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) +(-1165 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1164 |Coef|) +(-1166 |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."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1165 S |Coef| ULS) +(-1167 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1166 |Coef| ULS) +(-1168 |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)}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1167 |Coef| ULS) +(-1169 |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)}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3996 |has| |#1| (-312)) (-3990 |has| |#1| (-312)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-486)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-497)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486)))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-486)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-29 (-486)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -585) (QUOTE (-1092))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-486)))))) -(-1168 R FE |var| |cen|) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|)))) (|HasCategory| (-352 (-488)) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) +(-1170 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))}."))) -(((-4000 "*") |has| (-1162 |#2| |#3| |#4|) (-146)) (-3991 |has| (-1162 |#2| |#3| |#4|) (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-486))))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-486))))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-952 (-350 (-486)))))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-952 (-350 (-486))))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-952 (-486)))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-393))) (|HasCategory| (-1162 |#2| |#3| |#4|) (QUOTE (-497)))) -(-1169 A S) +(((-4003 "*") |has| (-1164 |#2| |#3| |#4|) (-148)) (-3994 |has| (-1164 |#2| |#3| |#4|) (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-38 (-352 (-488))))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-148))) (OR (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-38 (-352 (-488))))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-954 (-352 (-488)))))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-954 (-488)))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-314))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-395))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-499)))) +(-1171 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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -1037) (|devaluate| |#2|)))) -(-1170 S) +((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|)))) +(-1172 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1171 |Coef| |var| |cen|) +(-1173 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-497))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1092)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|)))) (|HasCategory| (-696) (QUOTE (-1027))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#1| (QUOTE (-29 (-486)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-486))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -585) (QUOTE (-1092))) (|devaluate| |#1|))))))) -(-1172 |Coef1| |Coef2| UTS1 UTS2) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-698)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-698)) (|devaluate| |#1|)))) (|HasCategory| (-698) (QUOTE (-1029))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-698))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-698))))) (|HasCategory| |#1| (QUOTE (-314))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) +(-1174 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1173 S |Coef|) +(-1175 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| (QUOTE (-29 (-486)))) (|HasCategory| |#2| (QUOTE (-873))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasSignature| |#2| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -585) (QUOTE (-1092))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1092))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-486))))) (|HasCategory| |#2| (QUOTE (-312)))) -(-1174 |Coef|) +((|HasCategory| |#2| (QUOTE (-29 (-488)))) (|HasCategory| |#2| (QUOTE (-875))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasSignature| |#2| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1094))))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314)))) +(-1176 |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."))) -(((-4000 "*") |has| |#1| (-146)) (-3991 |has| |#1| (-497)) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1175 |Coef| UTS) +(-1177 |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 -(-1176 -3095 UP L UTS) +(-1178 -3098 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 (-497)))) -(-1177) +((|HasCategory| |#1| (QUOTE (-499)))) +(-1179) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1178 |sym|) +(-1180 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1179 S R) +(-1181 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-917))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1180 R) +((|HasCategory| |#2| (QUOTE (-919))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-667))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1182 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})*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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL NIL -(-1181 R) +(-1183 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) NIL -((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-475)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-486) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-1015))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| $ (|%list| (QUOTE -1037) (|devaluate| |#1|))))) -(-1182 A B) +((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#1| (QUOTE (-965))) (-12 (|HasCategory| |#1| (QUOTE (-919))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) +(-1184 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1183) +(-1185) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1184) +(-1186) ((|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's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1185) +(-1187) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1186) +(-1188) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1187) +(-1189) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1188 A S) +(-1190 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1189 S) +(-1191 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}."))) -((-3993 . T) (-3992 . T)) +((-3996 . T) (-3995 . T)) NIL -(-1190 R) +(-1192 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]*v + A[2]\\spad{*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 -(-1191 K R UP -3095) +(-1193 K R UP -3098) ((|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 -(-1192) +(-1194) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1193) +(-1195) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1194 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1196 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: 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)"))) -((-3993 |has| |#1| (-146)) (-3992 |has| |#1| (-146)) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1195 R E V P) +((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314)))) +(-1197 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}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{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{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) NIL -((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-475)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-497))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-1015))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) -(-1196 R) +((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) +(-1198 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.fr)"))) -((-3992 . T) (-3993 . T) (-3995 . T)) +((-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1197 |vl| R) +(-1199 |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."))) -((-3995 . T) (-3991 |has| |#2| (-6 -3991)) (-3993 . T) (-3992 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3991))) -(-1198 R |VarSet| XPOLY) +((-3998 . T) (-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T)) +((|HasCategory| |#2| (QUOTE (-148))) (|HasAttribute| |#2| (QUOTE -3994))) +(-1200 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.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 -(-1199 S -3095) +(-1201 S -3098) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL -((|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) -(-1200 -3095) +((|HasCategory| |#2| (QUOTE (-322))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) +(-1202 -3098) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-3990 . T) (-3996 . T) (-3991 . T) ((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL -(-1201 |vl| R) +(-1203 |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|sh| (($ $ (|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-3991 |has| |#2| (-6 -3991)) (-3993 . T) (-3992 . T) (-3995 . T)) +((-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) NIL -(-1202 |VarSet| R) +(-1204 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}."))) -((-3991 |has| |#2| (-6 -3991)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-656 (-350 (-486))))) (|HasAttribute| |#2| (QUOTE -3991))) -(-1203 R) +((-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-658 (-352 (-488))))) (|HasAttribute| |#2| (QUOTE -3994))) +(-1205 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."))) -((-3991 |has| |#1| (-6 -3991)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3991))) -(-1204 |vl| R) +((-3994 |has| |#1| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasAttribute| |#1| (QUOTE -3994))) +(-1206 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-3991 |has| |#2| (-6 -3991)) (-3993 . T) (-3992 . T) (-3995 . T)) +((-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) NIL -(-1205 R E) +(-1207 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|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}."))) -((-3995 . T) (-3996 |has| |#1| (-6 -3996)) (-3991 |has| |#1| (-6 -3991)) (-3993 . T) (-3992 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasAttribute| |#1| (QUOTE -3996)) (|HasAttribute| |#1| (QUOTE -3991))) -(-1206 |VarSet| R) +((-3998 . T) (-3999 |has| |#1| (-6 -3999)) (-3994 |has| |#1| (-6 -3994)) (-3996 . T) (-3995 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3998)) (|HasAttribute| |#1| (QUOTE -3999)) (|HasAttribute| |#1| (QUOTE -3994))) +(-1208 |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."))) -((-3991 |has| |#2| (-6 -3991)) (-3993 . T) (-3992 . T) (-3995 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3991))) -(-1207) +((-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) +((|HasCategory| |#2| (QUOTE (-148))) (|HasAttribute| |#2| (QUOTE -3994))) +(-1209) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL NIL -(-1208 A) +(-1210 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1209 R |ls| |ls2|) +(-1211 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1210 R) +(-1212 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1211 |p|) +(-1213 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4000 "*") . T) (-3992 . T) (-3993 . T) (-3995 . T)) +(((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) NIL NIL NIL @@ -4792,4 +4800,4 @@ NIL NIL NIL NIL -((-3 NIL 1965537 1965542 1965547 1965552) (-2 NIL 1965517 1965522 1965527 1965532) (-1 NIL 1965497 1965502 1965507 1965512) (0 NIL 1965477 1965482 1965487 1965492) (-1211 "ZMOD.spad" 1965286 1965299 1965415 1965472) (-1210 "ZLINDEP.spad" 1964384 1964395 1965276 1965281) (-1209 "ZDSOLVE.spad" 1954345 1954367 1964374 1964379) (-1208 "YSTREAM.spad" 1953840 1953851 1954335 1954340) (-1207 "YDIAGRAM.spad" 1953474 1953483 1953830 1953835) (-1206 "XRPOLY.spad" 1952694 1952714 1953330 1953399) (-1205 "XPR.spad" 1950622 1950635 1952412 1952511) (-1204 "XPOLYC.spad" 1949941 1949957 1950548 1950617) (-1203 "XPOLY.spad" 1949496 1949507 1949797 1949866) (-1202 "XPBWPOLY.spad" 1947967 1947987 1949302 1949371) (-1201 "XFALG.spad" 1945148 1945164 1947893 1947962) (-1200 "XF.spad" 1943611 1943626 1945050 1945143) (-1199 "XF.spad" 1942054 1942071 1943495 1943500) (-1198 "XEXPPKG.spad" 1941313 1941339 1942044 1942049) (-1197 "XDPOLY.spad" 1940927 1940943 1941169 1941238) (-1196 "XALG.spad" 1940595 1940606 1940883 1940922) (-1195 "WUTSET.spad" 1936459 1936476 1940090 1940095) (-1194 "WP.spad" 1935666 1935710 1936317 1936384) (-1193 "WHILEAST.spad" 1935464 1935473 1935656 1935661) (-1192 "WHEREAST.spad" 1935135 1935144 1935454 1935459) (-1191 "WFFINTBS.spad" 1932798 1932820 1935125 1935130) (-1190 "WEIER.spad" 1931020 1931031 1932788 1932793) (-1189 "VSPACE.spad" 1930693 1930704 1930988 1931015) (-1188 "VSPACE.spad" 1930386 1930399 1930683 1930688) (-1187 "VOID.spad" 1930063 1930072 1930376 1930381) (-1186 "VIEWDEF.spad" 1925264 1925273 1930053 1930058) (-1185 "VIEW3D.spad" 1909225 1909234 1925254 1925259) (-1184 "VIEW2D.spad" 1897124 1897133 1909215 1909220) (-1183 "VIEW.spad" 1894844 1894853 1897114 1897119) (-1182 "VECTOR2.spad" 1893483 1893496 1894834 1894839) (-1181 "VECTOR.spad" 1891899 1891910 1892150 1892155) (-1180 "VECTCAT.spad" 1889833 1889844 1891889 1891894) (-1179 "VECTCAT.spad" 1887554 1887567 1889612 1889617) (-1178 "VARIABLE.spad" 1887334 1887349 1887544 1887549) (-1177 "UTYPE.spad" 1886978 1886987 1887324 1887329) (-1176 "UTSODETL.spad" 1886273 1886297 1886934 1886939) (-1175 "UTSODE.spad" 1884489 1884509 1886263 1886268) (-1174 "UTSCAT.spad" 1881968 1881984 1884387 1884484) (-1173 "UTSCAT.spad" 1879115 1879133 1881536 1881541) (-1172 "UTS2.spad" 1878710 1878745 1879105 1879110) (-1171 "UTS.spad" 1873722 1873750 1877242 1877339) (-1170 "URAGG.spad" 1868443 1868454 1873712 1873717) (-1169 "URAGG.spad" 1863100 1863113 1868371 1868376) (-1168 "UPXSSING.spad" 1860868 1860894 1862304 1862437) (-1167 "UPXSCONS.spad" 1858686 1858706 1859059 1859208) (-1166 "UPXSCCA.spad" 1857257 1857277 1858532 1858681) (-1165 "UPXSCCA.spad" 1855970 1855992 1857247 1857252) (-1164 "UPXSCAT.spad" 1854559 1854575 1855816 1855965) (-1163 "UPXS2.spad" 1854102 1854155 1854549 1854554) (-1162 "UPXS.spad" 1851457 1851485 1852293 1852442) (-1161 "UPSQFREE.spad" 1849872 1849886 1851447 1851452) (-1160 "UPSCAT.spad" 1847667 1847691 1849770 1849867) (-1159 "UPSCAT.spad" 1845163 1845189 1847268 1847273) (-1158 "UPOLYC2.spad" 1844634 1844653 1845153 1845158) (-1157 "UPOLYC.spad" 1839714 1839725 1844476 1844629) (-1156 "UPOLYC.spad" 1834712 1834725 1839476 1839481) (-1155 "UPMP.spad" 1833644 1833657 1834702 1834707) (-1154 "UPDIVP.spad" 1833209 1833223 1833634 1833639) (-1153 "UPDECOMP.spad" 1831470 1831484 1833199 1833204) (-1152 "UPCDEN.spad" 1830687 1830703 1831460 1831465) (-1151 "UP2.spad" 1830051 1830072 1830677 1830682) (-1150 "UP.spad" 1827521 1827536 1827908 1828061) (-1149 "UNISEG2.spad" 1827018 1827031 1827477 1827482) (-1148 "UNISEG.spad" 1826371 1826382 1826937 1826942) (-1147 "UNIFACT.spad" 1825474 1825486 1826361 1826366) (-1146 "ULSCONS.spad" 1819320 1819340 1819690 1819839) (-1145 "ULSCCAT.spad" 1817057 1817077 1819166 1819315) (-1144 "ULSCCAT.spad" 1814902 1814924 1817013 1817018) (-1143 "ULSCAT.spad" 1813142 1813158 1814748 1814897) (-1142 "ULS2.spad" 1812656 1812709 1813132 1813137) (-1141 "ULS.spad" 1804689 1804717 1805634 1806057) (-1140 "UINT8.spad" 1804566 1804575 1804679 1804684) (-1139 "UINT64.spad" 1804442 1804451 1804556 1804561) (-1138 "UINT32.spad" 1804318 1804327 1804432 1804437) (-1137 "UINT16.spad" 1804194 1804203 1804308 1804313) (-1136 "UFD.spad" 1803259 1803268 1804120 1804189) (-1135 "UFD.spad" 1802386 1802397 1803249 1803254) (-1134 "UDVO.spad" 1801267 1801276 1802376 1802381) (-1133 "UDPO.spad" 1798848 1798859 1801223 1801228) (-1132 "TYPEAST.spad" 1798767 1798776 1798838 1798843) (-1131 "TYPE.spad" 1798699 1798708 1798757 1798762) (-1130 "TWOFACT.spad" 1797351 1797366 1798689 1798694) (-1129 "TUPLE.spad" 1796858 1796869 1797263 1797268) (-1128 "TUBETOOL.spad" 1793725 1793734 1796848 1796853) (-1127 "TUBE.spad" 1792372 1792389 1793715 1793720) (-1126 "TSETCAT.spad" 1780465 1780482 1792362 1792367) (-1125 "TSETCAT.spad" 1768522 1768541 1780421 1780426) (-1124 "TS.spad" 1767150 1767166 1768116 1768213) (-1123 "TRMANIP.spad" 1761514 1761531 1766838 1766843) (-1122 "TRIMAT.spad" 1760477 1760502 1761504 1761509) (-1121 "TRIGMNIP.spad" 1759004 1759021 1760467 1760472) (-1120 "TRIGCAT.spad" 1758516 1758525 1758994 1758999) (-1119 "TRIGCAT.spad" 1758026 1758037 1758506 1758511) (-1118 "TREE.spad" 1756627 1756638 1757659 1757664) (-1117 "TRANFUN.spad" 1756466 1756475 1756617 1756622) (-1116 "TRANFUN.spad" 1756303 1756314 1756456 1756461) (-1115 "TOPSP.spad" 1755977 1755986 1756293 1756298) (-1114 "TOOLSIGN.spad" 1755640 1755651 1755967 1755972) (-1113 "TEXTFILE.spad" 1754201 1754210 1755630 1755635) (-1112 "TEX1.spad" 1753757 1753768 1754191 1754196) (-1111 "TEX.spad" 1750951 1750960 1753747 1753752) (-1110 "TBCMPPK.spad" 1749052 1749075 1750941 1750946) (-1109 "TBAGG.spad" 1748317 1748340 1749042 1749047) (-1108 "TBAGG.spad" 1747580 1747605 1748307 1748312) (-1107 "TANEXP.spad" 1746988 1746999 1747570 1747575) (-1106 "TALGOP.spad" 1746712 1746723 1746978 1746983) (-1105 "TABLEAU.spad" 1746193 1746204 1746702 1746707) (-1104 "TABLE.spad" 1743903 1743926 1744173 1744178) (-1103 "TABLBUMP.spad" 1740682 1740693 1743893 1743898) (-1102 "SYSTEM.spad" 1739910 1739919 1740672 1740677) (-1101 "SYSSOLP.spad" 1737393 1737404 1739900 1739905) (-1100 "SYSPTR.spad" 1737292 1737301 1737383 1737388) (-1099 "SYSNNI.spad" 1736515 1736526 1737282 1737287) (-1098 "SYSINT.spad" 1735919 1735930 1736505 1736510) (-1097 "SYNTAX.spad" 1732253 1732262 1735909 1735914) (-1096 "SYMTAB.spad" 1730321 1730330 1732243 1732248) (-1095 "SYMS.spad" 1726350 1726359 1730311 1730316) (-1094 "SYMPOLY.spad" 1725483 1725494 1725565 1725692) (-1093 "SYMFUNC.spad" 1724984 1724995 1725473 1725478) (-1092 "SYMBOL.spad" 1722479 1722488 1724974 1724979) (-1091 "SUTS.spad" 1719592 1719620 1721011 1721108) (-1090 "SUPXS.spad" 1716934 1716962 1717783 1717932) (-1089 "SUPFRACF.spad" 1716039 1716057 1716924 1716929) (-1088 "SUP2.spad" 1715431 1715444 1716029 1716034) (-1087 "SUP.spad" 1712515 1712526 1713288 1713441) (-1086 "SUMRF.spad" 1711489 1711500 1712505 1712510) (-1085 "SUMFS.spad" 1711118 1711135 1711479 1711484) (-1084 "SULS.spad" 1703138 1703166 1704096 1704519) (-1083 "syntax.spad" 1702907 1702916 1703128 1703133) (-1082 "SUCH.spad" 1702597 1702612 1702897 1702902) (-1081 "SUBSPACE.spad" 1694728 1694743 1702587 1702592) (-1080 "SUBRESP.spad" 1693898 1693912 1694684 1694689) (-1079 "STTFNC.spad" 1690366 1690382 1693888 1693893) (-1078 "STTF.spad" 1686465 1686481 1690356 1690361) (-1077 "STTAYLOR.spad" 1679142 1679153 1686372 1686377) (-1076 "STRTBL.spad" 1677015 1677032 1677164 1677169) (-1075 "STRING.spad" 1675656 1675665 1676041 1676046) (-1074 "STREAM3.spad" 1675229 1675244 1675646 1675651) (-1073 "STREAM2.spad" 1674357 1674370 1675219 1675224) (-1072 "STREAM1.spad" 1674063 1674074 1674347 1674352) (-1071 "STREAM.spad" 1671023 1671034 1673514 1673519) (-1070 "STINPROD.spad" 1669959 1669975 1671013 1671018) (-1069 "STEPAST.spad" 1669193 1669202 1669949 1669954) (-1068 "STEP.spad" 1668510 1668519 1669183 1669188) (-1067 "STBL.spad" 1666323 1666351 1666490 1666495) (-1066 "STAGG.spad" 1665022 1665033 1666313 1666318) (-1065 "STAGG.spad" 1663719 1663732 1665012 1665017) (-1064 "STACK.spad" 1663163 1663174 1663413 1663418) (-1063 "SRING.spad" 1662923 1662932 1663153 1663158) (-1062 "SREGSET.spad" 1660516 1660533 1662418 1662423) (-1061 "SRDCMPK.spad" 1659093 1659113 1660506 1660511) (-1060 "SRAGG.spad" 1654298 1654307 1659083 1659088) (-1059 "SRAGG.spad" 1649501 1649512 1654288 1654293) (-1058 "SQMATRIX.spad" 1647190 1647208 1648106 1648181) (-1057 "SPLTREE.spad" 1641850 1641863 1646646 1646651) (-1056 "SPLNODE.spad" 1638470 1638483 1641840 1641845) (-1055 "SPFCAT.spad" 1637279 1637288 1638460 1638465) (-1054 "SPECOUT.spad" 1635831 1635840 1637269 1637274) (-1053 "SPADXPT.spad" 1627922 1627931 1635821 1635826) (-1052 "spad-parser.spad" 1627387 1627396 1627912 1627917) (-1051 "SPADAST.spad" 1627088 1627097 1627377 1627382) (-1050 "SPACEC.spad" 1611303 1611314 1627078 1627083) (-1049 "SPACE3.spad" 1611079 1611090 1611293 1611298) (-1048 "SORTPAK.spad" 1610628 1610641 1611035 1611040) (-1047 "SOLVETRA.spad" 1608391 1608402 1610618 1610623) (-1046 "SOLVESER.spad" 1606847 1606858 1608381 1608386) (-1045 "SOLVERAD.spad" 1602873 1602884 1606837 1606842) (-1044 "SOLVEFOR.spad" 1601335 1601353 1602863 1602868) (-1043 "SNTSCAT.spad" 1600957 1600974 1601325 1601330) (-1042 "SMTS.spad" 1599274 1599300 1600551 1600648) (-1041 "SMP.spad" 1597082 1597102 1597472 1597599) (-1040 "SMITH.spad" 1595927 1595952 1597072 1597077) (-1039 "SMATCAT.spad" 1594057 1594087 1595883 1595922) (-1038 "SMATCAT.spad" 1592107 1592139 1593935 1593940) (-1037 "aggcat.spad" 1591793 1591804 1592097 1592102) (-1036 "SKAGG.spad" 1590784 1590795 1591783 1591788) (-1035 "SINT.spad" 1590083 1590092 1590650 1590779) (-1034 "SIMPAN.spad" 1589811 1589820 1590073 1590078) (-1033 "SIGNRF.spad" 1588936 1588947 1589801 1589806) (-1032 "SIGNEF.spad" 1588222 1588239 1588926 1588931) (-1031 "syntax.spad" 1587639 1587648 1588212 1588217) (-1030 "SIG.spad" 1587001 1587010 1587629 1587634) (-1029 "SHP.spad" 1584945 1584960 1586957 1586962) (-1028 "SHDP.spad" 1574288 1574315 1574805 1574890) (-1027 "SGROUP.spad" 1573896 1573905 1574278 1574283) (-1026 "SGROUP.spad" 1573502 1573513 1573886 1573891) (-1025 "catdef.spad" 1573212 1573224 1573323 1573497) (-1024 "catdef.spad" 1572768 1572780 1573033 1573207) (-1023 "SGCF.spad" 1565907 1565916 1572758 1572763) (-1022 "SFRTCAT.spad" 1564875 1564892 1565897 1565902) (-1021 "SFRGCD.spad" 1563938 1563958 1564865 1564870) (-1020 "SFQCMPK.spad" 1558751 1558771 1563928 1563933) (-1019 "SEXOF.spad" 1558594 1558634 1558741 1558746) (-1018 "SEXCAT.spad" 1556422 1556462 1558584 1558589) (-1017 "SEX.spad" 1556314 1556323 1556412 1556417) (-1016 "SETMN.spad" 1554774 1554791 1556304 1556309) (-1015 "SETCAT.spad" 1554259 1554268 1554764 1554769) (-1014 "SETCAT.spad" 1553742 1553753 1554249 1554254) (-1013 "SETAGG.spad" 1550291 1550302 1553722 1553737) (-1012 "SETAGG.spad" 1546848 1546861 1550281 1550286) (-1011 "SET.spad" 1545018 1545029 1546117 1546132) (-1010 "syntax.spad" 1544721 1544730 1545008 1545013) (-1009 "SEGXCAT.spad" 1543877 1543890 1544711 1544716) (-1008 "SEGCAT.spad" 1542802 1542813 1543867 1543872) (-1007 "SEGBIND2.spad" 1542500 1542513 1542792 1542797) (-1006 "SEGBIND.spad" 1542258 1542269 1542447 1542452) (-1005 "SEGAST.spad" 1541988 1541997 1542248 1542253) (-1004 "SEG2.spad" 1541423 1541436 1541944 1541949) (-1003 "SEG.spad" 1541236 1541247 1541342 1541347) (-1002 "SDVAR.spad" 1540512 1540523 1541226 1541231) (-1001 "SDPOL.spad" 1538204 1538215 1538495 1538622) (-1000 "SCPKG.spad" 1536293 1536304 1538194 1538199) (-999 "SCOPE.spad" 1535471 1535479 1536283 1536288) (-998 "SCACHE.spad" 1534168 1534178 1535461 1535466) (-997 "SASTCAT.spad" 1534078 1534086 1534158 1534163) (-996 "SAOS.spad" 1533951 1533959 1534068 1534073) (-995 "SAERFFC.spad" 1533665 1533684 1533941 1533946) (-994 "SAEFACT.spad" 1533367 1533386 1533655 1533660) (-993 "SAE.spad" 1531018 1531033 1531628 1531763) (-992 "RURPK.spad" 1528678 1528693 1531008 1531013) (-991 "RULESET.spad" 1528132 1528155 1528668 1528673) (-990 "RULECOLD.spad" 1527985 1527997 1528122 1528127) (-989 "RULE.spad" 1526234 1526257 1527975 1527980) (-988 "RTVALUE.spad" 1525970 1525978 1526224 1526229) (-987 "syntax.spad" 1525688 1525696 1525960 1525965) (-986 "RSETGCD.spad" 1522131 1522150 1525678 1525683) (-985 "RSETCAT.spad" 1512122 1512138 1522121 1522126) (-984 "RSETCAT.spad" 1502111 1502129 1512112 1512117) (-983 "RSDCMPK.spad" 1500612 1500631 1502101 1502106) (-982 "RRCC.spad" 1498997 1499026 1500602 1500607) (-981 "RRCC.spad" 1497380 1497411 1498987 1498992) (-980 "RPTAST.spad" 1497083 1497091 1497370 1497375) (-979 "RPOLCAT.spad" 1476588 1476602 1496951 1497078) (-978 "RPOLCAT.spad" 1455886 1455902 1476251 1476256) (-977 "ROMAN.spad" 1455215 1455223 1455752 1455881) (-976 "ROIRC.spad" 1454296 1454327 1455205 1455210) (-975 "RNS.spad" 1453273 1453281 1454198 1454291) (-974 "RNS.spad" 1452336 1452346 1453263 1453268) (-973 "RNGBIND.spad" 1451497 1451510 1452291 1452296) (-972 "RNG.spad" 1451106 1451114 1451487 1451492) (-971 "RNG.spad" 1450713 1450723 1451096 1451101) (-970 "RMODULE.spad" 1450495 1450505 1450703 1450708) (-969 "RMCAT2.spad" 1449916 1449972 1450485 1450490) (-968 "RMATRIX.spad" 1448738 1448756 1449080 1449107) (-967 "RMATCAT.spad" 1444520 1444550 1448706 1448733) (-966 "RMATCAT.spad" 1440180 1440212 1444368 1444373) (-965 "RLINSET.spad" 1439885 1439895 1440170 1440175) (-964 "RINTERP.spad" 1439774 1439793 1439875 1439880) (-963 "RING.spad" 1439245 1439253 1439754 1439769) (-962 "RING.spad" 1438724 1438734 1439235 1439240) (-961 "RIDIST.spad" 1438117 1438125 1438714 1438719) (-960 "RGCHAIN.spad" 1436384 1436399 1437277 1437282) (-959 "RGBCSPC.spad" 1436174 1436185 1436374 1436379) (-958 "RGBCMDL.spad" 1435737 1435748 1436164 1436169) (-957 "RFFACTOR.spad" 1435200 1435210 1435727 1435732) (-956 "RFFACT.spad" 1434936 1434947 1435190 1435195) (-955 "RFDIST.spad" 1433933 1433941 1434926 1434931) (-954 "RF.spad" 1431608 1431618 1433923 1433928) (-953 "RETSOL.spad" 1431028 1431040 1431598 1431603) (-952 "RETRACT.spad" 1430457 1430467 1431018 1431023) (-951 "RETRACT.spad" 1429884 1429896 1430447 1430452) (-950 "RETAST.spad" 1429697 1429705 1429874 1429879) (-949 "RESRING.spad" 1429045 1429091 1429635 1429692) (-948 "RESLATC.spad" 1428370 1428380 1429035 1429040) (-947 "REPSQ.spad" 1428102 1428112 1428360 1428365) (-946 "REPDB.spad" 1427810 1427820 1428092 1428097) (-945 "REP2.spad" 1417525 1417535 1427652 1427657) (-944 "REP1.spad" 1411746 1411756 1417475 1417480) (-943 "REP.spad" 1409301 1409309 1411736 1411741) (-942 "REGSET.spad" 1406988 1407004 1408796 1408801) (-941 "REF.spad" 1406507 1406517 1406978 1406983) (-940 "REDORDER.spad" 1405714 1405730 1406497 1406502) (-939 "RECLOS.spad" 1404611 1404630 1405314 1405407) (-938 "REALSOLV.spad" 1403752 1403760 1404601 1404606) (-937 "REAL0Q.spad" 1401051 1401065 1403742 1403747) (-936 "REAL0.spad" 1397896 1397910 1401041 1401046) (-935 "REAL.spad" 1397769 1397777 1397886 1397891) (-934 "RDUCEAST.spad" 1397491 1397499 1397759 1397764) (-933 "RDIV.spad" 1397147 1397171 1397481 1397486) (-932 "RDIST.spad" 1396715 1396725 1397137 1397142) (-931 "RDETRS.spad" 1395580 1395597 1396705 1396710) (-930 "RDETR.spad" 1393720 1393737 1395570 1395575) (-929 "RDEEFS.spad" 1392820 1392836 1393710 1393715) (-928 "RDEEF.spad" 1391831 1391847 1392810 1392815) (-927 "RCFIELD.spad" 1389050 1389058 1391733 1391826) (-926 "RCFIELD.spad" 1386355 1386365 1389040 1389045) (-925 "RCAGG.spad" 1384292 1384302 1386345 1386350) (-924 "RCAGG.spad" 1382130 1382142 1384185 1384190) (-923 "RATRET.spad" 1381491 1381501 1382120 1382125) (-922 "RATFACT.spad" 1381184 1381195 1381481 1381486) (-921 "RANDSRC.spad" 1380504 1380512 1381174 1381179) (-920 "RADUTIL.spad" 1380261 1380269 1380494 1380499) (-919 "RADIX.spad" 1377306 1377319 1378851 1378944) (-918 "RADFF.spad" 1375223 1375259 1375341 1375497) (-917 "RADCAT.spad" 1374819 1374827 1375213 1375218) (-916 "RADCAT.spad" 1374413 1374423 1374809 1374814) (-915 "QUEUE.spad" 1373849 1373859 1374107 1374112) (-914 "QUATCT2.spad" 1373470 1373488 1373839 1373844) (-913 "QUATCAT.spad" 1371641 1371651 1373400 1373465) (-912 "QUATCAT.spad" 1369577 1369589 1371338 1371343) (-911 "QUAT.spad" 1368184 1368194 1368526 1368591) (-910 "QUAGG.spad" 1367040 1367050 1368174 1368179) (-909 "QQUTAST.spad" 1366809 1366817 1367030 1367035) (-908 "QFORM.spad" 1366428 1366442 1366799 1366804) (-907 "QFCAT2.spad" 1366121 1366137 1366418 1366423) (-906 "QFCAT.spad" 1364824 1364834 1366023 1366116) (-905 "QFCAT.spad" 1363160 1363172 1364361 1364366) (-904 "QEQUAT.spad" 1362719 1362727 1363150 1363155) (-903 "QCMPACK.spad" 1357634 1357653 1362709 1362714) (-902 "QALGSET2.spad" 1355630 1355648 1357624 1357629) (-901 "QALGSET.spad" 1351735 1351767 1355544 1355549) (-900 "PWFFINTB.spad" 1349151 1349172 1351725 1351730) (-899 "PUSHVAR.spad" 1348490 1348509 1349141 1349146) (-898 "PTRANFN.spad" 1344626 1344636 1348480 1348485) (-897 "PTPACK.spad" 1341714 1341724 1344616 1344621) (-896 "PTFUNC2.spad" 1341537 1341551 1341704 1341709) (-895 "PTCAT.spad" 1340814 1340824 1341527 1341532) (-894 "PSQFR.spad" 1340129 1340153 1340804 1340809) (-893 "PSEUDLIN.spad" 1339015 1339025 1340119 1340124) (-892 "PSETPK.spad" 1325720 1325736 1338893 1338898) (-891 "PSETCAT.spad" 1320130 1320153 1325710 1325715) (-890 "PSETCAT.spad" 1314504 1314529 1320086 1320091) (-889 "PSCURVE.spad" 1313503 1313511 1314494 1314499) (-888 "PSCAT.spad" 1312286 1312315 1313401 1313498) (-887 "PSCAT.spad" 1311159 1311190 1312276 1312281) (-886 "PRTITION.spad" 1309857 1309865 1311149 1311154) (-885 "PRTDAST.spad" 1309576 1309584 1309847 1309852) (-884 "PRS.spad" 1299194 1299211 1309532 1309537) (-883 "PRQAGG.spad" 1298651 1298661 1299184 1299189) (-882 "PROPLOG.spad" 1298255 1298263 1298641 1298646) (-881 "PROPFUN2.spad" 1297878 1297891 1298245 1298250) (-880 "PROPFUN1.spad" 1297284 1297295 1297868 1297873) (-879 "PROPFRML.spad" 1295852 1295863 1297274 1297279) (-878 "PROPERTY.spad" 1295348 1295356 1295842 1295847) (-877 "PRODUCT.spad" 1293045 1293057 1293329 1293384) (-876 "PRINT.spad" 1292797 1292805 1293035 1293040) (-875 "PRIMES.spad" 1291058 1291068 1292787 1292792) (-874 "PRIMELT.spad" 1289179 1289193 1291048 1291053) (-873 "PRIMCAT.spad" 1288822 1288830 1289169 1289174) (-872 "PRIMARR2.spad" 1287589 1287601 1288812 1288817) (-871 "PRIMARR.spad" 1286341 1286351 1286511 1286516) (-870 "PREASSOC.spad" 1285723 1285735 1286331 1286336) (-869 "PR.spad" 1284241 1284253 1284940 1285067) (-868 "PPCURVE.spad" 1283378 1283386 1284231 1284236) (-867 "PORTNUM.spad" 1283169 1283177 1283368 1283373) (-866 "POLYROOT.spad" 1282018 1282040 1283125 1283130) (-865 "POLYLIFT.spad" 1281283 1281306 1282008 1282013) (-864 "POLYCATQ.spad" 1279409 1279431 1281273 1281278) (-863 "POLYCAT.spad" 1272911 1272932 1279277 1279404) (-862 "POLYCAT.spad" 1265933 1265956 1272301 1272306) (-861 "POLY2UP.spad" 1265385 1265399 1265923 1265928) (-860 "POLY2.spad" 1264982 1264994 1265375 1265380) (-859 "POLY.spad" 1262650 1262660 1263165 1263292) (-858 "POLUTIL.spad" 1261615 1261644 1262606 1262611) (-857 "POLTOPOL.spad" 1260363 1260378 1261605 1261610) (-856 "POINT.spad" 1258943 1258953 1259030 1259035) (-855 "PNTHEORY.spad" 1255645 1255653 1258933 1258938) (-854 "PMTOOLS.spad" 1254420 1254434 1255635 1255640) (-853 "PMSYM.spad" 1253969 1253979 1254410 1254415) (-852 "PMQFCAT.spad" 1253560 1253574 1253959 1253964) (-851 "PMPREDFS.spad" 1253022 1253044 1253550 1253555) (-850 "PMPRED.spad" 1252509 1252523 1253012 1253017) (-849 "PMPLCAT.spad" 1251586 1251604 1252438 1252443) (-848 "PMLSAGG.spad" 1251171 1251185 1251576 1251581) (-847 "PMKERNEL.spad" 1250750 1250762 1251161 1251166) (-846 "PMINS.spad" 1250330 1250340 1250740 1250745) (-845 "PMFS.spad" 1249907 1249925 1250320 1250325) (-844 "PMDOWN.spad" 1249197 1249211 1249897 1249902) (-843 "PMASSFS.spad" 1248172 1248188 1249187 1249192) (-842 "PMASS.spad" 1247190 1247198 1248162 1248167) (-841 "PLOTTOOL.spad" 1246970 1246978 1247180 1247185) (-840 "PLOT3D.spad" 1243434 1243442 1246960 1246965) (-839 "PLOT1.spad" 1242607 1242617 1243424 1243429) (-838 "PLOT.spad" 1237530 1237538 1242597 1242602) (-837 "PLEQN.spad" 1224932 1224959 1237520 1237525) (-836 "PINTERPA.spad" 1224716 1224732 1224922 1224927) (-835 "PINTERP.spad" 1224338 1224357 1224706 1224711) (-834 "PID.spad" 1223312 1223320 1224264 1224333) (-833 "PICOERCE.spad" 1222969 1222979 1223302 1223307) (-832 "PI.spad" 1222586 1222594 1222943 1222964) (-831 "PGROEB.spad" 1221195 1221209 1222576 1222581) (-830 "PGE.spad" 1212868 1212876 1221185 1221190) (-829 "PGCD.spad" 1211822 1211839 1212858 1212863) (-828 "PFRPAC.spad" 1210971 1210981 1211812 1211817) (-827 "PFR.spad" 1207674 1207684 1210873 1210966) (-826 "PFOTOOLS.spad" 1206932 1206948 1207664 1207669) (-825 "PFOQ.spad" 1206302 1206320 1206922 1206927) (-824 "PFO.spad" 1205721 1205748 1206292 1206297) (-823 "PFECAT.spad" 1203431 1203439 1205647 1205716) (-822 "PFECAT.spad" 1201169 1201179 1203387 1203392) (-821 "PFBRU.spad" 1199057 1199069 1201159 1201164) (-820 "PFBR.spad" 1196617 1196640 1199047 1199052) (-819 "PF.spad" 1196191 1196203 1196422 1196515) (-818 "PERMGRP.spad" 1190961 1190971 1196181 1196186) (-817 "PERMCAT.spad" 1189622 1189632 1190941 1190956) (-816 "PERMAN.spad" 1188178 1188192 1189612 1189617) (-815 "PERM.spad" 1183988 1183998 1188011 1188026) (-814 "PENDTREE.spad" 1183341 1183351 1183621 1183626) (-813 "PDSPC.spad" 1182154 1182164 1183331 1183336) (-812 "PDSPC.spad" 1180965 1180977 1182144 1182149) (-811 "PDRING.spad" 1180807 1180817 1180945 1180960) (-810 "PDMOD.spad" 1180623 1180635 1180775 1180802) (-809 "PDECOMP.spad" 1180093 1180110 1180613 1180618) (-808 "PDDOM.spad" 1179531 1179544 1180083 1180088) (-807 "PDDOM.spad" 1178967 1178982 1179521 1179526) (-806 "PCOMP.spad" 1178820 1178833 1178957 1178962) (-805 "PBWLB.spad" 1177418 1177435 1178810 1178815) (-804 "PATTERN2.spad" 1177156 1177168 1177408 1177413) (-803 "PATTERN1.spad" 1175500 1175516 1177146 1177151) (-802 "PATTERN.spad" 1170075 1170085 1175490 1175495) (-801 "PATRES2.spad" 1169747 1169761 1170065 1170070) (-800 "PATRES.spad" 1167330 1167342 1169737 1169742) (-799 "PATMATCH.spad" 1165571 1165602 1167082 1167087) (-798 "PATMAB.spad" 1165000 1165010 1165561 1165566) (-797 "PATLRES.spad" 1164086 1164100 1164990 1164995) (-796 "PATAB.spad" 1163850 1163860 1164076 1164081) (-795 "PARTPERM.spad" 1161906 1161914 1163840 1163845) (-794 "PARSURF.spad" 1161340 1161368 1161896 1161901) (-793 "PARSU2.spad" 1161137 1161153 1161330 1161335) (-792 "script-parser.spad" 1160657 1160665 1161127 1161132) (-791 "PARSCURV.spad" 1160091 1160119 1160647 1160652) (-790 "PARSC2.spad" 1159882 1159898 1160081 1160086) (-789 "PARPCURV.spad" 1159344 1159372 1159872 1159877) (-788 "PARPC2.spad" 1159135 1159151 1159334 1159339) (-787 "PARAMAST.spad" 1158263 1158271 1159125 1159130) (-786 "PAN2EXPR.spad" 1157675 1157683 1158253 1158258) (-785 "PALETTE.spad" 1156789 1156797 1157665 1157670) (-784 "PAIR.spad" 1155863 1155876 1156432 1156437) (-783 "PADICRC.spad" 1153268 1153286 1154431 1154524) (-782 "PADICRAT.spad" 1151328 1151340 1151541 1151634) (-781 "PADICCT.spad" 1149877 1149889 1151254 1151323) (-780 "PADIC.spad" 1149580 1149592 1149803 1149872) (-779 "PADEPAC.spad" 1148269 1148288 1149570 1149575) (-778 "PADE.spad" 1147021 1147037 1148259 1148264) (-777 "OWP.spad" 1146269 1146299 1146879 1146946) (-776 "OVERSET.spad" 1145842 1145850 1146259 1146264) (-775 "OVAR.spad" 1145623 1145646 1145832 1145837) (-774 "OUTFORM.spad" 1135031 1135039 1145613 1145618) (-773 "OUTBFILE.spad" 1134465 1134473 1135021 1135026) (-772 "OUTBCON.spad" 1133535 1133543 1134455 1134460) (-771 "OUTBCON.spad" 1132603 1132613 1133525 1133530) (-770 "OUT.spad" 1131721 1131729 1132593 1132598) (-769 "OSI.spad" 1131196 1131204 1131711 1131716) (-768 "OSGROUP.spad" 1131114 1131122 1131186 1131191) (-767 "ORTHPOL.spad" 1129625 1129635 1131057 1131062) (-766 "OREUP.spad" 1129119 1129147 1129346 1129385) (-765 "ORESUP.spad" 1128461 1128485 1128840 1128879) (-764 "OREPCTO.spad" 1126350 1126362 1128381 1128386) (-763 "OREPCAT.spad" 1120537 1120547 1126306 1126345) (-762 "OREPCAT.spad" 1114614 1114626 1120385 1120390) (-761 "ORDTYPE.spad" 1113851 1113859 1114604 1114609) (-760 "ORDTYPE.spad" 1113086 1113096 1113841 1113846) (-759 "ORDSTRCT.spad" 1112872 1112887 1113035 1113040) (-758 "ORDSET.spad" 1112572 1112580 1112862 1112867) (-757 "ORDRING.spad" 1112389 1112397 1112552 1112567) (-756 "ORDMON.spad" 1112244 1112252 1112379 1112384) (-755 "ORDFUNS.spad" 1111376 1111392 1112234 1112239) (-754 "ORDFIN.spad" 1111196 1111204 1111366 1111371) (-753 "ORDCOMP2.spad" 1110489 1110501 1111186 1111191) (-752 "ORDCOMP.spad" 1109015 1109025 1110097 1110126) (-751 "OPSIG.spad" 1108677 1108685 1109005 1109010) (-750 "OPQUERY.spad" 1108258 1108266 1108667 1108672) (-749 "OPERCAT.spad" 1107724 1107734 1108248 1108253) (-748 "OPERCAT.spad" 1107188 1107200 1107714 1107719) (-747 "OP.spad" 1106930 1106940 1107010 1107077) (-746 "ONECOMP2.spad" 1106354 1106366 1106920 1106925) (-745 "ONECOMP.spad" 1105160 1105170 1105962 1105991) (-744 "OMSAGG.spad" 1104972 1104982 1105140 1105155) (-743 "OMLO.spad" 1104405 1104417 1104858 1104897) (-742 "OINTDOM.spad" 1104168 1104176 1104331 1104400) (-741 "OFMONOID.spad" 1102307 1102317 1104124 1104129) (-740 "ODVAR.spad" 1101568 1101578 1102297 1102302) (-739 "ODR.spad" 1101212 1101238 1101380 1101529) (-738 "ODPOL.spad" 1098860 1098870 1099200 1099327) (-737 "ODP.spad" 1088347 1088367 1088720 1088805) (-736 "ODETOOLS.spad" 1086996 1087015 1088337 1088342) (-735 "ODESYS.spad" 1084690 1084707 1086986 1086991) (-734 "ODERTRIC.spad" 1080723 1080740 1084647 1084652) (-733 "ODERED.spad" 1080122 1080146 1080713 1080718) (-732 "ODERAT.spad" 1077755 1077772 1080112 1080117) (-731 "ODEPRRIC.spad" 1074848 1074870 1077745 1077750) (-730 "ODEPRIM.spad" 1072246 1072268 1074838 1074843) (-729 "ODEPAL.spad" 1071632 1071656 1072236 1072241) (-728 "ODEINT.spad" 1071067 1071083 1071622 1071627) (-727 "ODEEF.spad" 1066562 1066578 1071057 1071062) (-726 "ODECONST.spad" 1066107 1066125 1066552 1066557) (-725 "OCTCT2.spad" 1065748 1065766 1066097 1066102) (-724 "OCT.spad" 1064063 1064073 1064777 1064816) (-723 "OCAMON.spad" 1063911 1063919 1064053 1064058) (-722 "OC.spad" 1061707 1061717 1063867 1063906) (-721 "OC.spad" 1059242 1059254 1061404 1061409) (-720 "OASGP.spad" 1059057 1059065 1059232 1059237) (-719 "OAMONS.spad" 1058579 1058587 1059047 1059052) (-718 "OAMON.spad" 1058337 1058345 1058569 1058574) (-717 "OAMON.spad" 1058093 1058103 1058327 1058332) (-716 "OAGROUP.spad" 1057631 1057639 1058083 1058088) (-715 "OAGROUP.spad" 1057167 1057177 1057621 1057626) (-714 "NUMTUBE.spad" 1056758 1056774 1057157 1057162) (-713 "NUMQUAD.spad" 1044734 1044742 1056748 1056753) (-712 "NUMODE.spad" 1036086 1036094 1044724 1044729) (-711 "NUMFMT.spad" 1034926 1034934 1036076 1036081) (-710 "NUMERIC.spad" 1027041 1027051 1034732 1034737) (-709 "NTSCAT.spad" 1025571 1025587 1027031 1027036) (-708 "NTPOLFN.spad" 1025148 1025158 1025514 1025519) (-707 "NSUP2.spad" 1024540 1024552 1025138 1025143) (-706 "NSUP.spad" 1017977 1017987 1022397 1022550) (-705 "NSMP.spad" 1014889 1014908 1015181 1015308) (-704 "NREP.spad" 1013291 1013305 1014879 1014884) (-703 "NPCOEF.spad" 1012537 1012557 1013281 1013286) (-702 "NORMRETR.spad" 1012135 1012174 1012527 1012532) (-701 "NORMPK.spad" 1010077 1010096 1012125 1012130) (-700 "NORMMA.spad" 1009765 1009791 1010067 1010072) (-699 "NONE1.spad" 1009441 1009451 1009755 1009760) (-698 "NONE.spad" 1009182 1009190 1009431 1009436) (-697 "NODE1.spad" 1008669 1008685 1009172 1009177) (-696 "NNI.spad" 1007564 1007572 1008643 1008664) (-695 "NLINSOL.spad" 1006190 1006200 1007554 1007559) (-694 "NFINTBAS.spad" 1003750 1003767 1006180 1006185) (-693 "NETCLT.spad" 1003724 1003735 1003740 1003745) (-692 "NCODIV.spad" 1001948 1001964 1003714 1003719) (-691 "NCNTFRAC.spad" 1001590 1001604 1001938 1001943) (-690 "NCEP.spad" 999756 999770 1001580 1001585) (-689 "NASRING.spad" 999360 999368 999746 999751) (-688 "NASRING.spad" 998962 998972 999350 999355) (-687 "NARNG.spad" 998362 998370 998952 998957) (-686 "NARNG.spad" 997760 997770 998352 998357) (-685 "NAALG.spad" 997325 997335 997728 997755) (-684 "NAALG.spad" 996910 996922 997315 997320) (-683 "MULTSQFR.spad" 993868 993885 996900 996905) (-682 "MULTFACT.spad" 993251 993268 993858 993863) (-681 "MTSCAT.spad" 991345 991366 993149 993246) (-680 "MTHING.spad" 991004 991014 991335 991340) (-679 "MSYSCMD.spad" 990438 990446 990994 990999) (-678 "MSETAGG.spad" 990295 990305 990418 990433) (-677 "MSET.spad" 988105 988115 989852 989867) (-676 "MRING.spad" 985227 985239 987813 987880) (-675 "MRF2.spad" 984789 984803 985217 985222) (-674 "MRATFAC.spad" 984335 984352 984779 984784) (-673 "MPRFF.spad" 982375 982394 984325 984330) (-672 "MPOLY.spad" 980179 980194 980538 980665) (-671 "MPCPF.spad" 979443 979462 980169 980174) (-670 "MPC3.spad" 979260 979300 979433 979438) (-669 "MPC2.spad" 978914 978947 979250 979255) (-668 "MONOTOOL.spad" 977265 977282 978904 978909) (-667 "catdef.spad" 976698 976709 976919 977260) (-666 "catdef.spad" 976096 976107 976352 976693) (-665 "MONOID.spad" 975417 975425 976086 976091) (-664 "MONOID.spad" 974736 974746 975407 975412) (-663 "MONOGEN.spad" 973484 973497 974596 974731) (-662 "MONOGEN.spad" 972254 972269 973368 973373) (-661 "MONADWU.spad" 970334 970342 972244 972249) (-660 "MONADWU.spad" 968412 968422 970324 970329) (-659 "MONAD.spad" 967572 967580 968402 968407) (-658 "MONAD.spad" 966730 966740 967562 967567) (-657 "MOEBIUS.spad" 965466 965480 966710 966725) (-656 "MODULE.spad" 965336 965346 965434 965461) (-655 "MODULE.spad" 965226 965238 965326 965331) (-654 "MODRING.spad" 964561 964600 965206 965221) (-653 "MODOP.spad" 963218 963230 964383 964450) (-652 "MODMONOM.spad" 962949 962967 963208 963213) (-651 "MODMON.spad" 960019 960031 960734 960887) (-650 "MODFIELD.spad" 959381 959420 959921 960014) (-649 "MMLFORM.spad" 958241 958249 959371 959376) (-648 "MMAP.spad" 957983 958017 958231 958236) (-647 "MLO.spad" 956442 956452 957939 957978) (-646 "MLIFT.spad" 955054 955071 956432 956437) (-645 "MKUCFUNC.spad" 954589 954607 955044 955049) (-644 "MKRECORD.spad" 954177 954190 954579 954584) (-643 "MKFUNC.spad" 953584 953594 954167 954172) (-642 "MKFLCFN.spad" 952552 952562 953574 953579) (-641 "MKBCFUNC.spad" 952047 952065 952542 952547) (-640 "MHROWRED.spad" 950558 950568 952037 952042) (-639 "MFINFACT.spad" 949958 949980 950548 950553) (-638 "MESH.spad" 947753 947761 949948 949953) (-637 "MDDFACT.spad" 945972 945982 947743 947748) (-636 "MDAGG.spad" 945273 945283 945962 945967) (-635 "MCDEN.spad" 944483 944495 945263 945268) (-634 "MAYBE.spad" 943783 943794 944473 944478) (-633 "MATSTOR.spad" 941099 941109 943773 943778) (-632 "MATRIX.spad" 939900 939910 940384 940389) (-631 "MATLIN.spad" 937268 937292 939784 939789) (-630 "MATCAT2.spad" 936550 936598 937258 937263) (-629 "MATCAT.spad" 928268 928290 936540 936545) (-628 "MATCAT.spad" 919836 919860 928110 928115) (-627 "MAPPKG3.spad" 918751 918765 919826 919831) (-626 "MAPPKG2.spad" 918089 918101 918741 918746) (-625 "MAPPKG1.spad" 916917 916927 918079 918084) (-624 "MAPPAST.spad" 916256 916264 916907 916912) (-623 "MAPHACK3.spad" 916068 916082 916246 916251) (-622 "MAPHACK2.spad" 915837 915849 916058 916063) (-621 "MAPHACK1.spad" 915481 915491 915827 915832) (-620 "MAGMA.spad" 913287 913304 915471 915476) (-619 "MACROAST.spad" 912882 912890 913277 913282) (-618 "LZSTAGG.spad" 910136 910146 912872 912877) (-617 "LZSTAGG.spad" 907388 907400 910126 910131) (-616 "LWORD.spad" 904133 904150 907378 907383) (-615 "LSTAST.spad" 903917 903925 904123 904128) (-614 "LSQM.spad" 902207 902221 902601 902640) (-613 "LSPP.spad" 901742 901759 902197 902202) (-612 "LSMP1.spad" 899585 899599 901732 901737) (-611 "LSMP.spad" 898442 898470 899575 899580) (-610 "LSAGG.spad" 898133 898143 898432 898437) (-609 "LSAGG.spad" 897822 897834 898123 898128) (-608 "LPOLY.spad" 896784 896803 897678 897747) (-607 "LPEFRAC.spad" 896055 896065 896774 896779) (-606 "LOGIC.spad" 895597 895605 896045 896050) (-605 "LOGIC.spad" 895137 895147 895587 895592) (-604 "LODOOPS.spad" 894067 894079 895127 895132) (-603 "LODOF.spad" 893113 893130 894024 894029) (-602 "LODOCAT.spad" 891779 891789 893069 893108) (-601 "LODOCAT.spad" 890443 890455 891735 891740) (-600 "LODO2.spad" 889757 889769 890164 890203) (-599 "LODO1.spad" 889198 889208 889478 889517) (-598 "LODO.spad" 888623 888639 888919 888958) (-597 "LODEEF.spad" 887425 887443 888613 888618) (-596 "LO.spad" 886826 886840 887359 887386) (-595 "LNAGG.spad" 883013 883023 886816 886821) (-594 "LNAGG.spad" 879136 879148 882941 882946) (-593 "LMOPS.spad" 875904 875921 879126 879131) (-592 "LMODULE.spad" 875688 875698 875894 875899) (-591 "LMDICT.spad" 874930 874940 875178 875183) (-590 "LLINSET.spad" 874637 874647 874920 874925) (-589 "LITERAL.spad" 874543 874554 874627 874632) (-588 "LIST3.spad" 873854 873868 874533 874538) (-587 "LIST2MAP.spad" 870781 870793 873844 873849) (-586 "LIST2.spad" 869483 869495 870771 870776) (-585 "LIST.spad" 867062 867072 868405 868410) (-584 "LINSET.spad" 866841 866851 867052 867057) (-583 "LINFORM.spad" 866304 866316 866809 866836) (-582 "LINEXP.spad" 865047 865057 866294 866299) (-581 "LINELT.spad" 864418 864430 864930 864957) (-580 "LINDEP.spad" 863267 863279 864330 864335) (-579 "LINBASIS.spad" 862903 862918 863257 863262) (-578 "LIMITRF.spad" 860850 860860 862893 862898) (-577 "LIMITPS.spad" 859760 859773 860840 860845) (-576 "LIECAT.spad" 859244 859254 859686 859755) (-575 "LIECAT.spad" 858756 858768 859200 859205) (-574 "LIE.spad" 856760 856772 858034 858176) (-573 "LIB.spad" 854583 854591 855029 855034) (-572 "LGROBP.spad" 851936 851955 854573 854578) (-571 "LFCAT.spad" 850995 851003 851926 851931) (-570 "LF.spad" 849950 849966 850985 850990) (-569 "LEXTRIPK.spad" 845573 845588 849940 849945) (-568 "LEXP.spad" 843592 843619 845553 845568) (-567 "LETAST.spad" 843291 843299 843582 843587) (-566 "LEADCDET.spad" 841697 841714 843281 843286) (-565 "LAZM3PK.spad" 840441 840463 841687 841692) (-564 "LAUPOL.spad" 839108 839121 840008 840077) (-563 "LAPLACE.spad" 838691 838707 839098 839103) (-562 "LALG.spad" 838467 838477 838671 838686) (-561 "LALG.spad" 838251 838263 838457 838462) (-560 "LA.spad" 837691 837705 838173 838212) (-559 "KVTFROM.spad" 837434 837444 837681 837686) (-558 "KTVLOGIC.spad" 836978 836986 837424 837429) (-557 "KRCFROM.spad" 836724 836734 836968 836973) (-556 "KOVACIC.spad" 835455 835472 836714 836719) (-555 "KONVERT.spad" 835177 835187 835445 835450) (-554 "KOERCE.spad" 834914 834924 835167 835172) (-553 "KERNEL2.spad" 834617 834629 834904 834909) (-552 "KERNEL.spad" 833337 833347 834466 834471) (-551 "KDAGG.spad" 832456 832478 833327 833332) (-550 "KDAGG.spad" 831573 831597 832446 832451) (-549 "KAFILE.spad" 829949 829965 830184 830189) (-548 "JVMOP.spad" 829862 829870 829939 829944) (-547 "JVMMDACC.spad" 828916 828924 829852 829857) (-546 "JVMFDACC.spad" 828232 828240 828906 828911) (-545 "JVMCSTTG.spad" 826961 826969 828222 828227) (-544 "JVMCFACC.spad" 826407 826415 826951 826956) (-543 "JVMBCODE.spad" 826318 826326 826397 826402) (-542 "JORDAN.spad" 824135 824147 825596 825738) (-541 "JOINAST.spad" 823837 823845 824125 824130) (-540 "IXAGG.spad" 821970 821994 823827 823832) (-539 "IXAGG.spad" 819905 819931 821764 821769) (-538 "ITUPLE.spad" 819197 819207 819895 819900) (-537 "ITRIGMNP.spad" 818044 818063 819187 819192) (-536 "ITFUN3.spad" 817550 817564 818034 818039) (-535 "ITFUN2.spad" 817294 817306 817540 817545) (-534 "ITFORM.spad" 816649 816657 817284 817289) (-533 "ITAYLOR.spad" 814643 814658 816513 816610) (-532 "ISUPS.spad" 807092 807107 813629 813726) (-531 "ISUMP.spad" 806593 806609 807082 807087) (-530 "ISAST.spad" 806312 806320 806583 806588) (-529 "IRURPK.spad" 805029 805048 806302 806307) (-528 "IRSN.spad" 803033 803041 805019 805024) (-527 "IRRF2F.spad" 801526 801536 802989 802994) (-526 "IRREDFFX.spad" 801127 801138 801516 801521) (-525 "IROOT.spad" 799466 799476 801117 801122) (-524 "IRFORM.spad" 798790 798798 799456 799461) (-523 "IR2F.spad" 798004 798020 798780 798785) (-522 "IR2.spad" 797032 797048 797994 797999) (-521 "IR.spad" 794868 794882 796914 796941) (-520 "IPRNTPK.spad" 794628 794636 794858 794863) (-519 "IPF.spad" 794193 794205 794433 794526) (-518 "IPADIC.spad" 793962 793988 794119 794188) (-517 "IP4ADDR.spad" 793519 793527 793952 793957) (-516 "IOMODE.spad" 793041 793049 793509 793514) (-515 "IOBFILE.spad" 792426 792434 793031 793036) (-514 "IOBCON.spad" 792291 792299 792416 792421) (-513 "INVLAPLA.spad" 791940 791956 792281 792286) (-512 "INTTR.spad" 785334 785351 791930 791935) (-511 "INTTOOLS.spad" 783142 783158 784961 784966) (-510 "INTSLPE.spad" 782470 782478 783132 783137) (-509 "INTRVL.spad" 782036 782046 782384 782465) (-508 "INTRF.spad" 780468 780482 782026 782031) (-507 "INTRET.spad" 779900 779910 780458 780463) (-506 "INTRAT.spad" 778635 778652 779890 779895) (-505 "INTPM.spad" 777098 777114 778356 778361) (-504 "INTPAF.spad" 774974 774992 777027 777032) (-503 "INTHERTR.spad" 774248 774265 774964 