diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 1326 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1130 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1284 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8368 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31525 |
5 files changed, 21816 insertions, 21817 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index ce13be77..bd4d97f6 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2241668 . 3425075211) +(2241696 . 3427192338) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL NIL (-19 S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,23 +46,23 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4255 . T) (-4253 . T) (-4252 . T) ((-4260 "*") . T) (-4251 . T) (-4256 . T) (-4250 . T) (-1405 . T)) +((-4256 . T) (-4254 . T) (-4253 . T) ((-4261 "*") . T) (-4252 . T) (-4257 . T) (-4251 . T) (-1456 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) NIL NIL -(-31 R -3819) +(-31 R -1834) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (-32 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4258))) +((|HasAttribute| |#1| (QUOTE -4259))) (-33) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-1405 . T)) +((-1456 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -70,7 +70,7 @@ NIL NIL (-35 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4258 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4260 . T) (-1456 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -78,17 +78,17 @@ NIL NIL (-37 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) NIL (-38 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-39 -3819 UP UPUP -2152) +(-39 -1834 UP UPUP -2287) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4251 |has| (-385 |#2|) (-341)) (-4256 |has| (-385 |#2|) (-341)) (-4250 |has| (-385 |#2|) (-341)) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3254 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3254 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3254 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3254 (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) -(-40 R -3819) +((-4252 |has| (-385 |#2|) (-341)) (-4257 |has| (-385 |#2|) (-341)) (-4251 |has| (-385 |#2|) (-341)) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-2067 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-2067 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-2067 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-2067 (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) +(-40 R -1834) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) @@ -102,23 +102,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-286)))) (-43 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4255 |has| |#1| (-517)) (-4253 . T) (-4252 . T)) +((-4256 |has| |#1| (-517)) (-4254 . T) (-4253 . T)) ((|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-44 |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."))) -((-4258 . T) (-4259 . T)) -((-3254 (-12 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#2|))))))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-2067 (-12 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#2|))))))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-789))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-45 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-341)))) (-46 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-47) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| $ (QUOTE (-977))) (|HasCategory| $ (LIST (QUOTE -968) (QUOTE (-525))))) (-48) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -126,7 +126,7 @@ NIL NIL (-49 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4255 . T)) +((-4256 . T)) NIL (-50 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -140,7 +140,7 @@ 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 -(-53 |Base| R -3819) +(-53 |Base| R -1834) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4258 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4260 . T) (-1456 . T)) NIL (-56 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),{}...]}."))) @@ -158,65 +158,65 @@ NIL NIL (-57 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}"))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-58 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) -(-59 -3257) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +(-59 -2411) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-60 -3257) +(-60 -2411) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-61 -3257) +(-61 -2411) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3257) +(-62 -2411) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-63 -3257) +(-63 -2411) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3257) +(-64 -2411) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3257) +(-65 -2411) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3257) +(-66 -2411) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -3257) +(-67 -2411) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-68 -3257) +(-68 -2411) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3257) +(-69 -2411) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-70 -3257) +(-70 -2411) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-71 -3257) +(-71 -2411) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-72 -3257) +(-72 -2411) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -228,55 +228,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -3257) +(-75 -2411) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-76 -3257) +(-76 -2411) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-77 -3257) +(-77 -2411) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -3257) +(-78 -2411) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -3257) +(-79 -2411) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3257) +(-80 -2411) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3257) +(-81 -2411) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -3257) +(-82 -2411) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3257) +(-83 -2411) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3257) +(-84 -2411) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3257) +(-85 -2411) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3257) +(-86 -2411) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-87 -3257) +(-87 -2411) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -286,8 +286,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-341)))) (-89 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}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-90 S) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) NIL @@ -298,15 +298,15 @@ NIL NIL (-92) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4258 . T)) +((-4259 . T)) NIL (-93) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,{}b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4258 . T) ((-4260 "*") . T) (-4259 . T) (-4255 . T) (-4253 . T) (-4252 . T) (-4251 . T) (-4256 . T) (-4250 . T) (-4249 . T) (-4248 . T) (-4247 . T) (-4246 . T) (-4254 . T) (-4257 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4245 . T)) +((-4259 . T) ((-4261 "*") . T) (-4260 . T) (-4256 . T) (-4254 . T) (-4253 . T) (-4252 . T) (-4257 . T) (-4251 . T) (-4250 . T) (-4249 . T) (-4248 . T) (-4247 . T) (-4255 . T) (-4258 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4246 . T)) NIL (-94 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}."))) -((-4255 . T)) +((-4256 . T)) NIL (-95 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}."))) @@ -322,15 +322,15 @@ NIL NIL (-98 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-99 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 (-4260 "*")))) +((|HasAttribute| |#1| (QUOTE (-4261 "*")))) (-100) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4258 . T)) +((-4259 . T)) NIL (-101 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -338,12 +338,12 @@ NIL NIL (-102 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4259 . T) (-1405 . T)) +((-4260 . T) (-1456 . T)) NIL (-103) ((|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.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3254 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1068))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-2067 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1068))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) (-104) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -354,11 +354,11 @@ NIL NIL (-106) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4259 . T) (-4258 . T)) +((-4260 . T) (-4259 . T)) ((-12 (|HasCategory| (-108) (QUOTE (-1020))) (|HasCategory| (-108) (LIST (QUOTE -288) (QUOTE (-108))))) (|HasCategory| (-108) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-108) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-108) (QUOTE (-1020))) (|HasCategory| (-108) (LIST (QUOTE -566) (QUOTE (-798))))) (-107 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}"))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) NIL (-108) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -372,25 +372,25 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-111 -3819 UP) +(-111 -1834 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 (-112 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-113 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-112 |#1|) (QUOTE (-844))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-138))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-112 |#1|) (QUOTE (-953))) (|HasCategory| (-112 |#1|) (QUOTE (-762))) (-3254 (|HasCategory| (-112 |#1|) (QUOTE (-762))) (|HasCategory| (-112 |#1|) (QUOTE (-789)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-1068))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-213))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -486) (QUOTE (-1092)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-286))) (|HasCategory| (-112 |#1|) (QUOTE (-510))) (|HasCategory| (-112 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-844)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-112 |#1|) (QUOTE (-844))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-138))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-112 |#1|) (QUOTE (-953))) (|HasCategory| (-112 |#1|) (QUOTE (-762))) (-2067 (|HasCategory| (-112 |#1|) (QUOTE (-762))) (|HasCategory| (-112 |#1|) (QUOTE (-789)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-1068))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-213))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -486) (QUOTE (-1092)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-286))) (|HasCategory| (-112 |#1|) (QUOTE (-510))) (|HasCategory| (-112 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-844)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))))) (-114 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4259))) +((|HasAttribute| |#1| (QUOTE -4260))) (-115 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) -((-1405 . T)) +((-1456 . T)) NIL (-116 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) @@ -398,15 +398,15 @@ NIL NIL (-117 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"))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -414,20 +414,20 @@ NIL NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4258 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4260 . T) (-1456 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-123 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."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-124) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-3254 (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-125) (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1020)))) (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1020))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-2067 (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-125) (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1020)))) (|HasCategory| (-125) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-125) (QUOTE (-1020))) (-12 (|HasCategory| (-125) (QUOTE (-1020))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-798))))) (-125) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -442,13 +442,13 @@ NIL NIL (-128) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4260 "*") . T)) +(((-4261 "*") . T)) NIL -(-129 |minix| -2122 S T$) +(-129 |minix| -2041 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-130 |minix| -2122 R) +(-130 |minix| -2041 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -458,8 +458,8 @@ NIL NIL (-132) ((|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}."))) -((-4258 . T) (-4248 . T) (-4259 . T)) -((-3254 (-12 (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4249 . T) (-4260 . T)) +((-2067 (-12 (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) (-133 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -474,7 +474,7 @@ NIL NIL (-136) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4255 . T)) +((-4256 . T)) NIL (-137 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,{}r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -482,9 +482,9 @@ NIL NIL (-138) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4255 . T)) +((-4256 . T)) NIL -(-139 -3819 UP UPUP) +(-139 -1834 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 @@ -495,14 +495,14 @@ NIL (-141 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasAttribute| |#1| (QUOTE -4258))) +((|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasAttribute| |#1| (QUOTE -4259))) (-142 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-1405 . T)) +((-1456 . T)) NIL (-143 |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."))) -((-4253 . T) (-4252 . T) (-4255 . T)) +((-4254 . T) (-4253 . T) (-4256 . T)) NIL (-144) ((|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."))) @@ -516,7 +516,7 @@ 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 -(-147 R -3819) +(-147 R -1834) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -543,10 +543,10 @@ NIL (-153 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 (-844))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasCategory| |#2| (QUOTE (-986))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasAttribute| |#2| (QUOTE -4254)) (|HasAttribute| |#2| (QUOTE -4257)) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-789)))) +((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasCategory| |#2| (QUOTE (-986))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasAttribute| |#2| (QUOTE -4255)) (|HasAttribute| |#2| (QUOTE -4258)) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-789)))) (-154 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})"))) -((-4251 -3254 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-844)))) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-4254 |has| |#1| (-6 -4254)) (-4257 |has| |#1| (-6 -4257)) (-1466 . T) (-1405 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 -2067 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-844)))) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) (-4255 |has| |#1| (-6 -4255)) (-4258 |has| |#1| (-6 -4258)) (-1496 . T) (-1456 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-155 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."))) @@ -558,8 +558,8 @@ NIL NIL (-157 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}."))) -((-4251 -3254 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-844)))) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-4254 |has| |#1| (-6 -4254)) (-4257 |has| |#1| (-6 -4257)) (-1466 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3254 (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-346)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-770)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-953)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (QUOTE (-844))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| 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T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-2067 (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| 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(QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-770))) (|HasCategory| |#1| (QUOTE (-986))) (-12 (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-1114)))) (|HasCategory| |#1| (QUOTE (-510))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasAttribute| |#1| (QUOTE -4255)) (|HasAttribute| |#1| (QUOTE -4258)) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092))))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-327))))) (-158 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 @@ -570,11 +570,11 @@ NIL NIL (-160) ((|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."))) -(((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-161 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}."))) -(((-4260 "*") . T) (-4251 . T) (-4256 . T) (-4250 . T) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") . T) (-4252 . T) (-4257 . T) (-4251 . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-162) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -608,7 +608,7 @@ NIL ((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-170 R -3819) +(-170 R -1834) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -712,19 +712,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-196 -3819 UP UPUP R) +(-196 -1834 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 -(-197 -3819 FP) +(-197 -1834 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-198) ((|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.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3254 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1068))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) -(-199 R -3819) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-2067 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1068))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) +(-199 R -1834) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -738,19 +738,19 @@ NIL NIL (-202 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}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-203 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4255 . T)) +((-4256 . T)) NIL -(-204 R -3819) +(-204 R -1834) ((|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 (-205) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|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}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\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}."))) -((-1454 . T) (-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-1485 . T) (-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-206) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -758,15 +758,15 @@ NIL NIL (-207 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}"))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4260 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4261 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-208 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 (-209 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."))) -((-4259 . T) (-1405 . T)) +((-4260 . T) (-1456 . T)) NIL (-210 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -774,7 +774,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213)))) (-211 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4255 . T)) +((-4256 . T)) NIL (-212 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -782,36 +782,36 @@ NIL NIL (-213) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4255 . T)) +((-4256 . T)) NIL (-214 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4258))) +((|HasAttribute| |#1| (QUOTE -4259))) (-215 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}."))) -((-4259 . T) (-1405 . T)) +((-4260 . T) (-1456 . T)) NIL (-216) ((|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 -(-217 S -2122 R) +(-217 S -2041 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-735))) (|HasCategory| |#3| (QUOTE (-787))) (|HasAttribute| |#3| (QUOTE -4255)) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#3| (QUOTE (-669))) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (QUOTE (-1020)))) -(-218 -2122 R) +((|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-735))) (|HasCategory| |#3| (QUOTE (-787))) (|HasAttribute| |#3| (QUOTE -4256)) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#3| (QUOTE (-669))) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-977))) (|HasCategory| |#3| (QUOTE (-1020)))) +(-218 -2041 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4252 |has| |#2| (-977)) (-4253 |has| |#2| (-977)) (-4255 |has| |#2| (-6 -4255)) ((-4260 "*") |has| |#2| (-160)) (-4258 . T) (-1405 . T)) +((-4253 |has| |#2| (-977)) (-4254 |has| |#2| (-977)) (-4256 |has| |#2| (-6 -4256)) ((-4261 "*") |has| |#2| (-160)) (-4259 . T) (-1456 . T)) NIL -(-219 -2122 A B) +(-219 -2041 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-220 -2122 R) +(-220 -2041 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."))) -((-4252 |has| |#2| (-977)) (-4253 |has| |#2| (-977)) (-4255 |has| |#2| (-6 -4255)) ((-4260 "*") |has| |#2| (-160)) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-126))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-346))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-669))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-735))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-787))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (LIST 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -822,47 +822,47 @@ NIL NIL (-223) ((|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}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4251 . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-224 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."))) -((-1405 . T)) +((-1456 . T)) NIL (-225 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}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) -((-4259 . T) (-4258 . 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-213)))) (-232 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) NIL (-233 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}."))) -((-4258 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4260 . T) (-1456 . T)) NIL (-234) ((|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."))) @@ -902,8 +902,8 @@ NIL NIL (-243 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"))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#3| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#3| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#3| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-244 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -948,11 +948,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-255 R -3819) +(-255 R -1834) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-256 R -3819) +(-256 R -1834) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -974,7 +974,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020)))) (-261 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}."))) -((-4259 . T) (-1405 . T)) +((-4260 . T) (-1456 . T)) NIL (-262 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}."))) @@ -995,18 +995,18 @@ NIL (-266 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4259))) +((|HasAttribute| |#1| (QUOTE -4260))) (-267 |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 -(-268 S R |Mod| -2692 -1577 |exactQuo|) +(-268 S R |Mod| -2600 -3212 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-269) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4251 . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-270) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1022,21 +1022,21 @@ NIL NIL (-273 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#2|)))))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#2|)))))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-275) ((|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 -(-276 -3819 S) +(-276 -1834 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 -(-277 E -3819) +(-277 E -1834) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL NIL @@ -1074,7 +1074,7 @@ NIL NIL (-286) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-287 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1084,7 +1084,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-289 -3819) +(-289 -1834) ((|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 @@ -1094,8 +1094,8 @@ NIL NIL (-291 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))}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-953))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (-3254 (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-789)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-1068))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-213))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -486) (QUOTE (-1092)) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -288) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -265) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-286))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-510))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-789))) (-12 (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| $ (QUOTE (-136)))) (-3254 (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (-12 (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| $ (QUOTE (-136)))))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-953))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (-2067 (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-762))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-789)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-1068))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-213))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -486) (QUOTE (-1092)) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -288) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (LIST (QUOTE -265) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-286))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-510))) (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-789))) (-12 (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| $ (QUOTE (-136)))) (-2067 (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (-12 (|HasCategory| (-1160 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| $ (QUOTE (-136)))))) (-292 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1106,9 +1106,9 @@ NIL NIL (-294 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4255 -3254 (-3762 (|has| |#1| (-977)) (|has| |#1| (-588 (-525)))) (-12 (|has| |#1| (-517)) (-3254 (-3762 (|has| |#1| (-977)) (|has| |#1| (-588 (-525)))) (|has| |#1| (-977)) (|has| |#1| (-450)))) (|has| |#1| (-977)) (|has| |#1| (-450))) (-4253 |has| |#1| (-160)) (-4252 |has| |#1| (-160)) ((-4260 "*") |has| |#1| (-517)) (-4251 |has| |#1| (-517)) (-4256 |has| 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(QUOTE (-977))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))))) (-2067 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-977)))) (-2067 (-12 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| $ (QUOTE (-977))) (|HasCategory| $ (LIST (QUOTE -968) (QUOTE (-525))))) +(-295 R -1834) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1118,8 +1118,8 @@ NIL NIL (-297 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."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -1217) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3254 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1206) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -2897) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-2067 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2367) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -1296) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) (-298 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1130,7 +1130,7 @@ NIL NIL (-300 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) ((|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-734)))) (-301 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1146,19 +1146,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160)))) (-304 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-305 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."))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) -(-306 S -3819) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +(-306 S -1834) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-346)))) -(-307 -3819) +(-307 -1834) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-308) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) @@ -1176,15 +1176,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-312 S -3819 UP UPUP R) +(-312 S -1834 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-313 -3819 UP UPUP R) +(-313 -1834 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-314 -3819 UP UPUP R) +(-314 -1834 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1198,32 +1198,32 @@ NIL NIL (-317 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -968) (QUOTE (-357)))) (|HasCategory| $ (QUOTE (-977))) (|HasCategory| $ (LIST (QUOTE -968) (QUOTE (-525))))) (-318 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 -(-319 S -3819 UP UPUP) +(-319 S -1834 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|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 (-346))) (|HasCategory| |#2| (QUOTE (-341)))) -(-320 -3819 UP UPUP) +(-320 -1834 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|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."))) -((-4251 |has| (-385 |#2|) (-341)) (-4256 |has| (-385 |#2|) (-341)) (-4250 |has| (-385 |#2|) (-341)) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 |has| (-385 |#2|) (-341)) (-4257 |has| (-385 |#2|) (-341)) (-4251 |has| (-385 |#2|) (-341)) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-321 |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."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) (-322 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-323 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-324 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1238,33 +1238,33 @@ NIL NIL (-327) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL -(-328 R UP -3819) +(-328 R UP -1834) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-329 |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."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) (-330 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-331 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-332 |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}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| (-845 |#1|) (QUOTE (-136))) (|HasCategory| (-845 |#1|) (QUOTE (-346)))) (|HasCategory| (-845 |#1|) (QUOTE (-138))) (|HasCategory| (-845 |#1|) (QUOTE (-346))) (|HasCategory| (-845 |#1|) (QUOTE (-136)))) (-333 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) -(-334 -3819 GF) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +(-334 -1834 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1272,21 +1272,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-336 -3819 FP FPP) +(-336 -1834 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-337 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-338 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-339 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4255 . T)) +((-4256 . T)) NIL (-340 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1294,7 +1294,7 @@ NIL NIL (-341) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-342 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1310,7 +1310,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-517)))) (-345 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4255 |has| |#1| (-517)) (-4253 . T) (-4252 . T)) +((-4256 |has| |#1| (-517)) (-4254 . T) (-4253 . T)) NIL (-346) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1322,7 +1322,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-341)))) (-348 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) NIL (-349 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1331,14 +1331,14 @@ NIL (-350 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4259)) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020)))) +((|HasAttribute| |#1| (QUOTE -4260)) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020)))) (-351 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4258 . T) (-1405 . T)) +((-4259 . T) (-1456 . T)) NIL (-352 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4253 . T) (-4252 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4254 . T) (-4253 . T)) NIL (-353 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."))) @@ -1350,7 +1350,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-355 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}"))) -((-4255 . T)) +((-4256 . T)) NIL (-356 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1358,7 +1358,7 @@ NIL NIL (-357) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|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}."))) -((-4241 . T) (-4249 . T) (-1454 . T) (-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4242 . T) (-4250 . T) (-1485 . T) (-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-358 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1366,23 +1366,23 @@ NIL NIL (-359 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) ((|HasCategory| |#1| (QUOTE (-160)))) (-360 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) NIL (-361) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-1405 . T)) +((-1456 . T)) NIL (-362) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-1405 . T)) +((-1456 . T)) NIL (-363 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."))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) ((|HasCategory| |#1| (QUOTE (-160)))) (-364 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1390,7 +1390,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-789)))) (-365) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-366) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1402,13 +1402,13 @@ NIL NIL (-368 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) NIL (-369) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-370 -3819 UP UPUP R) +(-370 -1834 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 @@ -1422,27 +1422,27 @@ NIL NIL (-373) ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-1405 . T)) +((-1456 . T)) NIL (-374) ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-1405 . T)) +((-1456 . T)) NIL (-375) ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-376 -3257 |returnType| -1307 |symbols|) +(-376 -2411 |returnType| -1701 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-377 -3819 UP) +(-377 -1834 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-378 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-1405 . T)) +((-1456 . T)) NIL (-379 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1450,15 +1450,15 @@ NIL NIL (-380) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-381 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4241)) (|HasAttribute| |#1| (QUOTE -4249))) +((|HasAttribute| |#1| (QUOTE -4242)) (|HasAttribute| |#1| (QUOTE -4250))) (-382) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-1454 . T) (-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-1485 . T) (-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-383 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."))) @@ -1470,15 +1470,15 @@ NIL NIL (-385 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4245 -12 (|has| |#1| (-6 -4256)) (|has| |#1| (-429)) (|has| |#1| (-6 -4245))) (-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (QUOTE (-762))) (-3254 (|HasCategory| |#1| (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-789)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1068))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-510))) (-12 (|HasAttribute| |#1| (QUOTE -4256)) (|HasAttribute| |#1| (QUOTE -4245)) (|HasCategory| |#1| (QUOTE (-429)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +((-4246 -12 (|has| |#1| (-6 -4257)) (|has| |#1| (-429)) (|has| |#1| (-6 -4246))) (-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (QUOTE (-762))) (-2067 (|HasCategory| |#1| (QUOTE (-762))) (|HasCategory| |#1| (QUOTE (-789)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1068))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-770)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-510))) (-12 (|HasAttribute| |#1| (QUOTE -4257)) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-429)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-386 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-387 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) NIL (-388 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1492,11 +1492,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-391 R -3819 UP A) +(-391 R -1834 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4255 . T)) +((-4256 . T)) NIL -(-392 R -3819 UP A |ibasis|) +(-392 R -1834 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -968) (|devaluate| |#2|)))) @@ -1510,12 +1510,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-341)))) (-395 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4255 |has| |#1| (-517)) (-4253 . T) (-4252 . T)) +((-4256 |has| |#1| (-517)) (-4254 . T) (-4253 . T)) NIL (-396 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -288) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -265) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1132))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-429)))) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -288) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -265) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-953))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-429)))) (-397 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 @@ -1542,17 +1542,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-346)))) (-403 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4258 . T) (-4248 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4249 . T) (-4260 . T) (-1456 . T)) NIL -(-404 R -3819) +(-404 R -1834) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-405 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4245 -12 (|has| |#1| (-6 -4245)) (|has| |#2| (-6 -4245))) (-4252 . T) (-4253 . T) (-4255 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4245)) (|HasAttribute| |#2| (QUOTE -4245)))) -(-406 R -3819) +((-4246 -12 (|has| |#1| (-6 -4246)) (|has| |#2| (-6 -4246))) (-4253 . T) (-4254 . T) (-4256 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4246)) (|HasAttribute| |#2| (QUOTE -4246)))) +(-406 R -1834) ((|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 @@ -1562,17 +1562,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-1032))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (-408 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4255 -3254 (|has| |#1| (-977)) (|has| |#1| (-450))) (-4253 |has| |#1| (-160)) (-4252 |has| |#1| (-160)) ((-4260 "*") |has| |#1| (-517)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-517)) (-4250 |has| |#1| (-517)) (-1405 . T)) +((-4256 -2067 (|has| |#1| (-977)) (|has| |#1| (-450))) (-4254 |has| |#1| (-160)) (-4253 |has| |#1| (-160)) ((-4261 "*") |has| |#1| (-517)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-517)) (-4251 |has| |#1| (-517)) (-1456 . T)) NIL -(-409 R -3819) +(-409 R -1834) ((|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 -(-410 R -3819) +(-410 R -1834) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-411 R -3819) +(-411 R -1834) ((|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 @@ -1580,7 +1580,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-413 R -3819 UP) +(-413 R -1834 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-47))))) @@ -1598,17 +1598,17 @@ NIL NIL (-417) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-1405 . T)) +((-1456 . T)) NIL (-418) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-1405 . T)) +((-1456 . T)) NIL (-419 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\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-420 R UP -3819) +(-420 R UP -1834) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1646,16 +1646,16 @@ NIL NIL (-429) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-430 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"))) -((-4255 |has| (-385 (-887 |#1|)) (-517)) (-4253 . T) (-4252 . T)) +((-4256 |has| (-385 (-887 |#1|)) (-517)) (-4254 . T) (-4253 . T)) ((|HasCategory| (-385 (-887 |#1|)) (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| (-385 (-887 |#1|)) (QUOTE (-517)))) (-431 |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"))) -(((-4260 "*") |has| |#2| (-160)) (-4251 |has| |#2| (-517)) (-4256 |has| |#2| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#2| (QUOTE (-844))) (-3254 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3254 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3254 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4256)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +(((-4261 "*") |has| |#2| (-160)) (-4252 |has| |#2| (-517)) (-4257 |has| |#2| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#2| (QUOTE (-844))) (-2067 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-2067 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-2067 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4257)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) (-432 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1682,7 +1682,7 @@ NIL NIL (-438 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) NIL (-439 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1690,7 +1690,7 @@ NIL NIL (-440 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4259 . T) (-4258 . T)) +((-4260 . T) (-4259 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#4| (LIST (QUOTE -288) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#4| (LIST (QUOTE -566) (QUOTE (-798))))) (-441 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1720,7 +1720,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-448 |lv| -3819 R) +(-448 |lv| -1834 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1730,45 +1730,45 @@ NIL NIL (-450) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4255 . T)) +((-4256 . T)) NIL (-451 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") 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T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-2067 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2367) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -1296) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) (-452 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4259 . 