774969) (-502 "INTHERAL.spad" 773918 773942 774238 774243) (-501 "INTHEORY.spad" 770357 770365 773908 773913) (-500 "INTG0.spad" 764121 764139 770286 770291) (-499 "INTFACT.spad" 763188 763198 764111 764116) (-498 "INTEF.spad" 761599 761615 763178 763183) (-497 "INTDOM.spad" 760222 760230 761525 761594) (-496 "INTDOM.spad" 758907 758917 760212 760217) (-495 "INTCAT.spad" 757174 757184 758821 758902) (-494 "INTBIT.spad" 756681 756689 757164 757169) (-493 "INTALG.spad" 755869 755896 756671 756676) (-492 "INTAF.spad" 755369 755385 755859 755864) (-491 "INTABL.spad" 753186 753217 753349 753354) (-490 "INT8.spad" 753066 753074 753176 753181) (-489 "INT64.spad" 752945 752953 753056 753061) (-488 "INT32.spad" 752824 752832 752935 752940) (-487 "INT16.spad" 752703 752711 752814 752819) (-486 "INT.spad" 752229 752237 752569 752698) (-485 "INS.spad" 749732 749740 752131 752224) (-484 "INS.spad" 747321 747331 749722 749727) (-483 "INPSIGN.spad" 746791 746804 747311 747316) (-482 "INPRODPF.spad" 745887 745906 746781 746786) (-481 "INPRODFF.spad" 744975 744999 745877 745882) (-480 "INNMFACT.spad" 743950 743967 744965 744970) (-479 "INMODGCD.spad" 743454 743484 743940 743945) (-478 "INFSP.spad" 741751 741773 743444 743449) (-477 "INFPROD0.spad" 740831 740850 741741 741746) (-476 "INFORM1.spad" 740456 740466 740821 740826) (-475 "INFORM.spad" 737667 737675 740446 740451) (-474 "INFINITY.spad" 737219 737227 737657 737662) (-473 "INETCLTS.spad" 737196 737204 737209 737214) (-472 "INEP.spad" 735742 735764 737186 737191) (-471 "INDE.spad" 735391 735408 735652 735657) (-470 "INCRMAPS.spad" 734828 734838 735381 735386) (-469 "INBFILE.spad" 733924 733932 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(-407 "GRAY.spad" 648477 648485 649996 650001) (-406 "GRALG.spad" 647572 647584 648467 648472) (-405 "GRALG.spad" 646665 646679 647562 647567) (-404 "GPOLSET.spad" 645984 646007 646196 646201) (-403 "GOSPER.spad" 645261 645279 645974 645979) (-402 "GMODPOL.spad" 644409 644436 645229 645256) (-401 "GHENSEL.spad" 643492 643506 644399 644404) (-400 "GENUPS.spad" 639785 639798 643482 643487) (-399 "GENUFACT.spad" 639362 639372 639775 639780) (-398 "GENPGCD.spad" 638964 638981 639352 639357) (-397 "GENMFACT.spad" 638416 638435 638954 638959) (-396 "GENEEZ.spad" 636375 636388 638406 638411) (-395 "GDMP.spad" 633764 633781 634538 634665) (-394 "GCNAALG.spad" 627687 627714 633558 633625) (-393 "GCDDOM.spad" 626879 626887 627613 627682) (-392 "GCDDOM.spad" 626133 626143 626869 626874) (-391 "GBINTERN.spad" 622153 622191 626123 626128) (-390 "GBF.spad" 617936 617974 622143 622148) (-389 "GBEUCLID.spad" 615818 615856 617926 617931) (-388 "GB.spad" 613344 613382 615774 615779) (-387 "GAUSSFAC.spad" 612657 612665 613334 613339) (-386 "GALUTIL.spad" 610983 610993 612613 612618) (-385 "GALPOLYU.spad" 609437 609450 610973 610978) (-384 "GALFACTU.spad" 607650 607669 609427 609432) (-383 "GALFACT.spad" 597863 597874 607640 607645) (-382 "FUNDESC.spad" 597541 597549 597853 597858) (-381 "catdef.spad" 597152 597162 597531 597536) (-380 "FUNCTION.spad" 597001 597013 597142 597147) (-379 "FT.spad" 595301 595309 596991 596996) (-378 "FSUPFACT.spad" 594215 594234 595251 595256) (-377 "FST.spad" 592301 592309 594205 594210) (-376 "FSRED.spad" 591781 591797 592291 592296) (-375 "FSPRMELT.spad" 590647 590663 591738 591743) (-374 "FSPECF.spad" 588738 588754 590637 590642) (-373 "FSINT.spad" 588398 588414 588728 588733) (-372 "FSERIES.spad" 587589 587601 588218 588317) (-371 "FSCINT.spad" 586906 586922 587579 587584) (-370 "FSAGG2.spad" 585641 585657 586896 586901) (-369 "FSAGG.spad" 584782 584792 585621 585636) (-368 "FSAGG.spad" 583861 583873 584702 584707) (-367 "FS2UPS.spad" 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512174 512243) (-325 "FLAGG2.spad" 508635 508651 509908 509913) (-324 "FLAGG.spad" 505711 505721 508625 508630) (-323 "FLAGG.spad" 502652 502664 505568 505573) (-322 "FINRALG.spad" 500737 500750 502608 502647) (-321 "FINRALG.spad" 498748 498763 500621 500626) (-320 "FINITE.spad" 497900 497908 498738 498743) (-319 "FINITE.spad" 497050 497060 497890 497895) (-318 "aggcat.spad" 493775 493785 497040 497045) (-317 "FINAGG.spad" 490465 490477 493732 493737) (-316 "FINAALG.spad" 479650 479660 490407 490460) (-315 "FINAALG.spad" 468847 468859 479606 479611) (-314 "FILECAT.spad" 467381 467398 468837 468842) (-313 "FILE.spad" 466964 466974 467371 467376) (-312 "FIELD.spad" 466370 466378 466866 466959) (-311 "FIELD.spad" 465862 465872 466360 466365) (-310 "FGROUP.spad" 464525 464535 465842 465857) (-309 "FGLMICPK.spad" 463320 463335 464515 464520) (-308 "FFX.spad" 462706 462721 463039 463132) (-307 "FFSLPE.spad" 462217 462238 462696 462701) (-306 "FFPOLY2.spad" 461277 461294 462207 462212) (-305 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416223 416228) (-284 "FDIV2.spad" 413983 414023 414317 414322) (-283 "FDIV.spad" 413441 413465 413973 413978) (-282 "FCTRDATA.spad" 412449 412457 413431 413436) (-281 "FCOMP.spad" 411828 411838 412439 412444) (-280 "FAXF.spad" 404863 404877 411730 411823) (-279 "FAXF.spad" 397950 397966 404819 404824) (-278 "FARRAY.spad" 395839 395849 396872 396877) (-277 "FAMR.spad" 393983 393995 395737 395834) (-276 "FAMR.spad" 392111 392125 393867 393872) (-275 "FAMONOID.spad" 391795 391805 392065 392070) (-274 "FAMONC.spad" 390115 390127 391785 391790) (-273 "FAGROUP.spad" 389755 389765 390011 390038) (-272 "FACUTIL.spad" 387967 387984 389745 389750) (-271 "FACTFUNC.spad" 387169 387179 387957 387962) (-270 "EXPUPXS.spad" 384061 384084 385360 385509) (-269 "EXPRTUBE.spad" 381349 381357 384051 384056) (-268 "EXPRODE.spad" 378517 378533 381339 381344) (-267 "EXPR2UPS.spad" 374639 374652 378507 378512) (-266 "EXPR2.spad" 374344 374356 374629 374634) (-265 "EXPR.spad" 369989 369999 370703 370990) (-264 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"DIAGG.spad" 200161 200173 200513 200518) (-181 "DHMATRIX.spad" 198560 198570 199705 199710) (-180 "DFSFUN.spad" 192200 192208 198550 198555) (-179 "DFLOAT.spad" 188807 188815 192090 192195) (-178 "DFINTTLS.spad" 187038 187054 188797 188802) (-177 "DERHAM.spad" 185125 185157 187018 187033) (-176 "DEQUEUE.spad" 184536 184546 184819 184824) (-175 "DEGRED.spad" 184153 184167 184526 184531) (-174 "DEFINTRF.spad" 181735 181745 184143 184148) (-173 "DEFINTEF.spad" 180273 180289 181725 181730) (-172 "DEFAST.spad" 179657 179665 180263 180268) (-171 "DECIMAL.spad" 177886 177894 178247 178340) (-170 "DDFACT.spad" 175707 175724 177876 177881) (-169 "DBLRESP.spad" 175307 175331 175697 175702) (-168 "DBASIS.spad" 174933 174948 175297 175302) (-167 "DBASE.spad" 173597 173607 174923 174928) (-166 "DATAARY.spad" 173083 173096 173587 173592) (-165 "CYCLOTOM.spad" 172589 172597 173073 173078) (-164 "CYCLES.spad" 169372 169380 172579 172584) (-163 "CVMP.spad" 168789 168799 169362 169367) (-162 "CTRIGMNP.spad" 167289 167305 168779 168784) (-161 "CTORKIND.spad" 166892 166900 167279 167284) (-160 "CTORCAT.spad" 166133 166141 166882 166887) (-159 "CTORCAT.spad" 165372 165382 166123 166128) (-158 "CTORCALL.spad" 164961 164971 165362 165367) (-157 "CTOR.spad" 164652 164660 164951 164956) (-156 "CSTTOOLS.spad" 163897 163910 164642 164647) (-155 "CRFP.spad" 157669 157682 163887 163892) (-154 "CRCEAST.spad" 157389 157397 157659 157664) (-153 "CRAPACK.spad" 156456 156466 157379 157384) (-152 "CPMATCH.spad" 155957 155972 156378 156383) (-151 "CPIMA.spad" 155662 155681 155947 155952) (-150 "COORDSYS.spad" 150671 150681 155652 155657) (-149 "CONTOUR.spad" 150098 150106 150661 150666) (-148 "CONTFRAC.spad" 145848 145858 150000 150093) (-147 "CONDUIT.spad" 145606 145614 145838 145843) (-146 "COMRING.spad" 145280 145288 145544 145601) (-145 "COMPPROP.spad" 144798 144806 145270 145275) (-144 "COMPLPAT.spad" 144565 144580 144788 144793) (-143 "COMPLEX2.spad" 144280 144292 144555 144560) (-142 "COMPLEX.spad" 139986 139996 140230 140488) (-141 "COMPILER.spad" 139535 139543 139976 139981) (-140 "COMPFACT.spad" 139137 139151 139525 139530) (-139 "COMPCAT.spad" 137212 137222 138874 139132) (-138 "COMPCAT.spad" 135028 135040 136692 136697) (-137 "COMMUPC.spad" 134776 134794 135018 135023) (-136 "COMMONOP.spad" 134309 134317 134766 134771) (-135 "COMMAAST.spad" 134072 134080 134299 134304) (-134 "COMM.spad" 133883 133891 134062 134067) (-133 "COMBOPC.spad" 132806 132814 133873 133878) (-132 "COMBINAT.spad" 131573 131583 132796 132801) (-131 "COMBF.spad" 128995 129011 131563 131568) (-130 "COLOR.spad" 127832 127840 128985 128990) (-129 "COLONAST.spad" 127498 127506 127822 127827) (-128 "CMPLXRT.spad" 127209 127226 127488 127493) (-127 "CLLCTAST.spad" 126871 126879 127199 127204) (-126 "CLIP.spad" 122979 122987 126861 126866) (-125 "CLIF.spad" 121634 121650 122935 122974) (-124 "CLAGG.spad" 119840 119850 121624 121629) (-123 "CLAGG.spad" 117905 117917 119691 119696) (-122 "CINTSLPE.spad" 117260 117273 117895 117900) (-121 "CHVAR.spad" 115398 115420 117250 117255) (-120 "CHARZ.spad" 115313 115321 115378 115393) (-119 "CHARPOL.spad" 114839 114849 115303 115308) (-118 "CHARNZ.spad" 114601 114609 114819 114834) (-117 "CHAR.spad" 111969 111977 114591 114596) (-116 "CFCAT.spad" 111297 111305 111959 111964) (-115 "CDEN.spad" 110517 110531 111287 111292) (-114 "CCLASS.spad" 108598 108606 109860 109875) (-113 "CATEGORY.spad" 107672 107680 108588 108593) (-112 "CATCTOR.spad" 107563 107571 107662 107667) (-111 "CATAST.spad" 107189 107197 107553 107558) (-110 "CASEAST.spad" 106903 106911 107179 107184) (-109 "CARTEN2.spad" 106293 106320 106893 106898) (-108 "CARTEN.spad" 102045 102069 106283 106288) (-107 "CARD.spad" 99340 99348 102019 102040) (-106 "CAPSLAST.spad" 99122 99130 99330 99335) (-105 "CACHSET.spad" 98746 98754 99112 99117) (-104 "CABMON.spad" 98301 98309 98736 98741) (-103 "BYTEORD.spad" 97976 97984 98291 98296) (-102 "BYTEBUF.spad" 95796 95804 97002 97007) (-101 "BYTE.spad" 95271 95279 95786 95791) (-100 "BTREE.spad" 94370 94380 94904 94909) (-99 "BTOURN.spad" 93402 93411 94003 94008) (-98 "BTCAT.spad" 92982 92991 93392 93397) (-97 "BTCAT.spad" 92560 92571 92972 92977) (-96 "BTAGG.spad" 92049 92056 92550 92555) (-95 "BTAGG.spad" 91536 91545 92039 92044) (-94 "BSTREE.spad" 90304 90313 91169 91174) (-93 "BRILL.spad" 88510 88520 90294 90299) (-92 "BRAGG.spad" 87467 87476 88500 88505) (-91 "BRAGG.spad" 86360 86371 87395 87400) (-90 "BPADICRT.spad" 84420 84431 84666 84759) (-89 "BPADIC.spad" 84093 84104 84346 84415) (-88 "BOUNDZRO.spad" 83750 83766 84083 84088) (-87 "BOP1.spad" 81209 81218 83740 83745) (-86 "BOP.spad" 76352 76359 81199 81204) (-85 "BOOLEAN.spad" 75901 75908 76342 76347) (-84 "BOOLE.spad" 75552 75559 75891 75896) (-83 "BOOLE.spad" 75201 75210 75542 75547) (-82 "BMODULE.spad" 74914 74925 75169 75196) (-81 "BITS.spad" 74125 74132 74339 74344) (-80 "catdef.spad" 74008 74018 74115 74120) (-79 "catdef.spad" 73759 73769 73998 74003) (-78 "BINDING.spad" 73181 73188 73749 73754) (-77 "BINARY.spad" 71416 71423 71771 71864) (-76 "BGAGG.spad" 70746 70755 71406 71411) (-75 "BGAGG.spad" 70074 70085 70736 70741) (-74 "BEZOUT.spad" 69215 69241 70024 70029) (-73 "BBTREE.spad" 66119 66128 68848 68853) (-72 "BASTYPE.spad" 65619 65626 66109 66114) (-71 "BASTYPE.spad" 65117 65126 65609 65614) (-70 "BALFACT.spad" 64577 64589 65107 65112) (-69 "AUTOMOR.spad" 64028 64037 64557 64572) (-68 "ATTREG.spad" 61160 61167 63804 64023) (-67 "ATTRAST.spad" 60877 60884 61150 61155) (-66 "ATRIG.spad" 60347 60354 60867 60872) (-65 "ATRIG.spad" 59815 59824 60337 60342) (-64 "ASTCAT.spad" 59719 59726 59805 59810) (-63 "ASTCAT.spad" 59621 59630 59709 59714) (-62 "ASTACK.spad" 59047 59056 59315 59320) (-61 "ASSOCEQ.spad" 57881 57892 59003 59008) (-60 "ARRAY2.spad" 57426 57435 57575 57580) (-59 "ARRAY12.spad" 56139 56150 57416 57421) (-58 "ARRAY1.spad" 54715 54724 55061 55066) (-57 "ARR2CAT.spad" 51024 51045 54705 54710) (-56 "ARR2CAT.spad" 47331 47354 51014 51019) (-55 "ARITY.spad" 46703 46710 47321 47326) (-54 "APPRULE.spad" 45987 46009 46693 46698) (-53 "APPLYORE.spad" 45606 45619 45977 45982) (-52 "ANY1.spad" 44677 44686 45596 45601) (-51 "ANY.spad" 43528 43535 44667 44672) (-50 "ANTISYM.spad" 42101 42117 43508 43523) (-49 "ANON.spad" 41810 41817 42091 42096) (-48 "AN.spad" 40278 40285 41641 41734) (-47 "AMR.spad" 38608 38619 40176 40273) (-46 "AMR.spad" 36801 36814 38371 38376) (-45 "ALIST.spad" 33046 33067 33396 33401) (-44 "ALGSC.spad" 32181 32207 32918 32971) (-43 "ALGPKG.spad" 27964 27975 32137 32142) (-42 "ALGMFACT.spad" 27157 27171 27954 27959) (-41 "ALGMANIP.spad" 24658 24673 27001 27006) (-40 "ALGFF.spad" 22476 22503 22693 22849) (-39 "ALGFACT.spad" 21595 21605 22466 22471) (-38 "ALGEBRA.spad" 21428 21437 21551 21590) (-37 "ALGEBRA.spad" 21293 21304 21418 21423) (-36 "ALAGG.spad" 20831 20852 21283 21288) (-35 "AHYP.spad" 20212 20219 20821 20826) (-34 "AGG.spad" 19119 19126 20202 20207) (-33 "AGG.spad" 18024 18033 19109 19114) (-32 "AF.spad" 16469 16484 17973 17978) (-31 "ADDAST.spad" 16155 16162 16459 16464) (-30 "ACPLOT.spad" 15032 15039 16145 16150) (-29 "ACFS.spad" 12889 12898 14934 15027) (-28 "ACFS.spad" 10832 10843 12879 12884) (-27 "ACF.spad" 7586 7593 10734 10827) (-26 "ACF.spad" 4426 4435 7576 7581) (-25 "ABELSG.spad" 3967 3974 4416 4421) (-24 "ABELSG.spad" 3506 3515 3957 3962) (-23 "ABELMON.spad" 2934 2941 3496 3501) (-22 "ABELMON.spad" 2360 2369 2924 2929) (-21 "ABELGRP.spad" 2025 2032 2350 2355) (-20 "ABELGRP.spad" 1688 1697 2015 2020) (-19 "A1AGG.spad" 860 869 1678 1683) (-18 "A1AGG.spad" 30 41 850 855))
\ No newline at end of file +((-3 NIL 1966210 1966215 1966220 1966225) (-2 NIL 1966190 1966195 1966200 1966205) (-1 NIL 1966170 1966175 1966180 1966185) (0 NIL 1966150 1966155 1966160 1966165) (-1213 "ZMOD.spad" 1965959 1965972 1966088 1966145) (-1212 "ZLINDEP.spad" 1965057 1965068 1965949 1965954) (-1211 "ZDSOLVE.spad" 1955018 1955040 1965047 1965052) (-1210 "YSTREAM.spad" 1954513 1954524 1955008 1955013) (-1209 "YDIAGRAM.spad" 1954147 1954156 1954503 1954508) (-1208 "XRPOLY.spad" 1953367 1953387 1954003 1954072) (-1207 "XPR.spad" 1951295 1951308 1953085 1953184) (-1206 "XPOLYC.spad" 1950614 1950630 1951221 1951290) (-1205 "XPOLY.spad" 1950169 1950180 1950470 1950539) (-1204 "XPBWPOLY.spad" 1948640 1948660 1949975 1950044) (-1203 "XFALG.spad" 1945821 1945837 1948566 1948635) (-1202 "XF.spad" 1944284 1944299 1945723 1945816) (-1201 "XF.spad" 1942727 1942744 1944168 1944173) (-1200 "XEXPPKG.spad" 1941986 1942012 1942717 1942722) (-1199 "XDPOLY.spad" 1941600 1941616 1941842 1941911) (-1198 "XALG.spad" 1941268 1941279 1941556 1941595) (-1197 "WUTSET.spad" 1937132 1937149 1940763 1940768) (-1196 "WP.spad" 1936339 1936383 1936990 1937057) (-1195 "WHILEAST.spad" 1936137 1936146 1936329 1936334) (-1194 "WHEREAST.spad" 1935808 1935817 1936127 1936132) (-1193 "WFFINTBS.spad" 1933471 1933493 1935798 1935803) (-1192 "WEIER.spad" 1931693 1931704 1933461 1933466) (-1191 "VSPACE.spad" 1931366 1931377 1931661 1931688) (-1190 "VSPACE.spad" 1931059 1931072 1931356 1931361) (-1189 "VOID.spad" 1930736 1930745 1931049 1931054) (-1188 "VIEWDEF.spad" 1925937 1925946 1930726 1930731) (-1187 "VIEW3D.spad" 1909898 1909907 1925927 1925932) (-1186 "VIEW2D.spad" 1897797 1897806 1909888 1909893) (-1185 "VIEW.spad" 1895517 1895526 1897787 1897792) (-1184 "VECTOR2.spad" 1894156 1894169 1895507 1895512) (-1183 "VECTOR.spad" 1892572 1892583 1892823 1892828) (-1182 "VECTCAT.spad" 1890506 1890517 1892562 1892567) (-1181 "VECTCAT.spad" 1888227 1888240 1890285 1890290) (-1180 "VARIABLE.spad" 1888007 1888022 1888217 1888222) (-1179 "UTYPE.spad" 1887651 1887660 1887997 1888002) (-1178 "UTSODETL.spad" 1886946 1886970 1887607 1887612) (-1177 "UTSODE.spad" 1885162 1885182 1886936 1886941) (-1176 "UTSCAT.spad" 1882641 1882657 1885060 1885157) (-1175 "UTSCAT.spad" 1879788 1879806 1882209 1882214) (-1174 "UTS2.spad" 1879383 1879418 1879778 1879783) (-1173 "UTS.spad" 1874395 1874423 1877915 1878012) (-1172 "URAGG.spad" 1869116 1869127 1874385 1874390) (-1171 "URAGG.spad" 1863773 1863786 1869044 1869049) (-1170 "UPXSSING.spad" 1861541 1861567 1862977 1863110) (-1169 "UPXSCONS.spad" 1859359 1859379 1859732 1859881) (-1168 "UPXSCCA.spad" 1857930 1857950 1859205 1859354) (-1167 "UPXSCCA.spad" 1856643 1856665 1857920 1857925) (-1166 "UPXSCAT.spad" 1855232 1855248 1856489 1856638) (-1165 "UPXS2.spad" 1854775 1854828 1855222 1855227) (-1164 "UPXS.spad" 1852130 1852158 1852966 1853115) (-1163 "UPSQFREE.spad" 1850545 1850559 1852120 1852125) (-1162 "UPSCAT.spad" 1848340 1848364 1850443 1850540) (-1161 "UPSCAT.spad" 1845836 1845862 1847941 1847946) (-1160 "UPOLYC2.spad" 1845307 1845326 1845826 1845831) (-1159 "UPOLYC.spad" 1840387 1840398 1845149 1845302) (-1158 "UPOLYC.spad" 1835385 1835398 1840149 1840154) (-1157 "UPMP.spad" 1834317 1834330 1835375 1835380) (-1156 "UPDIVP.spad" 1833882 1833896 1834307 1834312) (-1155 "UPDECOMP.spad" 1832143 1832157 1833872 1833877) (-1154 "UPCDEN.spad" 1831360 1831376 1832133 1832138) (-1153 "UP2.spad" 1830724 1830745 1831350 1831355) (-1152 "UP.spad" 1828194 1828209 1828581 1828734) (-1151 "UNISEG2.spad" 1827691 1827704 1828150 1828155) (-1150 "UNISEG.spad" 1827044 1827055 1827610 1827615) (-1149 "UNIFACT.spad" 1826147 1826159 1827034 1827039) (-1148 "ULSCONS.spad" 1819993 1820013 1820363 1820512) (-1147 "ULSCCAT.spad" 1817730 1817750 1819839 1819988) (-1146 "ULSCCAT.spad" 1815575 1815597 1817686 1817691) (-1145 "ULSCAT.spad" 1813815 1813831 1815421 1815570) (-1144 "ULS2.spad" 1813329 1813382 1813805 1813810) (-1143 "ULS.spad" 1805362 1805390 1806307 1806730) (-1142 "UINT8.spad" 1805239 1805248 1805352 1805357) (-1141 "UINT64.spad" 1805115 1805124 1805229 1805234) (-1140 "UINT32.spad" 1804991 1805000 1805105 1805110) (-1139 "UINT16.spad" 1804867 1804876 1804981 1804986) (-1138 "UFD.spad" 1803932 1803941 1804793 1804862) (-1137 "UFD.spad" 1803059 1803070 1803922 1803927) (-1136 "UDVO.spad" 1801940 1801949 1803049 1803054) (-1135 "UDPO.spad" 1799521 1799532 1801896 1801901) (-1134 "TYPEAST.spad" 1799440 1799449 1799511 1799516) (-1133 "TYPE.spad" 1799372 1799381 1799430 1799435) (-1132 "TWOFACT.spad" 1798024 1798039 1799362 1799367) (-1131 "TUPLE.spad" 1797531 1797542 1797936 1797941) (-1130 "TUBETOOL.spad" 1794398 1794407 1797521 1797526) (-1129 "TUBE.spad" 1793045 1793062 1794388 1794393) (-1128 "TSETCAT.spad" 1781138 1781155 1793035 1793040) (-1127 "TSETCAT.spad" 1769195 1769214 1781094 1781099) (-1126 "TS.spad" 1767823 1767839 1768789 1768886) (-1125 "TRMANIP.spad" 1762187 1762204 1767511 1767516) (-1124 "TRIMAT.spad" 1761150 1761175 1762177 1762182) (-1123 "TRIGMNIP.spad" 1759677 1759694 1761140 1761145) (-1122 "TRIGCAT.spad" 1759189 1759198 1759667 1759672) (-1121 "TRIGCAT.spad" 1758699 1758710 1759179 1759184) (-1120 "TREE.spad" 1757300 1757311 1758332 1758337) (-1119 "TRANFUN.spad" 1757139 1757148 1757290 1757295) (-1118 "TRANFUN.spad" 1756976 1756987 1757129 1757134) (-1117 "TOPSP.spad" 1756650 1756659 1756966 1756971) (-1116 "TOOLSIGN.spad" 1756313 1756324 1756640 1756645) (-1115 "TEXTFILE.spad" 1754874 1754883 1756303 1756308) (-1114 "TEX1.spad" 1754430 1754441 1754864 1754869) (-1113 "TEX.spad" 1751624 1751633 1754420 1754425) (-1112 "TBCMPPK.spad" 1749725 1749748 1751614 1751619) (-1111 "TBAGG.spad" 1748990 1749013 1749715 1749720) (-1110 "TBAGG.spad" 1748253 1748278 1748980 1748985) (-1109 "TANEXP.spad" 1747661 1747672 1748243 1748248) (-1108 "TALGOP.spad" 1747385 1747396 1747651 1747656) (-1107 "TABLEAU.spad" 1746866 1746877 1747375 1747380) (-1106 "TABLE.spad" 1744576 1744599 1744846 1744851) (-1105 "TABLBUMP.spad" 1741355 1741366 1744566 1744571) (-1104 "SYSTEM.spad" 1740583 1740592 1741345 1741350) (-1103 "SYSSOLP.spad" 1738066 1738077 1740573 1740578) (-1102 "SYSPTR.spad" 1737965 1737974 1738056 1738061) (-1101 "SYSNNI.spad" 1737188 1737199 1737955 1737960) (-1100 "SYSINT.spad" 1736592 1736603 1737178 1737183) (-1099 "SYNTAX.spad" 1732926 1732935 1736582 1736587) (-1098 "SYMTAB.spad" 1730994 1731003 1732916 1732921) (-1097 "SYMS.spad" 1727023 1727032 1730984 1730989) (-1096 "SYMPOLY.spad" 1726156 1726167 1726238 1726365) (-1095 "SYMFUNC.spad" 1725657 1725668 1726146 1726151) (-1094 "SYMBOL.spad" 1723152 1723161 1725647 1725652) (-1093 "SUTS.spad" 1720265 1720293 1721684 1721781) (-1092 "SUPXS.spad" 1717607 1717635 1718456 1718605) (-1091 "SUPFRACF.spad" 1716712 1716730 1717597 1717602) (-1090 "SUP2.spad" 1716104 1716117 1716702 1716707) (-1089 "SUP.spad" 1713188 1713199 1713961 1714114) (-1088 "SUMRF.spad" 1712162 1712173 1713178 1713183) (-1087 "SUMFS.spad" 1711791 1711808 1712152 1712157) (-1086 "SULS.spad" 1703811 1703839 1704769 1705192) (-1085 "syntax.spad" 1703580 1703589 1703801 1703806) (-1084 "SUCH.spad" 1703270 1703285 1703570 1703575) (-1083 "SUBSPACE.spad" 1695401 1695416 1703260 1703265) (-1082 "SUBRESP.spad" 1694571 1694585 1695357 1695362) (-1081 "STTFNC.spad" 1691039 1691055 1694561 1694566) (-1080 "STTF.spad" 1687138 1687154 1691029 1691034) (-1079 "STTAYLOR.spad" 1679815 1679826 1687045 1687050) (-1078 "STRTBL.spad" 1677688 1677705 1677837 1677842) (-1077 "STRING.spad" 1676329 1676338 1676714 1676719) (-1076 "STREAM3.spad" 1675902 1675917 1676319 1676324) (-1075 "STREAM2.spad" 1675030 1675043 1675892 1675897) (-1074 "STREAM1.spad" 1674736 1674747 1675020 1675025) (-1073 "STREAM.spad" 1671696 1671707 1674187 1674192) (-1072 "STINPROD.spad" 1670632 1670648 1671686 1671691) (-1071 "STEPAST.spad" 1669866 1669875 1670622 1670627) (-1070 "STEP.spad" 1669183 1669192 1669856 1669861) (-1069 "STBL.spad" 1666996 1667024 1667163 1667168) (-1068 "STAGG.spad" 1665695 1665706 1666986 1666991) (-1067 "STAGG.spad" 1664392 1664405 1665685 1665690) (-1066 "STACK.spad" 1663836 1663847 1664086 1664091) (-1065 "SRING.spad" 1663596 1663605 1663826 1663831) (-1064 "SREGSET.spad" 1661189 1661206 1663091 1663096) (-1063 "SRDCMPK.spad" 1659766 1659786 1661179 1661184) (-1062 "SRAGG.spad" 1654971 1654980 1659756 1659761) (-1061 "SRAGG.spad" 1650174 1650185 1654961 1654966) (-1060 "SQMATRIX.spad" 1647863 1647881 1648779 1648854) (-1059 "SPLTREE.spad" 1642523 1642536 1647319 1647324) (-1058 "SPLNODE.spad" 1639143 1639156 1642513 1642518) (-1057 "SPFCAT.spad" 1637952 1637961 1639133 1639138) (-1056 "SPECOUT.spad" 1636504 1636513 1637942 1637947) (-1055 "SPADXPT.spad" 1628595 1628604 1636494 1636499) (-1054 "spad-parser.spad" 1628060 1628069 1628585 1628590) (-1053 "SPADAST.spad" 1627761 1627770 1628050 1628055) (-1052 "SPACEC.spad" 1611976 1611987 1627751 1627756) (-1051 "SPACE3.spad" 1611752 1611763 1611966 1611971) (-1050 "SORTPAK.spad" 1611301 1611314 1611708 1611713) (-1049 "SOLVETRA.spad" 1609064 1609075 1611291 1611296) (-1048 "SOLVESER.spad" 1607520 1607531 1609054 1609059) (-1047 "SOLVERAD.spad" 1603546 1603557 1607510 1607515) (-1046 "SOLVEFOR.spad" 1602008 1602026 1603536 1603541) (-1045 "SNTSCAT.spad" 1601630 1601647 1601998 1602003) (-1044 "SMTS.spad" 1599947 1599973 1601224 1601321) (-1043 "SMP.spad" 1597755 1597775 1598145 1598272) (-1042 "SMITH.spad" 1596600 1596625 1597745 1597750) (-1041 "SMATCAT.spad" 1594730 1594760 1596556 1596595) (-1040 "SMATCAT.spad" 1592780 1592812 1594608 1594613) (-1039 "aggcat.spad" 1592466 1592477 1592770 1592775) (-1038 "SKAGG.spad" 1591457 1591468 1592456 1592461) (-1037 "SINT.spad" 1590756 1590765 1591323 1591452) (-1036 "SIMPAN.spad" 1590484 1590493 1590746 1590751) (-1035 "SIGNRF.spad" 1589609 1589620 1590474 1590479) (-1034 "SIGNEF.spad" 1588895 1588912 1589599 1589604) (-1033 "syntax.spad" 1588312 1588321 1588885 1588890) (-1032 "SIG.spad" 1587674 1587683 1588302 1588307) (-1031 "SHP.spad" 1585618 1585633 1587630 1587635) (-1030 "SHDP.spad" 1574961 1574988 1575478 1575563) (-1029 "SGROUP.spad" 1574569 1574578 1574951 1574956) (-1028 "SGROUP.spad" 1574175 1574186 1574559 1574564) (-1027 "catdef.spad" 1573885 1573897 1573996 1574170) (-1026 "catdef.spad" 1573441 1573453 1573706 1573880) (-1025 "SGCF.spad" 1566580 1566589 1573431 1573436) (-1024 "SFRTCAT.spad" 1565548 1565565 1566570 1566575) (-1023 "SFRGCD.spad" 1564611 1564631 1565538 1565543) (-1022 "SFQCMPK.spad" 1559424 1559444 1564601 1564606) (-1021 "SEXOF.spad" 1559267 1559307 1559414 1559419) (-1020 "SEXCAT.spad" 1557095 1557135 1559257 1559262) (-1019 "SEX.spad" 1556987 1556996 1557085 1557090) (-1018 "SETMN.spad" 1555447 1555464 1556977 1556982) (-1017 "SETCAT.spad" 1554932 1554941 1555437 1555442) (-1016 "SETCAT.spad" 1554415 1554426 1554922 1554927) (-1015 "SETAGG.spad" 1550964 1550975 1554395 1554410) (-1014 "SETAGG.spad" 1547521 1547534 1550954 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1531704 1532299 1532434) (-994 "RURPK.spad" 1529349 1529364 1531679 1531684) (-993 "RULESET.spad" 1528803 1528826 1529339 1529344) (-992 "RULECOLD.spad" 1528656 1528668 1528793 1528798) (-991 "RULE.spad" 1526905 1526928 1528646 1528651) (-990 "RTVALUE.spad" 1526641 1526649 1526895 1526900) (-989 "syntax.spad" 1526359 1526367 1526631 1526636) (-988 "RSETGCD.spad" 1522802 1522821 1526349 1526354) (-987 "RSETCAT.spad" 1512793 1512809 1522792 1522797) (-986 "RSETCAT.spad" 1502782 1502800 1512783 1512788) (-985 "RSDCMPK.spad" 1501283 1501302 1502772 1502777) (-984 "RRCC.spad" 1499668 1499697 1501273 1501278) (-983 "RRCC.spad" 1498051 1498082 1499658 1499663) (-982 "RPTAST.spad" 1497754 1497762 1498041 1498046) (-981 "RPOLCAT.spad" 1477259 1477273 1497622 1497749) (-980 "RPOLCAT.spad" 1456557 1456573 1476922 1476927) (-979 "ROMAN.spad" 1455886 1455894 1456423 1456552) (-978 "ROIRC.spad" 1454967 1454998 1455876 1455881) (-977 "RNS.spad" 1453944 1453952 1454869 1454962) (-976 "RNS.spad" 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"REAL0.spad" 1398567 1398581 1401712 1401717) (-937 "REAL.spad" 1398440 1398448 1398557 1398562) (-936 "RDUCEAST.spad" 1398162 1398170 1398430 1398435) (-935 "RDIV.spad" 1397818 1397842 1398152 1398157) (-934 "RDIST.spad" 1397386 1397396 1397808 1397813) (-933 "RDETRS.spad" 1396251 1396268 1397376 1397381) (-932 "RDETR.spad" 1394391 1394408 1396241 1396246) (-931 "RDEEFS.spad" 1393491 1393507 1394381 1394386) (-930 "RDEEF.spad" 1392502 1392518 1393481 1393486) (-929 "RCFIELD.spad" 1389721 1389729 1392404 1392497) (-928 "RCFIELD.spad" 1387026 1387036 1389711 1389716) (-927 "RCAGG.spad" 1384963 1384973 1387016 1387021) (-926 "RCAGG.spad" 1382801 1382813 1384856 1384861) (-925 "RATRET.spad" 1382162 1382172 1382791 1382796) (-924 "RATFACT.spad" 1381855 1381866 1382152 1382157) (-923 "RANDSRC.spad" 1381175 1381183 1381845 1381850) (-922 "RADUTIL.spad" 1380932 1380940 1381165 1381170) (-921 "RADIX.spad" 1377977 1377990 1379522 1379615) (-920 "RADFF.spad" 1375894 1375930 1376012 1376168) (-919 "RADCAT.spad" 1375490 1375498 1375884 1375889) (-918 "RADCAT.spad" 1375084 1375094 1375480 1375485) (-917 "QUEUE.spad" 1374520 1374530 1374778 1374783) (-916 "QUATCT2.spad" 1374141 1374159 1374510 1374515) (-915 "QUATCAT.spad" 1372312 1372322 1374071 1374136) (-914 "QUATCAT.spad" 1370248 1370260 1372009 1372014) (-913 "QUAT.spad" 1368855 1368865 1369197 1369262) (-912 "QUAGG.spad" 1367711 1367721 1368845 1368850) (-911 "QQUTAST.spad" 1367480 1367488 1367701 1367706) (-910 "QFORM.spad" 1367099 1367113 1367470 1367475) (-909 "QFCAT2.spad" 1366792 1366808 1367089 1367094) (-908 "QFCAT.spad" 1365495 1365505 1366694 1366787) (-907 "QFCAT.spad" 1363831 1363843 1365032 1365037) (-906 "QEQUAT.spad" 1363390 1363398 1363821 1363826) (-905 "QCMPACK.spad" 1358305 1358324 1363380 1363385) (-904 "QALGSET2.spad" 1356301 1356319 1358295 1358300) (-903 "QALGSET.spad" 1352406 1352438 1356215 1356220) (-902 "PWFFINTB.spad" 1349822 1349843 1352396 1352401) (-901 "PUSHVAR.spad" 1349161 1349180 1349812 1349817) (-900 "PTRANFN.spad" 1345297 1345307 1349151 1349156) (-899 "PTPACK.spad" 1342385 1342395 1345287 1345292) (-898 "PTFUNC2.spad" 1342208 1342222 1342375 1342380) (-897 "PTCAT.spad" 1341485 1341495 1342198 1342203) (-896 "PSQFR.spad" 1340800 1340824 1341475 1341480) (-895 "PSEUDLIN.spad" 1339686 1339696 1340790 1340795) (-894 "PSETPK.spad" 1326391 1326407 1339564 1339569) (-893 "PSETCAT.spad" 1320801 1320824 1326381 1326386) (-892 "PSETCAT.spad" 1315175 1315200 1320757 1320762) (-891 "PSCURVE.spad" 1314174 1314182 1315165 1315170) (-890 "PSCAT.spad" 1312957 1312986 1314072 1314169) (-889 "PSCAT.spad" 1311830 1311861 1312947 1312952) (-888 "PRTITION.spad" 1310528 1310536 1311820 1311825) (-887 "PRTDAST.spad" 1310247 1310255 1310518 1310523) (-886 "PRS.spad" 1299865 1299882 1310203 1310208) (-885 "PRQAGG.spad" 1299322 1299332 1299855 1299860) (-884 "PROPLOG.spad" 1298926 1298934 1299312 1299317) (-883 "PROPFUN2.spad" 1298549 1298562 1298916 1298921) (-882 "PROPFUN1.spad" 1297955 1297966 1298539 1298544) (-881 "PROPFRML.spad" 1296523 1296534 1297945 1297950) (-880 "PROPERTY.spad" 1296019 1296027 1296513 1296518) (-879 "PRODUCT.spad" 1293716 1293728 1294000 1294055) (-878 "PRINT.spad" 1293468 1293476 1293706 1293711) (-877 "PRIMES.spad" 1291729 1291739 1293458 1293463) (-876 "PRIMELT.spad" 1289850 1289864 1291719 1291724) (-875 "PRIMCAT.spad" 1289493 1289501 1289840 1289845) (-874 "PRIMARR2.spad" 1288260 1288272 1289483 1289488) (-873 "PRIMARR.spad" 1287012 1287022 1287182 1287187) (-872 "PREASSOC.spad" 1286394 1286406 1287002 1287007) (-871 "PR.spad" 1284912 1284924 1285611 1285738) (-870 "PPCURVE.spad" 1284049 1284057 1284902 1284907) (-869 "PORTNUM.spad" 1283840 1283848 1284039 1284044) (-868 "POLYROOT.spad" 1282689 1282711 1283796 1283801) (-867 "POLYLIFT.spad" 1281954 1281977 1282679 1282684) (-866 "POLYCATQ.spad" 1280080 1280102 1281944 1281949) (-865 "POLYCAT.spad" 1273582 1273603 1279948 1280075) (-864 "POLYCAT.spad" 1266604 1266627 1272972 1272977) (-863 "POLY2UP.spad" 1266056 1266070 1266594 1266599) (-862 "POLY2.spad" 1265653 1265665 1266046 1266051) (-861 "POLY.spad" 1263321 1263331 1263836 1263963) (-860 "POLUTIL.spad" 1262286 1262315 1263277 1263282) (-859 "POLTOPOL.spad" 1261034 1261049 1262276 1262281) (-858 "POINT.spad" 1259614 1259624 1259701 1259706) (-857 "PNTHEORY.spad" 1256316 1256324 1259604 1259609) (-856 "PMTOOLS.spad" 1255091 1255105 1256306 1256311) (-855 "PMSYM.spad" 1254640 1254650 1255081 1255086) (-854 "PMQFCAT.spad" 1254231 1254245 1254630 1254635) (-853 "PMPREDFS.spad" 1253693 1253715 1254221 1254226) (-852 "PMPRED.spad" 1253180 1253194 1253683 1253688) (-851 "PMPLCAT.spad" 1252257 1252275 1253109 1253114) (-850 "PMLSAGG.spad" 1251842 1251856 1252247 1252252) (-849 "PMKERNEL.spad" 1251421 1251433 1251832 1251837) (-848 "PMINS.spad" 1251001 1251011 1251411 1251416) (-847 "PMFS.spad" 1250578 1250596 1250991 1250996) (-846 "PMDOWN.spad" 1249868 1249882 1250568 1250573) (-845 "PMASSFS.spad" 1248843 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(-769 "ORTHPOL.spad" 1130296 1130306 1131728 1131733) (-768 "OREUP.spad" 1129790 1129818 1130017 1130056) (-767 "ORESUP.spad" 1129132 1129156 1129511 1129550) (-766 "OREPCTO.spad" 1127021 1127033 1129052 1129057) (-765 "OREPCAT.spad" 1121208 1121218 1126977 1127016) (-764 "OREPCAT.spad" 1115285 1115297 1121056 1121061) (-763 "ORDTYPE.spad" 1114522 1114530 1115275 1115280) (-762 "ORDTYPE.spad" 1113757 1113767 1114512 1114517) (-761 "ORDSTRCT.spad" 1113543 1113558 1113706 1113711) (-760 "ORDSET.spad" 1113243 1113251 1113533 1113538) (-759 "ORDRING.spad" 1113060 1113068 1113223 1113238) (-758 "ORDMON.spad" 1112915 1112923 1113050 1113055) (-757 "ORDFUNS.spad" 1112047 1112063 1112905 1112910) (-756 "ORDFIN.spad" 1111867 1111875 1112037 1112042) (-755 "ORDCOMP2.spad" 1111160 1111172 1111857 1111862) (-754 "ORDCOMP.spad" 1109686 1109696 1110768 1110797) (-753 "OPSIG.spad" 1109348 1109356 1109676 1109681) (-752 "OPQUERY.spad" 1108929 1108937 1109338 1109343) (-751 "OPERCAT.spad" 1108395 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(-633 "MATLIN.spad" 937939 937963 940455 940460) (-632 "MATCAT2.spad" 937221 937269 937929 937934) (-631 "MATCAT.spad" 928939 928961 937211 937216) (-630 "MATCAT.spad" 920507 920531 928781 928786) (-629 "MAPPKG3.spad" 919422 919436 920497 920502) (-628 "MAPPKG2.spad" 918760 918772 919412 919417) (-627 "MAPPKG1.spad" 917588 917598 918750 918755) (-626 "MAPPAST.spad" 916927 916935 917578 917583) (-625 "MAPHACK3.spad" 916739 916753 916917 916922) (-624 "MAPHACK2.spad" 916508 916520 916729 916734) (-623 "MAPHACK1.spad" 916152 916162 916498 916503) (-622 "MAGMA.spad" 913958 913975 916142 916147) (-621 "MACROAST.spad" 913553 913561 913948 913953) (-620 "LZSTAGG.spad" 910807 910817 913543 913548) (-619 "LZSTAGG.spad" 908059 908071 910797 910802) (-618 "LWORD.spad" 904804 904821 908049 908054) (-617 "LSTAST.spad" 904588 904596 904794 904799) (-616 "LSQM.spad" 902878 902892 903272 903311) (-615 "LSPP.spad" 902413 902430 902868 902873) (-614 "LSMP1.spad" 900256 900270 902403 902408) (-613 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((-1168 . -592) 197621) ((-1168 . -590) 197495) ((-1168 . -972) T) ((-1168 . -1027) T) ((-1168 . -1063) T) ((-1168 . -665) T) ((-1168 . -963) T) ((-1168 . -82) 197345) ((-1168 . -965) 197234) ((-1168 . -970) 197123) ((-1168 . -21) T) ((-1168 . -23) T) ((-1168 . -1015) T) ((-1168 . -554) 197105) ((-1168 . -1131) T) ((-1168 . -13) T) ((-1168 . -72) T) ((-1168 . -25) T) ((-1168 . -104) T) ((-1168 . -584) 196962) ((-1168 . -656) 196819) ((-1168 . -118) 196780) ((-1168 . -120) 196741) ((-1168 . -146) T) ((-1168 . -381) 196707) ((-1168 . -497) T) ((-1168 . -246) T) ((-1168 . -47) 196651) ((-1167 . -1166) 196630) ((-1167 . -312) 196609) ((-1167 . -1136) 196588) ((-1167 . -834) 196567) ((-1167 . -497) 196521) ((-1167 . -146) 196455) ((-1167 . -557) 196274) ((-1167 . -656) 196121) ((-1167 . -584) 195968) ((-1167 . -38) 195815) ((-1167 . -393) 195794) ((-1167 . -258) 195773) ((-1167 . -592) 195673) ((-1167 . -590) 195558) ((-1167 . -972) T) ((-1167 . -1027) T) ((-1167 . -1063) T) ((-1167 . -665) T) ((-1167 . -963) T) ((-1167 . -82) 195378) ((-1167 . -965) 195219) ((-1167 . -970) 195060) ((-1167 . -21) T) ((-1167 . -23) T) ((-1167 . -1015) T) ((-1167 . -554) 195042) ((-1167 . -1131) T) ((-1167 . -13) T) ((-1167 . -72) T) ((-1167 . -25) T) ((-1167 . -104) T) ((-1167 . -246) 194996) ((-1167 . -201) 194975) ((-1167 . -917) 194941) ((-1167 . -1117) 194907) ((-1167 . -1120) 194873) ((-1167 . -434) 194839) ((-1167 . -239) 194805) ((-1167 . -66) 194771) ((-1167 . -35) 194737) ((-1167 . -1160) 194707) ((-1167 . -47) 194677) ((-1167 . -381) 194661) ((-1167 . -120) 194640) ((-1167 . -118) 194619) ((-1167 . -888) 194582) ((-1167 . -813) 194488) ((-1167 . -808) 194392) ((-1167 . -811) 194298) ((-1167 . -241) 194256) ((-1167 . -189) 194208) ((-1167 . -186) 194154) ((-1167 . -190) 194106) ((-1167 . -1164) 194090) ((-1167 . -952) 194074) ((-1162 . -1166) 194035) ((-1162 . -312) 194014) ((-1162 . -1136) 193993) ((-1162 . -834) 193972) ((-1162 . -497) 193926) ((-1162 . -146) 193860) ((-1162 . -557) 193609) ((-1162 . -656) 193456) ((-1162 . -584) 193303) ((-1162 . -38) 193150) ((-1162 . -393) 193129) ((-1162 . -258) 193108) ((-1162 . -592) 193008) ((-1162 . -590) 192893) ((-1162 . -972) T) ((-1162 . -1027) T) ((-1162 . -1063) T) ((-1162 . -665) T) ((-1162 . -963) T) ((-1162 . -82) 192713) ((-1162 . -965) 192554) ((-1162 . -970) 192395) ((-1162 . -21) T) ((-1162 . -23) T) ((-1162 . -1015) T) ((-1162 . -554) 192377) ((-1162 . -1131) T) ((-1162 . -13) T) ((-1162 . -72) T) ((-1162 . -25) T) ((-1162 . -104) T) ((-1162 . -246) 192331) ((-1162 . -201) 192310) ((-1162 . -917) 192276) ((-1162 . -1117) 192242) ((-1162 . -1120) 192208) ((-1162 . -434) 192174) ((-1162 . -239) 192140) ((-1162 . -66) 192106) ((-1162 . -35) 192072) ((-1162 . -1160) 192042) ((-1162 . -47) 192012) ((-1162 . -381) 191996) ((-1162 . -120) 191975) ((-1162 . -118) 191954) ((-1162 . -888) 191917) ((-1162 . -813) 191823) ((-1162 . -808) 191704) ((-1162 . -811) 191610) ((-1162 . -241) 191568) ((-1162 . -189) 191520) ((-1162 . -186) 191466) ((-1162 . -190) 191418) ((-1162 . -1164) 191402) ((-1162 . -952) 191337) ((-1150 . -1157) 191321) ((-1150 . -1068) 191299) ((-1150 . -555) NIL) ((-1150 . -260) 191286) ((-1150 . -457) 191234) ((-1150 . -277) 191211) ((-1150 . -952) 191094) ((-1150 . -355) 191078) ((-1150 . -38) 190910) ((-1150 . -82) 190715) ((-1150 . -965) 190541) ((-1150 . -970) 190367) ((-1150 . -590) 190277) ((-1150 . -592) 190166) ((-1150 . -584) 189998) ((-1150 . -656) 189830) ((-1150 . -557) 189586) ((-1150 . -118) 189565) ((-1150 . -120) 189544) ((-1150 . -381) 189528) ((-1150 . -47) 189505) ((-1150 . -329) 189489) ((-1150 . -582) 189437) ((-1150 . -811) 189381) ((-1150 . -808) 189288) ((-1150 . -813) 189199) ((-1150 . -798) NIL) ((-1150 . -823) 189178) ((-1150 . -1136) 189157) ((-1150 . -863) 189127) ((-1150 . -834) 189106) ((-1150 . -497) 189020) ((-1150 . -246) 188934) ((-1150 . -146) 188828) ((-1150 . -393) 188762) ((-1150 . -258) 188741) ((-1150 . -241) 188668) ((-1150 . -190) T) ((-1150 . -104) T) ((-1150 . -25) T) ((-1150 . -72) T) ((-1150 . -554) 188650) ((-1150 . -1015) T) ((-1150 . -23) T) ((-1150 . -21) T) ((-1150 . -972) T) ((-1150 . -1027) T) ((-1150 . -1063) T) ((-1150 . -665) T) ((-1150 . -963) T) ((-1150 . -186) 188637) ((-1150 . -13) T) ((-1150 . -1131) T) ((-1150 . -189) T) ((-1150 . -225) 188621) ((-1150 . -184) 188605) ((-1148 . -1008) 188589) ((-1148 . -559) 188573) ((-1148 . -1015) 188551) ((-1148 . -554) 188518) ((-1148 . -1131) 188496) ((-1148 . -13) 188474) ((-1148 . -72) 188452) ((-1148 . -1009) 188409) ((-1146 . -1145) 188388) ((-1146 . -917) 188354) ((-1146 . -1117) 188320) ((-1146 . -1120) 188286) ((-1146 . -434) 188252) ((-1146 . -239) 188218) ((-1146 . -66) 188184) ((-1146 . -35) 188150) ((-1146 . -1160) 188127) ((-1146 . -47) 188104) ((-1146 . -381) 188061) ((-1146 . -557) 187816) ((-1146 . -656) 187636) ((-1146 . -584) 187456) ((-1146 . -592) 187267) ((-1146 . -590) 187125) ((-1146 . -970) 186939) ((-1146 . -965) 186753) ((-1146 . -82) 186541) ((-1146 . -38) 186361) ((-1146 . -888) 186331) ((-1146 . -241) 186231) ((-1146 . -1143) 186215) ((-1146 . -972) T) ((-1146 . -1027) T) ((-1146 . -1063) T) ((-1146 . -665) T) ((-1146 . -963) T) ((-1146 . -21) T) ((-1146 . -23) T) ((-1146 . -1015) T) ((-1146 . -554) 186197) ((-1146 . -1131) T) ((-1146 . -13) T) ((-1146 . -72) T) ((-1146 . -25) T) ((-1146 . -104) T) ((-1146 . -118) 186125) ((-1146 . -120) 186007) ((-1146 . -555) 185680) ((-1146 . -184) 185650) ((-1146 . -811) 185504) ((-1146 . -813) 185304) ((-1146 . -808) 185102) ((-1146 . -225) 185072) ((-1146 . -189) 184934) ((-1146 . -186) 184790) ((-1146 . -190) 184698) ((-1146 . -312) 184677) ((-1146 . -1136) 184656) ((-1146 . -834) 184635) ((-1146 . -497) 184589) ((-1146 . -146) 184523) ((-1146 . -393) 184502) ((-1146 . -258) 184481) ((-1146 . -246) 184435) ((-1146 . -201) 184414) ((-1146 . -288) 184384) ((-1146 . -457) 184244) ((-1146 . -260) 184183) ((-1146 . -329) 184153) ((-1146 . -582) 184061) ((-1146 . -343) 184031) ((-1146 . -798) 183904) ((-1146 . -742) 183857) ((-1146 . -716) 183810) ((-1146 . -718) 183763) ((-1146 . -758) 183665) ((-1146 . -761) 183567) ((-1146 . -720) 183520) ((-1146 . -723) 183473) ((-1146 . -757) 183426) ((-1146 . -796) 183396) ((-1146 . -823) 183349) ((-1146 . -935) 183302) ((-1146 . -952) 183091) ((-1146 . -1068) 183043) ((-1146 . -906) 183013) ((-1141 . -1145) 182974) ((-1141 . -917) 182940) ((-1141 . -1117) 182906) ((-1141 . -1120) 182872) ((-1141 . -434) 182838) ((-1141 . -239) 182804) ((-1141 . -66) 182770) ((-1141 . -35) 182736) ((-1141 . -1160) 182713) ((-1141 . -47) 182690) ((-1141 . -381) 182629) ((-1141 . -557) 182430) ((-1141 . -656) 182232) ((-1141 . -584) 182034) ((-1141 . -592) 181889) ((-1141 . -590) 181729) ((-1141 . -970) 181525) ((-1141 . -965) 181321) ((-1141 . -82) 181073) ((-1141 . -38) 180875) ((-1141 . -888) 180845) ((-1141 . -241) 180673) ((-1141 . -1143) 180657) ((-1141 . -972) T) ((-1141 . -1027) T) ((-1141 . -1063) T) ((-1141 . -665) T) ((-1141 . -963) T) ((-1141 . -21) T) ((-1141 . -23) T) ((-1141 . -1015) T) ((-1141 . -554) 180639) ((-1141 . -1131) T) ((-1141 . -13) T) ((-1141 . -72) T) ((-1141 . -25) T) ((-1141 . -104) T) ((-1141 . -118) 180549) ((-1141 . -120) 180459) ((-1141 . -555) NIL) ((-1141 . -184) 180411) ((-1141 . -811) 180247) ((-1141 . -813) 180011) ((-1141 . -808) 179750) ((-1141 . -225) 179702) ((-1141 . -189) 179528) ((-1141 . -186) 179348) ((-1141 . -190) 179238) ((-1141 . -312) 179217) ((-1141 . -1136) 179196) ((-1141 . -834) 179175) ((-1141 . -497) 179129) ((-1141 . -146) 179063) ((-1141 . -393) 179042) ((-1141 . -258) 179021) ((-1141 . -246) 178975) ((-1141 . -201) 178954) ((-1141 . -288) 178906) ((-1141 . -457) 178640) ((-1141 . -260) 178525) ((-1141 . -329) 178477) ((-1141 . -582) 178429) ((-1141 . -343) 178381) ((-1141 . -798) NIL) ((-1141 . -742) NIL) ((-1141 . -716) NIL) ((-1141 . -718) NIL) ((-1141 . -758) NIL) ((-1141 . -761) NIL) ((-1141 . -720) NIL) ((-1141 . -723) NIL) ((-1141 . -757) NIL) ((-1141 . -796) 178333) ((-1141 . -823) NIL) ((-1141 . -935) NIL) ((-1141 . -952) 178299) ((-1141 . -1068) NIL) ((-1141 . -906) 178251) ((-1140 . -754) T) ((-1140 . -761) T) ((-1140 . -758) T) ((-1140 . -1015) T) ((-1140 . -554) 178233) ((-1140 . -1131) T) ((-1140 . -13) T) ((-1140 . -72) T) ((-1140 . -320) T) ((-1140 . -606) T) ((-1139 . -754) T) ((-1139 . -761) T) ((-1139 . -758) T) ((-1139 . -1015) T) ((-1139 . -554) 178215) ((-1139 . -1131) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -320) T) ((-1139 . -606) T) ((-1138 . -754) T) ((-1138 . -761) T) ((-1138 . -758) T) ((-1138 . -1015) T) ((-1138 . -554) 178197) ((-1138 . -1131) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -320) T) ((-1138 . -606) T) ((-1137 . -754) T) ((-1137 . -761) T) ((-1137 . -758) T) ((-1137 . -1015) T) ((-1137 . -554) 178179) ((-1137 . -1131) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -320) T) ((-1137 . -606) T) ((-1132 . -997) T) ((-1132 . -431) 178160) ((-1132 . -554) 178126) ((-1132 . -557) 178107) ((-1132 . -1015) T) ((-1132 . -1131) T) ((-1132 . -13) T) ((-1132 . -72) T) ((-1132 . -64) T) ((-1129 . -431) 178084) ((-1129 . -554) 178025) ((-1129 . -557) 178002) ((-1129 . -1015) 177980) ((-1129 . -1131) 177958) ((-1129 . -13) 177936) ((-1129 . -72) 177914) ((-1124 . -681) 177890) ((-1124 . -35) 177856) ((-1124 . -66) 177822) ((-1124 . -239) 177788) ((-1124 . -434) 177754) ((-1124 . -1120) 177720) ((-1124 . -1117) 177686) ((-1124 . -917) 177652) ((-1124 . -47) 177621) ((-1124 . -38) 177518) ((-1124 . -584) 177415) ((-1124 . -656) 177312) ((-1124 . -557) 177194) ((-1124 . -246) 177173) ((-1124 . -497) 177152) ((-1124 . -381) 177136) ((-1124 . -82) 177001) ((-1124 . -965) 176887) ((-1124 . -970) 176773) ((-1124 . -146) 176727) ((-1124 . -120) 176706) ((-1124 . -118) 176685) ((-1124 . -592) 176610) ((-1124 . -590) 176520) ((-1124 . -888) 176481) ((-1124 . -813) 176462) ((-1124 . -1131) T) ((-1124 . -13) T) ((-1124 . -808) 176441) ((-1124 . -963) T) ((-1124 . -665) T) ((-1124 . -1063) T) ((-1124 . -1027) T) ((-1124 . -972) T) ((-1124 . -21) T) ((-1124 . -23) T) ((-1124 . -1015) T) ((-1124 . -554) 176423) ((-1124 . -72) T) ((-1124 . -25) T) ((-1124 . -104) T) ((-1124 . -811) 176404) ((-1124 . -457) 176371) ((-1124 . -260) 176358) ((-1118 . -925) 176342) ((-1118 . -34) T) ((-1118 . -13) T) ((-1118 . -1131) T) ((-1118 . -72) 176296) ((-1118 . -554) 176231) ((-1118 . -260) 176169) ((-1118 . -457) 176102) ((-1118 . -381) 176086) ((-1118 . -1015) 176064) ((-1118 . -430) 176048) ((-1118 . -318) 176032) ((-1118 . -1037) 176016) ((-1113 . -314) 175990) ((-1113 . -72) T) ((-1113 . -13) T) ((-1113 . -1131) T) ((-1113 . -554) 175972) ((-1113 . -1015) T) ((-1111 . -1015) T) ((-1111 . -554) 175954) ((-1111 . -1131) T) ((-1111 . -13) T) ((-1111 . -72) T) ((-1111 . -557) 175936) ((-1106 . -749) 175920) ((-1106 . -72) T) ((-1106 . -13) T) ((-1106 . -1131) T) ((-1106 . -554) 175902) ((-1106 . -1015) T) ((-1104 . -1109) 175881) ((-1104 . -183) 175829) ((-1104 . -76) 175777) ((-1104 . -1037) 175712) ((-1104 . -124) 175660) ((-1104 . -555) NIL) ((-1104 . -193) 175608) ((-1104 . -540) 175587) ((-1104 . -260) 175385) ((-1104 . -457) 175137) ((-1104 . -381) 175072) ((-1104 . -430) 175007) ((-1104 . -241) 174986) ((-1104 . -243) 174965) ((-1104 . -551) 174944) ((-1104 . -1015) T) ((-1104 . -554) 174926) ((-1104 . -72) T) ((-1104 . -1131) T) ((-1104 . -13) T) ((-1104 . -34) T) ((-1104 . -318) 174874) ((-1100 . -1015) T) ((-1100 . -554) 174856) ((-1100 . -1131) T) ((-1100 . -13) T) ((-1100 . -72) T) ((-1099 . -754) T) ((-1099 . -761) T) ((-1099 . -758) T) ((-1099 . -1015) T) ((-1099 . -554) 174838) ((-1099 . -1131) T) ((-1099 . -13) T) ((-1099 . -72) T) ((-1099 . -320) T) ((-1099 . -606) T) ((-1098 . -754) T) ((-1098 . -761) T) ((-1098 . -758) T) ((-1098 . -1015) T) ((-1098 . -554) 174820) ((-1098 . -1131) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1098 . -320) T) ((-1097 . -1177) T) ((-1097 . -1015) T) ((-1097 . -554) 174787) ((-1097 . -1131) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -952) 174723) ((-1097 . -557) 174659) ((-1096 . -554) 174641) ((-1095 . -554) 174623) ((-1094 . -277) 174600) ((-1094 . -952) 174498) ((-1094 . -355) 174482) ((-1094 . -38) 174379) ((-1094 . -557) 174236) ((-1094 . -592) 174161) ((-1094 . -590) 174071) ((-1094 . -972) T) ((-1094 . -1027) T) ((-1094 . -1063) T) ((-1094 . -665) T) ((-1094 . -963) T) ((-1094 . -82) 173936) ((-1094 . -965) 173822) ((-1094 . -970) 173708) ((-1094 . -21) T) ((-1094 . -23) T) ((-1094 . -1015) T) ((-1094 . -554) 173690) ((-1094 . -1131) T) ((-1094 . -13) T) ((-1094 . -72) T) ((-1094 . -25) T) ((-1094 . -104) T) ((-1094 . -584) 173587) ((-1094 . -656) 173484) ((-1094 . -118) 173463) ((-1094 . -120) 173442) ((-1094 . -146) 173396) ((-1094 . -381) 173380) ((-1094 . -497) 173359) ((-1094 . -246) 173338) ((-1094 . -47) 173315) ((-1092 . -758) T) ((-1092 . -554) 173297) ((-1092 . -1015) T) ((-1092 . -72) T) ((-1092 . -13) T) ((-1092 . -1131) T) ((-1092 . -761) T) ((-1092 . -555) 173219) ((-1092 . -557) 173185) ((-1092 . -952) 173167) ((-1092 . -798) 173134) ((-1091 . -1174) 173118) ((-1091 . -190) 173077) ((-1091 . -557) 172959) ((-1091 . -592) 172884) ((-1091 . -590) 172794) ((-1091 . -104) T) ((-1091 . -25) T) ((-1091 . -72) T) ((-1091 . -554) 172776) ((-1091 . -1015) T) ((-1091 . -23) T) ((-1091 . -21) T) ((-1091 . -972) T) ((-1091 . -1027) T) ((-1091 . -1063) T) ((-1091 . -665) T) ((-1091 . -963) T) ((-1091 . -186) 172729) ((-1091 . -13) T) ((-1091 . -1131) T) ((-1091 . -189) 172688) ((-1091 . -241) 172653) ((-1091 . -811) 172566) ((-1091 . -808) 172454) ((-1091 . -813) 172367) ((-1091 . -888) 172337) ((-1091 . -38) 172234) ((-1091 . -82) 172099) ((-1091 . -965) 171985) ((-1091 . -970) 171871) ((-1091 . -584) 171768) ((-1091 . -656) 171665) ((-1091 . -118) 171644) ((-1091 . -120) 171623) ((-1091 . -146) 171577) ((-1091 . -381) 171561) ((-1091 . -497) 171540) ((-1091 . -246) 171519) ((-1091 . -47) 171496) ((-1091 . -1160) 171473) ((-1091 . -35) 171439) ((-1091 . -66) 171405) ((-1091 . -239) 171371) ((-1091 . -434) 171337) ((-1091 . -1120) 171303) ((-1091 . -1117) 171269) ((-1091 . -917) 171235) ((-1090 . -1166) 171196) ((-1090 . -312) 171175) ((-1090 . -1136) 171154) ((-1090 . -834) 171133) ((-1090 . -497) 171087) ((-1090 . -146) 171021) ((-1090 . -557) 170770) ((-1090 . -656) 170617) ((-1090 . -584) 170464) ((-1090 . -38) 170311) ((-1090 . -393) 170290) ((-1090 . -258) 170269) ((-1090 . -592) 170169) ((-1090 . -590) 170054) ((-1090 . -972) T) ((-1090 . -1027) T) ((-1090 . -1063) T) ((-1090 . -665) T) ((-1090 . -963) T) ((-1090 . -82) 169874) ((-1090 . -965) 169715) ((-1090 . -970) 169556) ((-1090 . -21) T) ((-1090 . -23) T) ((-1090 . -1015) T) ((-1090 . -554) 169538) ((-1090 . -1131) T) ((-1090 . -13) T) ((-1090 . -72) T) ((-1090 . -25) T) ((-1090 . -104) T) ((-1090 . -246) 169492) ((-1090 . -201) 169471) ((-1090 . -917) 169437) ((-1090 . -1117) 169403) ((-1090 . -1120) 169369) ((-1090 . -434) 169335) ((-1090 . -239) 169301) ((-1090 . -66) 169267) ((-1090 . -35) 169233) ((-1090 . -1160) 169203) ((-1090 . -47) 169173) ((-1090 . -381) 169157) ((-1090 . -120) 169136) ((-1090 . -118) 169115) ((-1090 . -888) 169078) ((-1090 . -813) 168984) ((-1090 . -808) 168865) ((-1090 . -811) 168771) ((-1090 . -241) 168729) ((-1090 . -189) 168681) ((-1090 . -186) 168627) ((-1090 . -190) 168579) ((-1090 . -1164) 168563) ((-1090 . -952) 168498) ((-1087 . -1157) 168482) ((-1087 . -1068) 168460) ((-1087 . -555) NIL) ((-1087 . -260) 168447) ((-1087 . -457) 168395) ((-1087 . -277) 168372) ((-1087 . -952) 168255) ((-1087 . -355) 168239) ((-1087 . -38) 168071) ((-1087 . -82) 167876) ((-1087 . -965) 167702) ((-1087 . -970) 167528) ((-1087 . -590) 167438) ((-1087 . -592) 167327) ((-1087 . -584) 167159) ((-1087 . -656) 166991) ((-1087 . -557) 166768) ((-1087 . -118) 166747) ((-1087 . -120) 166726) ((-1087 . -381) 166710) ((-1087 . -47) 166687) ((-1087 . -329) 166671) ((-1087 . -582) 166619) ((-1087 . -811) 166563) ((-1087 . -808) 166470) ((-1087 . -813) 166381) ((-1087 . -798) NIL) ((-1087 . -823) 166360) ((-1087 . -1136) 166339) ((-1087 . -863) 166309) ((-1087 . -834) 166288) ((-1087 . -497) 166202) ((-1087 . -246) 166116) ((-1087 . -146) 166010) ((-1087 . -393) 165944) ((-1087 . -258) 165923) ((-1087 . -241) 165850) ((-1087 . -190) T) ((-1087 . -104) T) ((-1087 . -25) T) ((-1087 . -72) T) ((-1087 . -554) 165832) ((-1087 . -1015) T) ((-1087 . -23) T) ((-1087 . -21) T) ((-1087 . -972) T) ((-1087 . -1027) T) ((-1087 . -1063) T) ((-1087 . -665) T) ((-1087 . -963) T) ((-1087 . -186) 165819) ((-1087 . -13) T) ((-1087 . -1131) T) ((-1087 . -189) T) ((-1087 . -225) 165803) ((-1087 . -184) 165787) ((-1084 . -1145) 165748) ((-1084 . -917) 165714) ((-1084 . -1117) 165680) ((-1084 . -1120) 165646) ((-1084 . -434) 165612) ((-1084 . -239) 165578) ((-1084 . -66) 165544) ((-1084 . -35) 165510) ((-1084 . -1160) 165487) ((-1084 . -47) 165464) ((-1084 . -381) 165403) ((-1084 . -557) 165204) ((-1084 . -656) 165006) ((-1084 . -584) 164808) ((-1084 . -592) 164663) ((-1084 . -590) 164503) ((-1084 . -970) 164299) ((-1084 . -965) 164095) ((-1084 . -82) 163847) ((-1084 . -38) 163649) ((-1084 . -888) 163619) ((-1084 . -241) 163447) ((-1084 . -1143) 163431) ((-1084 . -972) T) ((-1084 . -1027) T) ((-1084 . -1063) T) ((-1084 . -665) T) ((-1084 . -963) T) ((-1084 . -21) T) ((-1084 . -23) T) ((-1084 . -1015) T) ((-1084 . -554) 163413) ((-1084 . -1131) T) ((-1084 . -13) T) ((-1084 . -72) T) ((-1084 . -25) T) ((-1084 . -104) T) ((-1084 . -118) 163323) ((-1084 . -120) 163233) ((-1084 . -555) NIL) ((-1084 . -184) 163185) ((-1084 . -811) 163021) ((-1084 . -813) 162785) ((-1084 . -808) 162524) ((-1084 . -225) 162476) ((-1084 . -189) 162302) ((-1084 . -186) 162122) ((-1084 . -190) 162012) ((-1084 . -312) 161991) ((-1084 . -1136) 161970) ((-1084 . -834) 161949) ((-1084 . -497) 161903) ((-1084 . -146) 161837) ((-1084 . -393) 161816) ((-1084 . -258) 161795) ((-1084 . -246) 161749) ((-1084 . -201) 161728) ((-1084 . -288) 161680) ((-1084 . -457) 161414) ((-1084 . -260) 161299) ((-1084 . -329) 161251) ((-1084 . -582) 161203) ((-1084 . -343) 161155) ((-1084 . -798) NIL) ((-1084 . -742) NIL) ((-1084 . -716) NIL) ((-1084 . -718) NIL) ((-1084 . -758) NIL) ((-1084 . -761) NIL) ((-1084 . -720) NIL) ((-1084 . -723) NIL) ((-1084 . -757) NIL) ((-1084 . -796) 161107) ((-1084 . -823) NIL) ((-1084 . -935) NIL) ((-1084 . -952) 161073) ((-1084 . -1068) NIL) ((-1084 . -906) 161025) ((-1083 . -997) T) ((-1083 . -431) 161006) ((-1083 . -554) 160972) ((-1083 . -557) 160953) ((-1083 . -1015) T) ((-1083 . -1131) T) ((-1083 . -13) T) ((-1083 . -72) T) ((-1083 . -64) T) ((-1082 . -1015) T) ((-1082 . -554) 160935) ((-1082 . -1131) T) ((-1082 . -13) T) ((-1082 . -72) T) ((-1081 . -1015) T) ((-1081 . -554) 160917) ((-1081 . -1131) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1076 . -1109) 160893) ((-1076 . -183) 160838) ((-1076 . -76) 160783) ((-1076 . -1037) 160715) ((-1076 . -124) 160660) ((-1076 . -555) NIL) ((-1076 . -193) 160605) ((-1076 . -540) 160581) ((-1076 . -260) 160370) ((-1076 . -457) 160110) ((-1076 . -381) 160042) ((-1076 . -430) 159974) ((-1076 . -241) 159950) ((-1076 . -243) 159926) ((-1076 . -551) 159902) ((-1076 . -1015) T) ((-1076 . -554) 159884) ((-1076 . -72) T) ((-1076 . -1131) T) ((-1076 . -13) T) ((-1076 . -34) T) ((-1076 . -318) 159829) ((-1075 . -1060) T) ((-1075 . -324) 159811) ((-1075 . -761) T) ((-1075 . -758) T) ((-1075 . -124) 159793) ((-1075 . -555) NIL) ((-1075 . -241) 159743) ((-1075 . -540) 159718) ((-1075 . -243) 159693) ((-1075 . -595) 159675) ((-1075 . -430) 159657) ((-1075 . -1015) T) ((-1075 . -381) 159639) ((-1075 . -457) NIL) ((-1075 . -260) NIL) ((-1075 . -554) 159621) ((-1075 . -72) T) ((-1075 . -1131) T) ((-1075 . -13) T) ((-1075 . -34) T) ((-1075 . -318) 159603) ((-1075 . -1037) 159585) ((-1075 . -19) 159567) ((-1071 . -618) 159551) ((-1071 . -595) 159535) ((-1071 . -243) 159512) ((-1071 . -241) 159464) ((-1071 . -540) 159441) ((-1071 . -555) 159402) ((-1071 . -430) 159386) ((-1071 . -1015) 159364) ((-1071 . -381) 159348) ((-1071 . -457) 159281) ((-1071 . -260) 159219) ((-1071 . -554) 159154) ((-1071 . -72) 159108) ((-1071 . -1131) T) ((-1071 . -13) T) ((-1071 . -34) T) ((-1071 . -124) 159092) ((-1071 . -1170) 159076) ((-1071 . -925) 159060) ((-1071 . -1066) 159044) ((-1071 . -557) 159021) ((-1071 . -1037) 159005) ((-1069 . -997) T) ((-1069 . -431) 158986) ((-1069 . -554) 158952) ((-1069 . -557) 158933) ((-1069 . -1015) T) ((-1069 . -1131) T) ((-1069 . -13) T) ((-1069 . -72) T) ((-1069 . -64) T) ((-1067 . -1109) 158912) ((-1067 . -183) 158860) ((-1067 . -76) 158808) ((-1067 . -1037) 158743) ((-1067 . -124) 158691) ((-1067 . -555) NIL) ((-1067 . -193) 158639) ((-1067 . -540) 158618) ((-1067 . -260) 158416) ((-1067 . -457) 158168) ((-1067 . -381) 158103) ((-1067 . -430) 158038) ((-1067 . -241) 158017) ((-1067 . -243) 157996) ((-1067 . -551) 157975) ((-1067 . -1015) T) ((-1067 . -554) 157957) ((-1067 . -72) T) ((-1067 . -1131) T) ((-1067 . -13) T) ((-1067 . -34) T) ((-1067 . -318) 157905) ((-1064 . -1036) 157889) ((-1064 . -318) 157873) ((-1064 . -430) 157857) ((-1064 . -1015) 157835) ((-1064 . -381) 157819) ((-1064 . -457) 157752) ((-1064 . -260) 157690) ((-1064 . -554) 157625) ((-1064 . -72) 157579) ((-1064 . -1131) T) ((-1064 . -13) T) ((-1064 . -34) T) ((-1064 . -1037) 157563) ((-1064 . -76) 157547) ((-1062 . -1022) 157516) ((-1062 . -1126) 157485) ((-1062 . -1037) 157469) ((-1062 . -554) 157431) ((-1062 . -124) 157415) ((-1062 . -34) T) ((-1062 . -13) T) ((-1062 . -1131) T) ((-1062 . -72) T) ((-1062 . -260) 157353) ((-1062 . -457) 157286) ((-1062 . -381) 157270) ((-1062 . -1015) T) ((-1062 . -430) 157254) ((-1062 . -555) 157215) ((-1062 . -318) 157199) ((-1062 . -891) 157168) ((-1062 . -985) 157137) ((-1058 . -1039) 157082) ((-1058 . -318) 157066) ((-1058 . -34) T) ((-1058 . -260) 157004) ((-1058 . -457) 156937) ((-1058 . -381) 156921) ((-1058 . -430) 156905) ((-1058 . -967) 156845) ((-1058 . -952) 156743) ((-1058 . -557) 156662) ((-1058 . -355) 156646) ((-1058 . -582) 156594) ((-1058 . -592) 156532) ((-1058 . -329) 156516) ((-1058 . -190) 156495) ((-1058 . -186) 156443) ((-1058 . -189) 156397) ((-1058 . -225) 156381) ((-1058 . -808) 156305) ((-1058 . -813) 156231) ((-1058 . -811) 156190) ((-1058 . -184) 156174) ((-1058 . -656) 156109) ((-1058 . -584) 156044) ((-1058 . -590) 156003) ((-1058 . -104) T) ((-1058 . -25) T) ((-1058 . -72) T) ((-1058 . -13) T) ((-1058 . -1131) T) ((-1058 . -554) 155965) ((-1058 . -1015) T) ((-1058 . -23) T) ((-1058 . -21) T) ((-1058 . -970) 155949) ((-1058 . -965) 155933) ((-1058 . -82) 155912) ((-1058 . -963) T) ((-1058 . -665) T) ((-1058 . -1063) T) ((-1058 . -1027) T) ((-1058 . -972) T) ((-1058 . -38) 155872) ((-1058 . -555) 155833) ((-1057 . -925) 155804) ((-1057 . -34) T) ((-1057 . -13) T) ((-1057 . -1131) T) ((-1057 . -72) T) ((-1057 . -554) 155786) ((-1057 . -260) 155712) ((-1057 . -457) 155620) ((-1057 . -381) 155591) ((-1057 . -1015) T) ((-1057 . -430) 155562) ((-1057 . -318) 155533) ((-1057 . -1037) 155504) ((-1056 . -1015) T) ((-1056 . -554) 155486) ((-1056 . -1131) T) ((-1056 . -13) T) ((-1056 . -72) T) ((-1051 . -1053) T) ((-1051 . -1177) T) ((-1051 . -64) T) ((-1051 . -72) T) ((-1051 . -13) T) ((-1051 . -1131) T) ((-1051 . -554) 155452) ((-1051 . -1015) T) ((-1051 . -557) 155433) ((-1051 . -431) 155414) ((-1051 . -997) T) ((-1049 . -1050) 155398) ((-1049 . -72) T) ((-1049 . -13) T) ((-1049 . -1131) T) ((-1049 . -554) 155380) ((-1049 . -1015) T) ((-1042 . -681) 155359) ((-1042 . -35) 155325) ((-1042 . -66) 155291) ((-1042 . -239) 155257) ((-1042 . -434) 155223) ((-1042 . -1120) 155189) ((-1042 . -1117) 155155) ((-1042 . -917) 155121) ((-1042 . -47) 155093) ((-1042 . -38) 154990) ((-1042 . -584) 154887) ((-1042 . -656) 154784) ((-1042 . -557) 154666) ((-1042 . -246) 154645) ((-1042 . -497) 154624) ((-1042 . -381) 154608) ((-1042 . -82) 154473) ((-1042 . -965) 154359) ((-1042 . -970) 154245) ((-1042 . -146) 154199) ((-1042 . -120) 154178) ((-1042 . -118) 154157) ((-1042 . -592) 154082) ((-1042 . -590) 153992) ((-1042 . -888) 153959) ((-1042 . -813) 153943) ((-1042 . -1131) T) ((-1042 . -13) T) ((-1042 . -808) 153925) ((-1042 . -963) T) ((-1042 . -665) T) ((-1042 . -1063) T) ((-1042 . -1027) T) ((-1042 . -972) T) ((-1042 . -21) T) ((-1042 . -23) T) ((-1042 . -1015) T) ((-1042 . -554) 153907) ((-1042 . -72) T) ((-1042 . -25) T) ((-1042 . -104) T) ((-1042 . -811) 153891) ((-1042 . -457) 153861) ((-1042 . -260) 153848) ((-1041 . -863) 153815) ((-1041 . -557) 153614) ((-1041 . -952) 153499) ((-1041 . -1136) 153478) ((-1041 . -823) 153457) ((-1041 . -798) 153316) ((-1041 . -813) 153300) ((-1041 . -808) 153282) ((-1041 . -811) 153266) ((-1041 . -457) 153218) ((-1041 . -393) 153172) ((-1041 . -582) 153120) ((-1041 . -592) 153009) ((-1041 . -329) 152993) ((-1041 . -47) 152965) ((-1041 . -38) 152817) ((-1041 . -584) 152669) ((-1041 . -656) 152521) ((-1041 . -246) 152455) ((-1041 . -497) 152389) ((-1041 . -381) 152373) ((-1041 . -82) 152198) ((-1041 . -965) 152044) ((-1041 . -970) 151890) ((-1041 . -146) 151804) ((-1041 . -120) 151783) ((-1041 . -118) 151762) ((-1041 . -590) 151672) ((-1041 . -104) T) ((-1041 . -25) T) ((-1041 . -72) T) ((-1041 . -13) T) ((-1041 . -1131) T) ((-1041 . -554) 151654) ((-1041 . -1015) T) ((-1041 . -23) T) ((-1041 . -21) T) ((-1041 . -963) T) ((-1041 . -665) T) ((-1041 . -1063) T) ((-1041 . -1027) T) ((-1041 . -972) T) ((-1041 . -355) 151638) ((-1041 . -277) 151610) ((-1041 . -260) 151597) ((-1041 . -555) 151345) ((-1035 . -485) T) ((-1035 . -1136) T) ((-1035 . -1068) T) ((-1035 . -952) 151327) ((-1035 . -555) 151242) ((-1035 . -935) T) ((-1035 . -798) 151224) ((-1035 . -757) T) ((-1035 . -723) T) ((-1035 . -720) T) ((-1035 . -761) T) ((-1035 . -758) T) ((-1035 . -718) T) ((-1035 . -716) T) ((-1035 . -742) T) ((-1035 . -592) 151196) ((-1035 . -582) 151178) ((-1035 . -834) T) ((-1035 . -497) T) ((-1035 . -246) T) ((-1035 . -146) T) ((-1035 . -557) 151150) ((-1035 . -656) 151137) ((-1035 . -584) 151124) ((-1035 . -970) 151111) ((-1035 . -965) 151098) ((-1035 . -82) 151083) ((-1035 . -38) 151070) ((-1035 . -393) T) ((-1035 . -258) T) ((-1035 . -189) T) ((-1035 . -186) 151057) ((-1035 . -190) T) ((-1035 . -116) T) ((-1035 . -963) T) ((-1035 . -665) T) ((-1035 . -1063) T) ((-1035 . -1027) T) ((-1035 . -972) T) ((-1035 . -21) T) ((-1035 . -590) 151029) ((-1035 . -23) T) ((-1035 . -1015) T) ((-1035 . -554) 151011) ((-1035 . -1131) T) ((-1035 . -13) T) ((-1035 . -72) T) ((-1035 . -25) T) ((-1035 . -104) T) ((-1035 . -120) T) ((-1035 . -754) T) ((-1035 . -320) T) ((-1035 . -84) T) ((-1035 . -606) T) ((-1031 . -997) T) ((-1031 . -431) 150992) ((-1031 . -554) 150958) ((-1031 . -557) 150939) ((-1031 . -1015) T) ((-1031 . -1131) T) ((-1031 . -13) T) ((-1031 . -72) T) ((-1031 . -64) T) ((-1030 . -1015) T) ((-1030 . -554) 150921) ((-1030 . -1131) T) ((-1030 . -13) T) ((-1030 . -72) T) ((-1028 . -196) 150900) ((-1028 . -1189) 150870) ((-1028 . -723) 150849) ((-1028 . -720) 150828) ((-1028 . -761) 150782) ((-1028 . -758) 150736) ((-1028 . -718) 150715) ((-1028 . -719) 150694) ((-1028 . -656) 150639) ((-1028 . -584) 150564) ((-1028 . -243) 150541) ((-1028 . -241) 150518) ((-1028 . -540) 150495) ((-1028 . -952) 150324) ((-1028 . -557) 150128) ((-1028 . -355) 150097) ((-1028 . -582) 150005) ((-1028 . -592) 149844) ((-1028 . -329) 149814) ((-1028 . -430) 149798) ((-1028 . -381) 149782) ((-1028 . -457) 149715) ((-1028 . -260) 149653) ((-1028 . -34) T) ((-1028 . -318) 149637) ((-1028 . -320) 149616) ((-1028 . -190) 149569) ((-1028 . -590) 149357) ((-1028 . -972) 149336) ((-1028 . -1027) 149315) ((-1028 . -1063) 149294) ((-1028 . -665) 149273) ((-1028 . -963) 149252) ((-1028 . -186) 149148) ((-1028 . -189) 149050) ((-1028 . -225) 149020) ((-1028 . -808) 148892) ((-1028 . -813) 148766) ((-1028 . -811) 148699) ((-1028 . -184) 148669) ((-1028 . -554) 148366) ((-1028 . -970) 148291) ((-1028 . -965) 148196) ((-1028 . -82) 148116) ((-1028 . -104) 147991) ((-1028 . -25) 147828) ((-1028 . -72) 147565) ((-1028 . -13) T) ((-1028 . -1131) T) ((-1028 . -1015) 147321) ((-1028 . -23) 147177) ((-1028 . -21) 147092) ((-1024 . -1025) 147076) ((-1024 . |MappingCategory|) 147050) ((-1024 . -1131) T) ((-1024 . -80) 147034) ((-1024 . -1015) T) ((-1024 . -554) 147016) ((-1024 . -13) T) ((-1024 . -72) T) ((-1019 . -1018) 146980) ((-1019 . -72) T) ((-1019 . -554) 146962) ((-1019 . -1015) T) ((-1019 . -241) 146918) ((-1019 . -1131) T) ((-1019 . -13) T) ((-1019 . -559) 146833) ((-1017 . -1018) 146785) ((-1017 . -72) T) ((-1017 . -554) 146767) ((-1017 . -1015) T) ((-1017 . -241) 146723) ((-1017 . -1131) T) ((-1017 . -13) T) ((-1017 . -559) 146626) ((-1016 . -320) T) ((-1016 . -72) T) ((-1016 . -13) T) ((-1016 . -1131) T) ((-1016 . -554) 146608) ((-1016 . -1015) T) ((-1011 . -369) 146592) ((-1011 . -1013) 146576) ((-1011 . -318) 146560) ((-1011 . -320) 146539) ((-1011 . -193) 146523) ((-1011 . -555) 146484) ((-1011 . -124) 146468) ((-1011 . -430) 146452) ((-1011 . -1015) T) ((-1011 . -381) 146436) ((-1011 . -457) 146369) ((-1011 . -260) 146307) ((-1011 . -554) 146289) ((-1011 . -72) T) ((-1011 . -1131) T) ((-1011 . -13) T) ((-1011 . -34) T) ((-1011 . -1037) 146273) ((-1011 . -76) 146257) ((-1011 . -183) 146241) ((-1010 . -997) T) ((-1010 . -431) 146222) ((-1010 . -554) 146188) ((-1010 . -557) 146169) ((-1010 . -1015) T) ((-1010 . -1131) T) ((-1010 . -13) T) ((-1010 . -72) T) ((-1010 . -64) T) ((-1006 . -1131) T) ((-1006 . -13) T) ((-1006 . -1015) 146139) ((-1006 . -554) 146098) ((-1006 . -72) 146068) ((-1005 . -997) T) ((-1005 . -431) 146049) ((-1005 . -554) 146015) ((-1005 . -557) 145996) ((-1005 . -1015) T) ((-1005 . -1131) T) ((-1005 . -13) T) ((-1005 . -72) T) ((-1005 . -64) T) ((-1003 . -1008) 145980) ((-1003 . -559) 145964) ((-1003 . -1015) 145942) ((-1003 . -554) 145909) ((-1003 . -1131) 145887) ((-1003 . -13) 145865) ((-1003 . -72) 145843) ((-1003 . -1009) 145801) ((-1002 . -228) 145785) ((-1002 . -557) 145769) ((-1002 . -952) 145753) 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-104) T) ((-1001 . -25) T) ((-1001 . -72) T) ((-1001 . -554) 143068) ((-1001 . -1015) T) ((-1001 . -23) T) ((-1001 . -21) T) ((-1001 . -972) T) ((-1001 . -1027) T) ((-1001 . -1063) T) ((-1001 . -665) T) ((-1001 . -963) T) ((-1001 . -186) 143016) ((-1001 . -13) T) ((-1001 . -1131) T) ((-1001 . -189) 142970) ((-1001 . -225) 142954) ((-1001 . -184) 142938) ((-999 . -554) 142920) ((-996 . -758) T) ((-996 . -554) 142902) ((-996 . -1015) T) ((-996 . -72) T) ((-996 . -13) T) ((-996 . -1131) T) ((-996 . -761) T) ((-996 . -555) 142883) ((-993 . -663) 142862) ((-993 . -952) 142760) ((-993 . -355) 142744) ((-993 . -582) 142692) ((-993 . -592) 142569) ((-993 . -329) 142553) ((-993 . -322) 142532) ((-993 . -120) 142511) ((-993 . -557) 142336) ((-993 . -656) 142210) ((-993 . -584) 142084) ((-993 . -590) 141982) ((-993 . -970) 141895) ((-993 . -965) 141808) ((-993 . -82) 141700) ((-993 . -38) 141574) ((-993 . -353) 141553) ((-993 . -345) 141532) ((-993 . -118) 141486) ((-993 . -1068) 141465) ((-993 . 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. -72) T) ((-989 . -241) 140205) ((-989 . -952) 140182) ((-989 . -557) 140159) ((-988 . -1131) T) ((-988 . -13) T) ((-987 . -997) T) ((-987 . -431) 140140) ((-987 . -554) 140106) ((-987 . -557) 140087) ((-987 . -1015) T) ((-987 . -1131) T) ((-987 . -13) T) ((-987 . -72) T) ((-987 . -64) T) ((-980 . -997) T) ((-980 . -431) 140068) ((-980 . -554) 140034) ((-980 . -557) 140015) ((-980 . -1015) T) ((-980 . -1131) T) ((-980 . -13) T) ((-980 . -72) T) ((-980 . -64) T) ((-977 . -485) T) ((-977 . -1136) T) ((-977 . -1068) T) ((-977 . -952) 139997) ((-977 . -555) 139912) ((-977 . -935) T) ((-977 . -798) 139894) ((-977 . -757) T) ((-977 . -723) T) ((-977 . -720) T) ((-977 . -761) T) ((-977 . -758) T) ((-977 . -718) T) ((-977 . -716) T) ((-977 . -742) T) ((-977 . -592) 139866) ((-977 . -582) 139848) ((-977 . -834) T) ((-977 . -497) T) ((-977 . -246) T) ((-977 . -146) T) ((-977 . -557) 139820) ((-977 . -656) 139807) ((-977 . -584) 139794) ((-977 . -970) 139781) ((-977 . -965) 139768) ((-977 . -82) 139753) ((-977 . -38) 139740) ((-977 . -393) T) ((-977 . -258) T) ((-977 . -189) T) ((-977 . -186) 139727) ((-977 . -190) T) ((-977 . -116) T) ((-977 . -963) T) ((-977 . -665) T) ((-977 . -1063) T) ((-977 . -1027) T) ((-977 . -972) T) ((-977 . -21) T) ((-977 . -590) 139699) ((-977 . -23) T) ((-977 . -1015) T) ((-977 . -554) 139681) ((-977 . -1131) T) ((-977 . -13) T) ((-977 . -72) T) ((-977 . -25) T) ((-977 . -104) T) ((-977 . -120) T) ((-977 . -559) 139662) ((-976 . -982) 139641) ((-976 . -72) T) ((-976 . -13) T) ((-976 . -1131) T) ((-976 . -554) 139623) ((-976 . -1015) T) ((-973 . -1131) T) ((-973 . -13) T) ((-973 . -1015) 139601) ((-973 . -554) 139568) ((-973 . -72) 139546) ((-968 . -967) 139486) ((-968 . -584) 139431) ((-968 . -656) 139376) ((-968 . -430) 139360) ((-968 . -381) 139344) ((-968 . -457) 139277) ((-968 . -260) 139215) ((-968 . -34) T) ((-968 . -318) 139199) ((-968 . -592) 139183) ((-968 . -590) 139152) ((-968 . -104) T) ((-968 . -25) T) ((-968 . -72) T) ((-968 . -13) T) ((-968 . -1131) T) ((-968 . -554) 139114) ((-968 . -1015) T) ((-968 . -23) T) ((-968 . -21) T) ((-968 . -970) 139098) ((-968 . -965) 139082) ((-968 . -82) 139061) ((-968 . -1189) 139031) ((-968 . -555) 138992) ((-960 . -985) 138921) ((-960 . -891) 138850) ((-960 . -318) 138815) ((-960 . -555) 138757) ((-960 . -430) 138722) ((-960 . -1015) T) ((-960 . -381) 138687) ((-960 . -457) 138571) ((-960 . -260) 138479) ((-960 . -554) 138422) ((-960 . -72) T) ((-960 . -1131) T) ((-960 . -13) T) ((-960 . -34) T) ((-960 . -124) 138387) ((-960 . -1037) 138352) ((-960 . -1126) 138281) ((-950 . -997) T) ((-950 . -431) 138262) ((-950 . -554) 138228) ((-950 . -557) 138209) ((-950 . -1015) T) ((-950 . -1131) T) ((-950 . -13) T) ((-950 . -72) T) ((-950 . -64) T) ((-949 . -146) T) ((-949 . -557) 138178) ((-949 . -972) T) ((-949 . -1027) T) ((-949 . -1063) T) ((-949 . -665) T) ((-949 . -963) T) ((-949 . -592) 138152) ((-949 . -590) 138111) ((-949 . -104) T) ((-949 . -25) T) ((-949 . -72) T) ((-949 . -13) T) ((-949 . -1131) T) ((-949 . -554) 138093) ((-949 . -1015) T) ((-949 . -23) T) ((-949 . -21) T) ((-949 . -970) 138067) ((-949 . -965) 138041) ((-949 . -82) 138008) ((-949 . -38) 137992) ((-949 . -584) 137976) ((-949 . -656) 137960) ((-942 . -985) 137929) ((-942 . -891) 137898) ((-942 . -318) 137882) ((-942 . -555) 137843) ((-942 . -430) 137827) ((-942 . -1015) T) ((-942 . -381) 137811) ((-942 . -457) 137744) ((-942 . -260) 137682) ((-942 . -554) 137644) ((-942 . -72) T) ((-942 . -1131) T) ((-942 . -13) T) ((-942 . -34) T) ((-942 . -124) 137628) ((-942 . -1037) 137612) ((-942 . -1126) 137581) ((-941 . -1015) T) ((-941 . -554) 137563) ((-941 . -1131) T) ((-941 . -13) T) ((-941 . -72) T) ((-939 . -927) T) ((-939 . -917) T) ((-939 . -716) T) ((-939 . -718) T) ((-939 . -758) T) ((-939 . -761) T) ((-939 . -720) T) ((-939 . -723) T) ((-939 . -757) T) ((-939 . -952) 137448) ((-939 . -355) 137410) ((-939 . -201) T) ((-939 . -246) T) ((-939 . -258) T) ((-939 . -393) T) ((-939 . -38) 137347) ((-939 . -584) 137284) ((-939 . -656) 137221) ((-939 . -557) 137158) ((-939 . -497) T) ((-939 . -834) T) ((-939 . -1136) T) ((-939 . -312) T) ((-939 . -82) 137067) ((-939 . -965) 137004) ((-939 . -970) 136941) ((-939 . -146) T) ((-939 . -120) T) ((-939 . -592) 136878) ((-939 . -590) 136815) ((-939 . -104) T) ((-939 . -25) T) ((-939 . -72) T) ((-939 . -13) T) ((-939 . -1131) T) ((-939 . -554) 136797) ((-939 . -1015) T) ((-939 . -23) T) ((-939 . -21) T) ((-939 . -963) T) ((-939 . -665) T) ((-939 . -1063) T) ((-939 . -1027) T) ((-939 . -972) T) ((-934 . -997) T) ((-934 . -431) 136778) ((-934 . -554) 136744) ((-934 . -557) 136725) ((-934 . -1015) T) ((-934 . -1131) T) ((-934 . -13) T) ((-934 . -72) T) ((-934 . -64) T) ((-919 . -906) 136707) ((-919 . -1068) T) ((-919 . -557) 136657) ((-919 . -952) 136617) ((-919 . -555) 136547) ((-919 . -935) T) ((-919 . -823) NIL) ((-919 . -796) 136529) ((-919 . -757) T) ((-919 . -723) T) ((-919 . -720) T) ((-919 . -761) T) ((-919 . -758) T) ((-919 . -718) T) ((-919 . -716) T) ((-919 . -742) T) ((-919 . -798) 136511) ((-919 . -343) 136493) ((-919 . -582) 136475) ((-919 . -329) 136457) ((-919 . -241) NIL) ((-919 . -260) NIL) ((-919 . -457) NIL) ((-919 . -381) 136439) ((-919 . -288) 136421) ((-919 . -201) T) ((-919 . -82) 136348) ((-919 . -965) 136298) ((-919 . -970) 136248) ((-919 . -246) T) ((-919 . -656) 136198) ((-919 . -584) 136148) ((-919 . -592) 136098) ((-919 . -590) 136048) ((-919 . -38) 135998) ((-919 . -258) T) ((-919 . -393) T) ((-919 . -146) T) ((-919 . -497) T) ((-919 . -834) T) ((-919 . -1136) T) ((-919 . -312) T) ((-919 . -190) T) ((-919 . -186) 135985) ((-919 . -189) T) ((-919 . -225) 135967) ((-919 . -808) NIL) ((-919 . -813) NIL) ((-919 . -811) NIL) ((-919 . -184) 135949) ((-919 . -120) T) ((-919 . -118) NIL) ((-919 . -104) T) ((-919 . -25) T) ((-919 . -72) T) ((-919 . -13) T) ((-919 . -1131) T) ((-919 . -554) 135909) ((-919 . -1015) T) ((-919 . -23) T) ((-919 . -21) T) ((-919 . -963) T) ((-919 . -665) T) ((-919 . -1063) T) ((-919 . -1027) T) ((-919 . -972) T) ((-918 . -291) 135883) ((-918 . -146) T) ((-918 . -557) 135813) ((-918 . -972) T) ((-918 . -1027) T) ((-918 . -1063) T) ((-918 . -665) T) ((-918 . -963) T) ((-918 . -592) 135715) ((-918 . -590) 135645) ((-918 . -104) T) ((-918 . -25) T) ((-918 . -72) T) ((-918 . -13) T) ((-918 . -1131) T) ((-918 . -554) 135627) ((-918 . -1015) T) ((-918 . -23) T) ((-918 . -21) T) ((-918 . -970) 135572) ((-918 . -965) 135517) ((-918 . -82) 135434) ((-918 . -555) 135418) ((-918 . -184) 135395) ((-918 . -811) 135347) ((-918 . -813) 135259) ((-918 . -808) 135169) ((-918 . -225) 135146) ((-918 . -189) 135086) ((-918 . -186) 135020) ((-918 . -190) 134992) ((-918 . -312) T) ((-918 . -1136) T) ((-918 . -834) T) ((-918 . -497) T) ((-918 . -656) 134937) ((-918 . -584) 134882) ((-918 . -38) 134827) ((-918 . -393) T) ((-918 . -258) T) ((-918 . -246) T) ((-918 . -201) T) ((-918 . -320) NIL) ((-918 . -299) NIL) ((-918 . -1068) NIL) ((-918 . -118) 134799) ((-918 . -345) NIL) 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. -201) 132825) ((-911 . -190) 132804) ((-911 . -186) 132752) ((-911 . -189) 132706) ((-911 . -225) 132690) ((-911 . -808) 132614) ((-911 . -813) 132540) ((-911 . -811) 132499) ((-911 . -184) 132483) ((-911 . -555) 132444) ((-911 . -120) 132423) ((-911 . -118) 132402) ((-911 . -104) T) ((-911 . -25) T) ((-911 . -72) T) ((-911 . -13) T) ((-911 . -1131) T) ((-911 . -554) 132384) ((-911 . -1015) T) ((-911 . -23) T) ((-911 . -21) T) ((-911 . -963) T) ((-911 . -665) T) ((-911 . -1063) T) ((-911 . -1027) T) ((-911 . -972) T) ((-909 . -997) T) ((-909 . -431) 132365) ((-909 . -554) 132331) ((-909 . -557) 132312) ((-909 . -1015) T) ((-909 . -1131) T) ((-909 . -13) T) ((-909 . -72) T) ((-909 . -64) T) ((-908 . -21) T) ((-908 . -590) 132294) ((-908 . -23) T) ((-908 . -1015) T) ((-908 . -554) 132276) ((-908 . -1131) T) ((-908 . -13) T) ((-908 . -72) T) ((-908 . -25) T) ((-908 . -104) T) ((-908 . -241) 132243) ((-904 . -554) 132225) ((-901 . -1015) T) ((-901 . -554) 132207) ((-901 . -1131) T) ((-901 . -13) T) ((-901 . -72) T) ((-886 . -723) T) ((-886 . -720) T) ((-886 . -761) T) ((-886 . -758) T) ((-886 . -718) T) ((-886 . -23) T) ((-886 . -1015) T) ((-886 . -554) 132167) ((-886 . -1131) T) ((-886 . -13) T) ((-886 . -72) T) ((-886 . -25) T) ((-886 . -104) T) ((-885 . -997) T) ((-885 . -431) 132148) ((-885 . -554) 132114) ((-885 . -557) 132095) ((-885 . -1015) T) ((-885 . -1131) T) ((-885 . -13) T) ((-885 . -72) T) ((-885 . -64) T) ((-879 . -882) T) ((-879 . -72) T) ((-879 . -554) 132077) ((-879 . -1015) T) ((-879 . -606) T) ((-879 . -13) T) ((-879 . -1131) T) ((-879 . -84) T) ((-879 . -557) 132061) ((-878 . -554) 132043) ((-877 . -1015) T) ((-877 . -554) 132025) ((-877 . -1131) T) ((-877 . -13) T) ((-877 . -72) T) ((-877 . -320) 131978) ((-877 . -665) 131880) ((-877 . -1027) 131782) ((-877 . -23) 131596) ((-877 . -25) 131410) ((-877 . -104) 131268) ((-877 . -414) 131221) ((-877 . -21) 131176) ((-877 . -590) 131120) ((-877 . -719) 131073) ((-877 . -718) 131026) ((-877 . 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126628) ((-859 . -104) T) ((-859 . -25) T) ((-859 . -72) T) ((-859 . -13) T) ((-859 . -1131) T) ((-859 . -554) 126610) ((-859 . -1015) T) ((-859 . -23) T) ((-859 . -21) T) ((-859 . -963) T) ((-859 . -665) T) ((-859 . -1063) T) ((-859 . -1027) T) ((-859 . -972) T) ((-859 . -355) 126594) ((-859 . -277) 126563) ((-859 . -260) 126550) ((-859 . -555) 126411) ((-856 . -895) 126395) ((-856 . -19) 126379) ((-856 . -1037) 126363) ((-856 . -318) 126347) ((-856 . -34) T) ((-856 . -13) T) ((-856 . -1131) T) ((-856 . -72) 126281) ((-856 . -554) 126196) ((-856 . -260) 126134) ((-856 . -457) 126067) ((-856 . -381) 126051) ((-856 . -1015) 126004) ((-856 . -430) 125988) ((-856 . -595) 125972) ((-856 . -243) 125949) ((-856 . -241) 125901) ((-856 . -540) 125878) ((-856 . -555) 125839) ((-856 . -124) 125823) ((-856 . -758) 125802) ((-856 . -761) 125781) ((-856 . -324) 125765) ((-856 . -1180) 125749) ((-856 . -559) 125726) ((-840 . -889) T) ((-840 . -554) 125708) ((-838 . -868) T) ((-838 . -554) 125690) ((-832 . -720) T) ((-832 . -761) T) ((-832 . -758) T) ((-832 . -1015) T) ((-832 . -554) 125672) ((-832 . -1131) T) ((-832 . -13) T) ((-832 . -72) T) ((-832 . -25) T) ((-832 . -665) T) ((-832 . -1027) T) ((-827 . -312) T) ((-827 . -1136) T) ((-827 . -834) T) ((-827 . -497) T) ((-827 . -146) T) ((-827 . -557) 125609) ((-827 . -656) 125561) ((-827 . -584) 125513) ((-827 . -38) 125465) ((-827 . -393) T) ((-827 . -258) T) ((-827 . -592) 125417) ((-827 . -590) 125354) ((-827 . -972) T) ((-827 . -1027) T) ((-827 . -1063) T) ((-827 . -665) T) ((-827 . -963) T) ((-827 . -82) 125285) ((-827 . -965) 125237) ((-827 . -970) 125189) ((-827 . -21) T) ((-827 . -23) T) ((-827 . -1015) T) ((-827 . -554) 125171) ((-827 . -1131) T) ((-827 . -13) T) ((-827 . -72) T) ((-827 . -25) T) ((-827 . -104) T) ((-827 . -246) T) ((-827 . -201) T) ((-819 . -299) T) ((-819 . -1068) T) ((-819 . -320) T) ((-819 . -118) T) ((-819 . -312) T) ((-819 . -1136) T) ((-819 . -834) T) ((-819 . -497) T) ((-819 . -146) T) ((-819 . -557) 125121) ((-819 . -656) 125086) ((-819 . -584) 125051) ((-819 . -38) 125016) ((-819 . -393) T) ((-819 . -258) T) ((-819 . -82) 124965) ((-819 . -965) 124930) ((-819 . -970) 124895) ((-819 . -590) 124845) ((-819 . -592) 124810) ((-819 . -246) T) ((-819 . -201) T) ((-819 . -345) T) ((-819 . -189) T) ((-819 . -1131) T) ((-819 . -13) T) ((-819 . -186) 124797) ((-819 . -963) T) ((-819 . -665) T) ((-819 . -1063) T) ((-819 . -1027) T) ((-819 . -972) T) ((-819 . -21) T) ((-819 . -23) T) ((-819 . -1015) T) ((-819 . -554) 124779) ((-819 . -72) T) ((-819 . -25) T) ((-819 . -104) T) ((-819 . -190) T) ((-819 . -280) 124766) ((-819 . -120) 124748) ((-819 . -952) 124735) ((-819 . -1189) 124722) ((-819 . -1200) 124709) ((-819 . -555) 124691) ((-818 . -1015) T) ((-818 . -554) 124673) ((-818 . -1131) T) ((-818 . -13) T) ((-818 . -72) T) ((-815 . -817) 124657) ((-815 . -761) 124611) ((-815 . -758) 124565) ((-815 . -665) T) ((-815 . -1015) T) ((-815 . -554) 124547) ((-815 . -72) T) ((-815 . -1027) T) ((-815 . -414) T) ((-815 . -1131) T) ((-815 . -13) T) ((-815 . -241) 124526) ((-814 . -92) 124510) ((-814 . -430) 124494) ((-814 . -1015) 124472) ((-814 . -381) 124456) ((-814 . -457) 124389) ((-814 . -260) 124327) ((-814 . -554) 124241) ((-814 . -72) 124195) ((-814 . -1131) T) ((-814 . -13) T) ((-814 . -34) T) ((-814 . -925) 124179) ((-805 . -758) T) ((-805 . -554) 124161) ((-805 . -1015) T) ((-805 . -72) T) ((-805 . -13) T) ((-805 . -1131) T) ((-805 . -761) T) ((-805 . -952) 124138) ((-805 . -557) 124115) ((-802 . -1015) T) ((-802 . -554) 124097) ((-802 . -1131) T) ((-802 . -13) T) ((-802 . -72) T) ((-802 . -952) 124065) ((-802 . -557) 124033) ((-800 . -1015) T) ((-800 . -554) 124015) ((-800 . -1131) T) ((-800 . -13) T) ((-800 . -72) T) ((-797 . -1015) T) ((-797 . -554) 123997) ((-797 . -1131) T) ((-797 . -13) T) ((-797 . -72) T) ((-787 . -997) T) ((-787 . -431) 123978) ((-787 . -554) 123944) ((-787 . -557) 123925) ((-787 . -1015) T) ((-787 . -1131) T) ((-787 . -13) T) ((-787 . -72) T) ((-787 . -64) T) ((-787 . -1177) T) ((-785 . -1015) T) ((-785 . -554) 123907) ((-785 . -1131) T) ((-785 . -13) T) ((-785 . -72) T) ((-785 . -557) 123889) ((-784 . -1131) T) ((-784 . -13) T) ((-784 . -554) 123764) ((-784 . -1015) 123715) ((-784 . -72) 123666) ((-783 . -906) 123650) ((-783 . -1068) 123628) ((-783 . -952) 123495) ((-783 . -557) 123394) ((-783 . -555) 123197) ((-783 . -935) 123176) ((-783 . -823) 123155) ((-783 . -796) 123139) ((-783 . -757) 123118) ((-783 . -723) 123097) ((-783 . -720) 123076) ((-783 . -761) 123030) ((-783 . -758) 122984) ((-783 . -718) 122963) ((-783 . -716) 122942) ((-783 . -742) 122921) ((-783 . -798) 122846) ((-783 . -343) 122830) ((-783 . -582) 122778) ((-783 . -592) 122694) ((-783 . -329) 122678) ((-783 . -241) 122636) ((-783 . -260) 122601) ((-783 . -457) 122513) ((-783 . -381) 122497) ((-783 . -288) 122481) ((-783 . -201) T) ((-783 . -82) 122412) ((-783 . -965) 122364) ((-783 . -970) 122316) ((-783 . -246) T) ((-783 . -656) 122268) ((-783 . -584) 122220) ((-783 . -590) 122157) ((-783 . -38) 122109) ((-783 . -258) T) ((-783 . -393) T) ((-783 . -146) T) ((-783 . -497) T) ((-783 . -834) T) ((-783 . -1136) T) ((-783 . -312) T) ((-783 . -190) 122088) ((-783 . -186) 122036) ((-783 . -189) 121990) ((-783 . -225) 121974) ((-783 . -808) 121898) ((-783 . -813) 121824) ((-783 . -811) 121783) ((-783 . -184) 121767) ((-783 . -120) 121721) ((-783 . -118) 121700) ((-783 . -104) T) ((-783 . -25) T) ((-783 . -72) T) ((-783 . -13) T) ((-783 . -1131) T) ((-783 . -554) 121682) ((-783 . -1015) T) ((-783 . -23) T) ((-783 . -21) T) ((-783 . -963) T) ((-783 . -665) T) ((-783 . -1063) T) ((-783 . -1027) T) ((-783 . -972) T) ((-782 . -906) 121659) ((-782 . -1068) NIL) ((-782 . -952) 121636) ((-782 . -557) 121566) ((-782 . -555) NIL) ((-782 . -935) NIL) ((-782 . -823) NIL) ((-782 . -796) 121543) ((-782 . -757) NIL) ((-782 . -723) NIL) ((-782 . -720) NIL) ((-782 . -761) NIL) ((-782 . -758) NIL) ((-782 . -718) NIL) ((-782 . -716) NIL) ((-782 . -742) NIL) ((-782 . -798) NIL) ((-782 . -343) 121520) ((-782 . -582) 121497) ((-782 . -592) 121442) ((-782 . -329) 121419) ((-782 . -241) 121349) ((-782 . -260) 121293) ((-782 . -457) 121156) ((-782 . -381) 121133) ((-782 . -288) 121110) ((-782 . -201) T) ((-782 . -82) 121027) ((-782 . -965) 120972) ((-782 . -970) 120917) ((-782 . -246) T) ((-782 . -656) 120862) ((-782 . -584) 120807) ((-782 . -590) 120737) ((-782 . -38) 120682) ((-782 . -258) T) ((-782 . -393) T) ((-782 . -146) T) ((-782 . -497) T) ((-782 . -834) T) ((-782 . -1136) T) ((-782 . -312) T) ((-782 . -190) NIL) ((-782 . -186) NIL) ((-782 . -189) NIL) ((-782 . -225) 120659) ((-782 . -808) NIL) ((-782 . -813) NIL) ((-782 . -811) NIL) ((-782 . -184) 120636) ((-782 . -120) T) ((-782 . -118) NIL) ((-782 . -104) T) ((-782 . -25) T) ((-782 . -72) T) ((-782 . -13) T) ((-782 . -1131) T) ((-782 . -554) 120618) ((-782 . -1015) T) ((-782 . -23) T) ((-782 . -21) T) ((-782 . -963) T) ((-782 . -665) T) ((-782 . -1063) T) ((-782 . -1027) T) ((-782 . -972) T) ((-780 . -781) 120602) ((-780 . -834) T) ((-780 . -497) T) ((-780 . -246) T) ((-780 . -146) T) ((-780 . -557) 120574) ((-780 . -656) 120561) ((-780 . -584) 120548) ((-780 . -970) 120535) ((-780 . -965) 120522) ((-780 . -82) 120507) ((-780 . -38) 120494) ((-780 . -393) T) ((-780 . -258) T) ((-780 . -963) T) ((-780 . -665) T) ((-780 . -1063) T) ((-780 . -1027) T) ((-780 . -972) T) ((-780 . -21) T) ((-780 . -590) 120466) ((-780 . -23) T) ((-780 . -1015) T) ((-780 . -554) 120448) ((-780 . -1131) T) ((-780 . -13) T) ((-780 . -72) T) ((-780 . -25) T) ((-780 . -104) T) ((-780 . -592) 120435) ((-780 . -120) T) ((-777 . -963) T) ((-777 . -665) T) ((-777 . -1063) T) ((-777 . -1027) T) ((-777 . -972) T) ((-777 . -21) T) ((-777 . -590) 120380) ((-777 . -23) T) ((-777 . -1015) T) ((-777 . -554) 120342) ((-777 . -1131) T) ((-777 . -13) T) ((-777 . -72) T) ((-777 . -25) T) ((-777 . -104) T) ((-777 . -592) 120302) ((-777 . -557) 120237) ((-777 . -431) 120214) ((-777 . -38) 120184) ((-777 . -82) 120149) ((-777 . -965) 120119) ((-777 . -970) 120089) ((-777 . -584) 120059) ((-777 . -656) 120029) ((-776 . -1015) T) ((-776 . -554) 120011) ((-776 . -1131) T) ((-776 . -13) T) ((-776 . -72) T) ((-775 . -754) T) ((-775 . -761) T) ((-775 . -758) T) ((-775 . -1015) T) ((-775 . -554) 119993) ((-775 . -1131) T) ((-775 . -13) T) ((-775 . -72) T) ((-775 . -320) T) ((-775 . -555) 119915) ((-774 . -1015) T) ((-774 . -554) 119897) ((-774 . -1131) T) ((-774 . -13) T) ((-774 . -72) T) ((-773 . -772) T) ((-773 . -147) T) ((-773 . -554) 119879) ((-769 . -758) T) ((-769 . -554) 119861) ((-769 . -1015) T) ((-769 . -72) T) ((-769 . -13) T) ((-769 . -1131) T) ((-769 . -761) T) ((-766 . -763) 119845) ((-766 . -952) 119743) ((-766 . -557) 119641) ((-766 . -355) 119625) ((-766 . -656) 119595) ((-766 . -584) 119565) ((-766 . -592) 119539) ((-766 . -590) 119498) ((-766 . -104) T) ((-766 . -25) T) ((-766 . -72) T) ((-766 . -13) T) ((-766 . -1131) T) ((-766 . -554) 119480) ((-766 . -1015) T) 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118836) ((-752 . -557) 118709) ((-752 . -952) 118607) ((-752 . -21) 118562) ((-752 . -590) 118482) ((-752 . -23) 118437) ((-752 . -25) 118392) ((-752 . -104) 118347) ((-752 . -757) 118326) ((-752 . -723) 118305) ((-752 . -720) 118284) ((-752 . -761) 118263) ((-752 . -758) 118242) ((-752 . -718) 118221) ((-752 . -716) 118200) ((-752 . -963) 118179) ((-752 . -665) 118158) ((-752 . -1063) 118137) ((-752 . -1027) 118116) ((-752 . -972) 118095) ((-752 . -592) 118068) ((-752 . -120) 118047) ((-751 . -749) 118029) ((-751 . -72) T) ((-751 . -13) T) ((-751 . -1131) T) ((-751 . -554) 118011) ((-751 . -1015) T) ((-747 . -963) T) ((-747 . -665) T) ((-747 . -1063) T) ((-747 . -1027) T) ((-747 . -972) T) ((-747 . -21) T) ((-747 . -590) 117956) ((-747 . -23) T) ((-747 . -1015) T) ((-747 . -554) 117938) ((-747 . -1131) T) ((-747 . -13) T) ((-747 . -72) T) ((-747 . -25) T) ((-747 . -104) T) ((-747 . -592) 117898) ((-747 . -557) 117853) ((-747 . -952) 117823) ((-747 . -241) 117802) ((-747 . -120) 117781) ((-747 . -118) 117760) ((-747 . -38) 117730) ((-747 . -82) 117695) ((-747 . -965) 117665) ((-747 . -970) 117635) ((-747 . -584) 117605) ((-747 . -656) 117575) ((-745 . -1015) T) ((-745 . -554) 117557) ((-745 . -1131) T) ((-745 . -13) T) ((-745 . -72) T) ((-745 . -355) 117541) ((-745 . -557) 117414) ((-745 . -952) 117312) ((-745 . -21) 117267) ((-745 . -590) 117187) ((-745 . -23) 117142) ((-745 . -25) 117097) ((-745 . -104) 117052) ((-745 . -757) 117031) ((-745 . -723) 117010) ((-745 . -720) 116989) ((-745 . -761) 116968) ((-745 . -758) 116947) ((-745 . -718) 116926) ((-745 . -716) 116905) ((-745 . -963) 116884) ((-745 . -665) 116863) ((-745 . -1063) 116842) ((-745 . -1027) 116821) ((-745 . -972) 116800) ((-745 . -592) 116773) ((-745 . -120) 116752) ((-743 . -647) 116736) ((-743 . -557) 116691) ((-743 . -656) 116661) ((-743 . -584) 116631) ((-743 . -592) 116605) ((-743 . -590) 116564) ((-743 . -104) T) ((-743 . -25) T) ((-743 . -72) T) ((-743 . -13) T) ((-743 . -1131) T) ((-743 . -554) 116546) ((-743 . -1015) T) ((-743 . -23) T) ((-743 . -21) T) ((-743 . -970) 116530) ((-743 . -965) 116514) ((-743 . -82) 116493) ((-743 . -963) T) ((-743 . -665) T) ((-743 . -1063) T) ((-743 . -1027) T) ((-743 . -972) T) ((-743 . -38) 116463) ((-743 . -190) 116442) ((-743 . -186) 116415) ((-743 . -189) 116394) ((-741 . -336) 116378) ((-741 . -557) 116362) ((-741 . -952) 116346) ((-741 . -761) T) ((-741 . -758) T) ((-741 . -1027) T) ((-741 . -72) T) ((-741 . -13) T) ((-741 . -1131) T) ((-741 . -554) 116328) ((-741 . -1015) T) ((-741 . -665) T) ((-741 . -756) T) ((-741 . -768) T) ((-740 . -228) 116312) ((-740 . -557) 116296) ((-740 . -952) 116280) ((-740 . -761) T) ((-740 . -72) T) ((-740 . -1015) T) ((-740 . -554) 116262) ((-740 . -758) T) ((-740 . -186) 116249) ((-740 . -13) T) ((-740 . -1131) T) ((-740 . -189) T) ((-739 . -82) 116184) ((-739 . -965) 116135) ((-739 . -970) 116086) ((-739 . -21) T) ((-739 . -590) 116022) ((-739 . -23) T) ((-739 . -1015) T) ((-739 . -554) 115991) ((-739 . -1131) T) ((-739 . -13) T) ((-739 . -72) T) ((-739 . -25) T) ((-739 . -104) T) ((-739 . -592) 115942) ((-739 . -190) T) ((-739 . -557) 115851) ((-739 . -972) T) ((-739 . -1027) T) ((-739 . -1063) T) ((-739 . -665) T) ((-739 . -963) T) ((-739 . -186) 115838) ((-739 . -189) T) ((-739 . -431) 115822) ((-739 . -312) 115801) ((-739 . -1136) 115780) ((-739 . -834) 115759) ((-739 . -497) 115738) ((-739 . -146) 115717) ((-739 . -656) 115654) ((-739 . -584) 115591) ((-739 . -38) 115528) ((-739 . -393) 115507) ((-739 . -258) 115486) ((-739 . -246) 115465) ((-739 . -201) 115444) ((-738 . -213) 115383) ((-738 . -557) 115127) ((-738 . -952) 114957) ((-738 . -555) NIL) ((-738 . -277) 114919) ((-738 . -355) 114903) ((-738 . -38) 114755) ((-738 . -82) 114580) ((-738 . -965) 114426) ((-738 . -970) 114272) ((-738 . -590) 114182) ((-738 . -592) 114071) ((-738 . -584) 113923) ((-738 . -656) 113775) ((-738 . -118) 113754) ((-738 . -120) 113733) ((-738 . -146) 113647) ((-738 . -381) 113631) ((-738 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. -104) T) ((-532 . -190) 82584) ((-530 . -997) T) ((-530 . -431) 82565) ((-530 . -554) 82531) ((-530 . -557) 82512) ((-530 . -1015) T) ((-530 . -1131) T) ((-530 . -13) T) ((-530 . -72) T) ((-530 . -64) T) ((-524 . -1015) T) ((-524 . -554) 82478) ((-524 . -1131) T) ((-524 . -13) T) ((-524 . -72) T) ((-524 . -431) 82459) ((-524 . -557) 82440) ((-521 . -656) 82415) ((-521 . -584) 82390) ((-521 . -592) 82365) ((-521 . -590) 82325) ((-521 . -104) T) ((-521 . -25) T) ((-521 . -72) T) ((-521 . -13) T) ((-521 . -1131) T) ((-521 . -554) 82307) ((-521 . -1015) T) ((-521 . -23) T) ((-521 . -21) T) ((-521 . -970) 82282) ((-521 . -965) 82257) ((-521 . -82) 82218) ((-521 . -952) 82202) ((-521 . -557) 82186) ((-519 . -299) T) ((-519 . -1068) T) ((-519 . -320) T) ((-519 . -118) T) ((-519 . -312) T) ((-519 . -1136) T) ((-519 . -834) T) ((-519 . -497) T) ((-519 . -146) T) ((-519 . -557) 82136) ((-519 . -656) 82101) ((-519 . -584) 82066) ((-519 . -38) 82031) ((-519 . -393) T) ((-519 . -258) T) ((-519 . 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-116) T) ((-486 . -963) T) ((-486 . -665) T) ((-486 . -1063) T) ((-486 . -1027) T) ((-486 . -972) T) ((-486 . -21) T) ((-486 . -590) 79852) ((-486 . -23) T) ((-486 . -1015) T) ((-486 . -554) 79834) ((-486 . -1131) T) ((-486 . -13) T) ((-486 . -72) T) ((-486 . -25) T) ((-486 . -104) T) ((-486 . -120) T) ((-475 . -1018) 79786) ((-475 . -72) T) ((-475 . -554) 79768) ((-475 . -1015) T) ((-475 . -241) 79724) ((-475 . -1131) T) ((-475 . -13) T) ((-475 . -559) 79627) ((-475 . -555) 79608) ((-473 . -693) 79590) ((-473 . -467) T) ((-473 . -147) T) ((-473 . -772) T) ((-473 . -514) T) ((-473 . -554) 79572) ((-471 . -719) T) ((-471 . -104) T) ((-471 . -25) T) ((-471 . -72) T) ((-471 . -13) T) ((-471 . -1131) T) ((-471 . -554) 79554) ((-471 . -1015) T) ((-471 . -23) T) ((-471 . -718) T) ((-471 . -758) T) ((-471 . -761) T) ((-471 . -720) T) ((-471 . -723) T) ((-471 . -451) 79531) ((-471 . -381) 79513) ((-471 . -559) 79476) ((-469 . -467) T) ((-469 . -147) T) ((-469 . -554) 79458) ((-465 . -997) T) 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61244) ((-395 . -1136) 61223) ((-395 . -823) 61202) ((-395 . -798) NIL) ((-395 . -813) 61179) ((-395 . -808) 61154) ((-395 . -811) 61131) ((-395 . -457) 61069) ((-395 . -393) 61023) ((-395 . -582) 60971) ((-395 . -592) 60860) ((-395 . -329) 60844) ((-395 . -47) 60823) ((-395 . -38) 60675) ((-395 . -584) 60527) ((-395 . -656) 60379) ((-395 . -246) 60313) ((-395 . -497) 60247) ((-395 . -381) 60231) ((-395 . -82) 60056) ((-395 . -965) 59902) ((-395 . -970) 59748) ((-395 . -146) 59662) ((-395 . -120) 59641) ((-395 . -118) 59620) ((-395 . -590) 59530) ((-395 . -104) T) ((-395 . -25) T) ((-395 . -72) T) ((-395 . -13) T) ((-395 . -1131) T) ((-395 . -554) 59512) ((-395 . -1015) T) ((-395 . -23) T) ((-395 . -21) T) ((-395 . -963) T) ((-395 . -665) T) ((-395 . -1063) T) ((-395 . -1027) T) ((-395 . -972) T) ((-395 . -355) 59496) ((-395 . -277) 59475) ((-395 . -260) 59462) ((-395 . -555) 59323) ((-394 . -361) 59293) ((-394 . -685) 59263) ((-394 . -659) T) ((-394 . -687) T) ((-394 . -82) 59214) 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37445) ((-264 . -120) 37401) ((-264 . -118) 37357) ((-264 . -104) T) ((-264 . -25) T) ((-264 . -72) T) ((-264 . -13) T) ((-264 . -1131) T) ((-264 . -554) 37339) ((-264 . -1015) T) ((-264 . -23) T) ((-264 . -21) T) ((-264 . -963) T) ((-264 . -665) T) ((-264 . -1063) T) ((-264 . -1027) T) ((-264 . -972) T) ((-263 . -997) T) ((-263 . -431) 37320) ((-263 . -554) 37286) ((-263 . -557) 37267) ((-263 . -1015) T) ((-263 . -1131) T) ((-263 . -13) T) ((-263 . -72) T) ((-263 . -64) T) ((-262 . -1015) T) ((-262 . -554) 37249) ((-262 . -1131) T) ((-262 . -13) T) ((-262 . -72) T) ((-251 . -1109) 37228) ((-251 . -183) 37176) ((-251 . -76) 37124) ((-251 . -1037) 37059) ((-251 . -124) 37007) ((-251 . -555) NIL) ((-251 . -193) 36955) ((-251 . -540) 36934) ((-251 . -260) 36732) ((-251 . -457) 36484) ((-251 . -381) 36419) ((-251 . -430) 36354) ((-251 . -241) 36333) ((-251 . -243) 36312) ((-251 . -551) 36291) ((-251 . -1015) T) ((-251 . -554) 36273) ((-251 . -72) T) ((-251 . -1131) T) ((-251 . -13) T) 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18213) ((-181 . -554) 18148) ((-181 . -260) 18086) ((-181 . -457) 18019) ((-181 . -381) 18003) ((-181 . -1015) 17981) ((-181 . -430) 17965) ((-181 . -1037) 17949) ((-181 . -57) 17907) ((-179 . -347) T) ((-179 . -120) T) ((-179 . -557) 17857) ((-179 . -592) 17822) ((-179 . -590) 17772) ((-179 . -104) T) ((-179 . -25) T) ((-179 . -72) T) ((-179 . -13) T) ((-179 . -1131) T) ((-179 . -554) 17754) ((-179 . -1015) T) ((-179 . -23) T) ((-179 . -21) T) ((-179 . -972) T) ((-179 . -1027) T) ((-179 . -1063) T) ((-179 . -665) T) ((-179 . -963) T) ((-179 . -555) 17684) ((-179 . -312) T) ((-179 . -1136) T) ((-179 . -834) T) ((-179 . -497) T) ((-179 . -146) T) ((-179 . -656) 17649) ((-179 . -584) 17614) ((-179 . -38) 17579) ((-179 . -393) T) ((-179 . -258) T) ((-179 . -82) 17528) ((-179 . -965) 17493) ((-179 . -970) 17458) ((-179 . -246) T) ((-179 . -201) T) ((-179 . -757) T) ((-179 . -723) T) ((-179 . -720) T) ((-179 . -761) T) ((-179 . -758) T) ((-179 . -718) T) ((-179 . -716) T) ((-179 . -798) 17440) ((-179 . -917) T) ((-179 . -935) T) ((-179 . -952) 17400) ((-179 . -975) T) ((-179 . -190) T) ((-179 . -186) 17387) ((-179 . -189) T) ((-179 . -1117) T) ((-179 . -1120) T) ((-179 . -434) T) ((-179 . -239) T) ((-179 . -66) T) ((-179 . -35) T) ((-177 . -562) 17364) ((-177 . -557) 17326) ((-177 . -592) 17293) ((-177 . -590) 17245) ((-177 . -972) T) ((-177 . -1027) T) ((-177 . -1063) T) ((-177 . -665) T) ((-177 . -963) T) ((-177 . -21) T) ((-177 . -23) T) ((-177 . -1015) T) ((-177 . -554) 17227) ((-177 . -1131) T) ((-177 . -13) T) ((-177 . -72) T) ((-177 . -25) T) ((-177 . -104) T) ((-177 . -952) 17204) ((-177 . -381) 17181) ((-176 . -214) 17165) ((-176 . -1036) 17149) ((-176 . -76) 17133) ((-176 . -1037) 17117) ((-176 . -34) T) ((-176 . -13) T) ((-176 . -1131) T) ((-176 . -72) 17071) ((-176 . -554) 17006) ((-176 . -260) 16944) ((-176 . -457) 16877) ((-176 . -381) 16861) ((-176 . -1015) 16839) ((-176 . -430) 16823) ((-176 . -318) 16807) ((-176 . -910) 16791) ((-172 . -997) T) ((-172 . -431) 16772) ((-172 . -554) 16738) ((-172 . -557) 16719) ((-172 . -1015) T) ((-172 . -1131) T) ((-172 . -13) T) ((-172 . -72) T) ((-172 . -64) T) ((-171 . -906) 16701) ((-171 . -1068) T) ((-171 . -557) 16651) ((-171 . -952) 16611) ((-171 . -555) 16541) ((-171 . -935) T) ((-171 . -823) NIL) ((-171 . -796) 16523) ((-171 . -757) T) ((-171 . -723) T) ((-171 . -720) T) ((-171 . -761) T) ((-171 . -758) T) ((-171 . -718) T) ((-171 . -716) T) ((-171 . -742) T) ((-171 . -798) 16505) ((-171 . -343) 16487) ((-171 . -582) 16469) ((-171 . -329) 16451) ((-171 . -241) NIL) ((-171 . -260) NIL) ((-171 . -457) NIL) ((-171 . -381) 16433) ((-171 . -288) 16415) ((-171 . -201) T) ((-171 . -82) 16342) ((-171 . -965) 16292) ((-171 . -970) 16242) ((-171 . -246) T) ((-171 . -656) 16192) ((-171 . -584) 16142) ((-171 . -592) 16092) ((-171 . -590) 16042) ((-171 . -38) 15992) ((-171 . -258) T) ((-171 . -393) T) ((-171 . -146) T) ((-171 . -497) T) ((-171 . -834) T) ((-171 . -1136) T) ((-171 . -312) T) ((-171 . -190) T) ((-171 . -186) 15979) ((-171 . -189) T) ((-171 . -225) 15961) ((-171 . -808) NIL) ((-171 . -813) NIL) ((-171 . -811) NIL) ((-171 . -184) 15943) ((-171 . -120) T) ((-171 . -118) NIL) ((-171 . -104) T) ((-171 . -25) T) ((-171 . -72) T) ((-171 . -13) T) ((-171 . -1131) T) ((-171 . -554) 15885) ((-171 . -1015) T) ((-171 . -23) T) ((-171 . -21) T) ((-171 . -963) T) ((-171 . -665) T) ((-171 . -1063) T) ((-171 . -1027) T) ((-171 . -972) T) ((-168 . -754) T) ((-168 . -761) T) ((-168 . -758) T) ((-168 . -1015) T) ((-168 . -554) 15867) ((-168 . -1131) T) ((-168 . -13) T) ((-168 . -72) T) ((-168 . -320) T) ((-167 . -1015) T) ((-167 . -554) 15849) ((-167 . -1131) T) ((-167 . -13) T) ((-167 . -72) T) ((-167 . -557) 15826) ((-166 . -1015) T) ((-166 . -554) 15808) ((-166 . -1131) T) ((-166 . -13) T) ((-166 . -72) T) ((-161 . -1015) T) ((-161 . -554) 15790) ((-161 . -1131) T) ((-161 . -13) T) ((-161 . -72) T) ((-158 . -1015) T) ((-158 . -554) 15772) ((-158 . -1131) T) ((-158 . -13) T) ((-158 . -72) T) ((-157 . -160) T) ((-157 . -1015) T) ((-157 . -554) 15754) ((-157 . -1131) T) ((-157 . -13) T) ((-157 . -72) T) ((-157 . -749) 15736) ((-154 . -997) T) ((-154 . -431) 15717) ((-154 . -554) 15683) ((-154 . -557) 15664) ((-154 . -1015) T) ((-154 . -1131) T) ((-154 . -13) T) ((-154 . -72) T) ((-154 . -64) T) ((-149 . -554) 15646) ((-148 . -38) 15578) ((-148 . -557) 15495) ((-148 . -592) 15427) ((-148 . -590) 15344) ((-148 . -972) T) ((-148 . -1027) T) ((-148 . -1063) T) ((-148 . -665) T) ((-148 . -963) T) ((-148 . -82) 15243) ((-148 . -965) 15175) ((-148 . -970) 15107) ((-148 . -21) T) ((-148 . -23) T) ((-148 . -1015) T) ((-148 . -554) 15089) ((-148 . -1131) T) ((-148 . -13) T) ((-148 . -72) T) ((-148 . -25) T) ((-148 . -104) T) ((-148 . -584) 15021) ((-148 . -656) 14953) ((-148 . -312) T) ((-148 . -1136) T) ((-148 . -834) T) ((-148 . -497) T) ((-148 . -146) T) ((-148 . -393) T) ((-148 . -258) T) ((-148 . -246) T) ((-148 . -201) T) ((-145 . -1015) T) ((-145 . -554) 14935) ((-145 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-759) NIL) ((-1143 . -798) 178413) ((-1143 . -825) NIL) ((-1143 . -937) NIL) ((-1143 . -954) 178379) ((-1143 . -1070) NIL) ((-1143 . -908) 178331) ((-1142 . -756) T) ((-1142 . -763) T) ((-1142 . -760) T) ((-1142 . -1017) T) ((-1142 . -556) 178313) ((-1142 . -1133) T) ((-1142 . -13) T) ((-1142 . -72) T) ((-1142 . -322) T) ((-1142 . -608) T) ((-1141 . -756) T) ((-1141 . -763) T) ((-1141 . -760) T) ((-1141 . -1017) T) ((-1141 . -556) 178295) ((-1141 . -1133) T) ((-1141 . -13) T) ((-1141 . -72) T) ((-1141 . -322) T) ((-1141 . -608) T) ((-1140 . -756) T) ((-1140 . -763) T) ((-1140 . -760) T) ((-1140 . -1017) T) ((-1140 . -556) 178277) ((-1140 . -1133) T) ((-1140 . -13) T) ((-1140 . -72) T) ((-1140 . -322) T) ((-1140 . -608) T) ((-1139 . -756) T) ((-1139 . -763) T) ((-1139 . -760) T) ((-1139 . -1017) T) ((-1139 . -556) 178259) ((-1139 . -1133) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -322) T) ((-1139 . -608) T) ((-1134 . -999) T) ((-1134 . -433) 178240) ((-1134 . -556) 178206) ((-1134 . -559) 178187) ((-1134 . -1017) T) ((-1134 . -1133) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -64) T) ((-1131 . -433) 178164) ((-1131 . -556) 178105) ((-1131 . -559) 178082) ((-1131 . -1017) 178060) ((-1131 . -1133) 178038) ((-1131 . -13) 178016) ((-1131 . -72) 177994) ((-1126 . -683) 177970) ((-1126 . -35) 177936) ((-1126 . -66) 177902) ((-1126 . -241) 177868) ((-1126 . -436) 177834) ((-1126 . -1122) 177800) ((-1126 . -1119) 177766) ((-1126 . -919) 177732) ((-1126 . -47) 177701) ((-1126 . -38) 177598) ((-1126 . -586) 177495) ((-1126 . -658) 177392) ((-1126 . -559) 177274) ((-1126 . -248) 177253) ((-1126 . -499) 177232) ((-1126 . -383) 177216) ((-1126 . -82) 177081) ((-1126 . -967) 176967) ((-1126 . -972) 176853) ((-1126 . -148) 176807) ((-1126 . -120) 176786) ((-1126 . -118) 176765) ((-1126 . -594) 176690) ((-1126 . -592) 176600) ((-1126 . -890) 176561) ((-1126 . -815) 176542) ((-1126 . -1133) T) ((-1126 . -13) T) ((-1126 . -810) 176521) ((-1126 . -965) T) ((-1126 . -667) T) ((-1126 . -1065) T) ((-1126 . -1029) T) ((-1126 . -974) T) ((-1126 . -21) T) ((-1126 . -23) T) ((-1126 . -1017) T) ((-1126 . -556) 176503) ((-1126 . -72) T) ((-1126 . -25) T) ((-1126 . -104) T) ((-1126 . -813) 176484) ((-1126 . -459) 176451) ((-1126 . -262) 176438) ((-1120 . -927) 176422) ((-1120 . -34) T) ((-1120 . -13) T) ((-1120 . -1133) T) ((-1120 . -72) 176376) ((-1120 . -556) 176311) ((-1120 . -262) 176249) ((-1120 . -459) 176182) ((-1120 . -383) 176166) ((-1120 . -1017) 176144) ((-1120 . -432) 176128) ((-1120 . -320) 176112) ((-1120 . -1039) 176096) ((-1115 . -316) 176070) ((-1115 . -72) T) ((-1115 . -13) T) ((-1115 . -1133) T) ((-1115 . -556) 176052) ((-1115 . -1017) T) ((-1113 . -1017) T) ((-1113 . -556) 176034) ((-1113 . -1133) T) ((-1113 . -13) T) ((-1113 . -72) T) ((-1113 . -559) 176016) ((-1108 . -751) 176000) ((-1108 . -72) T) ((-1108 . -13) T) ((-1108 . -1133) T) ((-1108 . -556) 175982) ((-1108 . -1017) T) ((-1106 . -1111) 175961) ((-1106 . -185) 175909) ((-1106 . -76) 175857) ((-1106 . -1039) 175792) ((-1106 . -124) 175740) ((-1106 . -557) NIL) ((-1106 . -195) 175688) ((-1106 . -542) 175667) ((-1106 . -262) 175465) ((-1106 . -459) 175217) ((-1106 . -383) 175152) ((-1106 . -432) 175087) ((-1106 . -243) 175066) ((-1106 . -245) 175045) ((-1106 . -553) 175024) ((-1106 . -1017) T) ((-1106 . -556) 175006) ((-1106 . -72) T) ((-1106 . -1133) T) ((-1106 . -13) T) ((-1106 . -34) T) ((-1106 . -320) 174954) ((-1102 . -1017) T) ((-1102 . -556) 174936) ((-1102 . -1133) T) ((-1102 . -13) T) ((-1102 . -72) T) ((-1101 . -756) T) ((-1101 . -763) T) ((-1101 . -760) T) ((-1101 . -1017) T) ((-1101 . -556) 174918) ((-1101 . -1133) T) ((-1101 . -13) T) ((-1101 . -72) T) ((-1101 . -322) T) ((-1101 . -608) T) ((-1100 . -756) T) ((-1100 . -763) T) ((-1100 . -760) T) ((-1100 . -1017) T) ((-1100 . -556) 174900) ((-1100 . -1133) T) ((-1100 . -13) T) ((-1100 . -72) T) ((-1100 . -322) T) ((-1099 . -1179) T) ((-1099 . -1017) T) ((-1099 . -556) 174867) ((-1099 . -1133) T) ((-1099 . -13) T) ((-1099 . -72) T) ((-1099 . -954) 174803) ((-1099 . -559) 174739) ((-1098 . -556) 174721) ((-1097 . -556) 174703) ((-1096 . -279) 174680) ((-1096 . -954) 174578) ((-1096 . -357) 174562) ((-1096 . -38) 174459) ((-1096 . -559) 174316) ((-1096 . -594) 174241) ((-1096 . -592) 174151) ((-1096 . -974) T) ((-1096 . -1029) T) ((-1096 . -1065) T) ((-1096 . -667) T) ((-1096 . -965) T) ((-1096 . -82) 174016) ((-1096 . -967) 173902) ((-1096 . -972) 173788) ((-1096 . -21) T) ((-1096 . -23) T) ((-1096 . -1017) T) ((-1096 . -556) 173770) ((-1096 . -1133) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -25) T) ((-1096 . -104) T) ((-1096 . -586) 173667) ((-1096 . -658) 173564) ((-1096 . -118) 173543) ((-1096 . -120) 173522) ((-1096 . -148) 173476) ((-1096 . -383) 173460) ((-1096 . -499) 173439) ((-1096 . -248) 173418) ((-1096 . -47) 173395) ((-1094 . -760) T) ((-1094 . -556) 173377) ((-1094 . -1017) T) ((-1094 . -72) T) ((-1094 . -13) T) ((-1094 . -1133) T) ((-1094 . -763) T) ((-1094 . -557) 173299) ((-1094 . -559) 173265) ((-1094 . -954) 173247) ((-1094 . -800) 173214) ((-1093 . -1176) 173198) ((-1093 . -192) 173157) ((-1093 . -559) 173039) ((-1093 . -594) 172964) ((-1093 . -592) 172874) ((-1093 . -104) T) ((-1093 . -25) T) ((-1093 . -72) T) ((-1093 . -556) 172856) ((-1093 . -1017) T) ((-1093 . -23) T) ((-1093 . -21) T) ((-1093 . -974) T) ((-1093 . -1029) T) ((-1093 . -1065) T) ((-1093 . -667) T) ((-1093 . -965) T) ((-1093 . -188) 172809) ((-1093 . -13) T) ((-1093 . -1133) T) ((-1093 . -191) 172768) ((-1093 . -243) 172733) ((-1093 . -813) 172646) ((-1093 . -810) 172534) ((-1093 . -815) 172447) ((-1093 . -890) 172417) ((-1093 . -38) 172314) ((-1093 . -82) 172179) ((-1093 . -967) 172065) ((-1093 . -972) 171951) ((-1093 . -586) 171848) ((-1093 . -658) 171745) ((-1093 . -118) 171724) ((-1093 . -120) 171703) ((-1093 . -148) 171657) ((-1093 . -383) 171641) ((-1093 . -499) 171620) ((-1093 . -248) 171599) ((-1093 . -47) 171576) ((-1093 . -1162) 171553) ((-1093 . -35) 171519) ((-1093 . -66) 171485) ((-1093 . -241) 171451) ((-1093 . -436) 171417) ((-1093 . -1122) 171383) ((-1093 . -1119) 171349) ((-1093 . -919) 171315) ((-1092 . -1168) 171276) ((-1092 . -314) 171255) ((-1092 . -1138) 171234) ((-1092 . -836) 171213) ((-1092 . -499) 171167) ((-1092 . -148) 171101) ((-1092 . -559) 170850) ((-1092 . -658) 170697) ((-1092 . -586) 170544) ((-1092 . -38) 170391) ((-1092 . -395) 170370) ((-1092 . -260) 170349) ((-1092 . -594) 170249) ((-1092 . -592) 170134) ((-1092 . -974) T) ((-1092 . -1029) T) ((-1092 . -1065) T) ((-1092 . -667) T) ((-1092 . -965) T) ((-1092 . -82) 169954) ((-1092 . -967) 169795) ((-1092 . -972) 169636) ((-1092 . -21) T) ((-1092 . -23) T) ((-1092 . -1017) T) ((-1092 . -556) 169618) ((-1092 . -1133) T) ((-1092 . -13) T) ((-1092 . -72) T) ((-1092 . -25) T) ((-1092 . -104) T) ((-1092 . -248) 169572) ((-1092 . -203) 169551) ((-1092 . -919) 169517) ((-1092 . -1119) 169483) ((-1092 . -1122) 169449) ((-1092 . -436) 169415) ((-1092 . -241) 169381) ((-1092 . -66) 169347) ((-1092 . -35) 169313) ((-1092 . -1162) 169283) ((-1092 . -47) 169253) ((-1092 . -383) 169237) ((-1092 . -120) 169216) ((-1092 . -118) 169195) ((-1092 . -890) 169158) ((-1092 . -815) 169064) ((-1092 . -810) 168945) ((-1092 . -813) 168851) ((-1092 . -243) 168809) ((-1092 . -191) 168761) ((-1092 . -188) 168707) ((-1092 . -192) 168659) ((-1092 . -1166) 168643) ((-1092 . -954) 168578) ((-1089 . -1159) 168562) ((-1089 . -1070) 168540) ((-1089 . -557) NIL) ((-1089 . -262) 168527) ((-1089 . -459) 168475) ((-1089 . -279) 168452) ((-1089 . -954) 168335) ((-1089 . -357) 168319) ((-1089 . -38) 168151) ((-1089 . -82) 167956) ((-1089 . -967) 167782) ((-1089 . -972) 167608) ((-1089 . -592) 167518) ((-1089 . -594) 167407) ((-1089 . -586) 167239) ((-1089 . -658) 167071) ((-1089 . -559) 166848) ((-1089 . -118) 166827) ((-1089 . -120) 166806) ((-1089 . -383) 166790) ((-1089 . -47) 166767) ((-1089 . -331) 166751) ((-1089 . -584) 166699) ((-1089 . -813) 166643) ((-1089 . -810) 166550) ((-1089 . -815) 166461) ((-1089 . -800) NIL) ((-1089 . -825) 166440) ((-1089 . -1138) 166419) ((-1089 . -865) 166389) ((-1089 . -836) 166368) ((-1089 . -499) 166282) ((-1089 . -248) 166196) ((-1089 . -148) 166090) ((-1089 . -395) 166024) ((-1089 . -260) 166003) ((-1089 . -243) 165930) ((-1089 . -192) T) ((-1089 . -104) T) ((-1089 . -25) T) ((-1089 . -72) T) ((-1089 . -556) 165912) ((-1089 . -1017) T) ((-1089 . -23) T) ((-1089 . -21) T) ((-1089 . -974) T) ((-1089 . -1029) T) ((-1089 . -1065) T) ((-1089 . -667) T) ((-1089 . -965) T) ((-1089 . -188) 165899) ((-1089 . -13) T) ((-1089 . -1133) T) ((-1089 . -191) T) ((-1089 . -227) 165883) ((-1089 . -186) 165867) ((-1086 . -1147) 165828) ((-1086 . -919) 165794) ((-1086 . -1119) 165760) ((-1086 . -1122) 165726) ((-1086 . -436) 165692) ((-1086 . -241) 165658) ((-1086 . -66) 165624) ((-1086 . -35) 165590) ((-1086 . -1162) 165567) ((-1086 . -47) 165544) ((-1086 . -383) 165483) ((-1086 . -559) 165284) ((-1086 . -658) 165086) ((-1086 . -586) 164888) ((-1086 . -594) 164743) ((-1086 . -592) 164583) ((-1086 . -972) 164379) ((-1086 . -967) 164175) ((-1086 . -82) 163927) ((-1086 . -38) 163729) ((-1086 . -890) 163699) ((-1086 . -243) 163527) ((-1086 . -1145) 163511) ((-1086 . -974) T) ((-1086 . -1029) T) ((-1086 . -1065) T) ((-1086 . -667) T) ((-1086 . -965) T) ((-1086 . -21) T) ((-1086 . -23) T) ((-1086 . -1017) T) ((-1086 . -556) 163493) ((-1086 . -1133) T) ((-1086 . -13) T) ((-1086 . -72) T) ((-1086 . -25) T) ((-1086 . -104) T) ((-1086 . -118) 163403) ((-1086 . -120) 163313) ((-1086 . -557) NIL) ((-1086 . -186) 163265) ((-1086 . -813) 163101) ((-1086 . -815) 162865) ((-1086 . -810) 162604) ((-1086 . -227) 162556) ((-1086 . -191) 162382) ((-1086 . -188) 162202) ((-1086 . -192) 162092) ((-1086 . -314) 162071) ((-1086 . -1138) 162050) ((-1086 . -836) 162029) ((-1086 . -499) 161983) ((-1086 . -148) 161917) ((-1086 . -395) 161896) ((-1086 . -260) 161875) ((-1086 . -248) 161829) ((-1086 . -203) 161808) ((-1086 . -290) 161760) ((-1086 . -459) 161494) ((-1086 . -262) 161379) ((-1086 . -331) 161331) ((-1086 . -584) 161283) ((-1086 . -345) 161235) ((-1086 . -800) NIL) ((-1086 . -744) NIL) ((-1086 . -718) NIL) ((-1086 . -720) NIL) ((-1086 . -760) NIL) ((-1086 . -763) NIL) ((-1086 . -722) NIL) ((-1086 . -725) NIL) ((-1086 . -759) NIL) ((-1086 . -798) 161187) ((-1086 . -825) NIL) ((-1086 . -937) NIL) ((-1086 . -954) 161153) ((-1086 . -1070) NIL) ((-1086 . -908) 161105) ((-1085 . -999) T) ((-1085 . -433) 161086) ((-1085 . -556) 161052) ((-1085 . -559) 161033) ((-1085 . -1017) T) ((-1085 . -1133) T) ((-1085 . -13) T) ((-1085 . -72) T) ((-1085 . -64) T) ((-1084 . -1017) T) ((-1084 . -556) 161015) ((-1084 . -1133) T) ((-1084 . -13) T) ((-1084 . -72) T) ((-1083 . -1017) T) ((-1083 . -556) 160997) ((-1083 . -1133) T) ((-1083 . -13) T) ((-1083 . -72) T) ((-1078 . -1111) 160973) ((-1078 . -185) 160918) ((-1078 . -76) 160863) ((-1078 . -1039) 160795) ((-1078 . -124) 160740) ((-1078 . -557) NIL) ((-1078 . -195) 160685) ((-1078 . -542) 160661) ((-1078 . -262) 160450) ((-1078 . -459) 160190) ((-1078 . -383) 160122) ((-1078 . -432) 160054) ((-1078 . -243) 160030) ((-1078 . -245) 160006) ((-1078 . -553) 159982) ((-1078 . -1017) T) ((-1078 . -556) 159964) ((-1078 . -72) T) ((-1078 . -1133) T) ((-1078 . -13) T) ((-1078 . -34) T) ((-1078 . -320) 159909) ((-1077 . -1062) T) ((-1077 . -326) 159891) ((-1077 . -763) T) ((-1077 . -760) T) ((-1077 . -124) 159873) ((-1077 . -557) NIL) ((-1077 . -243) 159823) ((-1077 . -542) 159798) ((-1077 . -245) 159773) ((-1077 . -597) 159755) ((-1077 . -432) 159737) ((-1077 . -1017) T) ((-1077 . -383) 159719) ((-1077 . -459) NIL) ((-1077 . -262) NIL) ((-1077 . -556) 159701) ((-1077 . -72) T) ((-1077 . -1133) T) ((-1077 . -13) T) ((-1077 . -34) T) ((-1077 . -320) 159683) ((-1077 . -1039) 159665) ((-1077 . -19) 159647) ((-1073 . -620) 159631) ((-1073 . -597) 159615) ((-1073 . -245) 159592) ((-1073 . -243) 159544) ((-1073 . -542) 159521) ((-1073 . -557) 159482) ((-1073 . -432) 159466) ((-1073 . -1017) 159444) ((-1073 . -383) 159428) ((-1073 . -459) 159361) ((-1073 . -262) 159299) ((-1073 . -556) 159234) ((-1073 . -72) 159188) ((-1073 . -1133) T) ((-1073 . -13) T) ((-1073 . -34) T) ((-1073 . -124) 159172) ((-1073 . -1172) 159156) ((-1073 . -927) 159140) ((-1073 . -1068) 159124) ((-1073 . -559) 159101) ((-1073 . -1039) 159085) ((-1071 . -999) T) ((-1071 . -433) 159066) ((-1071 . -556) 159032) ((-1071 . -559) 159013) ((-1071 . -1017) T) ((-1071 . -1133) T) ((-1071 . -13) T) ((-1071 . -72) T) ((-1071 . -64) T) ((-1069 . -1111) 158992) ((-1069 . -185) 158940) ((-1069 . -76) 158888) ((-1069 . -1039) 158823) ((-1069 . -124) 158771) ((-1069 . -557) NIL) ((-1069 . -195) 158719) ((-1069 . -542) 158698) ((-1069 . -262) 158496) ((-1069 . -459) 158248) ((-1069 . -383) 158183) ((-1069 . -432) 158118) ((-1069 . -243) 158097) ((-1069 . -245) 158076) ((-1069 . -553) 158055) ((-1069 . -1017) T) ((-1069 . -556) 158037) ((-1069 . -72) T) ((-1069 . -1133) T) ((-1069 . -13) T) ((-1069 . -34) T) ((-1069 . -320) 157985) ((-1066 . -1038) 157969) ((-1066 . -320) 157953) ((-1066 . -432) 157937) ((-1066 . -1017) 157915) ((-1066 . -383) 157899) ((-1066 . -459) 157832) ((-1066 . -262) 157770) ((-1066 . -556) 157705) ((-1066 . -72) 157659) ((-1066 . -1133) T) ((-1066 . -13) T) ((-1066 . -34) T) ((-1066 . -1039) 157643) ((-1066 . -76) 157627) ((-1064 . -1024) 157596) ((-1064 . -1128) 157565) ((-1064 . -1039) 157549) ((-1064 . -556) 157511) ((-1064 . -124) 157495) ((-1064 . -34) T) ((-1064 . -13) T) ((-1064 . -1133) T) ((-1064 . -72) T) ((-1064 . -262) 157433) ((-1064 . -459) 157366) ((-1064 . -383) 157350) ((-1064 . -1017) T) ((-1064 . -432) 157334) ((-1064 . -557) 157295) ((-1064 . -320) 157279) ((-1064 . -893) 157248) ((-1064 . -987) 157217) ((-1060 . -1041) 157162) ((-1060 . -320) 157146) ((-1060 . -34) T) ((-1060 . -262) 157084) ((-1060 . -459) 157017) ((-1060 . -383) 157001) ((-1060 . -432) 156985) ((-1060 . -969) 156925) ((-1060 . -954) 156823) ((-1060 . -559) 156742) ((-1060 . -357) 156726) ((-1060 . -584) 156674) ((-1060 . -594) 156612) ((-1060 . -331) 156596) ((-1060 . -192) 156575) ((-1060 . -188) 156523) ((-1060 . -191) 156477) ((-1060 . -227) 156461) ((-1060 . -810) 156385) ((-1060 . -815) 156311) ((-1060 . -813) 156270) ((-1060 . -186) 156254) ((-1060 . -658) 156189) ((-1060 . -586) 156124) ((-1060 . -592) 156083) ((-1060 . -104) T) ((-1060 . -25) T) ((-1060 . -72) T) ((-1060 . -13) T) ((-1060 . -1133) T) ((-1060 . -556) 156045) ((-1060 . -1017) T) ((-1060 . -23) T) ((-1060 . -21) T) ((-1060 . -972) 156029) ((-1060 . -967) 156013) ((-1060 . -82) 155992) ((-1060 . -965) T) ((-1060 . -667) T) ((-1060 . -1065) T) ((-1060 . -1029) T) ((-1060 . -974) T) ((-1060 . -38) 155952) ((-1060 . -557) 155913) ((-1059 . -927) 155884) ((-1059 . -34) T) ((-1059 . -13) T) ((-1059 . -1133) T) ((-1059 . -72) T) ((-1059 . -556) 155866) ((-1059 . -262) 155792) ((-1059 . -459) 155700) ((-1059 . -383) 155671) ((-1059 . -1017) T) ((-1059 . -432) 155642) ((-1059 . -320) 155613) ((-1059 . -1039) 155584) ((-1058 . -1017) T) ((-1058 . -556) 155566) ((-1058 . -1133) T) ((-1058 . -13) T) ((-1058 . -72) T) ((-1053 . -1055) T) ((-1053 . -1179) T) ((-1053 . -64) T) ((-1053 . -72) T) ((-1053 . -13) T) ((-1053 . -1133) T) ((-1053 . -556) 155532) ((-1053 . -1017) T) ((-1053 . -559) 155513) ((-1053 . -433) 155494) ((-1053 . -999) T) ((-1051 . -1052) 155478) ((-1051 . -72) T) ((-1051 . -13) T) ((-1051 . -1133) T) ((-1051 . -556) 155460) ((-1051 . -1017) T) ((-1044 . -683) 155439) ((-1044 . -35) 155405) ((-1044 . -66) 155371) ((-1044 . -241) 155337) ((-1044 . -436) 155303) ((-1044 . -1122) 155269) ((-1044 . -1119) 155235) ((-1044 . -919) 155201) ((-1044 . -47) 155173) ((-1044 . -38) 155070) ((-1044 . -586) 154967) ((-1044 . -658) 154864) ((-1044 . -559) 154746) ((-1044 . -248) 154725) ((-1044 . -499) 154704) ((-1044 . -383) 154688) ((-1044 . -82) 154553) ((-1044 . -967) 154439) ((-1044 . -972) 154325) ((-1044 . -148) 154279) ((-1044 . -120) 154258) 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-104) T) ((-1003 . -25) T) ((-1003 . -72) T) ((-1003 . -556) 143148) ((-1003 . -1017) T) ((-1003 . -23) T) ((-1003 . -21) T) ((-1003 . -974) T) ((-1003 . -1029) T) ((-1003 . -1065) T) ((-1003 . -667) T) ((-1003 . -965) T) ((-1003 . -188) 143096) ((-1003 . -13) T) ((-1003 . -1133) T) ((-1003 . -191) 143050) ((-1003 . -227) 143034) ((-1003 . -186) 143018) ((-1001 . -556) 143000) ((-998 . -760) T) ((-998 . -556) 142982) ((-998 . -1017) T) ((-998 . -72) T) ((-998 . -13) T) ((-998 . -1133) T) ((-998 . -763) T) ((-998 . -557) 142963) ((-995 . -665) 142942) ((-995 . -954) 142840) ((-995 . -357) 142824) ((-995 . -584) 142772) ((-995 . -594) 142649) ((-995 . -331) 142633) ((-995 . -324) 142612) ((-995 . -120) 142591) ((-995 . -559) 142416) ((-995 . -658) 142290) ((-995 . -586) 142164) ((-995 . -592) 142062) ((-995 . -972) 141975) ((-995 . -967) 141888) ((-995 . -82) 141780) ((-995 . -38) 141654) ((-995 . -355) 141633) ((-995 . -347) 141612) ((-995 . -118) 141566) ((-995 . -1070) 141545) ((-995 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. -82) 139833) ((-979 . -38) 139820) ((-979 . -395) T) ((-979 . -260) T) ((-979 . -191) T) ((-979 . -188) 139807) ((-979 . -192) T) ((-979 . -116) T) ((-979 . -965) T) ((-979 . -667) T) ((-979 . -1065) T) ((-979 . -1029) T) ((-979 . -974) T) ((-979 . -21) T) ((-979 . -592) 139779) ((-979 . -23) T) ((-979 . -1017) T) ((-979 . -556) 139761) ((-979 . -1133) T) ((-979 . -13) T) ((-979 . -72) T) ((-979 . -25) T) ((-979 . -104) T) ((-979 . -120) T) ((-979 . -561) 139742) ((-978 . -984) 139721) ((-978 . -72) T) ((-978 . -13) T) ((-978 . -1133) T) ((-978 . -556) 139703) ((-978 . -1017) T) ((-975 . -1133) T) ((-975 . -13) T) ((-975 . -1017) 139681) ((-975 . -556) 139648) ((-975 . -72) 139626) ((-970 . -969) 139566) ((-970 . -586) 139511) ((-970 . -658) 139456) ((-970 . -432) 139440) ((-970 . -383) 139424) ((-970 . -459) 139357) ((-970 . -262) 139295) ((-970 . -34) T) ((-970 . -320) 139279) ((-970 . -594) 139263) ((-970 . -592) 139232) ((-970 . -104) T) ((-970 . -25) T) ((-970 . -72) T) ((-970 . 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137427) ((-941 . -586) 137364) ((-941 . -658) 137301) ((-941 . -559) 137238) ((-941 . -499) T) ((-941 . -836) T) ((-941 . -1138) T) ((-941 . -314) T) ((-941 . -82) 137147) ((-941 . -967) 137084) ((-941 . -972) 137021) ((-941 . -148) T) ((-941 . -120) T) ((-941 . -594) 136958) ((-941 . -592) 136895) ((-941 . -104) T) ((-941 . -25) T) ((-941 . -72) T) ((-941 . -13) T) ((-941 . -1133) T) ((-941 . -556) 136877) ((-941 . -1017) T) ((-941 . -23) T) ((-941 . -21) T) ((-941 . -965) T) ((-941 . -667) T) ((-941 . -1065) T) ((-941 . -1029) T) ((-941 . -974) T) ((-936 . -999) T) ((-936 . -433) 136858) ((-936 . -556) 136824) ((-936 . -559) 136805) ((-936 . -1017) T) ((-936 . -1133) T) ((-936 . -13) T) ((-936 . -72) T) ((-936 . -64) T) ((-921 . -908) 136787) ((-921 . -1070) T) ((-921 . -559) 136737) ((-921 . -954) 136697) ((-921 . -557) 136627) ((-921 . -937) T) ((-921 . -825) NIL) ((-921 . -798) 136609) ((-921 . -759) T) ((-921 . -725) T) ((-921 . -722) T) ((-921 . -763) T) ((-921 . -760) T) ((-921 . -720) T) ((-921 . -718) T) ((-921 . -744) T) ((-921 . -800) 136591) ((-921 . -345) 136573) ((-921 . -584) 136555) ((-921 . -331) 136537) ((-921 . -243) NIL) ((-921 . -262) NIL) ((-921 . -459) NIL) ((-921 . -383) 136519) ((-921 . -290) 136501) ((-921 . -203) T) ((-921 . -82) 136428) ((-921 . -967) 136378) ((-921 . -972) 136328) ((-921 . -248) T) ((-921 . -658) 136278) ((-921 . -586) 136228) ((-921 . -594) 136178) ((-921 . -592) 136128) ((-921 . -38) 136078) ((-921 . -260) T) ((-921 . -395) T) ((-921 . -148) T) ((-921 . -499) T) ((-921 . -836) T) ((-921 . -1138) T) ((-921 . -314) T) ((-921 . -192) T) ((-921 . -188) 136065) ((-921 . -191) T) ((-921 . -227) 136047) ((-921 . -810) NIL) ((-921 . -815) NIL) ((-921 . -813) NIL) ((-921 . -186) 136029) ((-921 . -120) T) ((-921 . -118) NIL) ((-921 . -104) T) ((-921 . -25) T) ((-921 . -72) T) ((-921 . -13) T) ((-921 . -1133) T) ((-921 . -556) 135989) ((-921 . -1017) T) ((-921 . -23) T) ((-921 . -21) T) ((-921 . -965) T) ((-921 . -667) T) ((-921 . -1065) T) ((-921 . -1029) T) ((-921 . -974) T) ((-920 . -293) 135963) ((-920 . -148) T) ((-920 . -559) 135893) ((-920 . -974) T) ((-920 . -1029) T) ((-920 . -1065) T) ((-920 . -667) T) ((-920 . -965) T) ((-920 . -594) 135795) ((-920 . -592) 135725) ((-920 . -104) T) ((-920 . -25) T) ((-920 . -72) T) ((-920 . -13) T) ((-920 . -1133) T) ((-920 . -556) 135707) ((-920 . -1017) T) ((-920 . -23) T) ((-920 . -21) T) ((-920 . -972) 135652) ((-920 . -967) 135597) ((-920 . -82) 135514) ((-920 . -557) 135498) ((-920 . -186) 135475) ((-920 . -813) 135427) ((-920 . -815) 135339) ((-920 . -810) 135249) ((-920 . -227) 135226) ((-920 . -191) 135166) ((-920 . -188) 135100) ((-920 . -192) 135072) ((-920 . -314) T) ((-920 . -1138) T) ((-920 . -836) T) ((-920 . -499) T) ((-920 . -658) 135017) ((-920 . -586) 134962) ((-920 . -38) 134907) ((-920 . -395) T) ((-920 . -260) T) ((-920 . -248) T) ((-920 . -203) T) ((-920 . -322) NIL) ((-920 . -301) NIL) ((-920 . -1070) NIL) ((-920 . -118) 134879) ((-920 . 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NIL) ((-784 . -744) NIL) ((-784 . -800) NIL) ((-784 . -345) 121600) ((-784 . -584) 121577) ((-784 . -594) 121522) ((-784 . -331) 121499) ((-784 . -243) 121429) ((-784 . -262) 121373) ((-784 . -459) 121236) ((-784 . -383) 121213) ((-784 . -290) 121190) ((-784 . -203) T) ((-784 . -82) 121107) ((-784 . -967) 121052) ((-784 . -972) 120997) ((-784 . -248) T) ((-784 . -658) 120942) ((-784 . -586) 120887) ((-784 . -592) 120817) ((-784 . -38) 120762) ((-784 . -260) T) ((-784 . -395) T) ((-784 . -148) T) ((-784 . -499) T) ((-784 . -836) T) ((-784 . -1138) T) ((-784 . -314) T) ((-784 . -192) NIL) ((-784 . -188) NIL) ((-784 . -191) NIL) ((-784 . -227) 120739) ((-784 . -810) NIL) ((-784 . -815) NIL) ((-784 . -813) NIL) ((-784 . -186) 120716) ((-784 . -120) T) ((-784 . -118) NIL) ((-784 . -104) T) ((-784 . -25) T) ((-784 . -72) T) ((-784 . -13) T) ((-784 . -1133) T) ((-784 . -556) 120698) ((-784 . -1017) T) ((-784 . -23) T) ((-784 . -21) T) ((-784 . -965) T) ((-784 . -667) T) ((-784 . -1065) T) 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. -120) 117861) ((-749 . -118) 117840) ((-749 . -38) 117810) ((-749 . -82) 117775) ((-749 . -967) 117745) ((-749 . -972) 117715) ((-749 . -586) 117685) ((-749 . -658) 117655) ((-747 . -1017) T) ((-747 . -556) 117637) ((-747 . -1133) T) ((-747 . -13) T) ((-747 . -72) T) ((-747 . -357) 117621) ((-747 . -559) 117494) ((-747 . -954) 117392) ((-747 . -21) 117347) ((-747 . -592) 117267) ((-747 . -23) 117222) ((-747 . -25) 117177) ((-747 . -104) 117132) ((-747 . -759) 117111) ((-747 . -725) 117090) ((-747 . -722) 117069) ((-747 . -763) 117048) ((-747 . -760) 117027) ((-747 . -720) 117006) ((-747 . -718) 116985) ((-747 . -965) 116964) ((-747 . -667) 116943) ((-747 . -1065) 116922) ((-747 . -1029) 116901) ((-747 . -974) 116880) ((-747 . -594) 116853) ((-747 . -120) 116832) ((-745 . -649) 116816) ((-745 . -559) 116771) ((-745 . -658) 116741) ((-745 . -586) 116711) ((-745 . -594) 116685) ((-745 . -592) 116644) ((-745 . -104) T) ((-745 . -25) T) ((-745 . -72) T) ((-745 . -13) T) ((-745 . -1133) T) 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116071) ((-741 . -1133) T) ((-741 . -13) T) ((-741 . -72) T) ((-741 . -25) T) ((-741 . -104) T) ((-741 . -594) 116022) ((-741 . -192) T) ((-741 . -559) 115931) ((-741 . -974) T) ((-741 . -1029) T) ((-741 . -1065) T) ((-741 . -667) T) ((-741 . -965) T) ((-741 . -188) 115918) ((-741 . -191) T) ((-741 . -433) 115902) ((-741 . -314) 115881) ((-741 . -1138) 115860) ((-741 . -836) 115839) ((-741 . -499) 115818) ((-741 . -148) 115797) ((-741 . -658) 115734) ((-741 . -586) 115671) ((-741 . -38) 115608) ((-741 . -395) 115587) ((-741 . -260) 115566) ((-741 . -248) 115545) ((-741 . -203) 115524) ((-740 . -215) 115463) ((-740 . -559) 115207) ((-740 . -954) 115037) ((-740 . -557) NIL) ((-740 . -279) 114999) ((-740 . -357) 114983) ((-740 . -38) 114835) ((-740 . -82) 114660) ((-740 . -967) 114506) ((-740 . -972) 114352) ((-740 . -592) 114262) ((-740 . -594) 114151) ((-740 . -586) 114003) ((-740 . -658) 113855) ((-740 . -118) 113834) ((-740 . -120) 113813) ((-740 . -148) 113727) ((-740 . -383) 113711) 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108512) ((-726 . -357) 108476) ((-726 . -243) 108434) ((-726 . -262) 108399) ((-726 . -459) 108311) ((-726 . -383) 108295) ((-726 . -290) 108279) ((-726 . -322) 108258) ((-726 . -557) 108219) ((-726 . -120) 108198) ((-726 . -118) 108177) ((-726 . -658) 108161) ((-726 . -586) 108145) ((-726 . -594) 108119) ((-726 . -592) 108078) ((-726 . -104) T) ((-726 . -25) T) ((-726 . -72) T) ((-726 . -13) T) ((-726 . -1133) T) ((-726 . -556) 108060) ((-726 . -1017) T) ((-726 . -23) T) ((-726 . -21) T) ((-726 . -972) 108044) ((-726 . -967) 108028) ((-726 . -82) 108007) ((-726 . -965) T) ((-726 . -667) T) ((-726 . -1065) T) ((-726 . -1029) T) ((-726 . -974) T) ((-726 . -38) 107991) ((-708 . -1159) 107975) ((-708 . -1070) 107953) ((-708 . -557) NIL) ((-708 . -262) 107940) ((-708 . -459) 107888) ((-708 . -279) 107865) ((-708 . -954) 107727) ((-708 . -357) 107711) ((-708 . -38) 107543) ((-708 . -82) 107348) ((-708 . -967) 107174) ((-708 . -972) 107000) ((-708 . -592) 106910) ((-708 . -594) 106799) 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104730) ((-707 . -954) 104589) ((-707 . -357) 104573) ((-707 . -38) 104425) ((-707 . -559) 104198) ((-707 . -594) 104087) ((-707 . -592) 103997) ((-707 . -974) T) ((-707 . -1029) T) ((-707 . -1065) T) ((-707 . -667) T) ((-707 . -965) T) ((-707 . -82) 103822) ((-707 . -967) 103668) ((-707 . -972) 103514) ((-707 . -21) T) ((-707 . -23) T) ((-707 . -1017) T) ((-707 . -556) 103428) ((-707 . -1133) T) ((-707 . -13) T) ((-707 . -72) T) ((-707 . -25) T) ((-707 . -104) T) ((-707 . -586) 103280) ((-707 . -658) 103132) ((-707 . -118) 103111) ((-707 . -120) 103090) ((-707 . -148) 103004) ((-707 . -383) 102988) ((-707 . -499) 102922) ((-707 . -248) 102856) ((-707 . -47) 102828) ((-707 . -331) 102812) ((-707 . -584) 102760) ((-707 . -395) 102714) ((-707 . -813) 102698) ((-707 . -810) 102680) ((-707 . -815) 102664) ((-707 . -800) 102523) ((-707 . -825) 102502) ((-707 . -1138) 102481) ((-707 . -865) 102448) ((-700 . -1017) T) ((-700 . -556) 102430) ((-700 . -1133) T) ((-700 . -13) T) ((-700 . -72) T) 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101953) ((-678 . -559) 101909) ((-678 . -954) 101880) ((-678 . -383) 101864) ((-678 . -120) 101843) ((-678 . -118) 101822) ((-678 . -38) 101792) ((-678 . -82) 101757) ((-678 . -967) 101727) ((-678 . -972) 101697) ((-678 . -586) 101667) ((-678 . -658) 101637) ((-678 . -322) 101590) ((-674 . -865) 101543) ((-674 . -559) 101335) ((-674 . -954) 101213) ((-674 . -1138) 101192) ((-674 . -825) 101171) ((-674 . -800) NIL) ((-674 . -815) 101148) ((-674 . -810) 101123) ((-674 . -813) 101100) ((-674 . -459) 101038) ((-674 . -395) 100992) ((-674 . -584) 100940) ((-674 . -594) 100829) ((-674 . -331) 100813) ((-674 . -47) 100778) ((-674 . -38) 100630) ((-674 . -586) 100482) ((-674 . -658) 100334) ((-674 . -248) 100268) ((-674 . -499) 100202) ((-674 . -383) 100186) ((-674 . -82) 100011) ((-674 . -967) 99857) ((-674 . -972) 99703) ((-674 . -148) 99617) ((-674 . -120) 99596) ((-674 . -118) 99575) ((-674 . -592) 99485) ((-674 . -104) T) ((-674 . -25) T) ((-674 . -72) T) ((-674 . -13) T) ((-674 . -1133) T) ((-674 . -556) 99467) ((-674 . -1017) T) ((-674 . -23) T) ((-674 . -21) T) ((-674 . -965) T) ((-674 . -667) T) ((-674 . -1065) T) ((-674 . -1029) T) ((-674 . -974) T) ((-674 . -357) 99451) ((-674 . -279) 99416) ((-674 . -262) 99403) ((-674 . -557) 99264) ((-668 . -669) 99248) ((-668 . -80) 99232) ((-668 . -1133) T) ((-668 . |MappingCategory|) 99206) ((-668 . -1027) 99190) ((-668 . -1017) T) ((-668 . -556) 99151) ((-668 . -13) T) ((-668 . -72) T) ((-659 . -416) T) ((-659 . -1029) T) ((-659 . -72) T) ((-659 . -13) T) ((-659 . -1133) T) ((-659 . -556) 99133) ((-659 . -1017) T) ((-659 . -667) T) ((-656 . -965) T) ((-656 . -667) T) ((-656 . -1065) T) ((-656 . -1029) T) ((-656 . -974) T) ((-656 . -21) T) ((-656 . -592) 99105) ((-656 . -23) T) ((-656 . -1017) T) ((-656 . -556) 99087) ((-656 . -1133) T) ((-656 . -13) T) ((-656 . -72) T) ((-656 . -25) T) ((-656 . -104) T) ((-656 . -594) 99074) ((-656 . -559) 99056) ((-655 . -965) T) ((-655 . -667) T) ((-655 . -1065) T) ((-655 . -1029) T) 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. -1133) T) ((-306 . -556) 52601) ((-306 . -1017) T) ((-306 . -23) T) ((-306 . -21) T) ((-306 . -974) T) ((-306 . -1029) T) ((-306 . -1065) T) ((-306 . -667) T) ((-306 . -965) T) ((-306 . -314) T) ((-306 . -1138) T) ((-306 . -836) T) ((-306 . -499) T) ((-306 . -148) T) ((-306 . -658) 52553) ((-306 . -586) 52505) ((-306 . -38) 52470) ((-306 . -395) T) ((-306 . -260) T) ((-306 . -82) 52401) ((-306 . -967) 52353) ((-306 . -972) 52305) ((-306 . -248) T) ((-306 . -203) T) ((-306 . -347) 52259) ((-306 . -118) 52213) ((-306 . -954) 52197) ((-306 . -1191) 52181) ((-306 . -1202) 52165) ((-305 . -282) 52149) ((-305 . -192) 52128) ((-305 . -188) 52101) ((-305 . -191) 52080) ((-305 . -322) 52059) ((-305 . -1070) 52038) ((-305 . -301) 52017) ((-305 . -120) 51996) ((-305 . -559) 51933) ((-305 . -594) 51885) ((-305 . -592) 51822) ((-305 . -104) T) ((-305 . -25) T) ((-305 . -72) T) ((-305 . -13) T) ((-305 . -1133) T) ((-305 . -556) 51804) ((-305 . -1017) T) ((-305 . -23) T) ((-305 . -21) T) ((-305 . 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. -72) T) ((-159 . -162) T) ((-159 . -1017) T) ((-159 . -556) 15834) ((-159 . -1133) T) ((-159 . -13) T) ((-159 . -72) T) ((-159 . -751) 15816) ((-156 . -999) T) ((-156 . -433) 15797) ((-156 . -556) 15763) ((-156 . -559) 15744) ((-156 . -1017) T) ((-156 . -1133) T) ((-156 . -13) T) ((-156 . -72) T) ((-156 . -64) T) ((-151 . -556) 15726) ((-150 . -38) 15658) ((-150 . -559) 15575) ((-150 . -594) 15507) ((-150 . -592) 15424) ((-150 . -974) T) ((-150 . -1029) T) ((-150 . -1065) T) ((-150 . -667) T) ((-150 . -965) T) ((-150 . -82) 15323) ((-150 . -967) 15255) ((-150 . -972) 15187) ((-150 . -21) T) ((-150 . -23) T) ((-150 . -1017) T) ((-150 . -556) 15169) ((-150 . -1133) T) ((-150 . -13) T) ((-150 . -72) T) ((-150 . -25) T) ((-150 . -104) T) ((-150 . -586) 15101) ((-150 . -658) 15033) ((-150 . -314) T) ((-150 . -1138) T) ((-150 . -836) T) ((-150 . -499) T) ((-150 . -148) T) ((-150 . -395) T) ((-150 . -260) T) ((-150 . -248) T) ((-150 . -203) T) ((-147 . -1017) T) ((-147 . -556) 15015) ((-147 . -1133) T) ((-147 . -13) T) ((-147 . -72) T) ((-144 . -141) 14999) ((-144 . -35) 14977) ((-144 . -66) 14955) ((-144 . -241) 14933) ((-144 . -436) 14911) ((-144 . -1122) 14889) ((-144 . -1119) 14867) ((-144 . -919) 14819) ((-144 . -825) 14772) ((-144 . -557) 14540) ((-144 . -798) 14524) ((-144 . -322) 14478) ((-144 . -301) 14457) ((-144 . -1070) 14436) ((-144 . -347) 14415) ((-144 . -355) 14386) ((-144 . -38) 14220) ((-144 . -82) 14112) ((-144 . -967) 14025) ((-144 . -972) 13938) ((-144 . -586) 13772) ((-144 . -658) 13606) ((-144 . -324) 13577) ((-144 . -665) 13548) ((-144 . -954) 13446) ((-144 . -559) 13231) ((-144 . -357) 13215) ((-144 . -800) 13140) ((-144 . -345) 13124) ((-144 . -584) 13072) ((-144 . -594) 12949) ((-144 . -592) 12847) ((-144 . -331) 12831) ((-144 . -243) 12789) ((-144 . -262) 12754) ((-144 . -459) 12666) ((-144 . -383) 12650) ((-144 . -290) 12634) ((-144 . -203) 12588) ((-144 . -1138) 12496) ((-144 . -314) 12450) ((-144 . -836) 12384) ((-144 . -499) 12298) ((-144 . 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NIL) ((-90 . -188) NIL) ((-90 . -191) NIL) ((-90 . -227) 7750) ((-90 . -810) NIL) ((-90 . -815) NIL) ((-90 . -813) NIL) ((-90 . -186) 7728) ((-90 . -120) T) ((-90 . -118) NIL) ((-90 . -104) T) ((-90 . -25) T) ((-90 . -72) T) ((-90 . -13) T) ((-90 . -1133) T) ((-90 . -556) 7710) ((-90 . -1017) T) ((-90 . -23) T) ((-90 . -21) T) ((-90 . -965) T) ((-90 . -667) T) ((-90 . -1065) T) ((-90 . -1029) T) ((-90 . -974) T) ((-89 . -783) 7694) ((-89 . -836) T) ((-89 . -499) T) ((-89 . -248) T) ((-89 . -148) T) ((-89 . -559) 7666) ((-89 . -658) 7653) ((-89 . -586) 7640) ((-89 . -972) 7627) ((-89 . -967) 7614) ((-89 . -82) 7599) ((-89 . -38) 7586) ((-89 . -395) T) ((-89 . -260) T) ((-89 . -965) T) ((-89 . -667) T) ((-89 . -1065) T) ((-89 . -1029) T) ((-89 . -974) T) ((-89 . -21) T) ((-89 . -592) 7558) ((-89 . -23) T) ((-89 . -1017) T) ((-89 . -556) 7540) ((-89 . -1133) T) ((-89 . -13) T) ((-89 . -72) T) ((-89 . -25) T) ((-89 . -104) T) ((-89 . -594) 7527) ((-89 . -120) T) ((-86 . -760) T) ((-86 . 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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 5fb4cad3..1d141e01 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3580468865) -(4001 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3580478883) +(4004 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| @@ -37,8 +37,9 @@ |ComplexRootPackage| |ColonAst| |Color| |CombinatorialFunction| |IntegerCombinatoricFunctions| |CombinatorialOpsCategory| |Commutator| |CommaAst| |CommonOperators| |CommuteUnivariatePolynomialCategory| - |ComplexCategory&| |ComplexCategory| |ComplexFactorization| |CompilerPackage| - |Complex| |ComplexFunctions2| |ComplexPattern| |SubSpaceComponentProperty| + |CommutativeOperation| |CommutativeOperatorCategory| |ComplexCategory&| + |ComplexCategory| |ComplexFactorization| |CompilerPackage| |Complex| + |ComplexFunctions2| |ComplexPattern| |SubSpaceComponentProperty| |CommutativeRing| |Conduit| |ContinuedFraction| |Contour| |CoordinateSystems| |CharacteristicPolynomialInMonogenicalAlgebra| |ComplexPatternMatch| |CRApackage| |CoerceAst| |ComplexRootFindingPackage| |CyclicStreamTools| @@ -427,101 +428,102 @@ |removeDuplicates| |e| |clipParametric| |clipWithRanges| |numberOfHues| |yellow| |iifact| |iibinom| |iiperm| |iipow| |iidsum| |iidprod| |ipow| |factorial| |multinomial| |permutation| |stirling1| |stirling2| |summation| - |factorials| |mkcomm| |polarCoordinates| |complex| |imaginary| |elaborateFile| - |elaborate| |macroExpand| |solid| |solid?| |denominators| |numerators| - |convergents| |approximants| |reducedForm| |partialQuotients| - |partialDenominators| |partialNumerators| |reducedContinuedFraction| |push| - |bindings| |cartesian| |polar| |cylindrical| |spherical| |parabolic| - |parabolicCylindrical| |paraboloidal| |ellipticCylindrical| - |prolateSpheroidal| |oblateSpheroidal| |bipolar| |bipolarCylindrical| - |toroidal| |conical| |modTree| |multiEuclideanTree| |complexZeros| - |divisorCascade| |graeffe| |pleskenSplit| |reciprocalPolynomial| |rootRadius| - |schwerpunkt| |setErrorBound| |startPolynomial| |cycleElt| - |computeCycleLength| |computeCycleEntry| |findConstructor| |arguments| - |operations| |dualSignature| |kind| |package| |domain| |category| |coerceP| - |powerSum| |elementary| |alternating| |cyclic| |dihedral| |cap| |cup| |wreath| - |SFunction| |skewSFunction| |cyclotomicDecomposition| - |cyclotomicFactorization| |qsetelt| |doubleResultant| |distdfact| - |separateDegrees| |trace2PowMod| |tracePowMod| |irreducible?| |decimal| - |innerint| |exteriorDifferential| |totalDifferential| |homogeneous?| - |leadingBasisTerm| |ignore?| |computeInt| |checkForZero| |nan?| |logGamma| - |hypergeometric0F1| |rotatez| |rotatey| |rotatex| |identity| |dictionary| - |dioSolve| |directProduct| |newLine| |copies| |say| |sayLength| |setnext!| - |setprevious!| |next| |previous| |datalist| |shanksDiscLogAlgorithm| - |showSummary| |reflect| |reify| |constructor| |functorData| |separant| - |initial| |leader| |isobaric?| |weights| |differentialVariables| - |extractBottom!| |extractTop!| |insertBottom!| |insertTop!| |bottom!| |top!| - |dequeue| |makeObject| |recolor| |drawComplex| |drawComplexVectorField| - |setRealSteps| |setImagSteps| |setClipValue| |draw| |option?| |range| - |colorFunction| |curveColor| |pointColor| |clip| |clipBoolean| |style| - |toScale| |pointColorPalette| |curveColorPalette| |var1Steps| |var2Steps| - |space| |tubePoints| |tubeRadius| |option| |weight| |makeVariable| |Nul| - |exponents| |iisqrt2| |iisqrt3| |iiexp| |iilog| |iisin| |iicos| |iitan| - |iicot| |iisec| |iicsc| |iiasin| |iiacos| |iiatan| |iiacot| |iiasec| |iiacsc| - |iisinh| |iicosh| |iitanh| |iicoth| |iisech| |iicsch| |iiasinh| |iiacosh| - |iiatanh| |iiacoth| |iiasech| |iiacsch| |specialTrigs| |localReal?| - |rischNormalize| |realElementary| |validExponential| |rootNormalize| |tanQ| - |callForm?| |getIdentifier| |variable?| |getConstant| |type| |environment| - |typeForm| |irForm| |elaboration| |select!| |delete!| |sn| |cn| |dn| |sncndn| - |qsetelt!| |categoryFrame| |interactiveEnv| |currentEnv| |putProperties| - |getProperties| |putProperty| |getProperty| |scopes| |eigenvalues| - |eigenvector| |generalizedEigenvector| |generalizedEigenvectors| - |eigenvectors| |factorAndSplit| |rightOne| |leftOne| |rightZero| |leftZero| - |swap| |error| |minPoly| |freeOf?| |operators| |tower| |kernels| |mainKernel| - |distribute| |subst| |multiEuclidean| |extendedEuclidean| |euclideanSize| - |sizeLess?| |simplifyPower| |number?| |seriesSolve| |constantToUnaryFunction| - |tubePlot| |exponentialOrder| |completeEval| |lowerPolynomial| - |raisePolynomial| |normalDeriv| |ran| |highCommonTerms| |mapCoef| |nthCoef| - |binomThmExpt| |pomopo!| |mapExponents| |linearAssociatedLog| - |linearAssociatedOrder| |linearAssociatedExp| |createNormalElement| |sin?| - |lookupFunction| |encodingDirectory| |attributeData| |domainTemplate| - |lSpaceBasis| |finiteBasis| |principal?| |divisor| |rationalPoints| - |nonSingularModel| |algSplitSimple| |hyperelliptic| |elliptic| - |integralDerivationMatrix| |integralRepresents| |integralCoordinates| - |yCoordinates| |inverseIntegralMatrixAtInfinity| |integralMatrixAtInfinity| - |inverseIntegralMatrix| |integralMatrix| |reduceBasisAtInfinity| - |normalizeAtInfinity| |complementaryBasis| |integral?| |integralAtInfinity?| - |integralBasisAtInfinity| |ramified?| |ramifiedAtInfinity?| |singular?| - |singularAtInfinity?| |branchPoint?| |branchPointAtInfinity?| |rationalPoint?| - |absolutelyIrreducible?| |genus| |getZechTable| |createZechTable| - |createMultiplicationTable| |createMultiplicationMatrix| - |createLowComplexityTable| |createLowComplexityNormalBasis| - |representationType| |createPrimitiveElement| |tableForDiscreteLogarithm| - |factorsOfCyclicGroupSize| |sizeMultiplication| |getMultiplicationMatrix| - |getMultiplicationTable| |primitive?| |numberOfIrreduciblePoly| - |numberOfPrimitivePoly| |numberOfNormalPoly| |createIrreduciblePoly| - |createPrimitivePoly| |createNormalPoly| |createNormalPrimitivePoly| - |createPrimitiveNormalPoly| |nextIrreduciblePoly| |nextPrimitivePoly| - |nextNormalPoly| |nextNormalPrimitivePoly| |nextPrimitiveNormalPoly| - |leastAffineMultiple| |reducedQPowers| |rootOfIrreduciblePoly| |write!| - |read!| |iomode| |close!| |reopen!| |open| |rightUnit| |leftUnit| - |rightMinimalPolynomial| |leftMinimalPolynomial| |associatorDependence| - |lieAlgebra?| |jordanAlgebra?| |noncommutativeJordanAlgebra?| - |jordanAdmissible?| |lieAdmissible?| |jacobiIdentity?| |powerAssociative?| - |alternative?| |flexible?| |rightAlternative?| |leftAlternative?| - |antiAssociative?| |associative?| |antiCommutative?| |commutative?| - |rightCharacteristicPolynomial| |leftCharacteristicPolynomial| |rightNorm| - |leftNorm| |rightTrace| |leftTrace| |someBasis| |find| |count| |every?| |any?| - |sort!| |copyInto!| |sorted?| |LiePoly| |quickSort| |heapSort| |shellSort| - |outputSpacing| |outputGeneral| |outputFixed| |outputFloating| |exp1| |log10| - |log2| |rationalApproximation| |relerror| |complexSolve| |complexRoots| - |realRoots| |leadingTerm| |overlap| |hcrf| |hclf| |writable?| |readable?| - |exists?| |extension| |directory| |filename| |shallowExpand| |deepExpand| - |fracPart| |polyPart| |fullPartialFraction| |primeFrobenius| |discreteLog| - |decreasePrecision| |increasePrecision| |precision| |bits| |mantissa| - |unitNormalize| |unit| |flagFactor| |sqfrFactor| |primeFactor| |nthFlag| - |nthExponent| |irreducibleFactor| |factors| |nilFactor| - |regularRepresentation| |traceMatrix| |randomLC| |minimize| |module| - |rightRegularRepresentation| |leftRegularRepresentation| |rightTraceMatrix| - |leftTraceMatrix| |rightDiscriminant| |leftDiscriminant| |represents| - |mergeFactors| |isMult| |applyQuote| |ground| |ground?| |exprToXXP| - |exprToUPS| |exprToGenUPS| |localAbs| |universe| |complement| |cardinality| - |internalIntegrate0| |makeCos| |makeSin| |iiGamma| |iiabs| |bringDown| - |newReduc| |logical?| |character?| |doubleComplex?| |complex?| |double?| - |ffactor| |qfactor| |UP2ifCan| |anfactor| |fortranCharacter| - |fortranDoubleComplex| |fortranComplex| |fortranLogical| |fortranInteger| - |fortranDouble| |fortranReal| |external?| |dimensionsOf| |scalarTypeOf| - |makeFR| |musserTrials| |stopMusserTrials| |numberOfFactors| |modularFactor| + |factorials| |mkcomm| |commutativeOperation| |polarCoordinates| |complex| + |imaginary| |elaborateFile| |elaborate| |macroExpand| |solid| |solid?| + |denominators| |numerators| |convergents| |approximants| |reducedForm| + |partialQuotients| |partialDenominators| |partialNumerators| + |reducedContinuedFraction| |push| |bindings| |cartesian| |polar| |cylindrical| + |spherical| |parabolic| |parabolicCylindrical| |paraboloidal| + |ellipticCylindrical| |prolateSpheroidal| |oblateSpheroidal| |bipolar| + |bipolarCylindrical| |toroidal| |conical| |modTree| |multiEuclideanTree| + |complexZeros| |divisorCascade| |graeffe| |pleskenSplit| + |reciprocalPolynomial| |rootRadius| |schwerpunkt| |setErrorBound| + |startPolynomial| |cycleElt| |computeCycleLength| |computeCycleEntry| + |findConstructor| |arguments| |operations| |dualSignature| |kind| |package| + |domain| |category| |coerceP| |powerSum| |elementary| |alternating| |cyclic| + |dihedral| |cap| |cup| |wreath| |SFunction| |skewSFunction| + |cyclotomicDecomposition| |cyclotomicFactorization| |qsetelt| + |doubleResultant| |distdfact| |separateDegrees| |trace2PowMod| |tracePowMod| + |irreducible?| |decimal| |innerint| |exteriorDifferential| |totalDifferential| + |homogeneous?| |leadingBasisTerm| |ignore?| |computeInt| |checkForZero| |nan?| + |logGamma| |hypergeometric0F1| |rotatez| |rotatey| |rotatex| |identity| + |dictionary| |dioSolve| |directProduct| |newLine| |copies| |say| |sayLength| + |setnext!| |setprevious!| |next| |previous| |datalist| + |shanksDiscLogAlgorithm| |showSummary| |reflect| |reify| |constructor| + |functorData| |separant| |initial| |leader| |isobaric?| |weights| + |differentialVariables| |extractBottom!| |extractTop!| |insertBottom!| + |insertTop!| |bottom!| |top!| |dequeue| |makeObject| |recolor| |drawComplex| + |drawComplexVectorField| |setRealSteps| |setImagSteps| |setClipValue| |draw| + |option?| |range| |colorFunction| |curveColor| |pointColor| |clip| + |clipBoolean| |style| |toScale| |pointColorPalette| |curveColorPalette| + |var1Steps| |var2Steps| |space| |tubePoints| |tubeRadius| |option| |weight| + |makeVariable| |Nul| |exponents| |iisqrt2| |iisqrt3| |iiexp| |iilog| |iisin| + |iicos| |iitan| |iicot| |iisec| |iicsc| |iiasin| |iiacos| |iiatan| |iiacot| + |iiasec| |iiacsc| |iisinh| |iicosh| |iitanh| |iicoth| |iisech| |iicsch| + |iiasinh| |iiacosh| |iiatanh| |iiacoth| |iiasech| |iiacsch| |specialTrigs| + |localReal?| |rischNormalize| |realElementary| |validExponential| + |rootNormalize| |tanQ| |callForm?| |getIdentifier| |variable?| |getConstant| + |type| |environment| |typeForm| |irForm| |elaboration| |select!| |delete!| + |sn| |cn| |dn| |sncndn| |qsetelt!| |categoryFrame| |interactiveEnv| + |currentEnv| |putProperties| |getProperties| |putProperty| |getProperty| + |scopes| |eigenvalues| |eigenvector| |generalizedEigenvector| + |generalizedEigenvectors| |eigenvectors| |factorAndSplit| |rightOne| |leftOne| + |rightZero| |leftZero| |swap| |error| |minPoly| |freeOf?| |operators| |tower| + |kernels| |mainKernel| |distribute| |subst| |multiEuclidean| + |extendedEuclidean| |euclideanSize| |sizeLess?| |simplifyPower| |number?| + |seriesSolve| |constantToUnaryFunction| |tubePlot| |exponentialOrder| + |completeEval| |lowerPolynomial| |raisePolynomial| |normalDeriv| |ran| + |highCommonTerms| |mapCoef| |nthCoef| |binomThmExpt| |pomopo!| |mapExponents| + |linearAssociatedLog| |linearAssociatedOrder| |linearAssociatedExp| + |createNormalElement| |sin?| |lookupFunction| |encodingDirectory| + |attributeData| |domainTemplate| |lSpaceBasis| |finiteBasis| |principal?| + |divisor| |rationalPoints| |nonSingularModel| |algSplitSimple| |hyperelliptic| + |elliptic| |integralDerivationMatrix| |integralRepresents| + |integralCoordinates| |yCoordinates| |inverseIntegralMatrixAtInfinity| + |integralMatrixAtInfinity| |inverseIntegralMatrix| |integralMatrix| + |reduceBasisAtInfinity| |normalizeAtInfinity| |complementaryBasis| |integral?| + |integralAtInfinity?| |integralBasisAtInfinity| |ramified?| + |ramifiedAtInfinity?| |singular?| |singularAtInfinity?| |branchPoint?| + |branchPointAtInfinity?| |rationalPoint?| |absolutelyIrreducible?| |genus| + |getZechTable| |createZechTable| |createMultiplicationTable| + |createMultiplicationMatrix| |createLowComplexityTable| + |createLowComplexityNormalBasis| |representationType| |createPrimitiveElement| + |tableForDiscreteLogarithm| |factorsOfCyclicGroupSize| |sizeMultiplication| + |getMultiplicationMatrix| |getMultiplicationTable| |primitive?| + |numberOfIrreduciblePoly| |numberOfPrimitivePoly| |numberOfNormalPoly| + |createIrreduciblePoly| |createPrimitivePoly| |createNormalPoly| + |createNormalPrimitivePoly| |createPrimitiveNormalPoly| |nextIrreduciblePoly| + |nextPrimitivePoly| |nextNormalPoly| |nextNormalPrimitivePoly| + |nextPrimitiveNormalPoly| |leastAffineMultiple| |reducedQPowers| + |rootOfIrreduciblePoly| |write!| |read!| |iomode| |close!| |reopen!| |open| + |rightUnit| |leftUnit| |rightMinimalPolynomial| |leftMinimalPolynomial| + |associatorDependence| |lieAlgebra?| |jordanAlgebra?| + |noncommutativeJordanAlgebra?| |jordanAdmissible?| |lieAdmissible?| + |jacobiIdentity?| |powerAssociative?| |alternative?| |flexible?| + |rightAlternative?| |leftAlternative?| |antiAssociative?| |associative?| + |antiCommutative?| |commutative?| |rightCharacteristicPolynomial| + |leftCharacteristicPolynomial| |rightNorm| |leftNorm| |rightTrace| |leftTrace| + |someBasis| |find| |count| |every?| |any?| |sort!| |copyInto!| |sorted?| + |LiePoly| |quickSort| |heapSort| |shellSort| |outputSpacing| |outputGeneral| + |outputFixed| |outputFloating| |exp1| |log10| |log2| |rationalApproximation| + |relerror| |complexSolve| |complexRoots| |realRoots| |leadingTerm| |overlap| + |hcrf| |hclf| |writable?| |readable?| |exists?| |extension| |directory| + |filename| |shallowExpand| |deepExpand| |fracPart| |polyPart| + |fullPartialFraction| |primeFrobenius| |discreteLog| |decreasePrecision| + |increasePrecision| |precision| |bits| |mantissa| |unitNormalize| |unit| + |flagFactor| |sqfrFactor| |primeFactor| |nthFlag| |nthExponent| + |irreducibleFactor| |factors| |nilFactor| |regularRepresentation| + |traceMatrix| |randomLC| |minimize| |module| |rightRegularRepresentation| + |leftRegularRepresentation| |rightTraceMatrix| |leftTraceMatrix| + |rightDiscriminant| |leftDiscriminant| |represents| |mergeFactors| |isMult| + |applyQuote| |ground| |ground?| |exprToXXP| |exprToUPS| |exprToGenUPS| + |localAbs| |universe| |complement| |cardinality| |internalIntegrate0| + |makeCos| |makeSin| |iiGamma| |iiabs| |bringDown| |newReduc| |logical?| + |character?| |doubleComplex?| |complex?| |double?| |ffactor| |qfactor| + |UP2ifCan| |anfactor| |fortranCharacter| |fortranDoubleComplex| + |fortranComplex| |fortranLogical| |fortranInteger| |fortranDouble| + |fortranReal| |external?| |dimensionsOf| |scalarTypeOf| |makeFR| + |musserTrials| |stopMusserTrials| |numberOfFactors| |modularFactor| |useSingleFactorBound?| |useSingleFactorBound| |useEisensteinCriterion?| |useEisensteinCriterion| |eisensteinIrreducible?| |tryFunctionalDecomposition?| |tryFunctionalDecomposition| |btwFact| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index b0ee8362..57156d5f 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4057 +1,4065 @@ -(2793086 . 3580468876) -((-1737 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1735 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3791 ((|#2| $ (-486) |#2|) NIL T ELT) ((|#2| $ (-1148 (-486)) |#2|) 44 T ELT)) (-2299 (($ $) 80 T ELT)) (-3845 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3422 (((-486) (-1 (-85) |#2|) $) 27 T ELT) (((-486) |#2| $) NIL T ELT) (((-486) |#2| $ (-486)) 96 T ELT)) (-3521 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2611 (((-585 |#2|) $) 13 T ELT)) (-3329 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3846 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2306 (($ |#2| $ (-486)) NIL T ELT) (($ $ $ (-486)) 67 T ELT)) (-1731 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1733 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) 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T) ((-23) . T) ((-25) . T) ((-38 (-350 (-486))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-38 |#1|) . T) ((-38 $) OR (|has| |#1| (-497)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-35) |has| |#1| (-1117)) ((-66) |has| |#1| (-1117)) ((-72) . T) ((-82 (-350 (-486)) (-350 (-486))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-82 |#1| |#1|) . T) ((-82 $ $) . T) ((-104) . T) ((-118) OR (|has| |#1| (-299)) (|has| |#1| (-118))) ((-120) |has| |#1| (-120)) ((-557 (-350 (-486))) OR (|has| |#1| (-952 (-350 (-486)))) (|has| |#1| (-299)) (|has| |#1| (-312))) ((-557 (-486)) . T) ((-557 |#1|) . T) ((-557 $) OR (|has| |#1| (-497)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-554 (-774)) . T) ((-146) . T) ((-555 (-142 (-179))) |has| |#1| (-935)) ((-555 (-142 (-330))) |has| |#1| (-935)) ((-555 (-475)) |has| |#1| (-555 (-475))) ((-555 (-802 (-330))) |has| |#1| (-555 (-802 (-330)))) ((-555 (-802 (-486))) |has| |#1| (-555 (-802 (-486)))) ((-555 (-1087 |#1|)) . T) ((-186 $) OR (|has| |#1| (-299)) (|has| |#1| (-189)) (|has| |#1| (-190))) ((-184 |#1|) . T) ((-190) OR (|has| |#1| (-299)) (|has| |#1| (-190))) ((-189) OR (|has| |#1| (-299)) (|has| |#1| (-189)) (|has| |#1| (-190))) ((-225 |#1|) . T) ((-201) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-239) |has| |#1| (-1117)) ((-241 |#1| $) |has| |#1| (-241 |#1| |#1|)) ((-246) OR (|has| |#1| (-497)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-258) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-260 |#1|) |has| |#1| (-260 |#1|)) ((-312) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-345) |has| |#1| (-299)) ((-320) OR (|has| |#1| (-299)) (|has| |#1| (-320))) ((-299) |has| |#1| (-299)) ((-322 |#1| (-1087 |#1|)) . T) ((-353 |#1| (-1087 |#1|)) . T) ((-288 |#1|) . T) ((-329 |#1|) . T) ((-343 |#1|) . T) ((-355 |#1|) . T) ((-381 |#1|) . 