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T)) +((-12 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#2|)))))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-453 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) -((-4259 . T) (-4258 . T)) +((-4260 . T) (-4259 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#4| (LIST (QUOTE -288) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#4| (LIST (QUOTE -566) (QUOTE (-798))))) (-454) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-455 |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."))) -((-4258 . T) (-4259 . 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Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-457 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(QUOTE (-525))))) (-12 (|HasCategory| |#2| (QUOTE (-735))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (QUOTE (-787))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))))) (|HasCategory| (-525) (QUOTE (-789))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (QUOTE (-977)))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092))))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525))))) (-2067 (|HasCategory| |#2| (QUOTE (-977))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-1020)))) (|HasAttribute| |#2| (QUOTE -4256)) (|HasCategory| |#2| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (-459 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}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) -(-460 -3819 UP UPUP R) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +(-460 -1834 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1778,15 +1778,15 @@ NIL NIL (-462) ((|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.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3254 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1068))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-2067 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1068))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) (-463 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4258)) (|HasAttribute| |#1| (QUOTE -4259)) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) +((|HasAttribute| |#1| (QUOTE -4259)) (|HasAttribute| |#1| (QUOTE -4260)) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (-464 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-1405 . T)) +((-1456 . T)) NIL (-465 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1796,33 +1796,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-467 -3819 UP |AlExt| |AlPol|) +(-467 -1834 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-468) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| $ (QUOTE (-977))) (|HasCategory| $ (LIST (QUOTE -968) (QUOTE (-525))))) (-469 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-470 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-471 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 -(-472 R UP -3819) +(-472 R UP -1834) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-473 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4259 . T) (-4258 . T)) +((-4260 . T) (-4259 . T)) ((-12 (|HasCategory| (-108) (QUOTE (-1020))) (|HasCategory| (-108) (LIST (QUOTE -288) (QUOTE (-108))))) (|HasCategory| (-108) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-108) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-108) (QUOTE (-1020))) (|HasCategory| (-108) (LIST (QUOTE -566) (QUOTE (-798))))) (-474 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)}."))) @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-477 -3819 |Expon| |VarSet| |DPoly|) +(-477 -1834 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-1092))))) @@ -1882,32 +1882,32 @@ NIL ((|HasCategory| |#2| (QUOTE (-734)))) (-488 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-489 |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}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((-3254 (|HasCategory| (-538 |#1|) (QUOTE (-136))) (|HasCategory| (-538 |#1|) (QUOTE (-346)))) (|HasCategory| (-538 |#1|) (QUOTE (-138))) (|HasCategory| (-538 |#1|) (QUOTE (-346))) (|HasCategory| (-538 |#1|) (QUOTE (-136)))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((-2067 (|HasCategory| (-538 |#1|) (QUOTE (-136))) (|HasCategory| (-538 |#1|) (QUOTE (-346)))) (|HasCategory| (-538 |#1|) (QUOTE (-138))) (|HasCategory| (-538 |#1|) (QUOTE (-346))) (|HasCategory| (-538 |#1|) (QUOTE (-136)))) (-490 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-491 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-492 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4259))) +((|HasAttribute| |#3| (QUOTE -4260))) (-493 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4259))) +((|HasAttribute| |#7| (QUOTE -4260))) (-494 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4260 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4261 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-495 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{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{\\spad{**}}{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 \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{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 \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{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 \\spad{GF}."))) NIL @@ -1920,7 +1920,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-498 K -3819 |Par|) +(-498 K -1834 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -1940,7 +1940,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-503 K -3819 |Par|) +(-503 K -1834 |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 @@ -1970,17 +1970,17 @@ NIL NIL (-510) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|hash| (($ $) "\\spad{hash(n)} returns the hash code of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4256 . T) (-4257 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4257 . T) (-4258 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-511 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#2|)))))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) -(-512 R -3819) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#2|)))))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +(-512 R -1834) ((|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 -(-513 R0 -3819 UP UPUP R) +(-513 R0 -1834 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 @@ -1990,7 +1990,7 @@ NIL NIL (-515 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-1454 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-1485 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-516 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."))) @@ -1998,9 +1998,9 @@ NIL NIL (-517) ((|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."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL -(-518 R -3819) +(-518 R -1834) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2012,7 +2012,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-521 R -3819 L) +(-521 R -1834 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -602) (|devaluate| |#2|)))) @@ -2020,31 +2020,31 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-523 -3819 UP UPUP R) +(-523 -1834 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 -(-524 -3819 UP) +(-524 -1834 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 (-525) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4240 . T) (-4246 . T) (-4250 . T) (-4245 . T) (-4256 . T) (-4257 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4241 . T) (-4247 . T) (-4251 . T) (-4246 . T) (-4257 . T) (-4258 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-526) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-527 R -3819 L) +(-527 R -1834 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -602) (|devaluate| |#2|)))) -(-528 R -3819) +(-528 R -1834) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1056)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-578))))) -(-529 -3819 UP) +(-529 -1834 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2052,53 +2052,53 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-531 -3819) +(-531 -1834) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-532 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."))) -((-1454 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-1485 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-533) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-534 R -3819) +(-534 R -1834) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-263))) (|HasCategory| |#2| (QUOTE (-578))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092))))) (-12 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-263)))) (|HasCategory| |#1| (QUOTE (-517)))) -(-535 -3819 UP) +(-535 -1834 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-536 R -3819) +(-536 R -1834) ((|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 (-537 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-538 |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."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| $ (QUOTE (-138))) (|HasCategory| $ (QUOTE (-136))) (|HasCategory| $ (QUOTE (-346)))) (-539) ((|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 -(-540 R -3819) +(-540 R -1834) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-541 E -3819) +(-541 E -1834) ((|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 -(-542 -3819) +(-542 -1834) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) ((|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-1092))))) (-543 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"))) @@ -2122,19 +2122,19 @@ NIL NIL (-548 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-3254 (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-2067 (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) (-549 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 (-550 |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}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|)))) (|HasCategory| (-525) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1217) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525)))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|)))) (|HasCategory| (-525) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525)))))) (-551 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4253 |has| |#1| (-517)) (-4252 |has| |#1| (-517)) ((-4260 "*") |has| |#1| (-517)) (-4251 |has| |#1| (-517)) (-4255 . T)) +((-4254 |has| |#1| (-517)) (-4253 |has| |#1| (-517)) ((-4261 "*") |has| |#1| (-517)) (-4252 |has| |#1| (-517)) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-517)))) (-552 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),{}..]}."))) @@ -2144,7 +2144,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-554 R -3819 FG) +(-554 R -1834 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2154,15 +2154,15 @@ NIL NIL (-556 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-557 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4259)) (|HasCategory| |#2| (QUOTE (-789))) (|HasAttribute| |#1| (QUOTE -4258)) (|HasCategory| |#3| (QUOTE (-1020)))) +((|HasAttribute| |#1| (QUOTE -4260)) (|HasCategory| |#2| (QUOTE (-789))) (|HasAttribute| |#1| (QUOTE -4259)) (|HasCategory| |#3| (QUOTE (-1020)))) (-558 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-1405 . T)) +((-1456 . T)) NIL (-559) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2170,19 +2170,19 @@ NIL NIL (-560 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)."))) -((-4255 -3254 (-3762 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4253 . T) (-4252 . T)) -((-3254 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) +((-4256 -2067 (-3944 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4254 . T) (-4253 . T)) +((-2067 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-561 |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."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (QUOTE (-1075))) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| (-1075) (QUOTE (-789))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (QUOTE (-1075))) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| (-1075) (QUOTE (-789))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-562 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 (-563 |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}."))) -((-4259 . T) (-1405 . T)) +((-4260 . T) (-1456 . T)) NIL (-564 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"))) @@ -2200,7 +2200,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-568 -3819 UP) +(-568 -1834 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2210,19 +2210,19 @@ NIL NIL (-570 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."))) -((-4255 . T)) +((-4256 . T)) NIL (-571 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}."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-787)))) -(-572 R -3819) +(-572 R -1834) ((|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 (-573 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"))) -((-4253 . T) (-4252 . T) ((-4260 "*") . T) (-4251 . T) (-4255 . T)) +((-4254 . T) (-4253 . T) ((-4261 "*") . T) (-4252 . T) (-4256 . T)) ((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (-574 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) @@ -2234,7 +2234,7 @@ NIL NIL (-576 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4255 . T)) +((-4256 . T)) NIL (-577 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2244,30 +2244,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-579 R -3819) +(-579 R -1834) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-580 |lv| -3819) +(-580 |lv| -1834) ((|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 (-581) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4259 . T)) -((-12 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (QUOTE (-1075))) (LIST (QUOTE |:|) (QUOTE -4201) (QUOTE (-51))))))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1075) (QUOTE (-789))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (QUOTE (-1075))) (LIST (QUOTE |:|) (QUOTE -3448) (QUOTE (-51))))))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1075) (QUOTE (-789))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) (-582 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-341)))) (-583 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4253 . T) (-4252 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4254 . T) (-4253 . T)) NIL (-584 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4255 -3254 (-3762 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4253 . T) (-4252 . T)) -((-3254 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) +((-4256 -2067 (-3944 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4254 . T) (-4253 . T)) +((-2067 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-585 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL @@ -2279,10 +2279,10 @@ NIL (-587 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1850 (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-341)))) +((-3272 (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-341)))) (-588 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4255 . T)) +((-4256 . T)) NIL (-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 \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) @@ -2298,12 +2298,12 @@ NIL NIL (-592 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-770))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-770))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-593 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-594 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2315,22 +2315,22 @@ NIL (-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{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4259))) +((|HasAttribute| |#1| (QUOTE -4260))) (-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{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) -((-1405 . T)) +((-1456 . T)) NIL -(-598 R -3819 L) +(-598 R -1834 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 (-599 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}}"))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) (-600 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) (-601 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2338,15 +2338,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-341)))) (-602 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}."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) NIL -(-603 -3819 UP) +(-603 -1834 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 -1718) +(-604 A -3470) ((|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}}"))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) (-605 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."))) @@ -2362,7 +2362,7 @@ NIL NIL (-608 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}."))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) ((|HasCategory| |#1| (QUOTE (-733)))) (-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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2370,7 +2370,7 @@ NIL NIL (-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.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4253 . T) (-4252 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4254 . T) (-4253 . T)) ((|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-160)))) (-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}."))) @@ -2378,13 +2378,13 @@ NIL NIL (-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}."))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL -(-613 -3819) +(-613 -1834) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-614 -3819 |Row| |Col| M) +(-614 -1834 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2394,8 +2394,8 @@ NIL NIL (-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."))) -((-4255 . T) (-4258 . T) (-4252 . T) (-4253 . T)) -((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4260 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (-3254 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517))) (-3254 (|HasAttribute| |#2| (QUOTE (-4260 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-160)))) +((-4256 . T) (-4259 . T) (-4253 . T) (-4254 . T)) +((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4261 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (-2067 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517))) (-2067 (|HasAttribute| |#2| (QUOTE (-4261 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-160)))) (-617 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2406,12 +2406,12 @@ NIL NIL (-619 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) -((-1405 . T)) +((-1456 . T)) NIL (-620 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-621 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL @@ -2447,10 +2447,10 @@ NIL (-629 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4260 "*"))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517)))) +((|HasAttribute| |#2| (QUOTE (-4261 "*"))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517)))) (-630 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4258 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4260 . T) (-1456 . T)) NIL (-631 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2458,13 +2458,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517)))) (-632 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."))) -((-4258 . T) (-4259 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4260 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4261 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-633 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL NIL -(-634 S -3819 FLAF FLAS) +(-634 S -1834 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2474,11 +2474,11 @@ NIL NIL (-636) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4251 . T) (-4256 |has| (-641) (-341)) (-4250 |has| (-641) (-341)) (-1466 . T) (-4257 |has| (-641) (-6 -4257)) (-4254 |has| (-641) (-6 -4254)) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-641) (QUOTE (-138))) (|HasCategory| (-641) (QUOTE (-136))) (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-346))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-641) (QUOTE (-213))) (-3254 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (LIST (QUOTE -265) (QUOTE (-641)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -288) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-641) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (-3254 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-641) (QUOTE (-953))) (|HasCategory| (-641) (QUOTE (-1114))) (-12 (|HasCategory| (-641) (QUOTE (-934))) (|HasCategory| (-641) (QUOTE (-1114)))) (-3254 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (-3254 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (-12 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-844)))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (|HasCategory| (-641) (QUOTE (-510))) (-12 (|HasCategory| (-641) (QUOTE (-986))) (|HasCategory| (-641) (QUOTE (-1114)))) (|HasCategory| (-641) (QUOTE (-986))) (-3254 (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844))) (-3254 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341)))) (-3254 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-517)))) (-12 (|HasCategory| (-641) (QUOTE (-213))) (|HasCategory| (-641) (QUOTE (-341)))) (-12 (|HasCategory| (-641) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-789))) (|HasCategory| (-641) (QUOTE (-517))) (|HasAttribute| (-641) (QUOTE -4257)) (|HasAttribute| (-641) (QUOTE -4254)) (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-136)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-327))))) +((-4252 . T) (-4257 |has| (-641) (-341)) (-4251 |has| (-641) (-341)) (-1496 . T) (-4258 |has| (-641) (-6 -4258)) (-4255 |has| (-641) (-6 -4255)) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-641) (QUOTE (-138))) (|HasCategory| (-641) (QUOTE (-136))) (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-346))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-641) (QUOTE (-213))) (-2067 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (LIST (QUOTE -265) (QUOTE (-641)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -288) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-641)))) (|HasCategory| (-641) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-641) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-641) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (-2067 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-327)))) (|HasCategory| (-641) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-641) (QUOTE (-953))) (|HasCategory| (-641) (QUOTE (-1114))) (-12 (|HasCategory| (-641) (QUOTE (-934))) (|HasCategory| (-641) (QUOTE (-1114)))) (-2067 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (-2067 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (-12 (|HasCategory| (-641) (QUOTE (-341))) (|HasCategory| (-641) (QUOTE (-844)))) (-12 (|HasCategory| (-641) (QUOTE (-327))) (|HasCategory| (-641) (QUOTE (-844))))) (|HasCategory| (-641) (QUOTE (-510))) (-12 (|HasCategory| (-641) (QUOTE (-986))) (|HasCategory| (-641) (QUOTE (-1114)))) (|HasCategory| (-641) (QUOTE (-986))) (-2067 (|HasCategory| (-641) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844))) (-2067 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-341)))) (-2067 (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-517)))) (-12 (|HasCategory| (-641) (QUOTE (-213))) (|HasCategory| (-641) (QUOTE (-341)))) (-12 (|HasCategory| (-641) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-641) (QUOTE (-341)))) (|HasCategory| (-641) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-641) (QUOTE (-789))) (|HasCategory| (-641) (QUOTE (-517))) (|HasAttribute| (-641) (QUOTE -4258)) (|HasAttribute| (-641) (QUOTE -4255)) (-12 (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-136)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-641) (QUOTE (-286))) (|HasCategory| (-641) (QUOTE (-844)))) (|HasCategory| (-641) (QUOTE (-327))))) (-637 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}."))) -((-4259 . T) (-1405 . T)) +((-4260 . T) (-1456 . T)) NIL (-638 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2488,13 +2488,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-640 OV E -3819 PG) +(-640 OV E -1834 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 (-641) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-1454 . T) (-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-1485 . T) (-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-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."))) @@ -2502,7 +2502,7 @@ NIL NIL (-643) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4257 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4258 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-644 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"))) @@ -2524,7 +2524,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-649 S -2022 I) +(-649 S -2401 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 @@ -2534,7 +2534,7 @@ NIL NIL (-651 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)}.}"))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) NIL (-652 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}."))) @@ -2544,25 +2544,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-654 R |Mod| -2692 -1577 |exactQuo|) +(-654 R |Mod| -2600 -3212 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-655 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(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"))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4254 |has| |#1| (-341)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-327))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4255 |has| |#1| (-341)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-327))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-656 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-657 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4253 |has| |#1| (-160)) (-4252 |has| |#1| (-160)) (-4255 . T)) +((-4254 |has| |#1| (-160)) (-4253 |has| |#1| (-160)) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138)))) -(-658 R |Mod| -2692 -1577 |exactQuo|) +(-658 R |Mod| -2600 -3212 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4255 . T)) +((-4256 . T)) NIL (-659 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2570,11 +2570,11 @@ NIL NIL (-660 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) NIL -(-661 -3819) +(-661 -1834) ((|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]]}."))) -((-4255 . T)) +((-4256 . T)) NIL (-662 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."))) @@ -2598,7 +2598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-327))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-346)))) (-667 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."))) -((-4251 |has| |#1| (-341)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 |has| |#1| (-341)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-668 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.")) (** (($ $ (|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."))) @@ -2608,7 +2608,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|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 -(-670 -3819 UP) +(-670 -1834 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 @@ -2626,8 +2626,8 @@ NIL NIL (-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."))) -(((-4260 "*") |has| |#2| (-160)) (-4251 |has| |#2| (-517)) (-4256 |has| |#2| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#2| (QUOTE (-844))) (-3254 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3254 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3254 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4256)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +(((-4261 "*") |has| |#2| (-160)) (-4252 |has| |#2| (-517)) (-4257 |has| |#2| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#2| (QUOTE (-844))) (-2067 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-2067 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-800 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-2067 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4257)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) (-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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2642,15 +2642,15 @@ NIL NIL (-678 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,{}m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4253 |has| |#1| (-160)) (-4252 |has| |#1| (-160)) (-4255 . T)) +((-4254 |has| |#1| (-160)) (-4253 |has| |#1| (-160)) (-4256 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-789)))) (-679 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4248 . T) (-4259 . T) (-1405 . T)) +((-4249 . T) (-4260 . T) (-1456 . T)) NIL (-680 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4258 . T) (-4248 . T) (-4259 . T)) +((-4259 . T) (-4249 . T) (-4260 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-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."))) @@ -2662,7 +2662,7 @@ NIL NIL (-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}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4253 . T) (-4252 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4254 . T) (-4253 . T) (-4256 . T)) NIL (-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"))) @@ -2678,7 +2678,7 @@ NIL NIL (-687 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) NIL (-688) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,{}n,{}scale,{}ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,{}n,{}scale,{}ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -2760,15 +2760,15 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-708 -3819) +(-708 -1834) ((|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 -(-709 P -3819) +(-709 P -1834) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL -(-710 UP -3819) +(-710 UP -1834) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -2782,9 +2782,9 @@ NIL NIL (-713) ((|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."))) -(((-4260 "*") . T)) +(((-4261 "*") . T)) NIL -(-714 R -3819) +(-714 R -1834) ((|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 @@ -2804,7 +2804,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-719 -3819 |ExtF| |SUEx| |ExtP| |n|) +(-719 -1834 |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 @@ -2818,23 +2818,23 @@ NIL NIL (-722 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL (-724 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4254 |has| |#1| (-341)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4255 |has| |#1| (-341)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-725 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-726 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-727 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}."))) @@ -2886,25 +2886,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-986))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-346)))) (-739 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) NIL -(-740 -3254 R OS S) +(-740 -2067 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-741 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-3254 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3254 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) +((-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-2067 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (-2067 (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-931 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (-742) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-743 R -3819 L) +(-743 R -1834 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-744 R -3819) +(-744 R -1834) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -2912,7 +2912,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-746 R -3819) +(-746 R -1834) ((|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 @@ -2920,11 +2920,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-748 -3819 UP UPUP R) +(-748 -1834 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 -(-749 -3819 UP L LQ) +(-749 -1834 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -2932,41 +2932,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-751 -3819 UP L LQ) +(-751 -1834 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-752 -3819 UP) +(-752 -1834 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-753 -3819 L UP A LO) +(-753 -1834 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 -(-754 -3819 UP) +(-754 -1834 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-755 -3819 LO) +(-755 -1834 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 -(-756 -3819 LODO) +(-756 -1834 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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(QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-1020)))) (|HasAttribute| |#2| (QUOTE -4256)) (|HasCategory| |#2| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (-758 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-760 (-1092)) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-759 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) -(((-4260 "*") |has| |#2| (-341)) (-4251 |has| |#2| (-341)) (-4256 |has| |#2| (-341)) (-4250 |has| |#2| (-341)) (-4255 . T) (-4253 . T) (-4252 . T)) +(((-4261 "*") |has| |#2| (-341)) (-4252 |has| |#2| (-341)) (-4257 |has| |#2| (-341)) (-4251 |has| |#2| (-341)) (-4256 . T) (-4254 . T) (-4253 . T)) ((|HasCategory| |#2| (QUOTE (-341)))) (-760 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}))."))) @@ -2978,7 +2978,7 @@ NIL NIL (-762) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-763) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -3006,7 +3006,7 @@ NIL NIL (-769 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-213)))) (-770) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3018,7 +3018,7 @@ NIL NIL (-772 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4258 . T) (-4248 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4249 . T) (-4260 . T) (-1456 . T)) NIL (-773) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3030,11 +3030,11 @@ NIL NIL (-775 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."))) -((-4255 |has| |#1| (-787))) -((|HasCategory| |#1| (QUOTE (-787))) (-3254 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3254 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4256 |has| |#1| (-787))) +((|HasCategory| |#1| (QUOTE (-787))) (-2067 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-2067 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) (-776 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4253 |has| |#1| (-160)) (-4252 |has| |#1| (-160)) (-4255 . T)) +((-4254 |has| |#1| (-160)) (-4253 |has| |#1| (-160)) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138)))) (-777) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3058,13 +3058,13 @@ NIL NIL (-782 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."))) -((-4255 |has| |#1| (-787))) -((|HasCategory| |#1| (QUOTE (-787))) (-3254 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3254 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4256 |has| |#1| (-787))) +((|HasCategory| |#1| (QUOTE (-787))) (-2067 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-2067 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) (-783) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-784 -2122 S) +(-784 -2041 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 @@ -3078,7 +3078,7 @@ NIL NIL (-787) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4255 . T)) +((-4256 . T)) NIL (-788 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3094,19 +3094,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160)))) (-791 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) NIL (-792 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) -(-793 R |sigma| -2178) +(-793 R |sigma| -2495) ((|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."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) -(-794 |x| R |sigma| -2178) +(-794 |x| R |sigma| -2495) ((|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}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-341)))) (-795 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..)}."))) @@ -3134,7 +3134,7 @@ NIL NIL (-801 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) -((-4253 |has| |#1| (-160)) (-4252 |has| |#1| (-160)) (-4255 . T)) +((-4254 |has| |#1| (-160)) (-4253 |has| |#1| (-160)) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341)))) (-802 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3146,24 +3146,24 @@ NIL NIL (-804 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-805 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-806 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-805 |#1|) (QUOTE (-844))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-805 |#1|) (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-138))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-805 |#1|) (QUOTE (-953))) (|HasCategory| (-805 |#1|) (QUOTE (-762))) (-3254 (|HasCategory| (-805 |#1|) (QUOTE (-762))) (|HasCategory| (-805 |#1|) (QUOTE (-789)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (QUOTE (-1068))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (QUOTE (-213))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -486) (QUOTE (-1092)) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -805) (|devaluate| |#1|)) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (QUOTE (-286))) (|HasCategory| (-805 |#1|) (QUOTE (-510))) (|HasCategory| (-805 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-844)))) (|HasCategory| (-805 |#1|) (QUOTE (-136))))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-805 |#1|) (QUOTE (-844))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-805 |#1|) (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-138))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-805 |#1|) (QUOTE (-953))) (|HasCategory| (-805 |#1|) (QUOTE (-762))) (-2067 (|HasCategory| (-805 |#1|) (QUOTE (-762))) (|HasCategory| (-805 |#1|) (QUOTE (-789)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (QUOTE (-1068))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-805 |#1|) (QUOTE (-213))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -486) (QUOTE (-1092)) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -805) (|devaluate| |#1|)) (LIST (QUOTE -805) (|devaluate| |#1|)))) (|HasCategory| (-805 |#1|) (QUOTE (-286))) (|HasCategory| (-805 |#1|) (QUOTE (-510))) (|HasCategory| (-805 |#1|) (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-805 |#1|) (QUOTE (-844)))) (|HasCategory| (-805 |#1|) (QUOTE (-136))))) (-807 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-762))) (-3254 (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789)))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -265) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-762))) (-2067 (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789)))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -265) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-789))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) (-808 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))))) (-809) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3219,7 +3219,7 @@ NIL (-822 |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 (-1850 (|HasCategory| |#2| (QUOTE (-977)))) (-1850 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092)))))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (-1850 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092)))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092))))) +((-12 (-3272 (|HasCategory| |#2| (QUOTE (-977)))) (-3272 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092)))))) (-12 (|HasCategory| |#2| (QUOTE (-977))) (-3272 (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092)))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092))))) (-823 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3228,7 +3228,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-825 R -2022) +(-825 R -2401) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3252,7 +3252,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-831 UP -3819) +(-831 UP -1834) ((|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 @@ -3270,19 +3270,19 @@ NIL NIL (-835 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4255 . T)) +((-4256 . T)) NIL (-836 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-837 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL (-838 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4255 . T)) +((-4256 . T)) NIL (-839 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3290,8 +3290,8 @@ NIL NIL (-840 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4255 . T)) -((-3254 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) +((-4256 . T)) +((-2067 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-789)))) (-841 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3306,13 +3306,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-136)))) (-844) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-845 |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."