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T) ((-656 $) OR (|has| |#1| (-497)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-663 |#1| (-1087 |#1|)) . T) ((-665) . T) ((-808 $ (-1092)) OR (|has| |#1| (-813 (-1092))) (|has| |#1| (-811 (-1092)))) ((-811 (-1092)) |has| |#1| (-811 (-1092))) ((-813 (-1092)) OR (|has| |#1| (-813 (-1092))) (|has| |#1| (-811 (-1092)))) ((-798 (-330)) |has| |#1| (-798 (-330))) ((-798 (-486)) |has| |#1| (-798 (-486))) ((-796 |#1|) . T) ((-823) -12 (|has| |#1| (-258)) (|has| |#1| (-823))) ((-834) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-917) -12 (|has| |#1| (-917)) (|has| |#1| (-1117))) ((-952 (-350 (-486))) |has| |#1| (-952 (-350 (-486)))) ((-952 (-486)) |has| |#1| (-952 (-486))) ((-952 |#1|) . T) ((-965 (-350 (-486))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-965 |#1|) . T) ((-965 $) . T) ((-970 (-350 (-486))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-970 |#1|) . T) ((-970 $) . T) ((-963) . T) ((-972) . T) ((-1027) . T) ((-1063) . T) ((-1015) . 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T) ((-186 $) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-963))) (-12 (|has| |#2| (-190)) (|has| |#2| (-963)))) ((-184 |#2|) |has| |#2| (-963)) ((-190) -12 (|has| |#2| (-190)) (|has| |#2| (-963))) ((-189) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-963))) (-12 (|has| |#2| (-190)) (|has| |#2| (-963)))) ((-225 |#2|) |has| |#2| (-963)) ((-241 (-486) |#2|) . T) ((-243 (-486) |#2|) . T) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1015))) ((-320) |has| |#2| (-320)) ((-318 |#2|) . T) ((-329 |#2|) |has| |#2| (-963)) ((-355 |#2|) |has| |#2| (-1015)) ((-381 |#2|) . T) ((-430 |#2|) . T) ((-540 (-486) |#2|) . T) ((-457 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1015))) ((-13) . T) ((-590 (-486)) OR (|has| |#2| (-963)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-21))) ((-590 |#2|) OR (|has| |#2| (-963)) (|has| |#2| (-665)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-590 $) |has| |#2| (-963)) ((-592 (-486)) -12 (|has| |#2| (-582 (-486))) (|has| |#2| (-963))) ((-592 |#2|) OR (|has| |#2| (-963)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-592 $) |has| |#2| (-963)) ((-584 |#2|) OR (|has| |#2| (-665)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-582 (-486)) -12 (|has| |#2| (-582 (-486))) (|has| |#2| (-963))) ((-582 |#2|) |has| |#2| (-963)) ((-656 |#2|) OR (|has| |#2| (-312)) (|has| |#2| (-146))) ((-665) |has| |#2| (-963)) ((-718) |has| |#2| (-719)) ((-719) |has| |#2| (-719)) ((-720) |has| |#2| (-719)) ((-723) |has| |#2| (-719)) ((-758) OR (|has| |#2| (-758)) (|has| |#2| (-719))) ((-761) OR (|has| |#2| (-758)) (|has| |#2| (-719))) ((-808 $ (-1092)) OR (-12 (|has| |#2| (-813 (-1092))) (|has| |#2| (-963))) (-12 (|has| |#2| (-811 (-1092))) (|has| |#2| (-963)))) ((-811 (-1092)) -12 (|has| |#2| (-811 (-1092))) (|has| |#2| (-963))) ((-813 (-1092)) OR (-12 (|has| |#2| (-813 (-1092))) (|has| |#2| (-963))) (-12 (|has| |#2| (-811 (-1092))) (|has| |#2| (-963)))) ((-952 (-350 (-486))) -12 (|has| |#2| (-952 (-350 (-486)))) (|has| |#2| (-1015))) ((-952 (-486)) -12 (|has| |#2| (-952 (-486))) (|has| |#2| (-1015))) ((-952 |#2|) |has| |#2| (-1015)) ((-965 |#2|) OR (|has| |#2| (-963)) (|has| |#2| (-665)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-970 |#2|) OR (|has| |#2| (-963)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-963) |has| |#2| (-963)) ((-972) |has| |#2| (-963)) ((-1027) |has| |#2| (-963)) ((-1063) |has| |#2| (-963)) ((-1015) OR (|has| |#2| (-1015)) (|has| |#2| (-963)) (|has| |#2| (-758)) (|has| |#2| (-719)) (|has| |#2| (-665)) (|has| |#2| (-320)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1131) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) OR (|has| |#1| (-823)) (|has| |#1| (-497)) (|has| |#1| (-393))) ((-72) . T) ((-82 (-350 (-486)) (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-823)) (|has| |#1| (-497)) (|has| |#1| (-393)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-557 (-350 (-486))) OR (|has| |#1| (-952 (-350 (-486)))) (|has| |#1| (-38 (-350 (-486))))) ((-557 (-486)) . T) ((-557 |#1|) . T) ((-557 |#2|) . T) ((-557 |#3|) . T) ((-557 $) OR (|has| |#1| (-823)) (|has| |#1| (-497)) (|has| |#1| (-393))) ((-554 (-774)) . T) ((-146) OR (|has| |#1| (-823)) (|has| |#1| (-497)) (|has| |#1| (-393)) (|has| |#1| (-146))) ((-555 (-475)) -12 (|has| |#1| (-555 (-475))) (|has| |#3| (-555 (-475)))) ((-555 (-802 (-330))) -12 (|has| |#1| (-555 (-802 (-330)))) (|has| |#3| (-555 (-802 (-330))))) ((-555 (-802 (-486))) -12 (|has| |#1| (-555 (-802 (-486)))) (|has| |#3| (-555 (-802 (-486))))) ((-186 $) OR (|has| |#1| (-189)) (|has| |#1| (-190))) ((-184 |#1|) . T) ((-190) |has| |#1| (-190)) ((-189) OR (|has| |#1| (-189)) (|has| |#1| (-190))) ((-225 |#1|) . T) ((-246) OR (|has| |#1| (-823)) (|has| |#1| (-497)) (|has| |#1| (-393))) ((-260 $) . T) ((-277 |#1| |#4|) . T) ((-329 |#1|) . T) ((-355 |#1|) . T) ((-381 |#1|) . T) ((-393) OR (|has| |#1| (-823)) (|has| |#1| (-393))) ((-457 |#2| |#1|) |has| |#1| (-190)) ((-457 |#2| $) |has| |#1| (-190)) ((-457 |#3| |#1|) . T) ((-457 |#3| $) . T) ((-457 $ $) . T) ((-497) OR (|has| |#1| (-823)) (|has| |#1| (-497)) (|has| |#1| (-393))) ((-13) . T) ((-590 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-590 (-486)) . T) ((-590 |#1|) . T) ((-590 $) . T) ((-592 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-592 (-486)) |has| |#1| (-582 (-486))) ((-592 |#1|) . T) ((-592 $) . T) ((-584 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-584 |#1|) |has| |#1| (-146)) ((-584 $) OR (|has| |#1| (-823)) (|has| |#1| (-497)) (|has| |#1| (-393))) ((-582 (-486)) |has| |#1| (-582 (-486))) ((-582 |#1|) . T) ((-656 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-656 |#1|) |has| |#1| (-146)) ((-656 $) OR (|has| |#1| (-823)) (|has| |#1| (-497)) (|has| |#1| (-393))) ((-665) . T) ((-808 $ (-1092)) OR (|has| |#1| (-813 (-1092))) (|has| |#1| (-811 (-1092)))) ((-808 $ |#3|) . T) ((-811 (-1092)) |has| |#1| (-811 (-1092))) ((-811 |#3|) . T) ((-813 (-1092)) OR (|has| |#1| (-813 (-1092))) (|has| |#1| (-811 (-1092)))) ((-813 |#3|) . 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T) ((-72) OR (|has| |#2| (-1017)) (|has| |#2| (-965)) (|has| |#2| (-760)) (|has| |#2| (-721)) (|has| |#2| (-667)) (|has| |#2| (-322)) (|has| |#2| (-314)) (|has| |#2| (-148)) (|has| |#2| (-104)) (|has| |#2| (-72)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-82 |#2| |#2|) OR (|has| |#2| (-965)) (|has| |#2| (-314)) (|has| |#2| (-148))) ((-104) OR (|has| |#2| (-965)) (|has| |#2| (-721)) (|has| |#2| (-314)) (|has| |#2| (-148)) (|has| |#2| (-104)) (|has| |#2| (-21))) ((-559 (-352 (-488))) -12 (|has| |#2| (-954 (-352 (-488)))) (|has| |#2| (-1017))) ((-559 (-488)) OR (|has| |#2| (-965)) (-12 (|has| |#2| (-954 (-488))) (|has| |#2| (-1017)))) ((-559 |#2|) |has| |#2| (-1017)) ((-556 (-776)) OR (|has| |#2| (-1017)) (|has| |#2| (-965)) (|has| |#2| (-760)) (|has| |#2| (-721)) (|has| |#2| (-667)) (|has| |#2| (-322)) (|has| |#2| (-314)) (|has| |#2| (-148)) (|has| |#2| (-556 (-776))) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-556 (-1183 |#2|)) . T) ((-188 $) OR (-12 (|has| |#2| (-191)) (|has| |#2| (-965))) (-12 (|has| |#2| (-192)) (|has| |#2| (-965)))) ((-186 |#2|) |has| |#2| (-965)) ((-192) -12 (|has| |#2| (-192)) (|has| |#2| (-965))) ((-191) OR (-12 (|has| |#2| (-191)) (|has| |#2| (-965))) (-12 (|has| |#2| (-192)) (|has| |#2| (-965)))) ((-227 |#2|) |has| |#2| (-965)) ((-243 (-488) |#2|) . T) ((-245 (-488) |#2|) . T) ((-262 |#2|) -12 (|has| |#2| (-262 |#2|)) (|has| |#2| (-1017))) ((-322) |has| |#2| (-322)) ((-320 |#2|) . T) ((-331 |#2|) |has| |#2| (-965)) ((-357 |#2|) |has| |#2| (-1017)) ((-383 |#2|) . T) ((-432 |#2|) . T) ((-542 (-488) |#2|) . T) ((-459 |#2| |#2|) -12 (|has| |#2| (-262 |#2|)) (|has| |#2| (-1017))) ((-13) . T) ((-592 (-488)) OR (|has| |#2| (-965)) (|has| |#2| (-314)) (|has| |#2| (-148)) (|has| |#2| (-21))) ((-592 |#2|) OR (|has| |#2| (-965)) (|has| |#2| (-667)) (|has| |#2| (-314)) (|has| |#2| (-148))) ((-592 $) |has| |#2| (-965)) ((-594 (-488)) -12 (|has| |#2| (-584 (-488))) (|has| |#2| (-965))) ((-594 |#2|) OR (|has| |#2| (-965)) (|has| |#2| (-314)) (|has| |#2| (-148))) ((-594 $) |has| |#2| (-965)) ((-586 |#2|) OR (|has| |#2| (-667)) (|has| |#2| (-314)) (|has| |#2| (-148))) ((-584 (-488)) -12 (|has| |#2| (-584 (-488))) (|has| |#2| (-965))) ((-584 |#2|) |has| |#2| (-965)) ((-658 |#2|) OR (|has| |#2| (-314)) (|has| |#2| (-148))) ((-667) |has| |#2| (-965)) ((-720) |has| |#2| (-721)) ((-721) |has| |#2| (-721)) ((-722) |has| |#2| (-721)) ((-725) |has| |#2| (-721)) ((-760) OR (|has| |#2| (-760)) (|has| |#2| (-721))) ((-763) OR (|has| |#2| (-760)) (|has| |#2| (-721))) ((-810 $ (-1094)) OR (-12 (|has| |#2| (-815 (-1094))) (|has| |#2| (-965))) (-12 (|has| |#2| (-813 (-1094))) (|has| |#2| (-965)))) ((-813 (-1094)) -12 (|has| |#2| (-813 (-1094))) (|has| |#2| (-965))) ((-815 (-1094)) OR (-12 (|has| |#2| (-815 (-1094))) (|has| |#2| (-965))) (-12 (|has| |#2| (-813 (-1094))) (|has| |#2| (-965)))) ((-954 (-352 (-488))) -12 (|has| |#2| (-954 (-352 (-488)))) (|has| |#2| (-1017))) ((-954 (-488)) -12 (|has| |#2| (-954 (-488))) (|has| |#2| (-1017))) ((-954 |#2|) |has| |#2| (-1017)) ((-967 |#2|) OR (|has| |#2| (-965)) (|has| |#2| (-667)) (|has| |#2| (-314)) (|has| |#2| (-148))) ((-972 |#2|) OR (|has| |#2| (-965)) (|has| |#2| (-314)) (|has| |#2| (-148))) ((-965) |has| |#2| (-965)) ((-974) |has| |#2| (-965)) ((-1029) |has| |#2| (-965)) ((-1065) |has| |#2| (-965)) ((-1017) OR (|has| |#2| (-1017)) (|has| |#2| (-965)) (|has| |#2| (-760)) (|has| |#2| (-721)) (|has| |#2| (-667)) (|has| |#2| (-322)) (|has| |#2| (-314)) (|has| |#2| (-148)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1133) . T) ((-1191 |#2|) |has| |#2| (-314))) +((-2574 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-3194 (((-85) $) NIL (|has| |#2| (-23)) ELT)) (-3713 (($ (-834)) 63 (|has| |#2| (-965)) ELT)) (-2203 (((-1189) $ (-488) (-488)) NIL (|has| $ (-1039 |#2|)) ELT)) (-2489 (($ $ $) 69 (|has| |#2| (-721)) ELT)) (-1316 (((-3 $ #1="failed") $ $) 54 (|has| |#2| (-104)) ELT)) (-3142 (((-698)) NIL (|has| |#2| (-322)) ELT)) (-3794 ((|#2| $ (-488) |#2|) NIL (|has| $ (-1039 |#2|)) ELT)) (-3730 (($) NIL T CONST)) (-3163 (((-3 (-488) #1#) $) NIL (-12 (|has| |#2| (-954 (-488))) (|has| |#2| (-1017))) ELT) (((-3 (-352 (-488)) #1#) $) NIL (-12 (|has| |#2| (-954 (-352 (-488)))) (|has| |#2| (-1017))) ELT) (((-3 |#2| #1#) $) 31 (|has| |#2| (-1017)) ELT)) (-3162 (((-488) $) NIL (-12 (|has| |#2| (-954 (-488))) (|has| |#2| (-1017))) ELT) (((-352 (-488)) $) NIL (-12 (|has| |#2| (-954 (-352 (-488)))) (|has| |#2| (-1017))) ELT) ((|#2| $) 29 (|has| |#2| (-1017)) ELT)) (-2284 (((-634 (-488)) (-634 $)) NIL (-12 (|has| |#2| (-584 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T) ((-76 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) . T) ((-72) OR (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-1017)) (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-1017)) (|has| |#2| (-72))) ((-556 (-776)) OR (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-1017)) (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-556 (-776))) (|has| |#2| (-1017)) (|has| |#2| (-556 (-776)))) ((-124 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) . T) ((-557 (-477)) |has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-557 (-477))) ((-185 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) . T) ((-195 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) . T) ((-243 |#1| |#2|) . T) ((-245 |#1| |#2|) . T) ((-262 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-262 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-1017))) ((-262 |#2|) -12 (|has| |#2| (-262 |#2|)) (|has| |#2| (-1017))) ((-320 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) . T) ((-383 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) . T) ((-383 |#2|) . T) ((-432 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) . T) ((-432 |#2|) . T) ((-542 |#1| |#2|) . T) ((-459 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-262 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-1017))) ((-459 |#2| |#2|) -12 (|has| |#2| (-262 |#2|)) (|has| |#2| (-1017))) ((-13) . T) ((-553 |#1| |#2|) . T) ((-1017) OR (|has| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (-1017)) (|has| |#2| (-1017))) ((-1039 (-2 (|:| -3867 |#1|) (|:| |entry| |#2|))) . T) ((-1039 |#2|) . T) ((-1133) . 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T) ((-592 (-350 (-486))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-486))))) ((-592 (-486)) -12 (|has| |#1| (-312)) (|has| |#2| (-582 (-486)))) ((-592 |#1|) . T) ((-592 |#2|) |has| |#1| (-312)) ((-592 $) . T) ((-584 (-350 (-486))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-486))))) ((-584 |#1|) |has| |#1| (-146)) ((-584 |#2|) |has| |#1| (-312)) ((-584 $) OR (|has| |#1| (-497)) (|has| |#1| (-312))) ((-582 (-486)) -12 (|has| |#1| (-312)) (|has| |#2| (-582 (-486)))) ((-582 |#2|) |has| |#1| (-312)) ((-656 (-350 (-486))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-486))))) ((-656 |#1|) |has| |#1| (-146)) ((-656 |#2|) |has| |#1| (-312)) ((-656 $) OR (|has| |#1| (-497)) (|has| |#1| (-312))) ((-665) . 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T) ((-23) . T) ((-47 |#1| (-696)) . T) ((-25) . T) ((-38 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-497)) ((-35) |has| |#1| (-38 (-350 (-486)))) ((-66) |has| |#1| (-38 (-350 (-486)))) ((-72) . T) ((-82 (-350 (-486)) (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-497)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-557 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-557 (-486)) . T) ((-557 |#1|) |has| |#1| (-146)) ((-557 $) |has| |#1| (-497)) ((-554 (-774)) . T) ((-146) OR (|has| |#1| (-497)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-696) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-696) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-696) |#1|))) ((-239) |has| |#1| (-38 (-350 (-486)))) ((-241 (-696) |#1|) . T) ((-241 $ $) |has| (-696) (-1027)) ((-246) |has| |#1| (-497)) ((-381 |#1|) . T) ((-434) |has| |#1| (-38 (-350 (-486)))) ((-497) |has| |#1| (-497)) ((-13) . T) ((-590 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-590 (-486)) . T) ((-590 |#1|) . T) ((-590 $) . T) ((-592 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-592 |#1|) . T) ((-592 $) . T) ((-584 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-584 |#1|) |has| |#1| (-146)) ((-584 $) |has| |#1| (-497)) ((-656 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-656 |#1|) |has| |#1| (-146)) ((-656 $) |has| |#1| (-497)) ((-665) . T) ((-808 $ (-1092)) -12 (|has| |#1| (-811 (-1092))) (|has| |#1| (-15 * (|#1| (-696) |#1|)))) ((-811 (-1092)) -12 (|has| |#1| (-811 (-1092))) (|has| |#1| (-15 * (|#1| (-696) |#1|)))) ((-813 (-1092)) -12 (|has| |#1| (-811 (-1092))) (|has| |#1| (-15 * (|#1| (-696) |#1|)))) ((-888 |#1| (-696) (-996)) . T) ((-917) |has| |#1| (-38 (-350 (-486)))) ((-965 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-965 |#1|) . T) ((-965 $) OR (|has| |#1| (-497)) (|has| |#1| (-146))) ((-970 (-350 (-486))) |has| |#1| (-38 (-350 (-486)))) ((-970 |#1|) . T) ((-970 $) OR (|has| |#1| (-497)) (|has| |#1| (-146))) ((-963) . T) ((-972) . T) ((-1027) . T) ((-1063) . T) ((-1015) . T) ((-1117) |has| |#1| (-38 (-350 (-486)))) ((-1120) |has| |#1| (-38 (-350 (-486)))) ((-1131) . T) ((-1160 |#1| (-696)) . 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NIL NIL) (-1181 2713575 2718005 2718097 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1180 2706901 2711230 2711273 "VECTCAT" 2712261 VECTCAT (NIL T) -9 NIL 2712845 NIL) (-1179 2706180 2706506 2706896 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1178 2705674 2705916 2706036 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1177 2705607 2705612 2705642 "UTYPE" 2705647 UTYPE (NIL) -9 NIL NIL NIL) (-1176 2704594 2704770 2705031 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1175 2702445 2702953 2703477 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1174 2692309 2698279 2698321 "UTSCAT" 2699419 UTSCAT (NIL T) -9 NIL 2700176 NIL) (-1173 2690374 2691317 2692304 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1172 2690048 2690097 2690228 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1171 2681759 2688244 2688723 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1170 2676303 2678576 2678619 "URAGG" 2680659 URAGG (NIL T) -9 NIL 2681384 NIL) (-1169 2674374 2675306 2676298 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1168 2670081 2673350 2673812 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1167 2662510 2670005 2670076 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1166 2651143 2658630 2658691 "UPXSCCA" 2659259 UPXSCCA (NIL T T) -9 NIL 2659491 NIL) (-1165 2650864 2650966 2651138 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1164 2639398 2646610 2646652 "UPXSCAT" 2647292 UPXSCAT (NIL T) -9 NIL 2647900 NIL) (-1163 2638911 2638996 2639173 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1162 2630597 2638502 2638764 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1161 2629492 2629762 2630112 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1160 2622177 2625662 2625716 "UPSCAT" 2626785 UPSCAT (NIL T T) -9 NIL 2627549 NIL) (-1159 2621597 2621849 2622172 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1158 2621271 2621320 2621451 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1157 2605382 2614337 2614379 "UPOLYC" 2616457 UPOLYC (NIL T) -9 NIL 2617677 NIL) (-1156 2599437 2602285 2605377 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1155 2598873 2598998 2599161 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1154 2598507 2598594 2598733 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1153 2597320 2597587 2597891 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1152 2596653 2596783 2596968 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1151 2596245 2596320 2596467 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1150 2587009 2596011 2596139 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1149 2586371 2586508 2586713 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1148 2584972 2585819 2586095 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1147 2584201 2584398 2584623 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1146 2571011 2584125 2584196 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1145 2550767 2564002 2564063 "ULSCCAT" 2564694 ULSCCAT (NIL T T) -9 NIL 2564981 NIL) (-1144 2550102 2550388 2550762 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1143 2538456 2545590 2545632 "ULSCAT" 2546485 ULSCAT (NIL T) -9 NIL 2547215 NIL) (-1142 2537969 2538054 2538231 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1141 2520086 2537468 2537709 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1140 2519120 2519813 2519927 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2520038) (-1139 2518153 2518846 2518960 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2519071) (-1138 2517186 2517879 2517993 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2518104) (-1137 2516219 2516912 2517026 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2517137) (-1136 2514226 2515447 2515477 "UFD" 2515688 UFD (NIL) -9 NIL 2515801 NIL) (-1135 2514070 2514127 2514221 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1134 2513322 2513529 2513745 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1133 2511542 2511995 2512460 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1132 2511267 2511507 2511537 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1131 2511205 2511210 2511240 "TYPE" 2511245 TYPE (NIL) -9 NIL 2511252 NIL) (-1130 2510364 2510584 2510824 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1129 2509542 2509973 2510208 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1128 2507696 2508269 2508808 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1127 2506730 2506966 2507202 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1126 2495328 2499505 2499601 "TSETCAT" 2504816 TSETCAT (NIL T T T T) -9 NIL 2506320 NIL) (-1125 2491665 2493481 2495323 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1124 2486057 2490891 2491173 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1123 2481394 2482407 2483336 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1122 2480891 2480966 2481129 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1121 2478967 2479257 2479612 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1120 2478451 2478600 2478630 "TRIGCAT" 2478843 TRIGCAT (NIL) -9 NIL NIL NIL) (-1119 2478202 2478305 2478446 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1118 2475198 2477308 2477589 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1117 2474304 2475000 2475030 "TRANFUN" 2475065 TRANFUN (NIL) -9 NIL 2475131 NIL) (-1116 2473768 2474019 2474299 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1115 2473605 2473643 2473704 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1114 2473062 2473193 2473344 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1113 2471803 2472460 2472696 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1112 2471615 2471652 2471724 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1111 2469829 2470475 2470904 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1110 2468209 2468546 2468868 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1109 2458194 2465898 2465954 "TBAGG" 2466271 TBAGG (NIL T T) -9 NIL 2466481 NIL) (-1108 2455599 2456854 2458189 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1107 2455076 2455201 2455346 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1106 2454586 2454906 2454996 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1105 2454083 2454200 2454338 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1104 2446587 2454011 2454078 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1103 2442340 2443635 2444880 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1102 2441709 2441868 2442049 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1101 2438863 2439616 2440399 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1100 2438637 2438827 2438858 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1099 2437591 2438276 2438402 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2438588) (-1098 2436855 2437403 2437482 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2437542) (-1097 2433678 2434837 2435537 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1096 2431361 2432044 2432678 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1095 2427439 2428485 2429462 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1094 2424538 2427094 2427323 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1093 2424134 2424221 2424343 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1092 2420758 2422232 2423051 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1091 2413718 2419955 2420248 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1090 2405404 2413309 2413571 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2404683 2404822 2405039 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1088 2404367 2404432 2404543 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1087 2395090 2404079 2404204 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1086 2393820 2394118 2394473 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1085 2393225 2393303 2393494 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1084 2375377 2392724 2392965 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1083 2374976 2375248 2375317 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1082 2374312 2374593 2374733 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1081 2368914 2370173 2371126 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1080 2368446 2368546 2368710 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1079 2363557 2364839 2365986 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1078 2358015 2359486 2360797 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1077 2350930 2352994 2354785 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1076 2343099 2350868 2350925 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1075 2338048 2342813 2342928 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1074 2337635 2337718 2337862 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1073 2336786 2336987 2337222 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1072 2336526 2336584 2336677 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1071 2330052 2334729 2335337 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1070 2329228 2329433 2329664 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1069 2328473 2328844 2328991 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1068 2327961 2328203 2328233 "STEP" 2328327 STEP (NIL) -9 NIL 2328398 NIL) (-1067 2320455 2327879 2327956 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1066 2315480 2319235 2319278 "STAGG" 2319705 STAGG (NIL T) -9 NIL 2319879 NIL) (-1065 2313938 2314646 2315475 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1064 2312100 2313765 2313857 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1063 2311380 2311919 2311949 "SRING" 2311954 SRING (NIL) -9 NIL 2311974 NIL) (-1062 2304295 2309918 2310357 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1061 2298069 2299508 2301012 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1060 2290686 2295344 2295374 "SRAGG" 2296673 SRAGG (NIL) -9 NIL 2297277 NIL) (-1059 2289983 2290303 2290681 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1058 2284089 2289305 2289728 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1057 2278018 2281442 2282193 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1056 2274447 2275266 2275903 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1055 2273422 2273727 2273757 "SPFCAT" 2274201 SPFCAT (NIL) -9 NIL NIL NIL) (-1054 2272359 2272611 2272875 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1053 2263117 2265391 2265421 "SPADXPT" 2270058 SPADXPT (NIL) -9 NIL 2272182 NIL) (-1052 2262919 2262965 2263034 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1051 2260575 2262883 2262914 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1050 2252249 2254338 2254380 "SPACEC" 2258695 SPACEC (NIL T) -9 NIL 2260500 NIL) (-1049 2250078 2252196 2252244 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1048 2249057 2249246 2249529 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1047 2247461 2247794 2248205 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1046 2246726 2246960 2247221 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1045 2242906 2243866 2244861 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1044 2239264 2239963 2240692 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1043 2233286 2238549 2238645 "SNTSCAT" 2238650 SNTSCAT (NIL T T T T) -9 NIL 2238720 NIL) (-1042 2227107 2231927 2232317 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1041 2220879 2227026 2227102 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1040 2219311 2219642 2220040 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1039 2210925 2215859 2215961 "SMATCAT" 2217304 SMATCAT (NIL NIL T T T) -9 NIL 2217852 NIL) (-1038 2208766 2209750 2210920 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1037 2208368 2208540 2208583 "SMAGG" 2208668 SMAGG (NIL T) -9 NIL 2208725 NIL) (-1036 2205911 2207517 2207560 "SKAGG" 2207821 SKAGG (NIL T) -9 NIL 2207957 NIL) (-1035 2201957 2205731 2205842 "SINT" NIL SINT (NIL) -8 NIL NIL 2205883) (-1034 2201767 2201811 2201877 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1033 2200842 2201074 2201342 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1032 2199846 2200008 2200284 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1031 2199192 2199532 2199655 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1030 2198538 2198845 2198985 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1029 2196649 2197141 2197647 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1028 2190133 2196568 2196644 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1027 2189636 2189873 2189903 "SGROUP" 2189996 SGROUP (NIL) -9 NIL 2190058 NIL) (-1026 2189526 2189558 2189631 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1025 2189164 2189204 2189245 "SGPOPC" 2189250 SGPOPC (NIL T) -9 NIL 2189451 NIL) (-1024 2188698 2188975 2189081 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1023 2186121 2186890 2187612 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1022 2180242 2185505 2185601 "SFRTCAT" 2185606 SFRTCAT (NIL T T T T) -9 NIL 2185644 NIL) (-1021 2174634 2175747 2176874 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1020 2168810 2169971 2171135 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2167782 2168684 2168805 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1018 2163390 2164285 2164380 "SEXCAT" 2166993 SEXCAT (NIL T T T T T) -9 NIL 2167544 NIL) (-1017 2162363 2163317 2163385 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1016 2160754 2161339 2161641 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1015 2160277 2160462 2160492 "SETCAT" 2160609 SETCAT (NIL) -9 NIL 2160693 NIL) (-1014 2160109 2160173 2160272 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1013 2157161 2158545 2158588 "SETAGG" 2159456 SETAGG (NIL T) -9 NIL 2159794 NIL) (-1012 2156767 2156919 2157156 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1011 2154012 2156714 2156762 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1010 2153478 2153788 2153888 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1009 2152605 2152971 2153032 "SEGXCAT" 2153318 SEGXCAT (NIL T T) -9 NIL 2153438 NIL) (-1008 2151530 2151798 2151841 "SEGCAT" 2152363 SEGCAT (NIL T) -9 NIL 2152584 NIL) (-1007 2151210 2151275 2151388 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1006 2150276 2150746 2150954 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1005 2149854 2150133 2150209 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1004 2149219 2149355 2149559 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1003 2148285 2149032 2149214 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1002 2147538 2148233 2148280 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1001 2139023 2147405 2147533 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1000 2137877 2138167 2138486 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-999 2137183 2137395 2137583 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-998 2136533 2136690 2136866 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-997 2136106 2136337 2136365 "SASTCAT" 2136370 SASTCAT (NIL) -9 NIL 2136383 NIL) (-996 2135573 2135998 2136072 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-995 2135176 2135217 2135388 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-994 2134807 2134848 2135005 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-993 2127888 2134724 2134802 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-992 2126538 2126867 2127263 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-991 2125299 2125660 2125960 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-990 2124923 2125144 2125225 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-989 2122383 2123017 2123470 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-988 2122222 2122255 2122323 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-987 2121713 2122016 2122107 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-986 2117341 2118209 2119120 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-985 2106396 2111659 2111753 "RSETCAT" 2115809 RSETCAT (NIL T T T T) -9 NIL 2116897 NIL) (-984 2104934 2105576 2106391 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-983 2098708 2100153 2101660 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-982 2096590 2097147 2097219 "RRCC" 2098292 RRCC (NIL T T) -9 NIL 2098633 NIL) (-981 2096115 2096314 2096585 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-980 2095585 2095895 2095993 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-979 2068118 2078832 2078896 "RPOLCAT" 2089370 RPOLCAT (NIL T T T) -9 NIL 2092515 NIL) (-978 2062217 2065040 2068113 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-977 2058384 2061965 2062103 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-976 2056712 2057451 2057707 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-975 2052355 2055167 2055195 "RNS" 2055457 RNS (NIL) -9 NIL 2055709 NIL) (-974 2051258 2051745 2052282 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-973 2050376 2050777 2050977 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-972 2049514 2050076 2050104 "RNG" 2050164 RNG (NIL) -9 NIL 2050218 NIL) (-971 2049403 2049437 2049509 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-970 2048665 2049170 2049210 "RMODULE" 2049215 RMODULE (NIL T) -9 NIL 2049241 NIL) (-969 2047604 2047710 2048040 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-968 2044501 2047194 2047487 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-967 2037342 2039786 2039898 "RMATCAT" 2043069 RMATCAT (NIL NIL NIL T T T) -9 NIL 2044000 NIL) (-966 2036859 2037038 2037337 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-965 2036427 2036638 2036679 "RLINSET" 2036740 RLINSET (NIL T) -9 NIL 2036784 NIL) (-964 2036072 2036153 2036279 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-963 2034918 2035649 2035677 "RING" 2035732 RING (NIL) -9 NIL 2035824 NIL) (-962 2034763 2034819 2034913 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-961 2033817 2034084 2034340 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-960 2025041 2033445 2033646 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-959 2024266 2024777 2024816 "RGBCSPC" 2024873 RGBCSPC (NIL T) -9 NIL 2024924 NIL) (-958 2023300 2023786 2023825 "RGBCMDL" 2024053 RGBCMDL (NIL T) -9 NIL 2024167 NIL) (-957 2023012 2023081 2023182 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-956 2022775 2022816 2022911 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-955 2021199 2021629 2022009 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-954 2018786 2019454 2020122 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-953 2018336 2018434 2018594 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-952 2017958 2018056 2018097 "RETRACT" 2018228 RETRACT (NIL T) -9 NIL 2018315 NIL) (-951 2017838 2017869 2017953 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-950 2017440 2017712 2017779 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-949 2015920 2016811 2017008 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-948 2015611 2015672 2015768 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-947 2015354 2015395 2015500 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-946 2015089 2015130 2015239 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-945 2010160 2011611 2012826 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-944 2007256 2008014 2008822 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-943 2005225 2005847 2006447 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-942 1998153 2003776 2004212 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-941 1997465 1997745 1997894 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-940 1996950 1997065 1997230 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-939 1992543 1996353 1996574 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-938 1991775 1991974 1992187 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-937 1989065 1989903 1990785 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-936 1985647 1986683 1987742 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-935 1985483 1985536 1985564 "REAL" 1985569 REAL (NIL) -9 NIL 1985604 NIL) (-934 1984973 1985277 1985368 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-933 1984453 1984531 1984736 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-932 1983686 1983878 1984089 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-931 1982574 1982871 1983238 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-930 1980841 1981311 1981844 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-929 1979765 1980042 1980429 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-928 1978594 1978903 1979322 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-927 1971942 1975454 1975482 "RCFIELD" 1976759 RCFIELD (NIL) -9 NIL 1977489 NIL) (-926 1970560 1971172 1971869 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-925 1967314 1968646 1968687 "RCAGG" 1969741 RCAGG (NIL T) -9 NIL 1970203 NIL) (-924 1967041 1967151 1967309 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-923 1966486 1966615 1966776 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-922 1966103 1966182 1966301 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-921 1965518 1965668 1965818 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-920 1965300 1965350 1965421 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-919 1957742 1964418 1964726 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-918 1947444 1957609 1957737 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-917 1947078 1947171 1947199 "RADCAT" 1947356 RADCAT (NIL) -9 NIL NIL NIL) (-916 1946916 1946976 1947073 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-915 1945021 1946747 1946836 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-914 1944702 1944751 1944878 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-913 1936971 1941055 1941095 "QUATCAT" 1941873 QUATCAT (NIL T) -9 NIL 1942637 NIL) (-912 1934221 1935501 1936877 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-911 1930061 1934171 1934216 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-910 1927399 1929058 1929099 "QUAGG" 1929474 QUAGG (NIL T) -9 NIL 1929650 NIL) (-909 1927001 1927273 1927340 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-908 1926007 1926637 1926800 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-907 1925688 1925737 1925864 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-906 1915270 1921439 1921479 "QFCAT" 1922137 QFCAT (NIL T) -9 NIL 1923130 NIL) (-905 1912154 1913593 1915176 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-904 1911700 1911834 1911964 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-903 1905896 1907057 1908219 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-902 1905315 1905495 1905727 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-901 1903137 1903665 1904088 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-900 1902036 1902278 1902595 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-899 1900397 1900595 1900948 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-898 1896153 1897369 1897410 "PTRANFN" 1899294 PTRANFN (NIL T) -9 NIL NIL NIL) (-897 1894800 1895145 1895466 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-896 1894493 1894556 1894663 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-895 1888790 1893234 1893274 "PTCAT" 1893566 PTCAT (NIL T) -9 NIL 1893719 NIL) (-894 1888483 1888524 1888648 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-893 1887362 1887678 1888012 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-892 1876241 1878802 1881111 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-891 1869443 1872006 1872100 "PSETCAT" 1875074 PSETCAT (NIL T T T T) -9 NIL 1875883 NIL) (-890 1867893 1868627 1869438 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-889 1867212 1867407 1867435 "PSCURVE" 1867703 PSCURVE (NIL) -9 NIL 1867870 NIL) (-888 1862796 1864616 1864680 "PSCAT" 1865515 PSCAT (NIL T T T) -9 NIL 1865754 NIL) (-887 1862110 1862392 1862791 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-886 1860507 1861422 1861685 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-885 1859998 1860301 1860392 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-884 1851018 1853440 1855628 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-883 1848712 1850281 1850321 "PRQAGG" 1850504 PRQAGG (NIL T) -9 NIL 1850607 NIL) (-882 1847885 1848331 1848359 "PROPLOG" 1848498 PROPLOG (NIL) -9 NIL 1848612 NIL) (-881 1847560 1847623 1847746 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-880 1846996 1847135 1847307 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-879 1845244 1846007 1846304 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-878 1844796 1844928 1845056 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-877 1839237 1843736 1844556 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-876 1839066 1839104 1839163 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-875 1838505 1838645 1838796 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-874 1836973 1837392 1837858 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-873 1836690 1836751 1836779 "PRIMCAT" 1836903 PRIMCAT (NIL) -9 NIL NIL NIL) (-872 1835861 1836057 1836285 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-871 1832022 1835811 1835856 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-870 1831721 1831783 1831894 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-869 1828857 1831370 1831603 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-868 1828308 1828465 1828493 "PPCURVE" 1828698 PPCURVE (NIL) -9 NIL 1828834 NIL) (-867 1827921 1828166 1828249 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-866 1825677 1826098 1826690 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-865 1825120 1825184 1825417 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-864 1821840 1822326 1822937 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-863 1807412 1813542 1813606 "POLYCAT" 1817091 POLYCAT (NIL T T T) -9 NIL 1818968 NIL) (-862 1802922 1805069 1807407 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-861 1802579 1802653 1802772 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-860 1802272 1802335 1802442 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-859 1795635 1802005 1802164 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-858 1794522 1794785 1795061 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-857 1793126 1793439 1793769 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-856 1788569 1793076 1793121 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-855 1787057 1787468 1787843 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-854 1785814 1786123 1786519 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-853 1785485 1785569 1785686 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-852 1785064 1785139 1785313 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-851 1784550 1784646 1784806 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-850 1784022 1784142 1784296 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-849 1782917 1783135 1783512 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-848 1782528 1782613 1782765 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-847 1782079 1782161 1782342 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-846 1781771 1781852 1781965 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-845 1781284 1781359 1781567 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-844 1780632 1780760 1780962 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-843 1779994 1780128 1780291 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-842 1779298 1779480 1779661 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-841 1779021 1779095 1779189 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-840 1775589 1776778 1777694 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-839 1774673 1774874 1775109 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-838 1770238 1771622 1772764 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-837 1750159 1755046 1759893 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-836 1749899 1749952 1750055 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-835 1749340 1749474 1749654 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-834 1747349 1748570 1748598 "PID" 1748795 PID (NIL) -9 NIL 1748922 NIL) (-833 1747137 1747180 1747255 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-832 1746324 1746984 1747071 "PI" NIL PI (NIL) -8 NIL NIL 1747111) (-831 1745776 1745927 1746103 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-830 1742104 1743062 1743967 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-829 1740468 1740757 1741123 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-828 1739910 1740025 1740186 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-827 1736451 1738779 1739132 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-826 1735057 1735337 1735662 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-825 1733822 1734076 1734424 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-824 1732532 1732759 1733111 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-823 1729542 1731102 1731130 "PFECAT" 1731723 PFECAT (NIL) -9 NIL 1732100 NIL) (-822 1729165 1729330 1729537 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-821 1727989 1728271 1728572 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-820 1726171 1726558 1726988 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-819 1722141 1726097 1726166 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-818 1718044 1719191 1720058 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-817 1715976 1717065 1717106 "PERMCAT" 1717505 PERMCAT (NIL T) -9 NIL 1717802 NIL) (-816 1715672 1715719 1715842 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-815 1712121 1713802 1714447 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-814 1710147 1711876 1711997 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-813 1709030 1709293 1709332 "PDSPC" 1709853 PDSPC (NIL T) -9 NIL 1710098 NIL) (-812 1708399 1708665 1709025 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-811 1707036 1708029 1708068 "PDRING" 1708073 PDRING (NIL T) -9 NIL 1708100 NIL) (-810 1705748 1706537 1706588 "PDMOD" 1706593 PDMOD (NIL T T) -9 NIL 1706696 NIL) (-809 1704841 1705053 1705302 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-808 1704446 1704513 1704567 "PDDOM" 1704732 PDDOM (NIL T T) -9 NIL 1704812 NIL) (-807 1704298 1704334 1704441 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-806 1704084 1704123 1704212 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-805 1702401 1703155 1703454 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-804 1702090 1702153 1702262 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-803 1700228 1700658 1701109 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-802 1693848 1695677 1696969 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-801 1693479 1693552 1693684 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-800 1691181 1691861 1692342 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-799 1689385 1689813 1690216 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-798 1688831 1689079 1689120 "PATMAB" 1689227 PATMAB (NIL T) -9 NIL 1689310 NIL) (-797 1687478 1687882 1688139 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-796 1687016 1687147 1687188 "PATAB" 1687193 PATAB (NIL T) -9 NIL 1687365 NIL) (-795 1685559 1685996 1686419 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-794 1685237 1685312 1685414 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-793 1684926 1684989 1685098 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-792 1684731 1684777 1684844 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-791 1684409 1684484 1684586 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-790 1684098 1684161 1684270 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-789 1683789 1683859 1683956 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-788 1683478 1683541 1683650 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-787 1682639 1683018 1683197 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-786 1682246 1682344 1682463 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-785 1681214 1681639 1681858 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-784 1679879 1680533 1680893 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-783 1672969 1679283 1679477 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-782 1665390 1672467 1672651 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-781 1662115 1664030 1664070 "PADICCT" 1664651 PADICCT (NIL NIL) -9 NIL 1664933 NIL) (-780 1660105 1662065 1662110 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-779 1659267 1659477 1659743 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-778 1658609 1658752 1658956 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-777 1656990 1658017 1658295 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-776 1656514 1656773 1656870 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-775 1655573 1656251 1656423 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-774 1645995 1648864 1651063 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-773 1645387 1645701 1645827 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-772 1644664 1644859 1644887 "OUTBCON" 1645205 OUTBCON (NIL) -9 NIL 1645371 NIL) (-771 1644372 1644502 1644659 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-770 1643753 1643898 1644059 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-769 1643124 1643551 1643640 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-768 1642539 1642954 1642982 "OSGROUP" 1642987 OSGROUP (NIL) -9 NIL 1643009 NIL) (-767 1641503 1641764 1642049 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-766 1638772 1641378 1641498 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-765 1635913 1638523 1638649 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-764 1633931 1634459 1635019 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-763 1627273 1629813 1629853 "OREPCAT" 1632174 OREPCAT (NIL T) -9 NIL 1633276 NIL) (-762 1625299 1626233 1627268 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-761 1624496 1624767 1624795 "ORDTYPE" 1625100 ORDTYPE (NIL) -9 NIL 1625258 NIL) (-760 1624030 1624241 1624491 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-759 1623492 1623868 1624025 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-758 1622986 1623349 1623377 "ORDSET" 1623382 ORDSET (NIL) -9 NIL 1623404 NIL) (-757 1621551 1622573 1622601 "ORDRING" 1622606 ORDRING (NIL) -9 NIL 1622634 NIL) (-756 1620799 1621356 1621384 "ORDMON" 1621389 ORDMON (NIL) -9 NIL 1621410 NIL) (-755 1620103 1620265 1620457 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-754 1619314 1619822 1619850 "ORDFIN" 1619915 ORDFIN (NIL) -9 NIL 1619989 NIL) (-753 1618708 1618847 1619033 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-752 1615383 1617676 1618082 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-751 1614790 1615145 1615250 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-750 1614598 1614643 1614709 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-749 1613899 1614175 1614216 "OPERCAT" 1614427 OPERCAT (NIL T) -9 NIL 1614523 NIL) (-748 1613711 1613778 1613894 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-747 1611077 1612513 1613009 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-746 1610498 1610625 1610799 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-745 1607399 1609637 1610003 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-744 1604265 1606774 1606814 "OMSAGG" 1606875 OMSAGG (NIL T) -9 NIL 1606939 NIL) (-743 1602677 1603936 1604104 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-742 1600873 1602114 1602142 "OINTDOM" 1602147 OINTDOM (NIL) -9 NIL 1602168 NIL) (-741 1598303 1599875 1600204 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-740 1597557 1598253 1598298 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-739 1594759 1597398 1597552 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-738 1586296 1594630 1594754 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-737 1579751 1586187 1586291 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-736 1578723 1578960 1579233 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-735 1576364 1577034 1577738 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-734 1572141 1573101 1574124 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-733 1571649 1571737 1571931 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-732 1569098 1569680 1570353 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-731 1566493 1567001 1567597 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-730 1563490 1564029 1564675 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-729 1562845 1562953 1563211 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-728 1562003 1562128 1562349 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-727 1558287 1559083 1559996 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-726 1557727 1557822 1558044 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-725 1557408 1557457 1557584 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-724 1554011 1557207 1557326 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-723 1553171 1553793 1553821 "OCAMON" 1553826 OCAMON (NIL) -9 NIL 1553847 NIL) (-722 1547365 1550179 1550219 "OC" 1551314 OC (NIL T) -9 NIL 1552170 NIL) (-721 1545365 1546291 1547271 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-720 1544781 1545199 1545227 "OASGP" 1545232 OASGP (NIL) -9 NIL 1545252 NIL) (-719 1543844 1544493 1544521 "OAMONS" 1544561 OAMONS (NIL) -9 NIL 1544604 NIL) (-718 1542989 1543570 1543598 "OAMON" 1543655 OAMON (NIL) -9 NIL 1543706 NIL) (-717 1542885 1542917 1542984 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-716 1541636 1542410 1542438 "OAGROUP" 1542584 OAGROUP (NIL) -9 NIL 1542676 NIL) (-715 1541427 1541514 1541631 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-714 1541167 1541223 1541311 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-713 1536229 1537792 1539319 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-712 1532924 1533958 1534993 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-711 1532034 1532267 1532485 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-710 1520895 1523923 1526371 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-709 1515018 1520281 1520375 "NTSCAT" 1520380 NTSCAT (NIL T T T T) -9 NIL 1520418 NIL) (-708 1514359 1514538 1514731 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-707 1514052 1514115 1514222 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-706 1501719 1511672 1512482 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-705 1490728 1501584 1501714 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-704 1489448 1489773 1490130 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-703 1488284 1488548 1488906 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-702 1487451 1487584 1487800 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-701 1485769 1486088 1486494 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-700 1485482 1485516 1485640 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-699 1485301 1485336 1485405 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-698 1485077 1485267 1485296 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-697 1484641 1484708 1484885 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-696 1482927 1484004 1484259 "NNI" NIL NNI (NIL) -8 NIL NIL 1484606) (-695 1481655 1481992 1482356 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-694 1480632 1480884 1481186 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-693 1479719 1480284 1480325 "NETCLT" 1480496 NETCLT (NIL T) -9 NIL 1480577 NIL) (-692 1478623 1478890 1479171 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-691 1478422 1478465 1478540 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-690 1476953 1477341 1477761 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-689 1475586 1476552 1476580 "NASRING" 1476690 NASRING (NIL) -9 NIL 1476770 NIL) (-688 1475431 1475487 1475581 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-687 1474360 1475038 1475066 "NARNG" 1475183 NARNG (NIL) -9 NIL 1475274 NIL) (-686 1474136 1474221 1474355 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-685 1472902 1473656 1473696 "NAALG" 1473775 NAALG (NIL T) -9 NIL 1473836 NIL) (-684 1472772 1472807 1472897 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-683 1467751 1468936 1470122 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-682 1467146 1467233 1467417 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-681 1459137 1463632 1463684 "MTSCAT" 1464744 MTSCAT (NIL T T) -9 NIL 1465258 NIL) (-680 1458903 1458963 1459055 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-679 1458729 1458768 1458828 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-678 1456358 1458243 1458284 "MSETAGG" 1458289 MSETAGG (NIL T) -9 NIL 1458323 NIL) (-677 1452728 1455401 1455722 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-676 1449121 1450944 1451663 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-675 1448758 1448831 1448960 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-674 1448411 1448452 1448596 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-673 1446276 1446613 1447044 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-672 1439674 1446175 1446271 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-671 1439199 1439240 1439448 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-670 1438758 1438807 1438990 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-669 1438032 1438125 1438344 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1436649 1437010 1437400 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-667 1436170 1436237 1436276 "MONOPC" 1436336 MONOPC (NIL T) -9 NIL 1436555 NIL) (-666 1435621 1435957 1436085 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-665 1434763 1435142 1435170 "MONOID" 1435388 MONOID (NIL) -9 NIL 1435532 NIL) (-664 1434422 1434572 1434758 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-663 1423360 1430230 1430289 "MONOGEN" 1430963 MONOGEN (NIL T T) -9 NIL 1431419 NIL) (-662 1421372 1422258 1423241 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-661 1420086 1420630 1420658 "MONADWU" 1421049 MONADWU (NIL) -9 NIL 1421284 NIL) (-660 1419634 1419834 1420081 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-659 1418911 1419212 1419240 "MONAD" 1419447 MONAD (NIL) -9 NIL 1419559 NIL) (-658 1418678 1418774 1418906 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-657 1417068 1417838 1418117 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-656 1416202 1416729 1416769 "MODULE" 1416774 MODULE (NIL T) -9 NIL 1416812 NIL) (-655 1415881 1416007 1416197 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-654 1413600 1414486 1414800 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-653 1410779 1412196 1412709 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-652 1409413 1409987 1410263 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-651 1398632 1408078 1408491 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-650 1395596 1397640 1397909 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-649 1394680 1395047 1395237 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-648 1394249 1394298 1394477 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-647 1392074 1393070 1393110 "MLO" 1393527 MLO (NIL T) -9 NIL 1393767 NIL) (-646 1389955 1390482 1391077 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-645 1389423 1389519 1389673 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-644 1389093 1389169 1389292 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-643 1388305 1388491 1388719 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-642 1387798 1387914 1388070 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-641 1387170 1387284 1387469 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-640 1386197 1386470 1386747 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-639 1385630 1385718 1385889 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-638 1382788 1383667 1384546 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-637 1381455 1381803 1382156 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-636 1378879 1380542 1380583 "MDAGG" 1380840 MDAGG (NIL T) -9 NIL 1380985 NIL) (-635 1378153 1378317 1378517 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-634 1377231 1377517 1377747 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-633 1375328 1375905 1376466 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-632 1371072 1374918 1375165 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-631 1367421 1368190 1368924 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-630 1366174 1366343 1366672 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-629 1355619 1359243 1359319 "MATCAT" 1364307 MATCAT (NIL T T T) -9 NIL 1365753 NIL) (-628 1352900 1354206 1355614 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-627 1351301 1351661 1352045 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-626 1350434 1350631 1350853 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-625 1349185 1349511 1349838 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-624 1348347 1348749 1348925 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-623 1348016 1348080 1348203 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-622 1347664 1347737 1347851 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-621 1347199 1347314 1347456 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-620 1345408 1346176 1346477 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-619 1344902 1345204 1345294 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-618 1339223 1343199 1343240 "LZSTAGG" 1344017 LZSTAGG (NIL T) -9 NIL 1344307 NIL) (-617 1336572 1337884 1339218 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-616 1333959 1334925 1335408 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-615 1333540 1333819 1333893 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-614 1325755 1333401 1333535 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-613 1325118 1325263 1325491 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-612 1322602 1323300 1324012 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-611 1320818 1321141 1321575 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-610 1314198 1319850 1319891 "LSAGG" 1319953 LSAGG (NIL T) -9 NIL 1320031 NIL) (-609 1311892 1312991 1314193 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-608 1309372 1311241 1311490 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-607 1309039 1309130 1309253 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-606 1308710 1308789 1308817 "LOGIC" 1308928 LOGIC (NIL) -9 NIL 1309010 NIL) (-605 1308605 1308634 1308705 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-604 1307924 1308082 1308275 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-603 1306709 1306958 1307309 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-602 1302531 1305330 1305370 "LODOCAT" 1305802 LODOCAT (NIL T) -9 NIL 1306013 NIL) (-601 1302324 1302400 1302526 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-600 1299324 1302201 1302319 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-599 1296422 1299274 1299319 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-598 1293509 1296352 1296417 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-597 1292562 1292737 1293039 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-596 1290694 1291824 1292077 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-595 1286609 1288835 1288876 "LNAGG" 1289735 LNAGG (NIL T) -9 NIL 1290173 NIL) (-594 1285996 1286263 1286604 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-593 1282568 1283509 1284146 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-592 1281830 1282335 1282375 "LMODULE" 1282380 LMODULE (NIL T) -9 NIL 1282406 NIL) (-591 1279299 1281566 1281689 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-590 1278867 1279078 1279119 "LLINSET" 1279180 LLINSET (NIL T) -9 NIL 1279224 NIL) (-589 1278543 1278803 1278862 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-588 1278142 1278222 1278361 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-587 1276593 1276941 1277340 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-586 1275764 1275960 1276188 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-585 1269078 1275020 1275274 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-584 1268655 1268888 1268929 "LINSET" 1268934 LINSET (NIL T) -9 NIL 1268967 NIL) (-583 1267556 1268278 1268445 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-582 1265822 1266577 1266617 "LINEXP" 1267103 LINEXP (NIL T) -9 NIL 1267376 NIL) (-581 1264444 1265431 1265612 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-580 1263271 1263543 1263845 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-579 1262484 1263073 1263183 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-578 1260042 1260764 1261514 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-577 1258677 1258974 1259365 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-576 1257470 1258072 1258112 "LIECAT" 1258252 LIECAT (NIL T) -9 NIL 1258403 NIL) (-575 1257344 1257377 1257465 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-574 1251600 1257034 1257262 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-573 1243240 1251276 1251432 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-572 1239692 1240641 1241576 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-571 1238316 1239224 1239252 "LFCAT" 1239459 LFCAT (NIL) -9 NIL 1239598 NIL) (-570 1236555 1236885 1237230 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-569 1234072 1234737 1235418 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-568 1231084 1232062 1232565 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-567 1230575 1230878 1230969 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-566 1229282 1229606 1230006 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-565 1228548 1228633 1228859 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-564 1223551 1227116 1227652 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-563 1223176 1223226 1223386 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-562 1221947 1222720 1222760 "LALG" 1222821 LALG (NIL T) -9 NIL 1222879 NIL) (-561 1221730 1221807 1221942 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-560 1219583 1220998 1221249 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-559 1219412 1219442 1219483 "KVTFROM" 1219545 KVTFROM (NIL T) -9 NIL NIL NIL) (-558 1218228 1218943 1219132 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-557 1218057 1218087 1218128 "KRCFROM" 1218190 KRCFROM (NIL T) -9 NIL NIL NIL) (-556 1217159 1217356 1217651 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-555 1216988 1217018 1217059 "KONVERT" 1217121 KONVERT (NIL T) -9 NIL NIL NIL) (-554 1216817 1216847 1216888 "KOERCE" 1216950 KOERCE (NIL T) -9 NIL NIL NIL) (-553 1216387 1216480 1216612 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-552 1214440 1215334 1215706 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-551 1207427 1212119 1212173 "KDAGG" 1212549 KDAGG (NIL T T) -9 NIL 1212789 NIL) (-550 1207085 1207220 1207422 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-549 1200389 1206877 1207023 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-548 1200039 1200321 1200384 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-547 1199009 1199508 1199757 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-546 1198135 1198584 1198789 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-545 1196999 1197491 1197791 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-544 1196281 1196680 1196841 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-543 1195991 1196227 1196276 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-542 1190246 1195681 1195909 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-541 1189664 1189997 1190117 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-540 1186392 1187852 1187904 "IXAGG" 1188801 IXAGG (NIL T T) -9 NIL 1189261 NIL) (-539 1185679 1186010 1186387 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-538 1184748 1185023 1185265 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-537 1183410 1183617 1183910 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-536 1182361 1182583 1182866 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-535 1182036 1182099 1182222 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-534 1181298 1181670 1181844 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-533 1179274 1180574 1180848 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-532 1168822 1174591 1175748 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-531 1168067 1168219 1168455 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-530 1167558 1167861 1167952 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-529 1166851 1166942 1167155 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-528 1165983 1166208 1166448 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-527 1164396 1164777 1165205 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-526 1164181 1164225 1164301 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-525 1163031 1163328 1163623 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-524 1162304 1162655 1162806 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-523 1161507 1161638 1161851 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-522 1159669 1160166 1160710 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-521 1156750 1158018 1158707 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-520 1156575 1156615 1156675 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-519 1152573 1156501 1156570 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-518 1150576 1152512 1152568 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-517 1149947 1150246 1150376 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-516 1149400 1149688 1149820 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-515 1148481 1149106 1149232 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-514 1147891 1148385 1148413 "IOBCON" 1148418 IOBCON (NIL) -9 NIL 1148439 NIL) (-513 1147462 1147526 1147708 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-512 1139521 1141892 1144217 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-511 1136632 1137415 1138279 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-510 1136309 1136406 1136523 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-509 1133751 1136245 1136304 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-508 1131863 1132392 1132959 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-507 1131365 1131479 1131619 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-506 1129749 1130155 1130617 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-505 1127528 1128122 1128733 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-504 1124901 1125511 1126231 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-503 1124305 1124463 1124671 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-502 1123824 1123910 1124098 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-501 1122029 1122550 1123007 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-500 1115119 1116772 1118501 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-499 1114485 1114647 1114820 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-498 1112358 1112822 1113366 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-497 1110484 1111434 1111462 "INTDOM" 1111761 INTDOM (NIL) -9 NIL 1111966 NIL) (-496 1110037 1110239 1110479 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-495 1105844 1108316 1108370 "INTCAT" 1109166 INTCAT (NIL T) -9 NIL 1109482 NIL) (-494 1105409 1105529 1105656 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-493 1104249 1104421 1104727 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-492 1103822 1103918 1104075 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-491 1096305 1103729 1103817 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-490 1095603 1096158 1096223 "INT8" NIL INT8 (NIL) -8 NIL NIL 1096257) (-489 1094900 1095455 1095520 "INT64" NIL INT64 (NIL) -8 NIL NIL 1095554) (-488 1094197 1094752 1094817 "INT32" NIL INT32 (NIL) -8 NIL NIL 1094851) (-487 1093494 1094049 1094114 "INT16" NIL INT16 (NIL) -8 NIL NIL 1094148) (-486 1089957 1093413 1093489 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-485 1084014 1087497 1087525 "INS" 1088455 INS (NIL) -9 NIL 1089114 NIL) (-484 1082076 1082994 1083941 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-483 1081135 1081358 1081633 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-482 1080349 1080490 1080687 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-481 1079339 1079480 1079717 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-480 1078491 1078655 1078915 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-479 1077771 1077886 1078074 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-478 1076510 1076779 1077103 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-477 1075790 1075931 1076114 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-476 1075453 1075525 1075623 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-475 1072531 1074017 1074540 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-474 1072130 1072237 1072351 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-473 1071286 1071931 1072032 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-472 1070136 1070404 1070725 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-471 1069126 1070066 1070131 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-470 1068751 1068831 1068948 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-469 1067665 1068210 1068414 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-468 1063760 1064815 1065758 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-467 1062614 1062937 1062965 "INBCON" 1063478 INBCON (NIL) -9 NIL 1063744 NIL) (-466 1062068 1062333 1062609 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-465 1061562 1061864 1061954 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-464 1061019 1061328 1061433 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-463 1059858 1059999 1060316 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-462 1058281 1058550 1058889 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-461 1053124 1058212 1058276 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-460 1052504 1052838 1052953 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-459 1047596 1051942 1052128 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-458 1046626 1047518 1047591 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-457 1046198 1046275 1046329 "IEVALAB" 1046536 IEVALAB (NIL T T) -9 NIL NIL NIL) (-456 1045953 1046033 1046193 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-455 1045338 1045565 1045722 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-454 1044331 1045258 1045333 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-453 1043394 1044251 1044326 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-452 1042477 1043123 1043260 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-451 1040941 1041512 1041563 "IDPC" 1041972 IDPC (NIL T T) -9 NIL 1042263 NIL) (-450 1040229 1040863 1040936 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-449 1039399 1040151 1040224 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-448 1039092 1039305 1039365 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-447 1038796 1038836 1038875 "IDEMOPC" 1038880 IDEMOPC (NIL T) -9 NIL 1039017 NIL) (-446 1035867 1036748 1037640 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-445 1029493 1030770 1031809 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-444 1028755 1028885 1029084 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-443 1027928 1028427 1028565 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-442 1026319 1026650 1027041 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-441 1022356 1026275 1026314 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-440 1019614 1020238 1020933 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-439 1017840 1018320 1018853 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-438 1015655 1017746 1017835 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-437 1011797 1015593 1015650 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-436 1005376 1010761 1011229 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-435 1004944 1005007 1005180 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-434 1004436 1004585 1004613 "HYPCAT" 1004820 HYPCAT (NIL) -9 NIL NIL NIL) (-433 1004092 1004245 1004431 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-432 1003705 1003950 1004033 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-431 1003538 1003587 1003628 "HOMOTOP" 1003633 HOMOTOP (NIL T) -9 NIL 1003666 NIL) (-430 1002041 1002853 1002894 "HOAGG" 1002899 HOAGG (NIL T) -9 NIL 1003199 NIL) (-429 1001668 1001815 1002036 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-428 994868 1001393 1001541 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-427 993803 994061 994324 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-426 992738 993668 993798 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-425 990937 992571 992659 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-424 990252 990604 990737 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-423 983750 990185 990247 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-422 976889 983486 983637 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-421 976342 976499 976662 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-420 968842 976259 976337 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-419 968333 968636 968727 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-418 965883 968120 968299 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-417 961569 965766 965878 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-416 954046 961466 961564 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-415 945983 953415 953670 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-414 945007 945516 945544 "GROUP" 945747 GROUP (NIL) -9 NIL 945881 NIL) (-413 944550 944751 945002 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-412 943222 943561 943948 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-411 942044 942401 942452 "GRMOD" 942981 GRMOD (NIL T T) -9 NIL 943147 NIL) (-410 941863 941911 942039 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-409 937986 939197 940197 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-408 936708 937032 937347 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-407 936261 936389 936530 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-406 935334 935833 935884 "GRALG" 936037 GRALG (NIL T T) -9 NIL 936127 NIL) (-405 935053 935154 935329 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-404 932072 934744 934911 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-403 931485 931548 931805 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-402 927339 928235 928760 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-401 926514 926716 926954 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-400 921517 922444 923463 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-399 921265 921322 921411 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-398 920747 920836 921001 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-397 920256 920297 920510 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-396 919057 919340 919644 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-395 912332 918747 918908 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-394 902115 907122 908226 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-393 900167 901270 901298 "GCDDOM" 901553 GCDDOM (NIL) -9 NIL 901710 NIL) (-392 899790 899947 900162 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-391 890583 893053 895441 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-390 888718 889043 889461 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-389 887659 887848 888115 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-388 886530 886737 887041 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-387 885993 886135 886283 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-386 884605 884953 885266 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-385 883150 883471 883793 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-384 880776 881132 881537 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-383 874028 875689 877267 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-382 873680 873901 873969 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-381 873425 873467 873508 "FUNCTOR" 873592 FUNCTOR (NIL T) -9 NIL 873651 NIL) (-380 873049 873270 873351 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 871146 871829 872289 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 869739 870046 870438 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 868394 868753 869077 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 867697 867821 868008 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 866671 866937 867284 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 864329 864859 865341 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 863912 863972 864141 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 862212 863126 863429 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 861360 861494 861717 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 860531 860692 860919 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 856747 859408 859449 "FSAGG" 859819 FSAGG (NIL T) -9 NIL 860080 NIL) (-368 855101 855860 856652 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 853057 853353 853897 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 852104 852286 852586 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 851785 851834 851961 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 831941 841442 841483 "FS" 845353 FS (NIL T) -9 NIL 847631 NIL) (-363 824172 827665 831644 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 823706 823833 823985 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 818229 821387 821427 "FRNAALG" 822747 FRNAALG (NIL T) -9 NIL 823345 NIL) (-360 814970 816221 817479 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 814651 814700 814827 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 813138 813695 813989 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 812424 812517 812804 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 810258 811024 811340 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 809367 809810 809851 "FRETRCT" 809856 FRETRCT (NIL T) -9 NIL 810027 NIL) (-354 808740 809018 809362 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 805484 807004 807063 "FRAMALG" 807945 FRAMALG (NIL T T) -9 NIL 808237 NIL) (-352 804080 804631 805261 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 803773 803836 803943 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 797414 803578 803768 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 797107 797170 797277 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 789516 794087 795394 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 783294 786797 786825 "FPS" 787944 FPS (NIL) -9 NIL 788500 NIL) (-346 782851 782984 783148 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 779661 781704 781732 "FPC" 781957 FPC (NIL) -9 NIL 782099 NIL) (-344 779507 779559 779656 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 778284 778993 779034 "FPATMAB" 779039 FPATMAB (NIL T) -9 NIL 779191 NIL) (-342 776714 777310 777657 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 776289 776347 776520 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 774792 775687 775861 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 773407 773912 773940 "FNCAT" 774397 FNCAT (NIL) -9 NIL 774654 NIL) (-338 772864 773374 773402 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 771451 772813 772859 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 768039 769397 769438 "FMONCAT" 770655 FMONCAT (NIL T) -9 NIL 771259 NIL) (-335 764998 766078 766131 "FMCAT" 767213 FMCAT (NIL T T) -9 NIL 767683 NIL) (-334 763698 764821 764920 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 762746 763546 763693 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 760933 761385 761879 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 758868 759404 759982 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 752254 757205 757819 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 750735 751836 751876 "FLINEXP" 751881 FLINEXP (NIL T) -9 NIL 751974 NIL) (-328 750144 750403 750730 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 749393 749552 749766 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 746276 747355 747407 "FLALG" 748634 FLALG (NIL T T) -9 NIL 749101 NIL) (-325 745447 745608 745835 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 739153 742843 742884 "FLAGG" 744123 FLAGG (NIL T) -9 NIL 744771 NIL) (-323 738261 738665 739148 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 734822 736086 736145 "FINRALG" 737273 FINRALG (NIL T T) -9 NIL 737781 NIL) (-321 734213 734478 734817 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 733511 733807 733835 "FINITE" 734031 FINITE (NIL) -9 NIL 734138 NIL) (-319 733419 733445 733506 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 730189 731515 731556 "FINAGG" 732555 FINAGG (NIL T) -9 NIL 733062 NIL) (-317 729108 729631 730184 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 721069 723660 723700 "FINAALG" 727352 FINAALG (NIL T) -9 NIL 728790 NIL) (-315 717336 718581 719704 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 715888 716307 716361 "FILECAT" 717045 FILECAT (NIL T T) -9 NIL 717261 NIL) (-313 715239 715713 715816 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 712487 714365 714393 "FIELD" 714433 FIELD (NIL) -9 NIL 714513 NIL) (-311 711512 711973 712482 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 709516 710462 710808 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 708759 708940 709159 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 704029 708697 708754 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 703691 703758 703893 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 703231 703273 703482 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 699911 700788 701565 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 695195 699843 699906 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 689874 694684 694874 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 684355 689155 689413 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 678562 683806 684017 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 677585 677795 678110 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 673025 675730 675758 "FFIELDC" 676377 FFIELDC (NIL) -9 NIL 676752 NIL) (-298 672094 672534 673020 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 671709 671767 671891 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 669853 670376 670893 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 664947 669652 669753 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 660047 664736 664843 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 654713 659838 659946 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 654167 654216 654451 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 632742 643776 643862 "FFCAT" 649012 FFCAT (NIL T T T) -9 NIL 650448 NIL) (-290 628982 630208 631514 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 623825 628913 628977 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 622848 623317 623358 "FEVALAB" 623363 FEVALAB (NIL T) -9 NIL 623602 NIL) (-287 622253 622505 622843 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 619080 619991 620106 "FDIVCAT" 621673 FDIVCAT (NIL T T T T) -9 NIL 622109 NIL) (-285 618874 618906 619075 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 618181 618274 618551 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 616667 617665 617868 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 615760 616144 616346 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 614882 615371 615511 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 606469 611112 611152 "FAXF" 612953 FAXF (NIL T) -9 NIL 613643 NIL) (-279 604385 605189 606004 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 599534 603907 604081 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 593973 596397 596449 "FAMR" 597460 FAMR (NIL T T) -9 NIL 597919 NIL) (-276 593172 593537 593968 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 592193 593114 593167 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 589787 590666 590719 "FAMONC" 591660 FAMONC (NIL T T) -9 NIL 592045 NIL) (-273 588343 589645 589782 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 586423 586784 587186 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 585700 585897 586119 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 577560 585147 585346 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 575579 576149 576735 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 572481 573123 573843 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 567638 568345 569150 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 567327 567390 567499 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 552120 566376 566802 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 542647 551440 551728 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 542141 542443 542533 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 541917 542107 542136 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 541606 541674 541787 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 541123 541265 541306 "EVALAB" 541476 EVALAB (NIL T) -9 NIL 541580 NIL) (-259 540751 540897 541118 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 537794 539389 539417 "EUCDOM" 539971 EUCDOM (NIL) -9 NIL 540320 NIL) (-257 536721 537214 537789 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 536446 536502 536602 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 536134 536198 536307 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 529905 531805 531833 "ES" 534575 ES (NIL) -9 NIL 535959 NIL) (-253 526420 527952 529744 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 525768 525921 526097 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 518274 525698 525763 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 517963 518026 518135 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 511700 514825 516229 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 508003 509099 510192 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 506832 507182 507487 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 505717 506448 506476 "ENTIRER" 506481 ENTIRER (NIL) -9 NIL 506525 NIL) (-245 505606 505640 505712 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 502247 504044 504393 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 501348 501563 501615 "ELTAGG" 501981 ELTAGG (NIL T T) -9 NIL 502195 NIL) (-242 501130 501204 501343 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 500876 500911 500965 "ELTAB" 501049 ELTAB (NIL T T) -9 NIL 501101 NIL) (-240 500127 500297 500496 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 499851 499925 499953 "ELEMFUN" 500058 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 499751 499778 499846 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 495068 497758 497799 "ELAGG" 498732 ELAGG (NIL T) -9 NIL 499193 NIL) (-236 493866 494404 495063 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 493284 493451 493607 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 492197 492516 492795 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 485590 487588 488415 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 479569 481565 482375 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 477383 477789 478260 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 468383 470296 471837 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 467496 467997 468146 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 466194 466868 466908 "DVARCAT" 467191 DVARCAT (NIL T) -9 NIL 467331 NIL) (-227 465613 465877 466189 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 457680 465481 465608 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 456018 456809 456850 "DSEXT" 457213 DSEXT (NIL T) -9 NIL 457507 NIL) (-224 454823 455347 456013 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 454547 454612 454710 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 450698 451914 453045 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 446344 447699 448763 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 445019 445380 445766 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 444705 444764 444882 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 443680 443978 444268 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 443265 443340 443490 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 435678 437790 439905 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 431195 432214 433293 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 427743 429804 429845 "DQAGG" 430474 DQAGG (NIL T) -9 NIL 430747 NIL) (-213 414267 421908 421990 "DPOLCAT" 423827 DPOLCAT (NIL T T T T) -9 NIL 424370 NIL) (-212 410675 412323 414262 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 403724 410573 410670 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 396682 403553 403719 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 396275 396535 396624 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 395689 396137 396217 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 394975 395300 395451 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 388114 394711 394862 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 385863 387180 387220 "DMEXT" 387225 DMEXT (NIL T) -9 NIL 387400 NIL) (-204 385519 385581 385725 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 379111 385004 385194 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 376319 377922 377963 "DLAGG" 378504 DLAGG (NIL T) -9 NIL 378736 NIL) (-201 374670 375541 375569 "DIVRING" 375661 DIVRING (NIL) -9 NIL 375744 NIL) (-200 374121 374365 374665 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 372549 372966 373372 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 371586 371807 372072 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 365104 371518 371581 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 353424 359846 359899 "DIRPCAT" 360155 DIRPCAT (NIL NIL T) -9 NIL 361030 NIL) (-195 351430 352200 353087 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 350877 351043 351229 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 348200 349736 349777 "DIOPS" 350197 DIOPS (NIL T) -9 NIL 350425 NIL) (-192 347860 348004 348195 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 346867 347613 347641 "DIOID" 347646 DIOID (NIL) -9 NIL 347668 NIL) (-190 345695 346524 346552 "DIFRING" 346557 DIFRING (NIL) -9 NIL 346578 NIL) (-189 345331 345429 345457 "DIFFSPC" 345576 DIFFSPC (NIL) -9 NIL 345651 NIL) (-188 345072 345174 345326 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 343975 344600 344640 "DIFFMOD" 344645 DIFFMOD (NIL T) -9 NIL 344742 NIL) (-186 343659 343716 343757 "DIFFDOM" 343878 DIFFDOM (NIL T) -9 NIL 343946 NIL) (-185 343540 343570 343654 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 341213 342734 342774 "DIFEXT" 342779 DIFEXT (NIL T) -9 NIL 342931 NIL) (-183 339141 340677 340718 "DIAGG" 340723 DIAGG (NIL T) -9 NIL 340743 NIL) (-182 338697 338887 339136 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 333881 337887 338164 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 330339 331392 332402 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 324889 329493 329820 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 323455 323747 324122 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 320737 321989 322357 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 318462 320568 320657 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 317845 317990 318172 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 315163 315887 316687 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 313272 313730 314292 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 312655 312988 313102 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 305855 312380 312528 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 303775 304285 304789 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 303414 303463 303614 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 302673 303235 303326 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 300697 301139 301499 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 299989 300278 300424 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 299440 299586 299738 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 296802 297595 298322 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 296241 296387 296558 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 294313 294624 294991 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 293870 294125 294226 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 293071 