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) ((|HasCategory| $ (QUOTE (-138))) (|HasCategory| $ (QUOTE (-136))) (|HasCategory| $ (QUOTE (-346)))) -(-846 R0 -3819 UP UPUP R) +(-846 R0 -1834 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 @@ -3326,7 +3326,7 @@ NIL NIL (-849 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,{}denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,{}x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,{}n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-850 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."))) @@ -3340,7 +3340,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-853 -3819) +(-853 -1834) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3350,17 +3350,17 @@ NIL NIL (-855) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-856) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4260 "*") . T)) +(((-4261 "*") . T)) NIL -(-857 -3819 P) +(-857 -1834 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-858 |xx| -3819) +(-858 |xx| -1834) ((|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 @@ -3384,7 +3384,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-864 R -3819) +(-864 R -1834) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3396,7 +3396,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-867 S R -3819) +(-867 S R -1834) ((|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 @@ -3416,11 +3416,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -821) (|devaluate| |#1|)))) -(-872 R -3819 -2022) +(-872 R -1834 -2401) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-873 -2022) +(-873 -2401) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3442,8 +3442,8 @@ NIL NIL (-878 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-879 |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 @@ -3463,12 +3463,12 @@ NIL (-883 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-844))) (|HasAttribute| |#2| (QUOTE -4256)) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#4| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#4| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#4| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#4| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#4| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-789)))) +((|HasCategory| |#2| (QUOTE (-844))) (|HasAttribute| |#2| (QUOTE -4257)) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#4| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#4| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#4| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#4| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#4| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-789)))) (-884 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) NIL -(-885 E V R P -3819) +(-885 E V R P -1834) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3478,9 +3478,9 @@ NIL NIL (-887 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}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) -(-888 E V R P -3819) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1092) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +(-888 E V R P -1834) ((|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)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-429)))) @@ -3498,13 +3498,13 @@ NIL NIL (-892 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-893) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-894 -3819) +(-894 -1834) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3518,12 +3518,12 @@ NIL NIL (-897 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}"))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-126)))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4256))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-126)))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4257))) (-898 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"))) -((-4255 -12 (|has| |#2| (-450)) (|has| |#1| (-450)))) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669))))) (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) +((-4256 -12 (|has| |#2| (-450)) (|has| |#1| (-450)))) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669))))) (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669)))) (-12 (|HasCategory| |#1| (QUOTE (-735))) (|HasCategory| |#2| (QUOTE (-735))))) (-12 (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-669)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-899) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3538,7 +3538,7 @@ NIL NIL (-902 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4258 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4260 . T) (-1456 . T)) NIL (-903 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3554,7 +3554,7 @@ NIL NIL (-906 |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}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-907) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3566,7 +3566,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-517)))) (-909 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4258 . T) (-1405 . T)) +((-4259 . T) (-1456 . T)) NIL (-910 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3582,7 +3582,7 @@ NIL NIL (-913 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| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|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}."))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-914 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3600,7 +3600,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-918 K R UP -3819) +(-918 K R UP -1834) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3630,7 +3630,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-953))) (|HasCategory| |#2| (QUOTE (-762))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1068)))) (-925 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}."))) -((-1405 . T) (-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-1456 . T) (-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-926 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3638,7 +3638,7 @@ NIL NIL (-927 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4258 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4260 . T) (-1456 . T)) NIL (-928 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}."))) @@ -3646,7 +3646,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-986))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-269)))) (-929 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}."))) -((-4251 |has| |#1| (-269)) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 |has| |#1| (-269)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-930 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}."))) @@ -3654,12 +3654,12 @@ NIL NIL (-931 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.}"))) -((-4251 |has| |#1| (-269)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-510))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))))) +((-4252 |has| |#1| (-269)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1092)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-986))) (|HasCategory| |#1| (QUOTE (-510))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))))) (-932 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}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-933 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3668,14 +3668,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-935 -3819 UP UPUP |radicnd| |n|) +(-935 -1834 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4251 |has| (-385 |#2|) (-341)) (-4256 |has| (-385 |#2|) (-341)) (-4250 |has| (-385 |#2|) (-341)) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3254 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3254 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3254 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3254 (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) +((-4252 |has| (-385 |#2|) (-341)) (-4257 |has| (-385 |#2|) (-341)) (-4251 |has| (-385 |#2|) (-341)) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-2067 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-2067 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-2067 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-2067 (|HasCategory| (-385 |#2|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) (-936 |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.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-3254 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1068))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-525) (QUOTE (-844))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-1092)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-953))) (|HasCategory| (-525) (QUOTE (-762))) (-2067 (|HasCategory| (-525) (QUOTE (-762))) (|HasCategory| (-525) (QUOTE (-789)))) (|HasCategory| (-525) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1068))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1092)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-525) (LIST (QUOTE -588) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-844)))) (|HasCategory| (-525) (QUOTE (-136))))) (-937) ((|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 @@ -3695,10 +3695,10 @@ NIL (-941 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4259)) (|HasCategory| |#2| (QUOTE (-1020)))) +((|HasAttribute| |#1| (QUOTE -4260)) (|HasCategory| |#2| (QUOTE (-1020)))) (-942 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) -((-1405 . T)) +((-1456 . T)) NIL (-943 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3706,21 +3706,21 @@ NIL NIL (-944) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4251 . T) (-4256 . T) (-4250 . T) (-4253 . T) (-4252 . T) ((-4260 "*") . T) (-4255 . T)) +((-4252 . T) (-4257 . T) (-4251 . T) (-4254 . T) (-4253 . T) ((-4261 "*") . T) (-4256 . T)) NIL -(-945 R -3819) +(-945 R -1834) ((|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 -(-946 R -3819) +(-946 R -1834) ((|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 -(-947 -3819 UP) +(-947 -1834 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 -(-948 -3819 UP) +(-948 -1834 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 @@ -3750,9 +3750,9 @@ NIL NIL (-955 |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"))) -((-4251 . T) (-4256 . T) (-4250 . T) (-4253 . T) (-4252 . T) ((-4260 "*") . T) (-4255 . T)) -((-3254 (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (QUOTE (-525))))) -(-956 -3819 L) +((-4252 . T) (-4257 . T) (-4251 . T) (-4254 . T) (-4253 . T) ((-4261 "*") . T) (-4256 . T)) +((-2067 (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -968) (QUOTE (-525))))) +(-956 -1834 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -3762,12 +3762,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1020)))) (-958 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4259 . T) (-4258 . T)) +((-4260 . T) (-4259 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#4| (LIST (QUOTE -288) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#4| (LIST (QUOTE -566) (QUOTE (-798))))) (-959 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4260 "*")))) +((|HasAttribute| |#1| (QUOTE (-4261 "*")))) (-960 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -3788,14 +3788,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-965 -3819 |Expon| |VarSet| |FPol| |LFPol|) +(-965 -1834 |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"))) -(((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-966) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (QUOTE (-1092))) (LIST (QUOTE |:|) (QUOTE -4201) (QUOTE (-51))))))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-1092) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (QUOTE (-1092))) (LIST (QUOTE |:|) (QUOTE -3448) (QUOTE (-51))))))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-1092) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) (-967 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") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL @@ -3826,7 +3826,7 @@ NIL NIL (-974 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4259 . T) (-4258 . T)) +((-4260 . T) (-4259 . T)) ((-12 (|HasCategory| (-722 |#1| (-800 |#2|)) (QUOTE (-1020))) (|HasCategory| (-722 |#1| (-800 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -722) (|devaluate| |#1|) (LIST (QUOTE -800) (|devaluate| |#2|)))))) (|HasCategory| (-722 |#1| (-800 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-722 |#1| (-800 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| (-800 |#2|) (QUOTE (-346))) (|HasCategory| (-722 |#1| (-800 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-975) ((|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"))) @@ -3838,9 +3838,9 @@ NIL NIL (-977) ((|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\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|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."))) -((-4255 . T)) +((-4256 . T)) NIL -(-978 |xx| -3819) +(-978 |xx| -1834) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3850,12 +3850,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-286))) (|HasCategory| |#4| (QUOTE (-341))) (|HasCategory| |#4| (QUOTE (-517))) (|HasCategory| |#4| (QUOTE (-160)))) (-980 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4258 . T) (-1405 . T) (-4253 . T) (-4252 . T)) +((-4259 . T) (-1456 . T) (-4254 . T) (-4253 . T)) NIL (-981 |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.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4258 . T) (-4253 . T) (-4252 . T)) -((-3254 (-12 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-341)))) (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (QUOTE (-286))) (|HasCategory| |#3| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) +((-4259 . T) (-4254 . T) (-4253 . T)) +((-2067 (-12 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-341)))) (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (QUOTE (-286))) (|HasCategory| |#3| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (-982 |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 @@ -3874,7 +3874,7 @@ NIL NIL (-986) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-987 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -3882,19 +3882,19 @@ NIL NIL (-988) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(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."))) -((-4246 . T) (-4250 . T) (-4245 . T) (-4256 . T) (-4257 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4247 . T) (-4251 . T) (-4246 . T) (-4257 . T) (-4258 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-989) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (QUOTE (-1092))) (LIST (QUOTE |:|) (QUOTE -4201) (QUOTE (-51))))))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (QUOTE (-1020))) (|HasCategory| (-1092) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (QUOTE (-1092))) (LIST (QUOTE |:|) (QUOTE -3448) (QUOTE (-51))))))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-51) (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1020))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (QUOTE (-1020))) (|HasCategory| (-1092) (QUOTE (-789))) (|HasCategory| (-51) (QUOTE (-1020))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-51) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (LIST (QUOTE -566) (QUOTE (-798))))) (-990 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -925) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#4| (LIST (QUOTE -567) (QUOTE (-1092))))) (-991 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) NIL (-992 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}"))) @@ -3914,7 +3914,7 @@ NIL NIL (-996 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-997 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -3924,11 +3924,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-999 |Base| R -3819) +(-999 |Base| R -1834) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1000 |Base| R -3819) +(-1000 |Base| R -1834) ((|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 @@ -3942,8 +3942,8 @@ NIL NIL (-1003 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."))) -((-4251 |has| |#1| (-341)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092))))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341))))) +((-4252 |has| |#1| (-341)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092))))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341))))) (-1004 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 @@ -3966,8 +3966,8 @@ NIL NIL (-1009 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"))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1010 (-1092)) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1010 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 @@ -3986,7 +3986,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1020)))) (-1014 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-1405 . T)) +((-1456 . T)) NIL (-1015 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -3994,15 +3994,15 @@ NIL ((|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1016 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-1405 . T)) +((-1456 . T)) NIL (-1017 A S) -((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) +((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL (-1018 S) -((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4248 . T) (-1405 . T)) +((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) +((-4249 . T) (-1456 . T)) NIL (-1019 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}."))) @@ -4018,8 +4018,8 @@ NIL NIL (-1022 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) -((-4258 . T) (-4248 . T) (-4259 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4249 . T) (-4260 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1023 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4046,7 +4046,7 @@ NIL NIL (-1029 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-1030) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4062,13 +4062,13 @@ NIL NIL (-1033 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4252 |has| |#3| (-977)) (-4253 |has| |#3| (-977)) (-4255 |has| |#3| (-6 -4255)) ((-4260 "*") |has| |#3| (-160)) (-4258 . 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\\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-429)))) -(-1035 R -3819) +(-1035 R -1834) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4086,19 +4086,19 @@ NIL NIL (-1039) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|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."))) -((-4246 . T) (-4250 . T) (-4245 . T) (-4256 . T) (-4257 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4247 . T) (-4251 . T) (-4246 . T) (-4257 . T) (-4258 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1040 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4258 . T) (-4259 . T) (-1405 . T)) +((-4259 . T) (-4260 . T) (-1456 . T)) NIL (-1041 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-341))) (|HasAttribute| |#3| (QUOTE (-4260 "*"))) (|HasCategory| |#3| (QUOTE (-160)))) +((|HasCategory| |#3| (QUOTE (-341))) (|HasAttribute| |#3| (QUOTE (-4261 "*"))) (|HasCategory| |#3| (QUOTE (-160)))) (-1042 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-1405 . T) (-4258 . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-1456 . T) (-4259 . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1043 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}."))) @@ -4106,17 +4106,17 @@ NIL NIL (-1044 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."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-844))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-844))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1045 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) (-1046 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}"))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL -(-1047 UP -3819) +(-1047 UP -1834) ((|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 @@ -4162,19 +4162,19 @@ NIL NIL (-1058 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| (-1057 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1057) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1057 |#1| |#2|) (QUOTE (-1020)))) (|HasCategory| (-1057 |#1| |#2|) (QUOTE (-1020))) (-3254 (|HasCategory| (-1057 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-1057 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1057) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1057 |#1| |#2|) (QUOTE (-1020))))) (|HasCategory| (-1057 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| (-1057 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1057) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1057 |#1| |#2|) (QUOTE (-1020)))) (|HasCategory| (-1057 |#1| |#2|) (QUOTE (-1020))) (-2067 (|HasCategory| (-1057 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-798)))) (-12 (|HasCategory| (-1057 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1057) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1057 |#1| |#2|) (QUOTE (-1020))))) (|HasCategory| (-1057 |#1| |#2|) (LIST (QUOTE -566) (QUOTE (-798))))) (-1059 |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.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|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}."))) -((-4255 . T) (-4247 |has| |#2| (-6 (-4260 "*"))) (-4258 . T) (-4252 . T) (-4253 . T)) -((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4260 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (-3254 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-341))) (-3254 (|HasAttribute| |#2| (QUOTE (-4260 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-160)))) +((-4256 . T) (-4248 |has| |#2| (-6 (-4261 "*"))) (-4259 . T) (-4253 . T) (-4254 . T)) +((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4261 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (-2067 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-341))) (-2067 (|HasAttribute| |#2| (QUOTE (-4261 "*"))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-160)))) (-1060 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1061) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-1062 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4182,24 +4182,24 @@ NIL NIL (-1063 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4259 . T) (-4258 . T)) +((-4260 . T) (-4259 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#4| (LIST (QUOTE -288) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#4| (LIST (QUOTE -566) (QUOTE (-798))))) (-1064 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}."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1065 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL (-1066 S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) -((-1405 . T)) +((-1456 . T)) NIL (-1067 |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."))) -((-4259 . T)) -((-12 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#2|)))))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#2|)))))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-789))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-1068) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4222,20 +4222,20 @@ NIL NIL (-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}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4259 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1074) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-1075) NIL -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| (-135) (QUOTE (-1020))) (-12 (|HasCategory| (-135) (QUOTE (-1020))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-798))))) (-1076 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4258 . T) (-4259 . T)) -((-12 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (QUOTE (-1075))) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#1|)))))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (QUOTE (-1020))) (|HasCategory| (-1075) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (QUOTE (-1075))) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#1|)))))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (QUOTE (-1020))) (|HasCategory| (-1075) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-1077 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4262,9 +4262,9 @@ NIL NIL (-1083 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|)))) (|HasCategory| (-713) (QUOTE (-1032))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -1217) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1206) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -2897) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|)))) (|HasCategory| (-713) (QUOTE (-1032))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2367) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -1296) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) (-1091) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4306,8 +4306,8 @@ NIL NIL (-1094 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-6 -4256)) (-4252 . T) (-4253 . T) (-4255 . 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(|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) 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T)) -((-12 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3364) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4201) (|devaluate| |#2|)))))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-3254 (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) +((-4259 . T) (-4260 . T)) +((-12 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1556) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3448) (|devaluate| |#2|)))))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-1020)))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -567) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-1020))) (-2067 (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-798)))) (|HasCategory| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (LIST (QUOTE -566) (QUOTE (-798))))) (-1103 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4350,7 +4350,7 @@ NIL NIL (-1105 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4259 . T) (-1405 . T)) +((-4260 . T) (-1456 . T)) NIL (-1106 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4390,8 +4390,8 @@ NIL NIL (-1115 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4259 . T) (-4258 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1020))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1116 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4400,7 +4400,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1118 R -3819) +(-1118 R -1834) ((|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 @@ -4408,7 +4408,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1120 R -3819) +(-1120 R -1834) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -567) (LIST (QUOTE -827) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -821) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -821) (|devaluate| |#1|))))) @@ -4418,12 +4418,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-346)))) (-1122 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-1123 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) (-1124 |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 @@ -4436,13 +4436,13 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) NIL ((|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) -(-1127 -3819) +(-1127 -1834) ((|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 (-1128) ((|constructor| (NIL "The fundamental Type."))) -((-1405 . T)) +((-1456 . T)) NIL (-1129 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) @@ -4458,7 +4458,7 @@ NIL NIL (-1132) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1133 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) @@ -4466,7 +4466,7 @@ NIL NIL (-1134 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,{}k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = n0..infinity,{}a[n] * x**n)) = sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1135 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) @@ -4474,16 +4474,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-341)))) (-1136 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-1405 |has| |#1| (-341)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) (-1456 |has| |#1| (-341)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1137 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4518,8 +4518,8 @@ NIL NIL (-1147 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) -(((-4260 "*") |has| |#2| (-160)) (-4251 |has| |#2| (-517)) (-4254 |has| |#2| (-341)) (-4256 |has| |#2| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3254 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-3254 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (-3254 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE -4256)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-3254 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) +(((-4261 "*") |has| |#2| (-160)) (-4252 |has| |#2| (-517)) (-4255 |has| |#2| (-341)) (-4257 |has| |#2| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-2067 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-357))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -821) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -821) (QUOTE (-525))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-357)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -567) (LIST (QUOTE -827) (QUOTE (-525)))))) (-12 (|HasCategory| (-1005) (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -567) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -588) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (-2067 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (-2067 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE -4257)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (-2067 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-136))))) (-1148 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 @@ -4530,15 +4530,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-1068)))) (-1150 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4254 |has| |#1| (-341)) (-4256 |has| |#1| (-6 -4256)) (-4253 . T) (-4252 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4255 |has| |#1| (-341)) (-4257 |has| |#1| (-6 -4257)) (-4254 . T) (-4253 . T) (-4256 . T)) NIL (-1151 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1032))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1217) (LIST (|devaluate| |#2|) (QUOTE (-1092)))))) +((|HasCategory| |#2| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1032))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4100) (LIST (|devaluate| |#2|) (QUOTE (-1092)))))) (-1152 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1153 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4550,7 +4550,7 @@ NIL NIL (-1155 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1156 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| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|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)}."))) @@ -4558,27 +4558,27 @@ NIL NIL (-1157 |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| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|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)}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1158 |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)}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -1217) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3254 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1206) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -2897) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-2067 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2367) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -1296) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-1159 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4256 |has| |#1| (-341)) (-4250 |has| |#1| (-341)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3254 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -1217) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3254 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1206) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -2897) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4257 |has| |#1| (-341)) (-4251 |has| |#1| (-341)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-2067 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-2067 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2367) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -1296) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) (-1160 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))}."))) -(((-4260 "*") |has| (-1159 |#2| |#3| |#4|) (-160)) (-4251 |has| (-1159 |#2| |#3| |#4|) (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-160))) (|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-341))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-429))) (-3254 (|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-517)))) +(((-4261 "*") |has| (-1159 |#2| |#3| |#4|) (-160)) (-4252 |has| (-1159 |#2| |#3| |#4|) (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-160))) (|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -968) (QUOTE (-525)))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-341))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-429))) (-2067 (|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (LIST (QUOTE -968) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-517)))) (-1161 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4259))) +((|HasAttribute| |#1| (QUOTE -4260))) (-1162 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-1405 . T)) +((-1456 . T)) NIL (-1163 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4587,26 +4587,26 @@ NIL (-1164 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-893))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasSignature| |#2| (LIST (QUOTE -2897) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1206) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1092))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-893))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasSignature| |#2| (LIST (QUOTE -1296) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2367) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1092))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341)))) (-1165 |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."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1166 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4260 "*") |has| |#1| (-160)) (-4251 |has| |#1| (-517)) (-4252 . T) (-4253 . T) (-4255 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3254 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|)))) (|HasCategory| (-713) (QUOTE (-1032))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -1217) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-3254 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -1206) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -2897) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) +(((-4261 "*") |has| |#1| (-160)) (-4252 |has| |#1| (-517)) (-4253 . T) (-4254 . T) (-4256 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-2067 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -835) (QUOTE (-1092)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-713)) (|devaluate| |#1|)))) (|HasCategory| (-713) (QUOTE (-1032))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasSignature| |#1| (LIST (QUOTE -4100) (LIST (|devaluate| |#1|) (QUOTE (-1092)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-713))))) (|HasCategory| |#1| (QUOTE (-341))) (-2067 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-893))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2367) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1092))))) (|HasSignature| |#1| (LIST (QUOTE -1296) (LIST (LIST (QUOTE -592) (QUOTE (-1092))) (|devaluate| |#1|))))))) (-1167 |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 -(-1168 -3819 UP L UTS) +(-1168 -1834 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 (-517)))) (-1169) ((|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."))) -((-1405 . T)) +((-1456 . T)) NIL (-1170 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4618,7 +4618,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-669))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1172 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4259 . T) (-4258 . T) (-1405 . T)) +((-4260 . T) (-4259 . T) (-1456 . T)) NIL (-1173 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4626,8 +4626,8 @@ NIL NIL (-1174 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4259 . T) (-4258 . T)) -((-3254 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3254 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-3254 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) +((-4260 . T) (-4259 . T)) +((-2067 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-2067 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (|HasCategory| |#1| (LIST (QUOTE -567) (QUOTE (-501)))) (-2067 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| (-525) (QUOTE (-789))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-669))) (|HasCategory| |#1| (QUOTE (-977))) (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-977)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-798))))) (-1175) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4654,68 +4654,68 @@ NIL NIL (-1181 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4253 . T) (-4252 . T)) +((-4254 . T) (-4253 . T)) NIL (-1182 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1183 K R UP -3819) +(-1183 K R UP -1834) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL (-1184 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights"))) -((-4253 |has| |#1| (-160)) (-4252 |has| |#1| (-160)) (-4255 . T)) +((-4254 |has| |#1| (-160)) (-4253 |has| |#1| (-160)) (-4256 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341)))) (-1185 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4259 . T) (-4258 . T)) +((-4260 . T) (-4259 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#4| (LIST (QUOTE -288) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -567) (QUOTE (-501)))) (|HasCategory| |#4| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#4| (LIST (QUOTE -566) (QUOTE (-798))))) (-1186 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) -((-4252 . T) (-4253 . T) (-4255 . T)) +((-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1187 |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."))) -((-4255 . T) (-4251 |has| |#2| (-6 -4251)) (-4253 . T) (-4252 . T)) -((|HasCategory| |#2| (QUOTE (-160))) (|HasAttribute| |#2| (QUOTE -4251))) +((-4256 . T) (-4252 |has| |#2| (-6 -4252)) (-4254 . T) (-4253 . T)) +((|HasCategory| |#2| (QUOTE (-160))) (|HasAttribute| |#2| (QUOTE -4252))) (-1188 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL (-1189 |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4251 |has| |#2| (-6 -4251)) (-4253 . T) (-4252 . T) (-4255 . T)) +((-4252 |has| |#2| (-6 -4252)) (-4254 . T) (-4253 . T) (-4256 . T)) NIL -(-1190 S -3819) +(-1190 S -1834) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138)))) -(-1191 -3819) +(-1191 -1834) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4250 . T) (-4256 . T) (-4251 . T) ((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +((-4251 . T) (-4257 . T) (-4252 . T) ((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL (-1192 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4251 |has| |#2| (-6 -4251)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (LIST (QUOTE -660) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasAttribute| |#2| (QUOTE -4251))) +((-4252 |has| |#2| (-6 -4252)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (LIST (QUOTE -660) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasAttribute| |#2| (QUOTE -4252))) (-1193 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4251 |has| |#2| (-6 -4251)) (-4253 . T) (-4252 . T) (-4255 . T)) +((-4252 |has| |#2| (-6 -4252)) (-4254 . T) (-4253 . T) (-4256 . T)) NIL (-1194 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4251 |has| |#1| (-6 -4251)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#1| (QUOTE (-160))) (|HasAttribute| |#1| (QUOTE -4251))) +((-4252 |has| |#1| (-6 -4252)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#1| (QUOTE (-160))) (|HasAttribute| |#1| (QUOTE -4252))) (-1195 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4255 . T) (-4256 |has| |#1| (-6 -4256)) (-4251 |has| |#1| (-6 -4251)) (-4253 . T) (-4252 . T)) -((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasAttribute| |#1| (QUOTE -4255)) (|HasAttribute| |#1| (QUOTE -4256)) (|HasAttribute| |#1| (QUOTE -4251))) +((-4256 . T) (-4257 |has| |#1| (-6 -4257)) (-4252 |has| |#1| (-6 -4252)) (-4254 . T) (-4253 . T)) +((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasAttribute| |#1| (QUOTE -4256)) (|HasAttribute| |#1| (QUOTE -4257)) (|HasAttribute| |#1| (QUOTE -4252))) (-1196 |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."))) -((-4251 |has| |#2| (-6 -4251)) (-4253 . T) (-4252 . T) (-4255 . T)) -((|HasCategory| |#2| (QUOTE (-160))) (|HasAttribute| |#2| (QUOTE -4251))) +((-4252 |has| |#2| (-6 -4252)) (-4254 . T) (-4253 . T) (-4256 . T)) +((|HasCategory| |#2| (QUOTE (-160))) (|HasAttribute| |#2| (QUOTE -4252))) (-1197 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 @@ -4730,7 +4730,7 @@ NIL NIL (-1200 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4260 "*") . T) (-4252 . T) (-4253 . T) (-4255 . T)) +(((-4261 "*") . T) (-4253 . T) (-4254 . T) (-4256 . T)) NIL NIL NIL @@ -4748,4 +4748,4 @@ NIL NIL NIL NIL -((-3 NIL 2241648 2241653 2241658 2241663) (-2 NIL 2241628 2241633 2241638 2241643) (-1 NIL 2241608 2241613 2241618 2241623) (0 NIL 2241588 2241593 2241598 2241603) (-1200 "ZMOD.spad" 2241397 2241410 2241526 2241583) (-1199 "ZLINDEP.spad" 2240441 2240452 2241387 2241392) (-1198 "ZDSOLVE.spad" 2230290 2230312 2240431 2240436) (-1197 "YSTREAM.spad" 2229783 2229794 2230280 2230285) (-1196 "XRPOLY.spad" 2229003 2229023 2229639 2229708) (-1195 "XPR.spad" 2226732 2226745 2228721 2228820) (-1194 "XPOLY.spad" 2226287 2226298 2226588 2226657) (-1193 "XPOLYC.spad" 2225604 2225620 2226213 2226282) (-1192 "XPBWPOLY.spad" 2224041 2224061 2225384 2225453) (-1191 "XF.spad" 2222502 2222517 2223943 2224036) (-1190 "XF.spad" 2220943 2220960 2222386 2222391) (-1189 "XFALG.spad" 2217967 2217983 2220869 2220938) (-1188 "XEXPPKG.spad" 2217218 2217244 2217957 2217962) (-1187 "XDPOLY.spad" 2216832 2216848 2217074 2217143) (-1186 "XALG.spad" 2216430 2216441 2216788 2216827) (-1185 "WUTSET.spad" 2212269 2212286 2216076 2216103) (-1184 "WP.spad" 2211283 2211327 2212127 2212194) (-1183 "WFFINTBS.spad" 2208846 2208868 2211273 2211278) (-1182 "WEIER.spad" 2207060 2207071 2208836 2208841) (-1181 "VSPACE.spad" 2206733 2206744 2207028 2207055) (-1180 "VSPACE.spad" 2206426 2206439 2206723 2206728) (-1179 "VOID.spad" 2206016 2206025 2206416 2206421) (-1178 "VIEW.spad" 2203638 2203647 2206006 2206011) (-1177 "VIEWDEF.spad" 2198835 2198844 2203628 2203633) (-1176 "VIEW3D.spad" 2182670 2182679 2198825 2198830) (-1175 "VIEW2D.spad" 2170407 2170416 2182660 2182665) (-1174 "VECTOR.spad" 2169084 2169095 2169335 2169362) (-1173 "VECTOR2.spad" 2167711 2167724 2169074 2169079) (-1172 "VECTCAT.spad" 2165599 2165610 2167667 2167706) (-1171 "VECTCAT.spad" 2163308 2163321 2165378 2165383) (-1170 "VARIABLE.spad" 2163088 2163103 2163298 2163303) (-1169 "UTYPE.spad" 2162722 2162731 2163068 2163083) (-1168 "UTSODETL.spad" 2162015 2162039 2162678 2162683) (-1167 "UTSODE.spad" 2160203 2160223 2162005 2162010) (-1166 "UTS.spad" 2154992 2155020 2158670 2158767) (-1165 "UTSCAT.spad" 2152443 2152459 2154890 2154987) (-1164 "UTSCAT.spad" 2149538 2149556 2151987 2151992) (-1163 "UTS2.spad" 2149131 2149166 2149528 2149533) (-1162 "URAGG.spad" 2143753 2143764 2149111 2149126) (-1161 "URAGG.spad" 2138349 2138362 2143709 2143714) (-1160 "UPXSSING.spad" 2135995 2136021 2137433 2137566) (-1159 "UPXS.spad" 2133022 2133050 2134127 2134276) (-1158 "UPXSCONS.spad" 2130779 2130799 2131154 2131303) (-1157 "UPXSCCA.spad" 2129237 2129257 2130625 2130774) (-1156 "UPXSCCA.spad" 2127837 2127859 2129227 2129232) (-1155 "UPXSCAT.spad" 2126418 2126434 2127683 2127832) (-1154 "UPXS2.spad" 2125959 2126012 2126408 2126413) (-1153 "UPSQFREE.spad" 2124371 2124385 2125949 2125954) (-1152 "UPSCAT.spad" 2121964 2121988 2124269 2124366) (-1151 "UPSCAT.spad" 2119263 2119289 2121570 2121575) (-1150 "UPOLYC.spad" 2114241 2114252 2119105 2119258) (-1149 "UPOLYC.spad" 2109111 2109124 2113977 2113982) (-1148 "UPOLYC2.spad" 2108580 2108599 2109101 2109106) (-1147 "UP.spad" 2105625 2105640 2106133 2106286) (-1146 "UPMP.spad" 2104515 2104528 2105615 2105620) (-1145 "UPDIVP.spad" 2104078 2104092 2104505 2104510) (-1144 "UPDECOMP.spad" 2102315 2102329 2104068 2104073) (-1143 "UPCDEN.spad" 2101522 2101538 2102305 2102310) (-1142 "UP2.spad" 2100884 2100905 2101512 2101517) (-1141 "UNISEG.spad" 2100237 2100248 2100803 2100808) (-1140 "UNISEG2.spad" 2099730 2099743 2100193 2100198) (-1139 "UNIFACT.spad" 2098831 2098843 2099720 2099725) (-1138 "ULS.spad" 2089390 2089418 2090483 2090912) (-1137 "ULSCONS.spad" 2083433 2083453 2083805 2083954) (-1136 "ULSCCAT.spad" 2081030 2081050 2083253 2083428) (-1135 "ULSCCAT.spad" 2078761 2078783 2080986 2080991) (-1134 "ULSCAT.spad" 2076977 2076993 2078607 2078756) (-1133 "ULS2.spad" 2076489 2076542 2076967 2076972) (-1132 "UFD.spad" 2075554 2075563 2076415 2076484) (-1131 "UFD.spad" 2074681 2074692 2075544 2075549) (-1130 "UDVO.spad" 2073528 2073537 2074671 2074676) (-1129 "UDPO.spad" 2070955 2070966 2073484 2073489) (-1128 "TYPE.spad" 2070877 2070886 2070935 2070950) (-1127 "TWOFACT.spad" 2069527 2069542 2070867 2070872) (-1126 "TUPLE.spad" 2068913 2068924 2069426 2069431) (-1125 "TUBETOOL.spad" 2065750 2065759 2068903 2068908) (-1124 "TUBE.spad" 2064391 2064408 2065740 2065745) (-1123 "TS.spad" 2062980 2062996 2063956 2064053) (-1122 "TSETCAT.spad" 2050095 2050112 2062936 2062975) (-1121 "TSETCAT.spad" 2037208 2037227 2050051 2050056) (-1120 "TRMANIP.spad" 2031574 2031591 2036914 2036919) (-1119 "TRIMAT.spad" 2030533 2030558 2031564 2031569) (-1118 "TRIGMNIP.spad" 2029050 2029067 2030523 2030528) (-1117 "TRIGCAT.spad" 2028562 2028571 2029040 2029045) (-1116 "TRIGCAT.spad" 2028072 2028083 2028552 2028557) (-1115 "TREE.spad" 2026643 2026654 2027679 2027706) (-1114 "TRANFUN.spad" 2026474 2026483 2026633 2026638) (-1113 "TRANFUN.spad" 2026303 2026314 2026464 2026469) (-1112 "TOPSP.spad" 2025977 2025986 2026293 2026298) (-1111 "TOOLSIGN.spad" 2025640 2025651 2025967 2025972) (-1110 "TEXTFILE.spad" 2024197 2024206 2025630 2025635) (-1109 "TEX.spad" 2021214 2021223 2024187 2024192) (-1108 "TEX1.spad" 2020770 2020781 2021204 2021209) (-1107 "TEMUTL.spad" 2020325 2020334 2020760 2020765) (-1106 "TBCMPPK.spad" 2018418 2018441 2020315 2020320) (-1105 "TBAGG.spad" 2017442 2017465 2018386 2018413) (-1104 "TBAGG.spad" 2016486 2016511 2017432 2017437) (-1103 "TANEXP.spad" 2015862 2015873 2016476 2016481) (-1102 "TABLE.spad" 2014273 2014296 2014543 2014570) (-1101 "TABLEAU.spad" 2013754 2013765 2014263 2014268) (-1100 "TABLBUMP.spad" 2010537 2010548 2013744 2013749) (-1099 "SYSTEM.spad" 2009811 2009820 2010527 2010532) (-1098 "SYSSOLP.spad" 2007284 2007295 2009801 2009806) (-1097 "SYNTAX.spad" 2003476 2003485 2007274 2007279) (-1096 "SYMTAB.spad" 2001532 2001541 2003466 2003471) (-1095 "SYMS.spad" 1997517 1997526 2001522 2001527) (-1094 "SYMPOLY.spad" 1996527 1996538 1996609 1996736) (-1093 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1942160 1942187) (-1074 "STRICAT.spad" 1941922 1941931 1942102 1942141) (-1073 "STREAM.spad" 1938690 1938701 1941447 1941462) (-1072 "STREAM3.spad" 1938235 1938250 1938680 1938685) (-1071 "STREAM2.spad" 1937303 1937316 1938225 1938230) (-1070 "STREAM1.spad" 1937007 1937018 1937293 1937298) (-1069 "STINPROD.spad" 1935913 1935929 1936997 1937002) (-1068 "STEP.spad" 1935114 1935123 1935903 1935908) (-1067 "STBL.spad" 1933640 1933668 1933807 1933822) (-1066 "STAGG.spad" 1932705 1932716 1933620 1933635) (-1065 "STAGG.spad" 1931778 1931791 1932695 1932700) (-1064 "STACK.spad" 1931129 1931140 1931385 1931412) (-1063 "SREGSET.spad" 1928833 1928850 1930775 1930802) (-1062 "SRDCMPK.spad" 1927378 1927398 1928823 1928828) (-1061 "SRAGG.spad" 1922463 1922472 1927334 1927373) (-1060 "SRAGG.spad" 1917580 1917591 1922453 1922458) (-1059 "SQMATRIX.spad" 1915206 1915224 1916114 1916201) (-1058 "SPLTREE.spad" 1909758 1909771 1914642 1914669) (-1057 "SPLNODE.spad" 1906346 1906359 1909748 1909753) (-1056 "SPFCAT.spad" 1905123 1905132 1906336 1906341) (-1055 "SPECOUT.spad" 1903673 1903682 1905113 1905118) (-1054 "spad-parser.spad" 1903138 1903147 1903663 1903668) (-1053 "SPACEC.spad" 1887151 1887162 1903128 1903133) (-1052 "SPACE3.spad" 1886927 1886938 1887141 1887146) (-1051 "SORTPAK.spad" 1886472 1886485 1886883 1886888) (-1050 "SOLVETRA.spad" 1884229 1884240 1886462 1886467) (-1049 "SOLVESER.spad" 1882749 1882760 1884219 1884224) (-1048 "SOLVERAD.spad" 1878759 1878770 1882739 1882744) (-1047 "SOLVEFOR.spad" 1877179 1877197 1878749 1878754) (-1046 "SNTSCAT.spad" 1876767 1876784 1877135 1877174) (-1045 "SMTS.spad" 1875027 1875053 1876332 1876429) (-1044 "SMP.spad" 1872469 1872489 1872859 1872986) (-1043 "SMITH.spad" 1871312 1871337 1872459 1872464) (-1042 "SMATCAT.spad" 1869410 1869440 1871244 1871307) (-1041 "SMATCAT.spad" 1867452 1867484 1869288 1869293) (-1040 "SKAGG.spad" 1866401 1866412 1867408 1867447) (-1039 "SINT.spad" 1864709 1864718 1866267 1866396) (-1038 "SIMPAN.spad" 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"SETCAT.spad" 1827768 1827779 1828275 1828280) (-1018 "SETAGG.spad" 1824291 1824302 1827736 1827763) (-1017 "SETAGG.spad" 1820834 1820847 1824281 1824286) (-1016 "SEGXCAT.spad" 1819946 1819959 1820814 1820829) (-1015 "SEG.spad" 1819759 1819770 1819865 1819870) (-1014 "SEGCAT.spad" 1818578 1818589 1819739 1819754) (-1013 "SEGBIND.spad" 1817650 1817661 1818533 1818538) (-1012 "SEGBIND2.spad" 1817346 1817359 1817640 1817645) (-1011 "SEG2.spad" 1816771 1816784 1817302 1817307) (-1010 "SDVAR.spad" 1816047 1816058 1816761 1816766) (-1009 "SDPOL.spad" 1813440 1813451 1813731 1813858) (-1008 "SCPKG.spad" 1811519 1811530 1813430 1813435) (-1007 "SCOPE.spad" 1810664 1810673 1811509 1811514) (-1006 "SCACHE.spad" 1809346 1809357 1810654 1810659) (-1005 "SAOS.spad" 1809218 1809227 1809336 1809341) (-1004 "SAERFFC.spad" 1808931 1808951 1809208 1809213) (-1003 "SAE.spad" 1807109 1807125 1807720 1807855) (-1002 "SAEFACT.spad" 1806810 1806830 1807099 1807104) (-1001 "RURPK.spad" 1804451 1804467 1806800 1806805) (-1000 "RULESET.spad" 1803892 1803916 1804441 1804446) (-999 "RULE.spad" 1802097 1802120 1803882 1803887) (-998 "RULECOLD.spad" 1801950 1801962 1802087 1802092) (-997 "RSETGCD.spad" 1798329 1798348 1801940 1801945) (-996 "RSETCAT.spad" 1788102 1788118 1798285 1798324) (-995 "RSETCAT.spad" 1777907 1777925 1788092 1788097) (-994 "RSDCMPK.spad" 1776360 1776379 1777897 1777902) (-993 "RRCC.spad" 1774745 1774774 1776350 1776355) (-992 "RRCC.spad" 1773128 1773159 1774735 1774740) (-991 "RPOLCAT.spad" 1752489 1752503 1772996 1773123) (-990 "RPOLCAT.spad" 1731565 1731581 1752074 1752079) (-989 "ROUTINE.spad" 1727429 1727437 1730212 1730239) (-988 "ROMAN.spad" 1726662 1726670 1727295 1727424) (-987 "ROIRC.spad" 1725743 1725774 1726652 1726657) (-986 "RNS.spad" 1724647 1724655 1725645 1725738) (-985 "RNS.spad" 1723637 1723647 1724637 1724642) (-984 "RNG.spad" 1723373 1723381 1723627 1723632) (-983 "RMODULE.spad" 1723012 1723022 1723363 1723368) (-982 "RMCAT2.spad" 1722421 1722477 1723002 1723007) (-981 "RMATRIX.spad" 1721101 1721119 1721588 1721627) (-980 "RMATCAT.spad" 1716623 1716653 1721045 1721096) (-979 "RMATCAT.spad" 1712047 1712079 1716471 1716476) (-978 "RINTERP.spad" 1711936 1711955 1712037 1712042) (-977 "RING.spad" 1711294 1711302 1711916 1711931) (-976 "RING.spad" 1710660 1710670 1711284 1711289) (-975 "RIDIST.spad" 1710045 1710053 1710650 1710655) (-974 "RGCHAIN.spad" 1708625 1708640 1709530 1709557) (-973 "RF.spad" 1706240 1706250 1708615 1708620) (-972 "RFFACTOR.spad" 1705703 1705713 1706230 1706235) (-971 "RFFACT.spad" 1705439 1705450 1705693 1705698) (-970 "RFDIST.spad" 1704428 1704436 1705429 1705434) (-969 "RETSOL.spad" 1703846 1703858 1704418 1704423) (-968 "RETRACT.spad" 1703196 1703206 1703836 1703841) (-967 "RETRACT.spad" 1702544 1702556 1703186 1703191) (-966 "RESULT.spad" 1700605 1700613 1701191 1701218) (-965 "RESRING.spad" 1699953 1699999 1700543 1700600) (-964 "RESLATC.spad" 1699278 1699288 1699943 1699948) (-963 "REPSQ.spad" 1699008 1699018 1699268 1699273) (-962 "REP.spad" 1696561 1696569 1698998 1699003) (-961 "REPDB.spad" 1696267 1696277 1696551 1696556) (-960 "REP2.spad" 1685840 1685850 1696109 1696114) (-959 "REP1.spad" 1679831 1679841 1685790 1685795) (-958 "REGSET.spad" 1677629 1677645 1679477 1679504) (-957 "REF.spad" 1676959 1676969 1677584 1677589) (-956 "REDORDER.spad" 1676136 1676152 1676949 1676954) (-955 "RECLOS.spad" 1674926 1674945 1675629 1675722) (-954 "REALSOLV.spad" 1674059 1674067 1674916 1674921) (-953 "REAL.spad" 1673932 1673940 1674049 1674054) (-952 "REAL0Q.spad" 1671215 1671229 1673922 1673927) (-951 "REAL0.spad" 1668044 1668058 1671205 1671210) (-950 "RDIV.spad" 1667696 1667720 1668034 1668039) (-949 "RDIST.spad" 1667260 1667270 1667686 1667691) (-948 "RDETRS.spad" 1666057 1666074 1667250 1667255) (-947 "RDETR.spad" 1664165 1664182 1666047 1666052) (-946 "RDEEFS.spad" 1663239 1663255 1664155 1664160) (-945 "RDEEF.spad" 1662236 1662252 1663229 1663234) (-944 "RCFIELD.spad" 1659423 1659431 1662138 1662231) (-943 "RCFIELD.spad" 1656696 1656706 1659413 1659418) (-942 "RCAGG.spad" 1654599 1654609 1656676 1656691) (-941 "RCAGG.spad" 1652439 1652451 1654518 1654523) (-940 "RATRET.spad" 1651800 1651810 1652429 1652434) (-939 "RATFACT.spad" 1651493 1651504 1651790 1651795) (-938 "RANDSRC.spad" 1650813 1650821 1651483 1651488) (-937 "RADUTIL.spad" 1650568 1650576 1650803 1650808) (-936 "RADIX.spad" 1647361 1647374 1649038 1649131) (-935 "RADFF.spad" 1645778 1645814 1645896 1646052) (-934 "RADCAT.spad" 1645372 1645380 1645768 1645773) (-933 "RADCAT.spad" 1644964 1644974 1645362 1645367) (-932 "QUEUE.spad" 1644307 1644317 1644571 1644598) (-931 "QUAT.spad" 1642893 1642903 1643235 1643300) (-930 "QUATCT2.spad" 1642512 1642530 1642883 1642888) (-929 "QUATCAT.spad" 1640677 1640687 1642442 1642507) (-928 "QUATCAT.spad" 1638594 1638606 1640361 1640366) (-927 "QUAGG.spad" 1637408 1637418 1638550 1638589) (-926 "QFORM.spad" 1636871 1636885 1637398 1637403) (-925 "QFCAT.spad" 1635562 1635572 1636761 1636866) (-924 "QFCAT.spad" 1633859 1633871 1635060 1635065) (-923 "QFCAT2.spad" 1633550 1633566 1633849 1633854) (-922 "QEQUAT.spad" 1633107 1633115 1633540 1633545) (-921 "QCMPACK.spad" 1627854 1627873 1633097 1633102) (-920 "QALGSET.spad" 1623929 1623961 1627768 1627773) (-919 "QALGSET2.spad" 1621925 1621943 1623919 1623924) (-918 "PWFFINTB.spad" 1619235 1619256 1621915 1621920) (-917 "PUSHVAR.spad" 1618564 1618583 1619225 1619230) (-916 "PTRANFN.spad" 1614690 1614700 1618554 1618559) (-915 "PTPACK.spad" 1611778 1611788 1614680 1614685) (-914 "PTFUNC2.spad" 1611599 1611613 1611768 1611773) (-913 "PTCAT.spad" 1610681 1610691 1611555 1611594) (-912 "PSQFR.spad" 1609988 1610012 1610671 1610676) (-911 "PSEUDLIN.spad" 1608846 1608856 1609978 1609983) (-910 "PSETPK.spad" 1594279 1594295 1608724 1608729) (-909 "PSETCAT.spad" 1588187 1588210 1594247 1594274) (-908 "PSETCAT.spad" 1582081 1582106 1588143 1588148) (-907 "PSCURVE.spad" 1581064 1581072 1582071 1582076) (-906 "PSCAT.spad" 1579831 1579860 1580962 1581059) (-905 "PSCAT.spad" 1578688 1578719 1579821 1579826) (-904 "PRTITION.spad" 1577531 1577539 1578678 1578683) (-903 "PRS.spad" 1567093 1567110 1577487 1577492) (-902 "PRQAGG.spad" 1566512 1566522 1567049 1567088) (-901 "PROPLOG.spad" 1565915 1565923 1566502 1566507) (-900 "PROPFRML.spad" 1563779 1563790 1565851 1565856) (-899 "PROPERTY.spad" 1563273 1563281 1563769 1563774) (-898 "PRODUCT.spad" 1560953 1560965 1561239 1561294) (-897 "PR.spad" 1559342 1559354 1560047 1560174) (-896 "PRINT.spad" 1559094 1559102 1559332 1559337) (-895 "PRIMES.spad" 1557345 1557355 1559084 1559089) (-894 "PRIMELT.spad" 1555326 1555340 1557335 1557340) (-893 "PRIMCAT.spad" 1554949 1554957 1555316 1555321) (-892 "PRIMARR.spad" 1553954 1553964 1554132 1554159) (-891 "PRIMARR2.spad" 1552677 1552689 1553944 1553949) (-890 "PREASSOC.spad" 1552049 1552061 1552667 1552672) (-889 "PPCURVE.spad" 1551186 1551194 1552039 1552044) (-888 "POLYROOT.spad" 1549958 1549980 1551142 1551147) (-887 "POLY.spad" 1547258 1547268 1547775 1547902) (-886 "POLYLIFT.spad" 1546519 1546542 1547248 1547253) (-885 "POLYCATQ.spad" 1544621 1544643 1546509 1546514) (-884 "POLYCAT.spad" 1538027 1538048 1544489 1544616) (-883 "POLYCAT.spad" 1530735 1530758 1537199 1537204) (-882 "POLY2UP.spad" 1530183 1530197 1530725 1530730) (-881 "POLY2.spad" 1529778 1529790 1530173 1530178) (-880 "POLUTIL.spad" 1528719 1528748 1529734 1529739) (-879 "POLTOPOL.spad" 1527467 1527482 1528709 1528714) (-878 "POINT.spad" 1526308 1526318 1526395 1526422) (-877 "PNTHEORY.spad" 1522974 1522982 1526298 1526303) (-876 "PMTOOLS.spad" 1521731 1521745 1522964 1522969) (-875 "PMSYM.spad" 1521276 1521286 1521721 1521726) (-874 "PMQFCAT.spad" 1520863 1520877 1521266 1521271) (-873 "PMPRED.spad" 1520332 1520346 1520853 1520858) (-872 "PMPREDFS.spad" 1519776 1519798 1520322 1520327) (-871 "PMPLCAT.spad" 1518846 1518864 1519708 1519713) (-870 "PMLSAGG.spad" 1518427 1518441 1518836 1518841) (-869 "PMKERNEL.spad" 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1416950) (-812 "PARPCURV.spad" 1416202 1416230 1416734 1416739) (-811 "PARPC2.spad" 1415991 1416007 1416192 1416197) (-810 "PAN2EXPR.spad" 1415403 1415411 1415981 1415986) (-809 "PALETTE.spad" 1414373 1414381 1415393 1415398) (-808 "PAIR.spad" 1413356 1413369 1413961 1413966) (-807 "PADICRC.spad" 1410689 1410707 1411864 1411957) (-806 "PADICRAT.spad" 1408707 1408719 1408928 1409021) (-805 "PADIC.spad" 1408402 1408414 1408633 1408702) (-804 "PADICCT.spad" 1406943 1406955 1408328 1408397) (-803 "PADEPAC.spad" 1405622 1405641 1406933 1406938) (-802 "PADE.spad" 1404362 1404378 1405612 1405617) (-801 "OWP.spad" 1403346 1403376 1404220 1404287) (-800 "OVAR.spad" 1403127 1403150 1403336 1403341) (-799 "OUT.spad" 1402211 1402219 1403117 1403122) (-798 "OUTFORM.spad" 1391625 1391633 1402201 1402206) (-797 "OSI.spad" 1391100 1391108 1391615 1391620) (-796 "OSGROUP.spad" 1391018 1391026 1391090 1391095) (-795 "ORTHPOL.spad" 1389479 1389489 1390935 1390940) (-794 "OREUP.spad" 1388839 1388867 1389161 1389200) (-793 "ORESUP.spad" 1388140 1388164 1388521 1388560) (-792 "OREPCTO.spad" 1385959 1385971 1388060 1388065) (-791 "OREPCAT.spad" 1380016 1380026 1385915 1385954) (-790 "OREPCAT.spad" 1373963 1373975 1379864 1379869) (-789 "ORDSET.spad" 1373129 1373137 1373953 1373958) (-788 "ORDSET.spad" 1372293 1372303 1373119 1373124) (-787 "ORDRING.spad" 1371683 1371691 1372273 1372288) (-786 "ORDRING.spad" 1371081 1371091 1371673 1371678) (-785 "ORDMON.spad" 1370936 1370944 1371071 1371076) (-784 "ORDFUNS.spad" 1370062 1370078 1370926 1370931) (-783 "ORDFIN.spad" 1369996 1370004 1370052 1370057) (-782 "ORDCOMP.spad" 1368464 1368474 1369546 1369575) (-781 "ORDCOMP2.spad" 1367749 1367761 1368454 1368459) (-780 "OPTPROB.spad" 1366329 1366337 1367739 1367744) (-779 "OPTPACK.spad" 1358714 1358722 1366319 1366324) (-778 "OPTCAT.spad" 1356389 1356397 1358704 1358709) (-777 "OPQUERY.spad" 1355938 1355946 1356379 1356384) (-776 "OP.spad" 1355680 1355690 1355760 1355827) (-775 "ONECOMP.spad" 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(-718 "NORMPK.spad" 1223805 1223824 1225893 1225898) (-717 "NORMMA.spad" 1223493 1223519 1223795 1223800) (-716 "NONE.spad" 1223234 1223242 1223483 1223488) (-715 "NONE1.spad" 1222910 1222920 1223224 1223229) (-714 "NODE1.spad" 1222379 1222395 1222900 1222905) (-713 "NNI.spad" 1221266 1221274 1222353 1222374) (-712 "NLINSOL.spad" 1219888 1219898 1221256 1221261) (-711 "NIPROB.spad" 1218371 1218379 1219878 1219883) (-710 "NFINTBAS.spad" 1215831 1215848 1218361 1218366) (-709 "NCODIV.spad" 1214029 1214045 1215821 1215826) (-708 "NCNTFRAC.spad" 1213671 1213685 1214019 1214024) (-707 "NCEP.spad" 1211831 1211845 1213661 1213666) (-706 "NASRING.spad" 1211427 1211435 1211821 1211826) (-705 "NASRING.spad" 1211021 1211031 1211417 1211422) (-704 "NARNG.spad" 1210365 1210373 1211011 1211016) (-703 "NARNG.spad" 1209707 1209717 1210355 1210360) (-702 "NAGSP.spad" 1208780 1208788 1209697 1209702) (-701 "NAGS.spad" 1198305 1198313 1208770 1208775) (-700 "NAGF07.spad" 