293454 293482 "CTORCAT" 293663 CTORCAT (NIL) -9 NIL 293775 NIL) (-159 292774 292908 293066 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 292267 292524 292632 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 291683 292114 292187 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 291142 291259 291412 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 287536 288292 289047 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 287027 287330 287421 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 286246 286455 286683 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 285750 285855 286059 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 285503 285537 285643 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 282442 283204 283922 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 281961 282103 282242 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 277854 280424 280916 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 277728 277755 277783 "CONDUIT" 277820 CONDUIT (NIL) -9 NIL NIL NIL) (-146 276607 277338 277366 "COMRING" 277371 COMRING (NIL) -9 NIL 277421 NIL) (-145 275772 276139 276317 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 275468 275509 275637 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 275161 275224 275331 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 264003 275111 275156 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 263464 263603 263763 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 263217 263258 263356 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 244630 256880 256920 "COMPCAT" 257921 COMPCAT (NIL T) -9 NIL 259263 NIL) (-138 237168 240681 244274 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 236927 236961 237063 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 236757 236796 236854 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 236338 236617 236691 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 235915 236156 236243 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 235110 235358 235386 "COMBOPC" 235724 COMBOPC (NIL) -9 NIL 235899 NIL) (-132 234174 234426 234668 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 231106 231790 232413 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 229986 230437 230672 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 229477 229780 229871 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 229164 229217 229342 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 228634 228944 229042 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 225154 226224 227304 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 223449 224434 224672 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 221053 222214 222255 "CLAGG" 222724 CLAGG (NIL T) -9 NIL 223051 NIL) (-123 220723 220855 221048 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220352 220443 220583 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218289 218796 219344 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217250 217981 218009 "CHARZ" 218014 CHARZ (NIL) -9 NIL 218028 NIL) (-119 217044 217090 217168 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 215883 216646 216674 "CHARNZ" 216735 CHARNZ (NIL) -9 NIL 216783 NIL) (-117 213361 214458 214981 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 213069 213148 213176 "CFCAT" 213287 CFCAT (NIL) -9 NIL NIL NIL) (-115 212412 212541 212723 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208680 211825 212105 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208058 208245 208422 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207586 208005 208053 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207059 207368 207465 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206550 206853 206944 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205799 205959 206180 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 201899 203156 203864 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200265 201296 201547 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199846 200125 200199 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199280 199533 199561 "CACHSET" 199693 CACHSET (NIL) -9 NIL 199771 NIL) (-104 198632 199047 199075 "CABMON" 199125 CABMON (NIL) -9 NIL 199181 NIL) (-103 198162 198426 198536 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193651 197830 197991 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192621 193325 193460 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193623) (-100 190087 192388 192494 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187524 189841 189949 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184702 186908 186947 "BTCAT" 187014 BTCAT (NIL T) -9 NIL 187095 NIL) (-97 184453 184551 184697 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179770 183626 183652 "BTAGG" 183763 BTAGG (NIL) -9 NIL 183871 NIL) (-95 179401 179562 179765 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176480 178893 179083 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175750 175902 176080 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172826 174447 174486 "BRAGG" 175115 BRAGG (NIL T) -9 NIL 175375 NIL) (-91 171901 172332 172821 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164435 171406 171587 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162427 164387 164430 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 162160 162196 162307 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160399 160832 161280 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156365 157781 158671 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 155241 156132 156254 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154827 154984 155010 "BOOLE" 155118 BOOLE (NIL) -9 NIL 155199 NIL) (-83 154620 154701 154822 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153758 154285 154335 "BMODULE" 154340 BMODULE (NIL T T) -9 NIL 154404 NIL) (-81 149643 153615 153684 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 149456 149496 149535 "BINOPC" 149540 BINOPC (NIL T) -9 NIL 149585 NIL) (-79 148998 149271 149373 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 148519 148663 148801 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141725 148249 148394 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 139941 140914 140953 "BGAGG" 141209 BGAGG (NIL T) -9 NIL 141349 NIL) (-75 139810 139848 139936 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 138661 138862 139147 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 135316 137841 138146 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 134901 134994 135020 "BASTYPE" 135191 BASTYPE (NIL) -9 NIL 135287 NIL) (-71 134671 134767 134896 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 134186 134274 134424 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 133085 133760 133945 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 132833 132838 132864 "ATTREG" 132869 ATTREG (NIL) -9 NIL NIL NIL) (-67 132438 132710 132775 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 131938 132087 132113 "ATRIG" 132314 ATRIG (NIL) -9 NIL NIL NIL) (-65 131793 131846 131933 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 131363 131594 131620 "ASTCAT" 131625 ASTCAT (NIL) -9 NIL 131655 NIL) (-63 131162 131239 131358 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 129326 130995 131083 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 128133 128446 128811 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 125926 128063 128128 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 125117 125308 125529 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 120985 124848 124962 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 115535 117597 117672 "ARR2CAT" 119940 ARR2CAT (NIL T T T) -9 NIL 120591 NIL) (-56 114496 114978 115530 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 113864 114235 114357 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 112796 112964 113260 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 112497 112551 112669 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 111880 112026 112182 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 111285 111575 111695 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 108980 110141 110443 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 108505 108765 108861 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 102200 107567 108009 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 97835 99498 99548 "AMR" 100189 AMR (NIL T T) -9 NIL 100764 NIL) (-46 97189 97469 97830 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 79174 97123 97184 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 75577 78850 79019 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 72587 73247 73854 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 71966 72079 72263 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68378 69003 69595 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 57867 68071 68221 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 57184 57338 57516 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 55897 56692 56730 "ALGEBRA" 56735 ALGEBRA (NIL T) -9 NIL 56775 NIL) (-37 55683 55760 55892 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 33898 52685 52737 "ALAGG" 52872 ALAGG (NIL T T) -9 NIL 53044 NIL) (-35 33398 33547 33573 "AHYP" 33774 AHYP (NIL) -9 NIL NIL NIL) (-34 32880 33012 33038 "AGG" 33243 AGG (NIL) -9 NIL 33369 NIL) (-33 32723 32781 32875 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30862 31322 31722 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30357 30660 30749 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29727 30022 30178 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17285 26564 26602 "ACFS" 27209 ACFS (NIL T) -9 NIL 27448 NIL) (-28 15908 16518 17280 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11460 13839 13865 "ACF" 14744 ACF (NIL) -9 NIL 15156 NIL) (-26 10556 10962 11455 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10058 10298 10324 "ABELSG" 10416 ABELSG (NIL) -9 NIL 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T) ((-148) OR (|has| |#1| (-499)) (|has| |#1| (-314)) (|has| |#1| (-148))) ((-557 (-181)) -12 (|has| |#1| (-314)) (|has| |#2| (-937))) ((-557 (-332)) -12 (|has| |#1| (-314)) (|has| |#2| (-937))) ((-557 (-477)) -12 (|has| |#1| (-314)) (|has| |#2| (-557 (-477)))) ((-557 (-804 (-332))) -12 (|has| |#1| (-314)) (|has| |#2| (-557 (-804 (-332))))) ((-557 (-804 (-488))) -12 (|has| |#1| (-314)) (|has| |#2| (-557 (-804 (-488))))) ((-188 $) OR (|has| |#1| (-15 * (|#1| (-488) |#1|))) (-12 (|has| |#1| (-314)) (|has| |#2| (-191))) (-12 (|has| |#1| (-314)) (|has| |#2| (-192)))) ((-186 |#2|) |has| |#1| (-314)) ((-192) OR (|has| |#1| (-15 * (|#1| (-488) |#1|))) (-12 (|has| |#1| (-314)) (|has| |#2| (-192)))) ((-191) OR (|has| |#1| (-15 * (|#1| (-488) |#1|))) (-12 (|has| |#1| (-314)) (|has| |#2| (-191))) (-12 (|has| |#1| (-314)) (|has| |#2| (-192)))) ((-227 |#2|) |has| |#1| (-314)) ((-203) |has| |#1| (-314)) ((-241) |has| |#1| (-38 (-352 (-488)))) ((-243 (-488) |#1|) . T) ((-243 |#2| $) -12 (|has| |#1| (-314)) (|has| |#2| (-243 |#2| |#2|))) ((-243 $ $) |has| (-488) (-1029)) ((-248) OR (|has| |#1| (-499)) (|has| |#1| (-314))) ((-260) |has| |#1| (-314)) ((-262 |#2|) -12 (|has| |#1| (-314)) (|has| |#2| (-262 |#2|))) ((-314) |has| |#1| (-314)) ((-290 |#2|) |has| |#1| (-314)) ((-331 |#2|) |has| |#1| (-314)) ((-345 |#2|) |has| |#1| (-314)) ((-383 |#1|) . T) ((-383 |#2|) |has| |#1| (-314)) ((-395) |has| |#1| (-314)) ((-436) |has| |#1| (-38 (-352 (-488)))) ((-459 (-1094) |#2|) -12 (|has| |#1| (-314)) (|has| |#2| (-459 (-1094) |#2|))) ((-459 |#2| |#2|) -12 (|has| |#1| (-314)) (|has| |#2| (-262 |#2|))) ((-499) OR (|has| |#1| (-499)) (|has| |#1| (-314))) ((-13) . T) ((-592 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-592 (-488)) . T) ((-592 |#1|) . T) ((-592 |#2|) |has| |#1| (-314)) ((-592 $) . T) ((-594 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-594 (-488)) -12 (|has| |#1| (-314)) (|has| |#2| (-584 (-488)))) ((-594 |#1|) . T) ((-594 |#2|) |has| |#1| (-314)) ((-594 $) . T) ((-586 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-586 |#1|) |has| |#1| (-148)) ((-586 |#2|) |has| |#1| (-314)) ((-586 $) OR (|has| |#1| (-499)) (|has| |#1| (-314))) ((-584 (-488)) -12 (|has| |#1| (-314)) (|has| |#2| (-584 (-488)))) ((-584 |#2|) |has| |#1| (-314)) ((-658 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-658 |#1|) |has| |#1| (-148)) ((-658 |#2|) |has| |#1| (-314)) ((-658 $) OR (|has| |#1| (-499)) (|has| |#1| (-314))) ((-667) . T) ((-718) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-720) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-722) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-725) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-744) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-759) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-760) OR (-12 (|has| |#1| (-314)) (|has| |#2| (-760))) (-12 (|has| |#1| (-314)) (|has| |#2| (-744)))) ((-763) OR (-12 (|has| |#1| (-314)) (|has| |#2| (-760))) (-12 (|has| |#1| (-314)) (|has| |#2| (-744)))) ((-810 $ (-1094)) OR (-12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-488) |#1|)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-815 (-1094)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-813 (-1094))))) ((-813 (-1094)) OR (-12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-488) |#1|)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-813 (-1094))))) ((-815 (-1094)) OR (-12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-488) |#1|)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-815 (-1094)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-813 (-1094))))) ((-800 (-332)) -12 (|has| |#1| (-314)) (|has| |#2| (-800 (-332)))) ((-800 (-488)) -12 (|has| |#1| (-314)) (|has| |#2| (-800 (-488)))) ((-798 |#2|) |has| |#1| (-314)) ((-825) -12 (|has| |#1| (-314)) (|has| |#2| (-825))) ((-890 |#1| (-488) (-998)) . T) ((-836) |has| |#1| (-314)) ((-908 |#2|) |has| |#1| (-314)) ((-919) |has| |#1| (-38 (-352 (-488)))) ((-937) -12 (|has| |#1| (-314)) (|has| |#2| (-937))) ((-954 (-352 (-488))) -12 (|has| |#1| (-314)) (|has| |#2| (-954 (-488)))) ((-954 (-488)) -12 (|has| |#1| (-314)) (|has| |#2| (-954 (-488)))) ((-954 (-1094)) -12 (|has| |#1| (-314)) (|has| |#2| (-954 (-1094)))) ((-954 |#2|) . T) ((-967 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-967 |#1|) . T) ((-967 |#2|) |has| |#1| (-314)) ((-967 $) OR (|has| |#1| (-499)) (|has| |#1| (-314)) (|has| |#1| (-148))) ((-972 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-972 |#1|) . T) ((-972 |#2|) |has| |#1| (-314)) ((-972 $) OR (|has| |#1| (-499)) (|has| |#1| (-314)) (|has| |#1| (-148))) ((-965) . T) ((-974) . T) ((-1029) . T) ((-1065) . T) ((-1017) . T) ((-1070) -12 (|has| |#1| (-314)) (|has| |#2| (-1070))) ((-1119) |has| |#1| (-38 (-352 (-488)))) ((-1122) |has| |#1| (-38 (-352 (-488)))) ((-1133) . T) ((-1138) |has| |#1| (-314)) ((-1145 |#1|) . T) ((-1162 |#1| (-488)) . 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2421412 2422886 2423705 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1093 2414372 2420609 2420902 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1092 2406058 2413963 2414225 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1091 2405337 2405476 2405693 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1090 2405021 2405086 2405197 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1089 2395744 2404733 2404858 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1088 2394474 2394772 2395127 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1087 2393879 2393957 2394148 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1086 2376031 2393378 2393619 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1085 2375630 2375902 2375971 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1084 2374966 2375247 2375387 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1083 2369568 2370827 2371780 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1082 2369100 2369200 2369364 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1081 2364211 2365493 2366640 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1080 2358669 2360140 2361451 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1079 2351584 2353648 2355439 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1078 2343753 2351522 2351579 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1077 2338702 2343467 2343582 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1076 2338289 2338372 2338516 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1075 2337440 2337641 2337876 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1074 2337180 2337238 2337331 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1073 2330706 2335383 2335991 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1072 2329882 2330087 2330318 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1071 2329127 2329498 2329645 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1070 2328615 2328857 2328887 "STEP" 2328981 STEP (NIL) -9 NIL 2329052 NIL) (-1069 2321109 2328533 2328610 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1068 2316134 2319889 2319932 "STAGG" 2320359 STAGG (NIL T) -9 NIL 2320533 NIL) (-1067 2314592 2315300 2316129 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1066 2312754 2314419 2314511 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1065 2312034 2312573 2312603 "SRING" 2312608 SRING (NIL) -9 NIL 2312628 NIL) (-1064 2304949 2310572 2311011 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1063 2298723 2300162 2301666 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2291340 2295998 2296028 "SRAGG" 2297327 SRAGG (NIL) -9 NIL 2297931 NIL) (-1061 2290637 2290957 2291335 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1060 2284743 2289959 2290382 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1059 2278672 2282096 2282847 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1058 2275101 2275920 2276557 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1057 2274076 2274381 2274411 "SPFCAT" 2274855 SPFCAT (NIL) -9 NIL NIL NIL) (-1056 2273013 2273265 2273529 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1055 2263771 2266045 2266075 "SPADXPT" 2270712 SPADXPT (NIL) -9 NIL 2272836 NIL) (-1054 2263573 2263619 2263688 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1053 2261229 2263537 2263568 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1052 2252903 2254992 2255034 "SPACEC" 2259349 SPACEC (NIL T) -9 NIL 2261154 NIL) (-1051 2250732 2252850 2252898 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1050 2249711 2249900 2250183 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1049 2248115 2248448 2248859 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1048 2247380 2247614 2247875 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1047 2243560 2244520 2245515 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1046 2239918 2240617 2241346 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1045 2233940 2239203 2239299 "SNTSCAT" 2239304 SNTSCAT (NIL T T T T) -9 NIL 2239374 NIL) (-1044 2227761 2232581 2232971 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1043 2221533 2227680 2227756 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1042 2219965 2220296 2220694 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1041 2211579 2216513 2216615 "SMATCAT" 2217958 SMATCAT (NIL NIL T T T) -9 NIL 2218506 NIL) (-1040 2209420 2210404 2211574 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1039 2209022 2209194 2209237 "SMAGG" 2209322 SMAGG (NIL T) -9 NIL 2209379 NIL) (-1038 2206565 2208171 2208214 "SKAGG" 2208475 SKAGG (NIL T) -9 NIL 2208611 NIL) (-1037 2202611 2206385 2206496 "SINT" NIL SINT (NIL) -8 NIL NIL 2206537) (-1036 2202421 2202465 2202531 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1035 2201496 2201728 2201996 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1034 2200500 2200662 2200938 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1033 2199846 2200186 2200309 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1032 2199192 2199499 2199639 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1031 2197303 2197795 2198301 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1030 2190787 2197222 2197298 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1029 2190290 2190527 2190557 "SGROUP" 2190650 SGROUP (NIL) -9 NIL 2190712 NIL) (-1028 2190180 2190212 2190285 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1027 2189818 2189858 2189899 "SGPOPC" 2189904 SGPOPC (NIL T) -9 NIL 2190105 NIL) (-1026 2189352 2189629 2189735 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1025 2186775 2187544 2188266 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1024 2180896 2186159 2186255 "SFRTCAT" 2186260 SFRTCAT (NIL T T T T) -9 NIL 2186298 NIL) (-1023 2175288 2176401 2177528 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1022 2169464 2170625 2171789 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1021 2168436 2169338 2169459 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1020 2164044 2164939 2165034 "SEXCAT" 2167647 SEXCAT (NIL T T T T T) -9 NIL 2168198 NIL) (-1019 2163017 2163971 2164039 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1018 2161408 2161993 2162295 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1017 2160931 2161116 2161146 "SETCAT" 2161263 SETCAT (NIL) -9 NIL 2161347 NIL) (-1016 2160763 2160827 2160926 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1015 2157815 2159199 2159242 "SETAGG" 2160110 SETAGG (NIL T) -9 NIL 2160448 NIL) (-1014 2157421 2157573 2157810 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1013 2154666 2157368 2157416 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1012 2154132 2154442 2154542 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1011 2153259 2153625 2153686 "SEGXCAT" 2153972 SEGXCAT (NIL T T) -9 NIL 2154092 NIL) (-1010 2152184 2152452 2152495 "SEGCAT" 2153017 SEGCAT (NIL T) -9 NIL 2153238 NIL) (-1009 2151864 2151929 2152042 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1008 2150930 2151400 2151608 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1007 2150508 2150787 2150863 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1006 2149873 2150009 2150213 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1005 2148939 2149686 2149868 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1004 2148192 2148887 2148934 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1003 2139677 2148059 2148187 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1002 2138531 2138821 2139140 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1001 2137829 2138041 2138231 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-1000 2137173 2137330 2137508 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-999 2136746 2136977 2137005 "SASTCAT" 2137010 SASTCAT (NIL) -9 NIL 2137023 NIL) (-998 2136213 2136638 2136712 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-997 2135816 2135857 2136028 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-996 2135447 2135488 2135645 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-995 2128528 2135364 2135442 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-994 2127178 2127507 2127903 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-993 2125939 2126300 2126600 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-992 2125563 2125784 2125865 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-991 2123023 2123657 2124110 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-990 2122862 2122895 2122963 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-989 2122353 2122656 2122747 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-988 2117981 2118849 2119760 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-987 2107036 2112299 2112393 "RSETCAT" 2116449 RSETCAT (NIL T T T T) -9 NIL 2117537 NIL) (-986 2105574 2106216 2107031 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-985 2099348 2100793 2102300 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-984 2097230 2097787 2097859 "RRCC" 2098932 RRCC (NIL T T) -9 NIL 2099273 NIL) (-983 2096755 2096954 2097225 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-982 2096225 2096535 2096633 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-981 2068758 2079472 2079536 "RPOLCAT" 2090010 RPOLCAT (NIL T T T) -9 NIL 2093155 NIL) (-980 2062857 2065680 2068753 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-979 2059024 2062605 2062743 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-978 2057352 2058091 2058347 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-977 2052995 2055807 2055835 "RNS" 2056097 RNS (NIL) -9 NIL 2056349 NIL) (-976 2051898 2052385 2052922 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-975 2051016 2051417 2051617 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-974 2050154 2050716 2050744 "RNG" 2050804 RNG (NIL) -9 NIL 2050858 NIL) (-973 2050043 2050077 2050149 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-972 2049305 2049810 2049850 "RMODULE" 2049855 RMODULE (NIL T) -9 NIL 2049881 NIL) (-971 2048244 2048350 2048680 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-970 2045141 2047834 2048127 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-969 2037982 2040426 2040538 "RMATCAT" 2043709 RMATCAT (NIL NIL NIL T T T) -9 NIL 2044640 NIL) (-968 2037499 2037678 2037977 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-967 2037067 2037278 2037319 "RLINSET" 2037380 RLINSET (NIL T) -9 NIL 2037424 NIL) (-966 2036712 2036793 2036919 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-965 2035558 2036289 2036317 "RING" 2036372 RING (NIL) -9 NIL 2036464 NIL) (-964 2035403 2035459 2035553 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-963 2034457 2034724 2034980 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-962 2025681 2034085 2034286 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-961 2024906 2025417 2025456 "RGBCSPC" 2025513 RGBCSPC (NIL T) -9 NIL 2025564 NIL) (-960 2023940 2024426 2024465 "RGBCMDL" 2024693 RGBCMDL (NIL T) -9 NIL 2024807 NIL) (-959 2023652 2023721 2023822 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-958 2023415 2023456 2023551 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-957 2021839 2022269 2022649 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-956 2019426 2020094 2020762 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-955 2018976 2019074 2019234 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-954 2018598 2018696 2018737 "RETRACT" 2018868 RETRACT (NIL T) -9 NIL 2018955 NIL) (-953 2018478 2018509 2018593 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-952 2018080 2018352 2018419 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-951 2016560 2017451 2017648 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-950 2016251 2016312 2016408 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-949 2015994 2016035 2016140 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-948 2015729 2015770 2015879 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-947 2010800 2012251 2013466 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-946 2007896 2008654 2009462 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-945 2005865 2006487 2007087 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-944 1998793 2004416 2004852 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-943 1998105 1998385 1998534 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-942 1997590 1997705 1997870 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-941 1993183 1996993 1997214 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-940 1992415 1992614 1992827 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-939 1989705 1990543 1991425 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-938 1986287 1987323 1988382 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-937 1986123 1986176 1986204 "REAL" 1986209 REAL (NIL) -9 NIL 1986244 NIL) (-936 1985613 1985917 1986008 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-935 1985093 1985171 1985376 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-934 1984326 1984518 1984729 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-933 1983214 1983511 1983878 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-932 1981481 1981951 1982484 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-931 1980405 1980682 1981069 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-930 1979234 1979543 1979962 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-929 1972582 1976094 1976122 "RCFIELD" 1977399 RCFIELD (NIL) -9 NIL 1978129 NIL) (-928 1971200 1971812 1972509 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-927 1967954 1969286 1969327 "RCAGG" 1970381 RCAGG (NIL T) -9 NIL 1970843 NIL) (-926 1967681 1967791 1967949 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-925 1967126 1967255 1967416 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-924 1966743 1966822 1966941 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-923 1966158 1966308 1966458 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-922 1965940 1965990 1966061 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-921 1958382 1965058 1965366 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-920 1948084 1958249 1958377 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-919 1947718 1947811 1947839 "RADCAT" 1947996 RADCAT (NIL) -9 NIL NIL NIL) (-918 1947556 1947616 1947713 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-917 1945661 1947387 1947476 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-916 1945342 1945391 1945518 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-915 1937611 1941695 1941735 "QUATCAT" 1942513 QUATCAT (NIL T) -9 NIL 1943277 NIL) (-914 1934861 1936141 1937517 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-913 1930701 1934811 1934856 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-912 1928039 1929698 1929739 "QUAGG" 1930114 QUAGG (NIL T) -9 NIL 1930290 NIL) (-911 1927641 1927913 1927980 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-910 1926647 1927277 1927440 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-909 1926328 1926377 1926504 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-908 1915910 1922079 1922119 "QFCAT" 1922777 QFCAT (NIL T) -9 NIL 1923770 NIL) (-907 1912794 1914233 1915816 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-906 1912340 1912474 1912604 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-905 1906536 1907697 1908859 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-904 1905955 1906135 1906367 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-903 1903777 1904305 1904728 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-902 1902676 1902918 1903235 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-901 1901037 1901235 1901588 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-900 1896793 1898009 1898050 "PTRANFN" 1899934 PTRANFN (NIL T) -9 NIL NIL NIL) (-899 1895440 1895785 1896106 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-898 1895133 1895196 1895303 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-897 1889430 1893874 1893914 "PTCAT" 1894206 PTCAT (NIL T) -9 NIL 1894359 NIL) (-896 1889123 1889164 1889288 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-895 1888002 1888318 1888652 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-894 1876881 1879442 1881751 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-893 1870083 1872646 1872740 "PSETCAT" 1875714 PSETCAT (NIL T T T T) -9 NIL 1876523 NIL) (-892 1868533 1869267 1870078 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-891 1867852 1868047 1868075 "PSCURVE" 1868343 PSCURVE (NIL) -9 NIL 1868510 NIL) (-890 1863436 1865256 1865320 "PSCAT" 1866155 PSCAT (NIL T T T) -9 NIL 1866394 NIL) (-889 1862750 1863032 1863431 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-888 1861147 1862062 1862325 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-887 1860638 1860941 1861032 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-886 1851658 1854080 1856268 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-885 1849352 1850921 1850961 "PRQAGG" 1851144 PRQAGG (NIL T) -9 NIL 1851247 NIL) (-884 1848525 1848971 1848999 "PROPLOG" 1849138 PROPLOG (NIL) -9 NIL 1849252 NIL) (-883 1848200 1848263 1848386 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-882 1847636 1847775 1847947 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-881 1845884 1846647 1846944 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-880 1845436 1845568 1845696 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-879 1839877 1844376 1845196 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-878 1839706 1839744 1839803 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-877 1839145 1839285 1839436 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-876 1837613 1838032 1838498 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-875 1837330 1837391 1837419 "PRIMCAT" 1837543 PRIMCAT (NIL) -9 NIL NIL NIL) (-874 1836501 1836697 1836925 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-873 1832662 1836451 1836496 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-872 1832361 1832423 1832534 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-871 1829497 1832010 1832243 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-870 1828948 1829105 1829133 "PPCURVE" 1829338 PPCURVE (NIL) -9 NIL 1829474 NIL) (-869 1828561 1828806 1828889 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-868 1826317 1826738 1827330 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-867 1825760 1825824 1826057 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-866 1822480 1822966 1823577 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-865 1808052 1814182 1814246 "POLYCAT" 1817731 POLYCAT (NIL T T T) -9 NIL 1819608 NIL) (-864 1803562 1805709 1808047 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-863 1803219 1803293 1803412 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-862 1802912 1802975 1803082 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-861 1796275 1802645 1802804 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-860 1795162 1795425 1795701 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-859 1793766 1794079 1794409 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-858 1789209 1793716 1793761 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-857 1787697 1788108 1788483 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-856 1786454 1786763 1787159 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-855 1786125 1786209 1786326 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-854 1785704 1785779 1785953 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-853 1785190 1785286 1785446 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-852 1784662 1784782 1784936 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-851 1783557 1783775 1784152 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-850 1783168 1783253 1783405 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-849 1782719 1782801 1782982 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-848 1782411 1782492 1782605 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-847 1781924 1781999 1782207 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-846 1781272 1781400 1781602 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-845 1780634 1780768 1780931 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-844 1779938 1780120 1780301 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-843 1779661 1779735 1779829 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-842 1776229 1777418 1778334 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-841 1775313 1775514 1775749 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-840 1770878 1772262 1773404 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-839 1750799 1755686 1760533 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-838 1750539 1750592 1750695 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-837 1749980 1750114 1750294 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-836 1747989 1749210 1749238 "PID" 1749435 PID (NIL) -9 NIL 1749562 NIL) (-835 1747777 1747820 1747895 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-834 1746964 1747624 1747711 "PI" NIL PI (NIL) -8 NIL NIL 1747751) (-833 1746416 1746567 1746743 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-832 1742744 1743702 1744607 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-831 1741108 1741397 1741763 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-830 1740550 1740665 1740826 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-829 1737091 1739419 1739772 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-828 1735697 1735977 1736302 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-827 1734462 1734716 1735064 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-826 1733172 1733399 1733751 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-825 1730182 1731742 1731770 "PFECAT" 1732363 PFECAT (NIL) -9 NIL 1732740 NIL) (-824 1729805 1729970 1730177 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-823 1728629 1728911 1729212 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-822 1726811 1727198 1727628 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-821 1722781 1726737 1726806 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-820 1718684 1719831 1720698 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-819 1716616 1717705 1717746 "PERMCAT" 1718145 PERMCAT (NIL T) -9 NIL 1718442 NIL) (-818 1716312 1716359 1716482 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-817 1712761 1714442 1715087 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-816 1710787 1712516 1712637 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-815 1709670 1709933 1709972 "PDSPC" 1710493 PDSPC (NIL T) -9 NIL 1710738 NIL) (-814 1709039 1709305 1709665 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-813 1707676 1708669 1708708 "PDRING" 1708713 PDRING (NIL T) -9 NIL 1708740 NIL) (-812 1706388 1707177 1707228 "PDMOD" 1707233 PDMOD (NIL T T) -9 NIL 1707336 NIL) (-811 1705481 1705693 1705942 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-810 1705086 1705153 1705207 "PDDOM" 1705372 PDDOM (NIL T T) -9 NIL 1705452 NIL) (-809 1704938 1704974 1705081 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-808 1704724 1704763 1704852 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-807 1703041 1703795 1704094 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-806 1702730 1702793 1702902 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-805 1700868 1701298 1701749 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-804 1694488 1696317 1697609 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-803 1694119 1694192 1694324 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-802 1691821 1692501 1692982 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-801 1690025 1690453 1690856 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-800 1689471 1689719 1689760 "PATMAB" 1689867 PATMAB (NIL T) -9 NIL 1689950 NIL) (-799 1688118 1688522 1688779 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-798 1687656 1687787 1687828 "PATAB" 1687833 PATAB (NIL T) -9 NIL 1688005 NIL) (-797 1686199 1686636 1687059 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-796 1685877 1685952 1686054 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-795 1685566 1685629 1685738 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-794 1685371 1685417 1685484 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-793 1685049 1685124 1685226 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-792 1684738 1684801 1684910 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-791 1684429 1684499 1684596 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-790 1684118 1684181 1684290 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-789 1683279 1683658 1683837 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-788 1682886 1682984 1683103 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-787 1681854 1682279 1682498 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-786 1680519 1681173 1681533 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-785 1673609 1679923 1680117 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-784 1666030 1673107 1673291 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-783 1662755 1664670 1664710 "PADICCT" 1665291 PADICCT (NIL NIL) -9 NIL 1665573 NIL) (-782 1660745 1662705 1662750 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-781 1659907 1660117 1660383 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-780 1659249 1659392 1659596 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-779 1657630 1658657 1658935 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-778 1657154 1657413 1657510 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-777 1656213 1656891 1657063 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-776 1646635 1649504 1651703 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-775 1646027 1646341 1646467 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-774 1645304 1645499 1645527 "OUTBCON" 1645845 OUTBCON (NIL) -9 NIL 1646011 NIL) (-773 1645012 1645142 1645299 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-772 1644393 1644538 1644699 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-771 1643764 1644191 1644280 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-770 1643179 1643594 1643622 "OSGROUP" 1643627 OSGROUP (NIL) -9 NIL 1643649 NIL) (-769 1642143 1642404 1642689 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-768 1639412 1642018 1642138 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-767 1636553 1639163 1639289 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-766 1634571 1635099 1635659 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-765 1627913 1630453 1630493 "OREPCAT" 1632814 OREPCAT (NIL T) -9 NIL 1633916 NIL) (-764 1625939 1626873 1627908 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-763 1625136 1625407 1625435 "ORDTYPE" 1625740 ORDTYPE (NIL) -9 NIL 1625898 NIL) (-762 1624670 1624881 1625131 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-761 1624132 1624508 1624665 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-760 1623626 1623989 1624017 "ORDSET" 1624022 ORDSET (NIL) -9 NIL 1624044 NIL) (-759 1622191 1623213 1623241 "ORDRING" 1623246 ORDRING (NIL) -9 NIL 1623274 NIL) (-758 1621439 1621996 1622024 "ORDMON" 1622029 ORDMON (NIL) -9 NIL 1622050 NIL) (-757 1620743 1620905 1621097 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-756 1619954 1620462 1620490 "ORDFIN" 1620555 ORDFIN (NIL) -9 NIL 1620629 NIL) (-755 1619348 1619487 1619673 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-754 1616023 1618316 1618722 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-753 1615430 1615785 1615890 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-752 1615238 1615283 1615349 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-751 1614539 1614815 1614856 "OPERCAT" 1615067 OPERCAT (NIL T) -9 NIL 1615163 NIL) (-750 1614351 1614418 1614534 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-749 1611717 1613153 1613649 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-748 1611138 1611265 1611439 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-747 1608039 1610277 1610643 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-746 1604905 1607414 1607454 "OMSAGG" 1607515 OMSAGG (NIL T) -9 NIL 1607579 NIL) (-745 1603317 1604576 1604744 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-744 1601513 1602754 1602782 "OINTDOM" 1602787 OINTDOM (NIL) -9 NIL 1602808 NIL) (-743 1598943 1600515 1600844 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-742 1598197 1598893 1598938 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-741 1595399 1598038 1598192 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-740 1586936 1595270 1595394 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-739 1580391 1586827 1586931 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-738 1579363 1579600 1579873 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-737 1577004 1577674 1578378 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-736 1572781 1573741 1574764 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-735 1572289 1572377 1572571 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-734 1569738 1570320 1570993 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-733 1567133 1567641 1568237 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-732 1564130 1564669 1565315 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-731 1563485 1563593 1563851 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-730 1562643 1562768 1562989 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-729 1558927 1559723 1560636 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-728 1558367 1558462 1558684 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-727 1558048 1558097 1558224 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-726 1554651 1557847 1557966 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-725 1553811 1554433 1554461 "OCAMON" 1554466 OCAMON (NIL) -9 NIL 1554487 NIL) (-724 1548005 1550819 1550859 "OC" 1551954 OC (NIL T) -9 NIL 1552810 NIL) (-723 1546005 1546931 1547911 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-722 1545421 1545839 1545867 "OASGP" 1545872 OASGP (NIL) -9 NIL 1545892 NIL) (-721 1544484 1545133 1545161 "OAMONS" 1545201 OAMONS (NIL) -9 NIL 1545244 NIL) (-720 1543629 1544210 1544238 "OAMON" 1544295 OAMON (NIL) -9 NIL 1544346 NIL) (-719 1543525 1543557 1543624 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-718 1542276 1543050 1543078 "OAGROUP" 1543224 OAGROUP (NIL) -9 NIL 1543316 NIL) (-717 1542067 1542154 1542271 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-716 1541807 1541863 1541951 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-715 1536869 1538432 1539959 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-714 1533564 1534598 1535633 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-713 1532674 1532907 1533125 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-712 1521535 1524563 1527011 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-711 1515658 1520921 1521015 "NTSCAT" 1521020 NTSCAT (NIL T T T T) -9 NIL 1521058 NIL) (-710 1514999 1515178 1515371 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-709 1514692 1514755 1514862 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-708 1502359 1512312 1513122 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-707 1491368 1502224 1502354 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-706 1490088 1490413 1490770 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-705 1488924 1489188 1489546 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-704 1488091 1488224 1488440 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-703 1486409 1486728 1487134 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-702 1486122 1486156 1486280 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-701 1485941 1485976 1486045 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-700 1485717 1485907 1485936 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-699 1485281 1485348 1485525 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-698 1483567 1484644 1484899 "NNI" NIL NNI (NIL) -8 NIL NIL 1485246) (-697 1482295 1482632 1482996 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-696 1481272 1481524 1481826 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-695 1480359 1480924 1480965 "NETCLT" 1481136 NETCLT (NIL T) -9 NIL 1481217 NIL) (-694 1479263 1479530 1479811 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-693 1479062 1479105 1479180 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-692 1477593 1477981 1478401 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-691 1476226 1477192 1477220 "NASRING" 1477330 NASRING (NIL) -9 NIL 1477410 NIL) (-690 1476071 1476127 1476221 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-689 1475000 1475678 1475706 "NARNG" 1475823 NARNG (NIL) -9 NIL 1475914 NIL) (-688 1474776 1474861 1474995 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-687 1473542 1474296 1474336 "NAALG" 1474415 NAALG (NIL T) -9 NIL 1474476 NIL) (-686 1473412 1473447 1473537 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-685 1468391 1469576 1470762 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-684 1467786 1467873 1468057 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-683 1459777 1464272 1464324 "MTSCAT" 1465384 MTSCAT (NIL T T) -9 NIL 1465898 NIL) (-682 1459543 1459603 1459695 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-681 1459369 1459408 1459468 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-680 1456998 1458883 1458924 "MSETAGG" 1458929 MSETAGG (NIL T) -9 NIL 1458963 NIL) (-679 1453368 1456041 1456362 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-678 1449761 1451584 1452303 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-677 1449398 1449471 1449600 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-676 1449051 1449092 1449236 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-675 1446916 1447253 1447684 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-674 1440314 1446815 1446911 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-673 1439839 1439880 1440088 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-672 1439398 1439447 1439630 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-671 1438672 1438765 1438984 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-670 1437289 1437650 1438040 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-669 1436810 1436877 1436916 "MONOPC" 1436976 MONOPC (NIL T) -9 NIL 1437195 NIL) (-668 1436261 1436597 1436725 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-667 1435403 1435782 1435810 "MONOID" 1436028 MONOID (NIL) -9 NIL 1436172 NIL) (-666 1435062 1435212 1435398 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-665 1424000 1430870 1430929 "MONOGEN" 1431603 MONOGEN (NIL T T) -9 NIL 1432059 NIL) (-664 1422012 1422898 1423881 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-663 1420726 1421270 1421298 "MONADWU" 1421689 MONADWU (NIL) -9 NIL 1421924 NIL) (-662 1420274 1420474 1420721 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-661 1419551 1419852 1419880 "MONAD" 1420087 MONAD (NIL) -9 NIL 1420199 NIL) (-660 1419318 1419414 1419546 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-659 1417708 1418478 1418757 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-658 1416842 1417369 1417409 "MODULE" 1417414 MODULE (NIL T) -9 NIL 1417452 NIL) (-657 1416521 1416647 1416837 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-656 1414240 1415126 1415440 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-655 1411419 1412836 1413349 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-654 1410053 1410627 1410903 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-653 1399272 1408718 1409131 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-652 1396236 1398280 1398549 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-651 1395320 1395687 1395877 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-650 1394889 1394938 1395117 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-649 1392714 1393710 1393750 "MLO" 1394167 MLO (NIL T) -9 NIL 1394407 NIL) (-648 1390595 1391122 1391717 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-647 1390063 1390159 1390313 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-646 1389733 1389809 1389932 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-645 1388945 1389131 1389359 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-644 1388438 1388554 1388710 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-643 1387810 1387924 1388109 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-642 1386837 1387110 1387387 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-641 1386270 1386358 1386529 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-640 1383428 1384307 1385186 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-639 1382095 1382443 1382796 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-638 1379519 1381182 1381223 "MDAGG" 1381480 MDAGG (NIL T) -9 NIL 1381625 NIL) (-637 1378793 1378957 1379157 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-636 1377871 1378157 1378387 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-635 1375968 1376545 1377106 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-634 1371712 1375558 1375805 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-633 1368061 1368830 1369564 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-632 1366814 1366983 1367312 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-631 1356259 1359883 1359959 "MATCAT" 1364947 MATCAT (NIL T T T) -9 NIL 1366393 NIL) (-630 1353540 1354846 1356254 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-629 1351941 1352301 1352685 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-628 1351074 1351271 1351493 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-627 1349825 1350151 1350478 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-626 1348987 1349389 1349565 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-625 1348656 1348720 1348843 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-624 1348304 1348377 1348491 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-623 1347839 1347954 1348096 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-622 1346048 1346816 1347117 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-621 1345542 1345844 1345934 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-620 1339863 1343839 1343880 "LZSTAGG" 1344657 LZSTAGG (NIL T) -9 NIL 1344947 NIL) (-619 1337212 1338524 1339858 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-618 1334599 1335565 1336048 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-617 1334180 1334459 1334533 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-616 1326395 1334041 1334175 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-615 1325758 1325903 1326131 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-614 1323242 1323940 1324652 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-613 1321458 1321781 1322215 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-612 1314838 1320490 1320531 "LSAGG" 1320593 LSAGG (NIL T) -9 NIL 1320671 NIL) (-611 1312532 1313631 1314833 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-610 1310012 1311881 1312130 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-609 1309679 1309770 1309893 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-608 1309350 1309429 1309457 "LOGIC" 1309568 LOGIC (NIL) -9 NIL 1309650 NIL) (-607 1309245 1309274 1309345 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-606 1308564 1308722 1308915 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-605 1307349 1307598 1307949 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-604 1303171 1305970 1306010 "LODOCAT" 1306442 LODOCAT (NIL T) -9 NIL 1306653 NIL) (-603 1302964 1303040 1303166 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-602 1299964 1302841 1302959 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-601 1297062 1299914 1299959 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-600 1294149 1296992 1297057 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-599 1293202 1293377 1293679 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-598 1291334 1292464 1292717 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-597 1287249 1289475 1289516 "LNAGG" 1290375 LNAGG (NIL T) -9 NIL 1290813 NIL) (-596 1286636 1286903 1287244 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-595 1283208 1284149 1284786 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-594 1282470 1282975 1283015 "LMODULE" 1283020 LMODULE (NIL T) -9 NIL 1283046 NIL) (-593 1279939 1282206 1282329 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-592 1279507 1279718 1279759 "LLINSET" 1279820 LLINSET (NIL T) -9 NIL 1279864 NIL) (-591 1279183 1279443 1279502 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-590 1278782 1278862 1279001 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-589 1277233 1277581 1277980 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-588 1276404 1276600 1276828 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-587 1269718 1275660 1275914 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-586 1269295 1269528 1269569 "LINSET" 1269574 LINSET (NIL T) -9 NIL 1269607 NIL) (-585 1268196 1268918 1269085 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-584 1266462 1267217 1267257 "LINEXP" 1267743 LINEXP (NIL T) -9 NIL 1268016 NIL) (-583 1265084 1266071 1266252 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-582 1263911 1264183 1264485 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-581 1263124 1263713 1263823 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-580 1260682 1261404 1262154 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-579 1259317 1259614 1260005 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-578 1258110 1258712 1258752 "LIECAT" 1258892 LIECAT (NIL T) -9 NIL 1259043 NIL) (-577 1257984 1258017 1258105 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-576 1252240 1257674 1257902 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-575 1243880 1251916 1252072 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-574 1240332 1241281 1242216 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-573 1238956 1239864 1239892 "LFCAT" 1240099 LFCAT (NIL) -9 NIL 1240238 NIL) (-572 1237195 1237525 1237870 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-571 1234712 1235377 1236058 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-570 1231724 1232702 1233205 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-569 1231215 1231518 1231609 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-568 1229922 1230246 1230646 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-567 1229188 1229273 1229499 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-566 1224191 1227756 1228292 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-565 1223816 1223866 1224026 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-564 1222587 1223360 1223400 "LALG" 1223461 LALG (NIL T) -9 NIL 1223519 NIL) (-563 1222370 1222447 1222582 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-562 1220223 1221638 1221889 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-561 1220052 1220082 1220123 "KVTFROM" 1220185 KVTFROM (NIL T) -9 NIL NIL NIL) (-560 1218868 1219583 1219772 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-559 1218697 1218727 1218768 "KRCFROM" 1218830 KRCFROM (NIL T) -9 NIL NIL NIL) (-558 1217799 1217996 1218291 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-557 1217628 1217658 1217699 "KONVERT" 1217761 KONVERT (NIL T) -9 NIL NIL NIL) (-556 1217457 1217487 1217528 "KOERCE" 1217590 KOERCE (NIL T) -9 NIL NIL NIL) (-555 1217027 1217120 1217252 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-554 1215080 1215974 1216346 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-553 1208067 1212759 1212813 "KDAGG" 1213189 KDAGG (NIL T T) -9 NIL 1213429 NIL) (-552 1207725 1207860 1208062 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-551 1201029 1207517 1207663 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-550 1200679 1200961 1201024 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-549 1199649 1200148 1200397 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-548 1198775 1199224 1199429 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-547 1197639 1198131 1198431 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-546 1196921 1197320 1197481 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-545 1196631 1196867 1196916 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-544 1190886 1196321 1196549 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-543 1190304 1190637 1190757 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-542 1187032 1188492 1188544 "IXAGG" 1189441 IXAGG (NIL T T) -9 NIL 1189901 NIL) (-541 1186319 1186650 1187027 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-540 1185388 1185663 1185905 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-539 1184050 1184257 1184550 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-538 1183001 1183223 1183506 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-537 1182676 1182739 1182862 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-536 1181938 1182310 1182484 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-535 1179914 1181214 1181488 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-534 1169462 1175231 1176388 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-533 1168707 1168859 1169095 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-532 1168198 1168501 1168592 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-531 1167491 1167582 1167795 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-530 1166623 1166848 1167088 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-529 1165036 1165417 1165845 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-528 1164821 1164865 1164941 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-527 1163671 1163968 1164263 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-526 1162944 1163295 1163446 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-525 1162147 1162278 1162491 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-524 1160309 1160806 1161350 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-523 1157390 1158658 1159347 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-522 1157215 1157255 1157315 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-521 1153213 1157141 1157210 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-520 1151216 1153152 1153208 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-519 1150587 1150886 1151016 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-518 1150040 1150328 1150460 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-517 1149121 1149746 1149872 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-516 1148531 1149025 1149053 "IOBCON" 1149058 IOBCON (NIL) -9 NIL 1149079 NIL) (-515 1148102 1148166 1148348 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-514 1140161 1142532 1144857 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-513 1137272 1138055 1138919 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-512 1136949 1137046 1137163 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-511 1134391 1136885 1136944 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-510 1132503 1133032 1133599 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-509 1132005 1132119 1132259 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-508 1130389 1130795 1131257 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-507 1128168 1128762 1129373 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-506 1125541 1126151 1126871 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-505 1124945 1125103 1125311 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-504 1124464 1124550 1124738 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-503 1122669 1123190 1123647 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-502 1115759 1117412 1119141 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-501 1115125 1115287 1115460 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-500 1112998 1113462 1114006 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-499 1111124 1112074 1112102 "INTDOM" 1112401 INTDOM (NIL) -9 NIL 1112606 NIL) (-498 1110677 1110879 1111119 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-497 1106484 1108956 1109010 "INTCAT" 1109806 INTCAT (NIL T) -9 NIL 1110122 NIL) (-496 1106049 1106169 1106296 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-495 1104889 1105061 1105367 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-494 1104462 1104558 1104715 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-493 1096945 1104369 1104457 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-492 1096243 1096798 1096863 "INT8" NIL INT8 (NIL) -8 NIL NIL 1096897) (-491 1095540 1096095 1096160 "INT64" NIL INT64 (NIL) -8 NIL NIL 1096194) (-490 1094837 1095392 1095457 "INT32" NIL INT32 (NIL) -8 NIL NIL 1095491) (-489 1094134 1094689 1094754 "INT16" NIL INT16 (NIL) -8 NIL NIL 1094788) (-488 1090597 1094053 1094129 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-487 1084654 1088137 1088165 "INS" 1089095 INS (NIL) -9 NIL 1089754 NIL) (-486 1082716 1083634 1084581 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-485 1081775 1081998 1082273 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-484 1080989 1081130 1081327 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-483 1079979 1080120 1080357 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-482 1079131 1079295 1079555 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-481 1078411 1078526 1078714 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-480 1077150 1077419 1077743 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-479 1076430 1076571 1076754 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-478 1076093 1076165 1076263 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-477 1073171 1074657 1075180 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-476 1072770 1072877 1072991 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-475 1071926 1072571 1072672 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-474 1070776 1071044 1071365 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-473 1069766 1070706 1070771 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-472 1069391 1069471 1069588 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-471 1068305 1068850 1069054 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-470 1064400 1065455 1066398 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-469 1063254 1063577 1063605 "INBCON" 1064118 INBCON (NIL) -9 NIL 1064384 NIL) (-468 1062708 1062973 1063249 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-467 1062202 1062504 1062594 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-466 1061659 1061968 1062073 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-465 1060498 1060639 1060956 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-464 1058921 1059190 1059529 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-463 1053764 1058852 1058916 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-462 1053144 1053478 1053593 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-461 1048236 1052582 1052768 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-460 1047266 1048158 1048231 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-459 1046838 1046915 1046969 "IEVALAB" 1047176 IEVALAB (NIL T T) -9 NIL NIL NIL) (-458 1046593 1046673 1046833 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-457 1045978 1046205 1046362 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-456 1044971 1045898 1045973 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-455 1044034 1044891 1044966 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-454 1043117 1043763 1043900 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-453 1041581 1042152 1042203 "IDPC" 1042612 IDPC (NIL T T) -9 NIL 1042903 NIL) (-452 1040869 1041503 1041576 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-451 1040039 1040791 1040864 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-450 1039732 1039945 1040005 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-449 1039436 1039476 1039515 "IDEMOPC" 1039520 IDEMOPC (NIL T) -9 NIL 1039657 NIL) (-448 1036507 1037388 1038280 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-447 1030133 1031410 1032449 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-446 1029395 1029525 1029724 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-445 1028568 1029067 1029205 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-444 1026959 1027290 1027681 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-443 1022996 1026915 1026954 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-442 1020254 1020878 1021573 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-441 1018480 1018960 1019493 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-440 1016295 1018386 1018475 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-439 1012437 1016233 1016290 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-438 1006016 1011401 1011869 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-437 1005584 1005647 1005820 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-436 1005076 1005225 1005253 "HYPCAT" 1005460 HYPCAT (NIL) -9 NIL NIL NIL) (-435 1004732 1004885 1005071 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-434 1004345 1004590 1004673 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-433 1004178 1004227 1004268 "HOMOTOP" 1004273 HOMOTOP (NIL T) -9 NIL 1004306 NIL) (-432 1002681 1003493 1003534 "HOAGG" 1003539 HOAGG (NIL T) -9 NIL 1003839 NIL) (-431 1002308 1002455 1002676 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-430 995508 1002033 1002181 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-429 994443 994701 994964 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-428 993378 994308 994438 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-427 991577 993211 993299 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-426 990892 991244 991377 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-425 984390 990825 990887 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-424 977529 984126 984277 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-423 976982 977139 977302 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-422 969482 976899 976977 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-421 968973 969276 969367 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-420 966523 968760 968939 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-419 962209 966406 966518 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-418 954686 962106 962204 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-417 946623 954055 954310 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-416 945647 946156 946184 "GROUP" 946387 GROUP (NIL) -9 NIL 946521 NIL) (-415 945190 945391 945642 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-414 943862 944201 944588 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-413 942684 943041 943092 "GRMOD" 943621 GRMOD (NIL T T) -9 NIL 943787 NIL) (-412 942503 942551 942679 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-411 938626 939837 940837 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-410 937348 937672 937987 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-409 936901 937029 937170 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-408 935974 936473 936524 "GRALG" 936677 GRALG (NIL T T) -9 NIL 936767 NIL) (-407 935693 935794 935969 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-406 932712 935384 935551 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-405 932125 932188 932445 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-404 927979 928875 929400 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-403 927154 927356 927594 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-402 922157 923084 924103 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-401 921905 921962 922051 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-400 921387 921476 921641 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-399 920896 920937 921150 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-398 919697 919980 920284 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-397 912972 919387 919548 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-396 902755 907762 908866 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-395 900807 901910 901938 "GCDDOM" 902193 GCDDOM (NIL) -9 NIL 902350 NIL) (-394 900430 900587 900802 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-393 891223 893693 896081 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-392 889358 889683 890101 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-391 888299 888488 888755 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-390 887170 887377 887681 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-389 886633 886775 886923 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-388 885245 885593 885906 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-387 883790 884111 884433 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-386 881416 881772 882177 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-385 874668 876329 877907 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-384 874320 874541 874609 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-383 874065 874107 874148 "FUNCTOR" 874232 FUNCTOR (NIL T) -9 NIL 874291 NIL) (-382 873689 873910 873991 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-381 871786 872469 872929 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-380 870379 870686 871078 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-379 869034 869393 869717 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-378 868337 868461 868648 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-377 867311 867577 867924 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-376 864969 865499 865981 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-375 864552 864612 864781 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-374 862852 863766 864069 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-373 862000 862134 862357 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-372 861171 861332 861559 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-371 857387 860048 860089 "FSAGG" 860459 FSAGG (NIL T) -9 NIL 860720 NIL) (-370 855741 856500 857292 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-369 853697 853993 854537 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-368 852744 852926 853226 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-367 852425 852474 852601 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-366 832581 842082 842123 "FS" 845993 FS (NIL T) -9 NIL 848271 NIL) (-365 824812 828305 832284 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-364 824346 824473 824625 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-363 818869 822027 822067 "FRNAALG" 823387 FRNAALG (NIL T) -9 NIL 823985 NIL) (-362 815610 816861 818119 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-361 815291 815340 815467 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-360 813778 814335 814629 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-359 813064 813157 813444 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-358 810898 811664 811980 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-357 810007 810450 810491 "FRETRCT" 810496 FRETRCT (NIL T) -9 NIL 810667 NIL) (-356 809380 809658 810002 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-355 806124 807644 807703 "FRAMALG" 808585 FRAMALG (NIL T T) -9 NIL 808877 NIL) (-354 804720 805271 805901 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-353 804413 804476 804583 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-352 798054 804218 804408 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-351 797747 797810 797917 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-350 790156 794727 796034 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-349 783934 787437 787465 "FPS" 788584 FPS (NIL) -9 NIL 789140 NIL) (-348 783491 783624 783788 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-347 780301 782344 782372 "FPC" 782597 FPC (NIL) -9 NIL 782739 NIL) (-346 780147 780199 780296 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-345 778924 779633 779674 "FPATMAB" 779679 FPATMAB (NIL T) -9 NIL 779831 NIL) (-344 777354 777950 778297 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-343 776929 776987 777160 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-342 775432 776327 776501 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-341 774047 774552 774580 "FNCAT" 775037 FNCAT (NIL) -9 NIL 775294 NIL) (-340 773504 774014 774042 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-339 772091 773453 773499 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-338 768679 770037 770078 "FMONCAT" 771295 FMONCAT (NIL T) -9 NIL 771899 NIL) (-337 765638 766718 766771 "FMCAT" 767853 FMCAT (NIL T T) -9 NIL 768323 NIL) (-336 764338 765461 765560 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-335 763386 764186 764333 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-334 761573 762025 762519 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-333 759508 760044 760622 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-332 752894 757845 758459 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-331 751375 752476 752516 "FLINEXP" 752521 FLINEXP (NIL T) -9 NIL 752614 NIL) (-330 750784 751043 751370 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-329 750033 750192 750406 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-328 746916 747995 748047 "FLALG" 749274 FLALG (NIL T T) -9 NIL 749741 NIL) (-327 746087 746248 746475 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-326 739793 743483 743524 "FLAGG" 744763 FLAGG (NIL T) -9 NIL 745411 NIL) (-325 738901 739305 739788 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-324 735462 736726 736785 "FINRALG" 737913 FINRALG (NIL T T) -9 NIL 738421 NIL) (-323 734853 735118 735457 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-322 734151 734447 734475 "FINITE" 734671 FINITE (NIL) -9 NIL 734778 NIL) (-321 734059 734085 734146 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-320 730829 732155 732196 "FINAGG" 733195 FINAGG (NIL T) -9 NIL 733702 NIL) (-319 729748 730271 730824 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-318 721709 724300 724340 "FINAALG" 727992 FINAALG (NIL T) -9 NIL 729430 NIL) (-317 717976 719221 720344 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-316 716528 716947 717001 "FILECAT" 717685 FILECAT (NIL T T) -9 NIL 717901 NIL) (-315 715879 716353 716456 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-314 713127 715005 715033 "FIELD" 715073 FIELD (NIL) -9 NIL 715153 NIL) (-313 712152 712613 713122 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-312 710156 711102 711448 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-311 709399 709580 709799 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-310 704669 709337 709394 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-309 704331 704398 704533 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-308 703871 703913 704122 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-307 700551 701428 702205 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-306 695835 700483 700546 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-305 690514 695324 695514 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-304 684995 689795 690053 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-303 679202 684446 684657 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-302 678225 678435 678750 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-301 673665 676370 676398 "FFIELDC" 677017 FFIELDC (NIL) -9 NIL 677392 NIL) (-300 672734 673174 673660 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-299 672349 672407 672531 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-298 670493 671016 671533 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-297 665587 670292 670393 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-296 660687 665376 665483 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-295 655353 660478 660586 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-294 654807 654856 655091 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-293 633382 644416 644502 "FFCAT" 649652 FFCAT (NIL T T T) -9 NIL 651088 NIL) (-292 629622 630848 632154 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-291 624465 629553 629617 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-290 623488 623957 623998 "FEVALAB" 624003 FEVALAB (NIL T) -9 NIL 624242 NIL) (-289 622893 623145 623483 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-288 619720 620631 620746 "FDIVCAT" 622313 FDIVCAT (NIL T T T T) -9 NIL 622749 NIL) (-287 619514 619546 619715 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-286 618821 618914 619191 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-285 617307 618305 618508 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-284 616400 616784 616986 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-283 615522 616011 616151 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-282 607109 611752 611792 "FAXF" 613593 FAXF (NIL T) -9 NIL 614283 NIL) (-281 605025 605829 606644 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-280 600174 604547 604721 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-279 594613 597037 597089 "FAMR" 598100 FAMR (NIL T T) -9 NIL 598559 NIL) (-278 593812 594177 594608 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-277 592833 593754 593807 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-276 590427 591306 591359 "FAMONC" 592300 FAMONC (NIL T T) -9 NIL 592685 NIL) (-275 588983 590285 590422 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-274 587063 587424 587826 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-273 586340 586537 586759 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-272 578200 585787 585986 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-271 576219 576789 577375 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-270 573121 573763 574483 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-269 568278 568985 569790 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-268 567967 568030 568139 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-267 552760 567016 567442 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-266 543287 552080 552368 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-265 542781 543083 543173 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-264 542557 542747 542776 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-263 542246 542314 542427 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-262 541763 541905 541946 "EVALAB" 542116 EVALAB (NIL T) -9 NIL 542220 NIL) (-261 541391 541537 541758 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-260 538434 540029 540057 "EUCDOM" 540611 EUCDOM (NIL) -9 NIL 540960 NIL) (-259 537361 537854 538429 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-258 537086 537142 537242 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-257 536774 536838 536947 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-256 530545 532445 532473 "ES" 535215 ES (NIL) -9 NIL 536599 NIL) (-255 527060 528592 530384 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-254 526408 526561 526737 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-253 518914 526338 526403 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-252 518603 518666 518775 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-251 512340 515465 516869 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-250 508643 509739 510832 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-249 507469 507820 508126 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-248 506354 507085 507113 "ENTIRER" 507118 ENTIRER (NIL) -9 NIL 507162 NIL) (-247 506243 506277 506349 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-246 502884 504681 505030 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-245 501985 502200 502252 "ELTAGG" 502618 ELTAGG (NIL T T) -9 NIL 502832 NIL) (-244 501767 501841 501980 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-243 501513 501548 501602 "ELTAB" 501686 ELTAB (NIL T T) -9 NIL 501738 NIL) (-242 500764 500934 501133 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-241 500488 500562 500590 "ELEMFUN" 500695 ELEMFUN (NIL) -9 NIL NIL NIL) (-240 500388 500415 500483 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-239 495705 498395 498436 "ELAGG" 499369 ELAGG (NIL T) -9 NIL 499830 NIL) (-238 494503 495041 495700 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-237 493921 494088 494244 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-236 492834 493153 493432 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-235 486227 488225 489052 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-234 480206 482202 483012 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-233 478020 478426 478897 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-232 469020 470933 472474 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-231 468133 468634 468783 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-230 466831 467505 467545 "DVARCAT" 467828 DVARCAT (NIL T) -9 NIL 467968 NIL) (-229 466250 466514 466826 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-228 458317 466118 466245 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-227 456655 457446 457487 "DSEXT" 457850 DSEXT (NIL T) -9 NIL 458144 NIL) (-226 455460 455984 456650 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-225 455184 455249 455347 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-224 451335 452551 453682 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-223 446981 448336 449400 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-222 445656 446017 446403 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-221 445342 445401 445519 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-220 444317 444615 444905 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-219 443902 443977 444127 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-218 436315 438427 440542 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-217 431832 432851 433930 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-216 428380 430441 430482 "DQAGG" 431111 DQAGG (NIL T) -9 NIL 431384 NIL) (-215 414904 422545 422627 "DPOLCAT" 424464 DPOLCAT (NIL T T T T) -9 NIL 425007 NIL) (-214 411312 412960 414899 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-213 404361 411210 411307 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-212 397319 404190 404356 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-211 396912 397172 397261 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-210 396326 396774 396854 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-209 395612 395937 396088 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-208 388751 395348 395499 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-207 386500 387817 387857 "DMEXT" 387862 DMEXT (NIL T) -9 NIL 388037 NIL) (-206 386156 386218 386362 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-205 379748 385641 385831 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-204 376956 378559 378600 "DLAGG" 379141 DLAGG (NIL T) -9 NIL 379373 NIL) (-203 375307 376178 376206 "DIVRING" 376298 DIVRING (NIL) -9 NIL 376381 NIL) (-202 374758 375002 375302 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-201 373186 373603 374009 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-200 372223 372444 372709 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-199 365741 372155 372218 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-198 354061 360483 360536 "DIRPCAT" 360792 DIRPCAT (NIL NIL T) -9 NIL 361667 NIL) (-197 352067 352837 353724 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-196 351514 351680 351866 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-195 348837 350373 350414 "DIOPS" 350834 DIOPS (NIL T) -9 NIL 351062 NIL) (-194 348497 348641 348832 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-193 347504 348250 348278 "DIOID" 348283 DIOID (NIL) -9 NIL 348305 NIL) (-192 346332 347161 347189 "DIFRING" 347194 DIFRING (NIL) -9 NIL 347215 NIL) (-191 345968 346066 346094 "DIFFSPC" 346213 DIFFSPC (NIL) -9 NIL 346288 NIL) (-190 345709 345811 345963 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-189 344612 345237 345277 "DIFFMOD" 345282 DIFFMOD (NIL T) -9 NIL 345379 NIL) (-188 344296 344353 344394 "DIFFDOM" 344515 DIFFDOM (NIL T) -9 NIL 344583 NIL) (-187 344177 344207 344291 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-186 341850 343371 343411 "DIFEXT" 343416 DIFEXT (NIL T) -9 NIL 343568 NIL) (-185 339778 341314 341355 "DIAGG" 341360 DIAGG (NIL T) -9 NIL 341380 NIL) (-184 339334 339524 339773 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-183 334518 338524 338801 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-182 330976 332029 333039 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-181 325526 330130 330457 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-180 324092 324384 324759 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-179 321374 322626 322994 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-178 319099 321205 321294 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-177 318482 318627 318809 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-176 315800 316524 317324 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-175 313909 314367 314929 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-174 313292 313625 313739 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-173 306492 313017 313165 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-172 304412 304922 305426 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-171 304051 304100 304251 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-170 303310 303872 303963 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-169 301334 301776 302136 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-168 300626 300915 301061 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-167 300077 300223 300375 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-166 297439 298232 298959 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-165 296878 297024 297195 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-164 294950 295261 295628 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-163 294507 294762 294863 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-162 293708 294091 294119 "CTORCAT" 294300 CTORCAT (NIL) -9 NIL 294412 NIL) (-161 293411 293545 293703 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-160 292904 293161 293269 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-159 292320 292751 292824 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-158 291779 291896 292049 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-157 288173 288929 289684 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-156 287664 287967 288058 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-155 286883 287092 287320 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-154 286387 286492 286696 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-153 286140 286174 286280 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-152 283079 283841 284559 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-151 282598 282740 282879 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-150 278491 281061 281553 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-149 278365 278392 278420 "CONDUIT" 278457 CONDUIT (NIL) -9 NIL NIL NIL) (-148 277244 277975 278003 "COMRING" 278008 COMRING (NIL) -9 NIL 278058 NIL) (-147 276409 276776 276954 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-146 276105 276146 276274 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-145 275798 275861 275968 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-144 264640 275748 275793 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-143 264101 264240 264400 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-142 263854 263895 263993 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-141 245267 257517 257557 "COMPCAT" 258558 COMPCAT (NIL T) -9 NIL 259900 NIL) (-140 237805 241318 244911 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-139 237481 237521 237560 "COMOPC" 237565 COMOPC (NIL T) -9 NIL 237730 NIL) (-138 237168 237286 237399 "COMOP" NIL COMOP (NIL T) -8 NIL NIL NIL) (-137 236927 236961 237063 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 236757 236796 236854 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 236338 236617 236691 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 235915 236156 236243 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 235110 235358 235386 "COMBOPC" 235724 COMBOPC (NIL) -9 NIL 235899 NIL) (-132 234174 234426 234668 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 231106 231790 232413 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 229986 230437 230672 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 229477 229780 229871 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 229164 229217 229342 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 228634 228944 229042 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 225154 226224 227304 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 223449 224434 224672 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 221053 222214 222255 "CLAGG" 222724 CLAGG (NIL T) -9 NIL 223051 NIL) (-123 220723 220855 221048 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220352 220443 220583 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218289 218796 219344 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217250 217981 218009 "CHARZ" 218014 CHARZ (NIL) -9 NIL 218028 NIL) (-119 217044 217090 217168 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 215883 216646 216674 "CHARNZ" 216735 CHARNZ (NIL) -9 NIL 216783 NIL) (-117 213361 214458 214981 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 213069 213148 213176 "CFCAT" 213287 CFCAT (NIL) -9 NIL NIL NIL) (-115 212412 212541 212723 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208680 211825 212105 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208058 208245 208422 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207586 208005 208053 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207059 207368 207465 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206550 206853 206944 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205799 205959 206180 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 201899 203156 203864 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200265 201296 201547 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199846 200125 200199 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199280 199533 199561 "CACHSET" 199693 CACHSET (NIL) -9 NIL 199771 NIL) (-104 198632 199047 199075 "CABMON" 199125 CABMON (NIL) -9 NIL 199181 NIL) (-103 198162 198426 198536 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193651 197830 197991 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192621 193325 193460 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193623) (-100 190087 192388 192494 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187524 189841 189949 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184702 186908 186947 "BTCAT" 187014 BTCAT (NIL T) -9 NIL 187095 NIL) (-97 184453 184551 184697 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179770 183626 183652 "BTAGG" 183763 BTAGG (NIL) -9 NIL 183871 NIL) (-95 179401 179562 179765 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176480 178893 179083 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175750 175902 176080 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172826 174447 174486 "BRAGG" 175115 BRAGG (NIL T) -9 NIL 175375 NIL) (-91 171901 172332 172821 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164435 171406 171587 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162427 164387 164430 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 162160 162196 162307 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160399 160832 161280 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156365 157781 158671 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 155241 156132 156254 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154827 154984 155010 "BOOLE" 155118 BOOLE (NIL) 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index db55e819..7ed631cd 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,13100 +1,13101 @@ -(628638 . 3580468867) +(628725 . 3580478884) (((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1181 *4)) (-4 *4 (-13 (-963) (-582 (-486)))) - (-5 *2 (-1181 (-350 (-486)))) (-5 *1 (-1210 *4))))) + (|partial| -12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488)))) + (-5 *2 (-1183 (-352 (-488)))) (-5 *1 (-1212 *4))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-1181 *4)) (-4 *4 (-13 (-963) (-582 (-486)))) - (-5 *2 (-1181 (-486))) (-5 *1 (-1210 *4))))) + (|partial| -12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488)))) + (-5 *2 (-1183 (-488))) (-5 *1 (-1212 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-1181 *4)) (-4 *4 (-13 (-963) (-582 (-486)))) (-5 *2 (-85)) - (-5 *1 (-1210 *4))))) + (-12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488)))) (-5 *2 (-85)) + (-5 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\ No newline at end of file |