1196698 1196706 1198295 1198300) (-699 "NAGF04.spad" 1190930 1190938 1196688 1196693) (-698 "NAGF02.spad" 1184739 1184747 1190920 1190925) (-697 "NAGF01.spad" 1180342 1180350 1184729 1184734) (-696 "NAGE04.spad" 1173802 1173810 1180332 1180337) (-695 "NAGE02.spad" 1164144 1164152 1173792 1173797) (-694 "NAGE01.spad" 1160028 1160036 1164134 1164139) (-693 "NAGD03.spad" 1157948 1157956 1160018 1160023) (-692 "NAGD02.spad" 1150479 1150487 1157938 1157943) (-691 "NAGD01.spad" 1144592 1144600 1150469 1150474) (-690 "NAGC06.spad" 1140379 1140387 1144582 1144587) (-689 "NAGC05.spad" 1138848 1138856 1140369 1140374) (-688 "NAGC02.spad" 1138103 1138111 1138838 1138843) (-687 "NAALG.spad" 1137638 1137648 1138071 1138098) (-686 "NAALG.spad" 1137193 1137205 1137628 1137633) (-685 "MULTSQFR.spad" 1134151 1134168 1137183 1137188) (-684 "MULTFACT.spad" 1133534 1133551 1134141 1134146) (-683 "MTSCAT.spad" 1131568 1131589 1133432 1133529) (-682 "MTHING.spad" 1131225 1131235 1131558 1131563) (-681 "MSYSCMD.spad" 1130659 1130667 1131215 1131220) (-680 "MSET.spad" 1128601 1128611 1130365 1130404) (-679 "MSETAGG.spad" 1128434 1128444 1128557 1128596) (-678 "MRING.spad" 1125405 1125417 1128142 1128209) (-677 "MRF2.spad" 1124973 1124987 1125395 1125400) (-676 "MRATFAC.spad" 1124519 1124536 1124963 1124968) (-675 "MPRFF.spad" 1122549 1122568 1124509 1124514) (-674 "MPOLY.spad" 1119987 1120002 1120346 1120473) (-673 "MPCPF.spad" 1119251 1119270 1119977 1119982) (-672 "MPC3.spad" 1119066 1119106 1119241 1119246) (-671 "MPC2.spad" 1118708 1118741 1119056 1119061) (-670 "MONOTOOL.spad" 1117043 1117060 1118698 1118703) (-669 "MONOID.spad" 1116217 1116225 1117033 1117038) (-668 "MONOID.spad" 1115389 1115399 1116207 1116212) (-667 "MONOGEN.spad" 1114135 1114148 1115249 1115384) (-666 "MONOGEN.spad" 1112903 1112918 1114019 1114024) (-665 "MONADWU.spad" 1110917 1110925 1112893 1112898) (-664 "MONADWU.spad" 1108929 1108939 1110907 1110912) (-663 "MONAD.spad" 1108073 1108081 1108919 1108924) (-662 "MONAD.spad" 1107215 1107225 1108063 1108068) (-661 "MOEBIUS.spad" 1105901 1105915 1107195 1107210) (-660 "MODULE.spad" 1105771 1105781 1105869 1105896) (-659 "MODULE.spad" 1105661 1105673 1105761 1105766) (-658 "MODRING.spad" 1104992 1105031 1105641 1105656) (-657 "MODOP.spad" 1103651 1103663 1104814 1104881) (-656 "MODMONOM.spad" 1103183 1103201 1103641 1103646) (-655 "MODMON.spad" 1099888 1099904 1100664 1100817) (-654 "MODFIELD.spad" 1099246 1099285 1099790 1099883) (-653 "MMLFORM.spad" 1098106 1098114 1099236 1099241) (-652 "MMAP.spad" 1097846 1097880 1098096 1098101) (-651 "MLO.spad" 1096273 1096283 1097802 1097841) (-650 "MLIFT.spad" 1094845 1094862 1096263 1096268) (-649 "MKUCFUNC.spad" 1094378 1094396 1094835 1094840) (-648 "MKRECORD.spad" 1093980 1093993 1094368 1094373) (-647 "MKFUNC.spad" 1093361 1093371 1093970 1093975) (-646 "MKFLCFN.spad" 1092317 1092327 1093351 1093356) (-645 "MKCHSET.spad" 1092093 1092103 1092307 1092312) (-644 "MKBCFUNC.spad" 1091578 1091596 1092083 1092088) (-643 "MINT.spad" 1091017 1091025 1091480 1091573) (-642 "MHROWRED.spad" 1089518 1089528 1091007 1091012) (-641 "MFLOAT.spad" 1087963 1087971 1089408 1089513) (-640 "MFINFACT.spad" 1087363 1087385 1087953 1087958) (-639 "MESH.spad" 1085095 1085103 1087353 1087358) (-638 "MDDFACT.spad" 1083288 1083298 1085085 1085090) (-637 "MDAGG.spad" 1082563 1082573 1083256 1083283) (-636 "MCMPLX.spad" 1078543 1078551 1079157 1079358) (-635 "MCDEN.spad" 1077751 1077763 1078533 1078538) (-634 "MCALCFN.spad" 1074853 1074879 1077741 1077746) (-633 "MATSTOR.spad" 1072129 1072139 1074843 1074848) (-632 "MATRIX.spad" 1070833 1070843 1071317 1071344) (-631 "MATLIN.spad" 1068159 1068183 1070717 1070722) (-630 "MATCAT.spad" 1059732 1059754 1068115 1068154) (-629 "MATCAT.spad" 1051189 1051213 1059574 1059579) (-628 "MATCAT2.spad" 1050457 1050505 1051179 1051184) (-627 "MAPPKG3.spad" 1049356 1049370 1050447 1050452) (-626 "MAPPKG2.spad" 1048690 1048702 1049346 1049351) (-625 "MAPPKG1.spad" 1047508 1047518 1048680 1048685) (-624 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"LODOOPS.spad" 1022831 1022843 1023903 1023908) (-604 "LODO.spad" 1022217 1022233 1022513 1022552) (-603 "LODOF.spad" 1021261 1021278 1022174 1022179) (-602 "LODOCAT.spad" 1019919 1019929 1021217 1021256) (-601 "LODOCAT.spad" 1018575 1018587 1019875 1019880) (-600 "LODO2.spad" 1017850 1017862 1018257 1018296) (-599 "LODO1.spad" 1017252 1017262 1017532 1017571) (-598 "LODEEF.spad" 1016024 1016042 1017242 1017247) (-597 "LNAGG.spad" 1011816 1011826 1016004 1016019) (-596 "LNAGG.spad" 1007582 1007594 1011772 1011777) (-595 "LMOPS.spad" 1004318 1004335 1007572 1007577) (-594 "LMODULE.spad" 1003960 1003970 1004308 1004313) (-593 "LMDICT.spad" 1003243 1003253 1003511 1003538) (-592 "LIST.spad" 1000961 1000971 1002390 1002417) (-591 "LIST3.spad" 1000252 1000266 1000951 1000956) (-590 "LIST2.spad" 998892 998904 1000242 1000247) (-589 "LIST2MAP.spad" 995769 995781 998882 998887) (-588 "LINEXP.spad" 995201 995211 995749 995764) (-587 "LINDEP.spad" 993978 993990 995113 995118) (-586 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967391 967396) (-565 "KERNEL.spad" 965673 965683 966922 966927) (-564 "KERNEL2.spad" 965376 965388 965663 965668) (-563 "KDAGG.spad" 964467 964489 965344 965371) (-562 "KDAGG.spad" 963578 963602 964457 964462) (-561 "KAFILE.spad" 962541 962557 962776 962803) (-560 "JORDAN.spad" 960368 960380 961831 961976) (-559 "JAVACODE.spad" 960134 960142 960358 960363) (-558 "IXAGG.spad" 958247 958271 960114 960129) (-557 "IXAGG.spad" 956225 956251 958094 958099) (-556 "IVECTOR.spad" 954998 955013 955153 955180) (-555 "ITUPLE.spad" 954143 954153 954988 954993) (-554 "ITRIGMNP.spad" 952954 952973 954133 954138) (-553 "ITFUN3.spad" 952448 952462 952944 952949) (-552 "ITFUN2.spad" 952178 952190 952438 952443) (-551 "ITAYLOR.spad" 949970 949985 952014 952139) (-550 "ISUPS.spad" 942381 942396 948944 949041) (-549 "ISUMP.spad" 941878 941894 942371 942376) (-548 "ISTRING.spad" 940881 940894 941047 941074) (-547 "IRURPK.spad" 939594 939613 940871 940876) (-546 "IRSN.spad" 937554 937562 939584 939589) (-545 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901298 901439) (-524 "INTHERTR.spad" 900071 900088 900795 900800) (-523 "INTHERAL.spad" 899737 899761 900061 900066) (-522 "INTHEORY.spad" 896150 896158 899727 899732) (-521 "INTG0.spad" 889613 889631 896082 896087) (-520 "INTFTBL.spad" 883642 883650 889603 889608) (-519 "INTFACT.spad" 882701 882711 883632 883637) (-518 "INTEF.spad" 881016 881032 882691 882696) (-517 "INTDOM.spad" 879631 879639 880942 881011) (-516 "INTDOM.spad" 878308 878318 879621 879626) (-515 "INTCAT.spad" 876561 876571 878222 878303) (-514 "INTBIT.spad" 876064 876072 876551 876556) (-513 "INTALG.spad" 875246 875273 876054 876059) (-512 "INTAF.spad" 874738 874754 875236 875241) (-511 "INTABL.spad" 873256 873287 873419 873446) (-510 "INS.spad" 870652 870660 873158 873251) (-509 "INS.spad" 868134 868144 870642 870647) (-508 "INPSIGN.spad" 867568 867581 868124 868129) (-507 "INPRODPF.spad" 866634 866653 867558 867563) (-506 "INPRODFF.spad" 865692 865716 866624 866629) (-505 "INNMFACT.spad" 864663 864680 865682 865687) (-504 "INMODGCD.spad" 864147 864177 864653 864658) (-503 "INFSP.spad" 862432 862454 864137 864142) (-502 "INFPROD0.spad" 861482 861501 862422 862427) (-501 "INFORM.spad" 858750 858758 861472 861477) (-500 "INFORM1.spad" 858375 858385 858740 858745) (-499 "INFINITY.spad" 857927 857935 858365 858370) (-498 "INEP.spad" 856459 856481 857917 857922) (-497 "INDE.spad" 856188 856205 856449 856454) (-496 "INCRMAPS.spad" 855609 855619 856178 856183) (-495 "INBFF.spad" 851379 851390 855599 855604) (-494 "IMATRIX.spad" 850324 850350 850836 850863) (-493 "IMATQF.spad" 849418 849462 850280 850285) (-492 "IMATLIN.spad" 848023 848047 849374 849379) (-491 "ILIST.spad" 846679 846694 847206 847233) (-490 "IIARRAY2.spad" 846067 846105 846286 846313) (-489 "IFF.spad" 845477 845493 845748 845841) (-488 "IFARRAY.spad" 842964 842979 844660 844687) (-487 "IFAMON.spad" 842826 842843 842920 842925) (-486 "IEVALAB.spad" 842215 842227 842816 842821) (-485 "IEVALAB.spad" 841602 841616 842205 842210) (-484 "IDPO.spad" 841400 841412 841592 841597) (-483 "IDPOAMS.spad" 841156 841168 841390 841395) (-482 "IDPOAM.spad" 840876 840888 841146 841151) (-481 "IDPC.spad" 839810 839822 840866 840871) (-480 "IDPAM.spad" 839555 839567 839800 839805) (-479 "IDPAG.spad" 839302 839314 839545 839550) (-478 "IDECOMP.spad" 836539 836557 839292 839297) (-477 "IDEAL.spad" 831462 831501 836474 836479) (-476 "ICDEN.spad" 830613 830629 831452 831457) (-475 "ICARD.spad" 829802 829810 830603 830608) (-474 "IBPTOOLS.spad" 828395 828412 829792 829797) (-473 "IBITS.spad" 827594 827607 828031 828058) (-472 "IBATOOL.spad" 824469 824488 827584 827589) (-471 "IBACHIN.spad" 822956 822971 824459 824464) (-470 "IARRAY2.spad" 821944 821970 822563 822590) (-469 "IARRAY1.spad" 820989 821004 821127 821154) (-468 "IAN.spad" 819204 819212 820807 820900) (-467 "IALGFACT.spad" 818805 818838 819194 819199) (-466 "HYPCAT.spad" 818229 818237 818795 818800) (-465 "HYPCAT.spad" 817651 817661 818219 818224) (-464 "HOAGG.spad" 814909 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"GRAY.spad" 770410 770418 771941 771946) (-442 "GRALG.spad" 769457 769469 770400 770405) (-441 "GRALG.spad" 768502 768516 769447 769452) (-440 "GPOLSET.spad" 767956 767979 768184 768211) (-439 "GOSPER.spad" 767221 767239 767946 767951) (-438 "GMODPOL.spad" 766359 766386 767189 767216) (-437 "GHENSEL.spad" 765428 765442 766349 766354) (-436 "GENUPS.spad" 761529 761542 765418 765423) (-435 "GENUFACT.spad" 761106 761116 761519 761524) (-434 "GENPGCD.spad" 760690 760707 761096 761101) (-433 "GENMFACT.spad" 760142 760161 760680 760685) (-432 "GENEEZ.spad" 758081 758094 760132 760137) (-431 "GDMP.spad" 755102 755119 755878 756005) (-430 "GCNAALG.spad" 748997 749024 754896 754963) (-429 "GCDDOM.spad" 748169 748177 748923 748992) (-428 "GCDDOM.spad" 747403 747413 748159 748164) (-427 "GB.spad" 744921 744959 747359 747364) (-426 "GBINTERN.spad" 740941 740979 744911 744916) (-425 "GBF.spad" 736698 736736 740931 740936) (-424 "GBEUCLID.spad" 734572 734610 736688 736693) (-423 "GAUSSFAC.spad" 733869 733877 734562 734567) (-422 "GALUTIL.spad" 732191 732201 733825 733830) (-421 "GALPOLYU.spad" 730637 730650 732181 732186) (-420 "GALFACTU.spad" 728802 728821 730627 730632) (-419 "GALFACT.spad" 718935 718946 728792 728797) (-418 "FVFUN.spad" 715948 715956 718915 718930) (-417 "FVC.spad" 714990 714998 715928 715943) (-416 "FUNCTION.spad" 714839 714851 714980 714985) (-415 "FT.spad" 713051 713059 714829 714834) (-414 "FTEM.spad" 712214 712222 713041 713046) (-413 "FSUPFACT.spad" 711115 711134 712151 712156) (-412 "FST.spad" 709201 709209 711105 711110) (-411 "FSRED.spad" 708679 708695 709191 709196) (-410 "FSPRMELT.spad" 707503 707519 708636 708641) (-409 "FSPECF.spad" 705580 705596 707493 707498) (-408 "FS.spad" 699631 699641 705344 705575) (-407 "FS.spad" 693473 693485 699188 699193) (-406 "FSINT.spad" 693131 693147 693463 693468) (-405 "FSERIES.spad" 692318 692330 692951 693050) (-404 "FSCINT.spad" 691631 691647 692308 692313) (-403 "FSAGG.spad" 690736 690746 691575 691626) (-402 "FSAGG.spad" 689815 689827 690656 690661) (-401 "FSAGG2.spad" 688514 688530 689805 689810) (-400 "FS2UPS.spad" 682903 682937 688504 688509) (-399 "FS2.spad" 682548 682564 682893 682898) (-398 "FS2EXPXP.spad" 681671 681694 682538 682543) (-397 "FRUTIL.spad" 680613 680623 681661 681666) (-396 "FR.spad" 674310 674320 679640 679709) (-395 "FRNAALG.spad" 669397 669407 674252 674305) (-394 "FRNAALG.spad" 664496 664508 669353 669358) (-393 "FRNAAF2.spad" 663950 663968 664486 664491) (-392 "FRMOD.spad" 663345 663375 663882 663887) (-391 "FRIDEAL.spad" 662540 662561 663325 663340) (-390 "FRIDEAL2.spad" 662142 662174 662530 662535) (-389 "FRETRCT.spad" 661653 661663 662132 662137) (-388 "FRETRCT.spad" 661032 661044 661513 661518) (-387 "FRAMALG.spad" 659360 659373 660988 661027) (-386 "FRAMALG.spad" 657720 657735 659350 659355) (-385 "FRAC.spad" 654823 654833 655226 655399) (-384 "FRAC2.spad" 654426 654438 654813 654818) (-383 "FR2.spad" 653760 653772 654416 654421) (-382 "FPS.spad" 650569 650577 653650 653755) (-381 "FPS.spad" 647406 647416 650489 650494) (-380 "FPC.spad" 646448 646456 647308 647401) (-379 "FPC.spad" 645576 645586 646438 646443) (-378 "FPATMAB.spad" 645328 645338 645556 645571) (-377 "FPARFRAC.spad" 643801 643818 645318 645323) (-376 "FORTRAN.spad" 642307 642350 643791 643796) (-375 "FORT.spad" 641236 641244 642297 642302) (-374 "FORTFN.spad" 638396 638404 641216 641231) (-373 "FORTCAT.spad" 638070 638078 638376 638391) (-372 "FORMULA.spad" 635408 635416 638060 638065) (-371 "FORMULA1.spad" 634887 634897 635398 635403) (-370 "FORDER.spad" 634578 634602 634877 634882) (-369 "FOP.spad" 633779 633787 634568 634573) (-368 "FNLA.spad" 633203 633225 633747 633774) (-367 "FNCAT.spad" 631531 631539 633193 633198) (-366 "FNAME.spad" 631423 631431 631521 631526) (-365 "FMTC.spad" 631221 631229 631349 631418) (-364 "FMONOID.spad" 628276 628286 631177 631182) (-363 "FM.spad" 627971 627983 628210 628237) (-362 "FMFUN.spad" 624991 624999 627951 627966) (-361 "FMC.spad" 624033 624041 624971 624986) (-360 "FMCAT.spad" 621687 621705 624001 624028) (-359 "FM1.spad" 621044 621056 621621 621648) (-358 "FLOATRP.spad" 618765 618779 621034 621039) (-357 "FLOAT.spad" 611929 611937 618631 618760) (-356 "FLOATCP.spad" 609346 609360 611919 611924) (-355 "FLINEXP.spad" 609058 609068 609326 609341) (-354 "FLINEXP.spad" 608724 608736 608994 608999) (-353 "FLASORT.spad" 608044 608056 608714 608719) (-352 "FLALG.spad" 605690 605709 607970 608039) (-351 "FLAGG.spad" 602696 602706 605658 605685) (-350 "FLAGG.spad" 599615 599627 602579 602584) (-349 "FLAGG2.spad" 598296 598312 599605 599610) (-348 "FINRALG.spad" 596325 596338 598252 598291) (-347 "FINRALG.spad" 594280 594295 596209 596214) (-346 "FINITE.spad" 593432 593440 594270 594275) (-345 "FINAALG.spad" 582413 582423 593374 593427) (-344 "FINAALG.spad" 571406 571418 582369 582374) (-343 "FILE.spad" 570989 570999 571396 571401) (-342 "FILECAT.spad" 569507 569524 570979 570984) (-341 "FIELD.spad" 568913 568921 569409 569502) (-340 "FIELD.spad" 568405 568415 568903 568908) (-339 "FGROUP.spad" 567014 567024 568385 568400) (-338 "FGLMICPK.spad" 565801 565816 567004 567009) (-337 "FFX.spad" 565176 565191 565517 565610) (-336 "FFSLPE.spad" 564665 564686 565166 565171) (-335 "FFPOLY.spad" 555917 555928 564655 564660) (-334 "FFPOLY2.spad" 554977 554994 555907 555912) (-333 "FFP.spad" 554374 554394 554693 554786) (-332 "FF.spad" 553822 553838 554055 554148) (-331 "FFNBX.spad" 552334 552354 553538 553631) (-330 "FFNBP.spad" 550847 550864 552050 552143) (-329 "FFNB.spad" 549312 549333 550528 550621) (-328 "FFINTBAS.spad" 546726 546745 549302 549307) (-327 "FFIELDC.spad" 544301 544309 546628 546721) (-326 "FFIELDC.spad" 541962 541972 544291 544296) (-325 "FFHOM.spad" 540710 540727 541952 541957) (-324 "FFF.spad" 538145 538156 540700 540705) (-323 "FFCGX.spad" 536992 537012 537861 537954) (-322 "FFCGP.spad" 535881 535901 536708 536801) (-321 "FFCG.spad" 534673 534694 535562 535655) (-320 "FFCAT.spad" 527574 527596 534512 534668) (-319 "FFCAT.spad" 520554 520578 527494 527499) (-318 "FFCAT2.spad" 520299 520339 520544 520549) (-317 "FEXPR.spad" 512012 512058 520059 520098) (-316 "FEVALAB.spad" 511718 511728 512002 512007) (-315 "FEVALAB.spad" 511209 511221 511495 511500) (-314 "FDIV.spad" 510651 510675 511199 511204) (-313 "FDIVCAT.spad" 508693 508717 510641 510646) (-312 "FDIVCAT.spad" 506733 506759 508683 508688) (-311 "FDIV2.spad" 506387 506427 506723 506728) (-310 "FCPAK1.spad" 504940 504948 506377 506382) (-309 "FCOMP.spad" 504319 504329 504930 504935) (-308 "FC.spad" 494144 494152 504309 504314) (-307 "FAXF.spad" 487079 487093 494046 494139) (-306 "FAXF.spad" 480066 480082 487035 487040) (-305 "FARRAY.spad" 478212 478222 479249 479276) (-304 "FAMR.spad" 476332 476344 478110 478207) (-303 "FAMR.spad" 474436 474450 476216 476221) (-302 "FAMONOID.spad" 474086 474096 474390 474395) (-301 "FAMONC.spad" 472308 472320 474076 474081) (-300 "FAGROUP.spad" 471914 471924 472204 472231) (-299 "FACUTIL.spad" 470110 470127 471904 471909) (-298 "FACTFUNC.spad" 469286 469296 470100 470105) (-297 "EXPUPXS.spad" 466119 466142 467418 467567) (-296 "EXPRTUBE.spad" 463347 463355 466109 466114) (-295 "EXPRODE.spad" 460219 460235 463337 463342) (-294 "EXPR.spad" 455521 455531 456235 456638) (-293 "EXPR2UPS.spad" 451613 451626 455511 455516) (-292 "EXPR2.spad" 451316 451328 451603 451608) (-291 "EXPEXPAN.spad" 448257 448282 448891 448984) (-290 "EXIT.spad" 447928 447936 448247 448252) (-289 "EVALCYC.spad" 447386 447400 447918 447923) (-288 "EVALAB.spad" 446950 446960 447376 447381) (-287 "EVALAB.spad" 446512 446524 446940 446945) (-286 "EUCDOM.spad" 444054 444062 446438 446507) (-285 "EUCDOM.spad" 441658 441668 444044 444049) (-284 "ESTOOLS.spad" 433498 433506 441648 441653) (-283 "ESTOOLS2.spad" 433099 433113 433488 433493) (-282 "ESTOOLS1.spad" 432784 432795 433089 433094) (-281 "ES.spad" 425331 425339 432774 432779) (-280 "ES.spad" 417786 417796 425231 425236) 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388099) (-258 "EFUPXS.spad" 383811 383841 386991 386996) (-257 "EFULS.spad" 380647 380670 383767 383772) (-256 "EFSTRUC.spad" 378602 378618 380637 380642) (-255 "EF.spad" 373368 373384 378592 378597) (-254 "EAB.spad" 371644 371652 373358 373363) (-253 "E04UCFA.spad" 371180 371188 371634 371639) (-252 "E04NAFA.spad" 370757 370765 371170 371175) (-251 "E04MBFA.spad" 370337 370345 370747 370752) (-250 "E04JAFA.spad" 369873 369881 370327 370332) (-249 "E04GCFA.spad" 369409 369417 369863 369868) (-248 "E04FDFA.spad" 368945 368953 369399 369404) (-247 "E04DGFA.spad" 368481 368489 368935 368940) (-246 "E04AGNT.spad" 364323 364331 368471 368476) (-245 "DVARCAT.spad" 361008 361018 364313 364318) (-244 "DVARCAT.spad" 357691 357703 360998 361003) (-243 "DSMP.spad" 355125 355139 355430 355557) (-242 "DROPT.spad" 349070 349078 355115 355120) (-241 "DROPT1.spad" 348733 348743 349060 349065) (-240 "DROPT0.spad" 343560 343568 348723 348728) (-239 "DRAWPT.spad" 341715 341723 343550 343555) (-238 "DRAW.spad" 334315 334328 341705 341710) (-237 "DRAWHACK.spad" 333623 333633 334305 334310) (-236 "DRAWCX.spad" 331065 331073 333613 333618) (-235 "DRAWCURV.spad" 330602 330617 331055 331060) (-234 "DRAWCFUN.spad" 319774 319782 330592 330597) (-233 "DQAGG.spad" 317930 317940 319730 319769) (-232 "DPOLCAT.spad" 313271 313287 317798 317925) (-231 "DPOLCAT.spad" 308698 308716 313227 313232) (-230 "DPMO.spad" 302048 302064 302186 302482) (-229 "DPMM.spad" 295411 295429 295536 295832) (-228 "DOMAIN.spad" 294682 294690 295401 295406) (-227 "DMP.spad" 291907 291922 292479 292606) (-226 "DLP.spad" 291255 291265 291897 291902) (-225 "DLIST.spad" 289667 289677 290438 290465) (-224 "DLAGG.spad" 288068 288078 289647 289662) (-223 "DIVRING.spad" 287515 287523 288012 288063) (-222 "DIVRING.spad" 287006 287016 287505 287510) (-221 "DISPLAY.spad" 285186 285194 286996 287001) (-220 "DIRPROD.spad" 276091 276107 276731 276860) (-219 "DIRPROD2.spad" 274899 274917 276081 276086) (-218 "DIRPCAT.spad" 273831 273847 274753 274894) (-217 "DIRPCAT.spad" 272503 272521 273427 273432) (-216 "DIOSP.spad" 271328 271336 272493 272498) (-215 "DIOPS.spad" 270300 270310 271296 271323) (-214 "DIOPS.spad" 269258 269270 270256 270261) (-213 "DIFRING.spad" 268550 268558 269238 269253) (-212 "DIFRING.spad" 267850 267860 268540 268545) (-211 "DIFEXT.spad" 267009 267019 267830 267845) (-210 "DIFEXT.spad" 266085 266097 266908 266913) (-209 "DIAGG.spad" 265703 265713 266053 266080) (-208 "DIAGG.spad" 265341 265353 265693 265698) (-207 "DHMATRIX.spad" 263645 263655 264798 264825) (-206 "DFSFUN.spad" 257053 257061 263635 263640) (-205 "DFLOAT.spad" 253576 253584 256943 257048) (-204 "DFINTTLS.spad" 251785 251801 253566 253571) (-203 "DERHAM.spad" 249695 249727 251765 251780) (-202 "DEQUEUE.spad" 249013 249023 249302 249329) (-201 "DEGRED.spad" 248628 248642 249003 249008) (-200 "DEFINTRF.spad" 246153 246163 248618 248623) (-199 "DEFINTEF.spad" 244649 244665 246143 246148) (-198 "DECIMAL.spad" 242533 242541 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225116 225121) (-177 "D01ALFA.spad" 224176 224184 224626 224631) (-176 "D01AKFA.spad" 223702 223710 224166 224171) (-175 "D01AJFA.spad" 223225 223233 223692 223697) (-174 "D01AGNT.spad" 219284 219292 223215 223220) (-173 "CYCLOTOM.spad" 218790 218798 219274 219279) (-172 "CYCLES.spad" 215622 215630 218780 218785) (-171 "CVMP.spad" 215039 215049 215612 215617) (-170 "CTRIGMNP.spad" 213529 213545 215029 215034) (-169 "CTORCALL.spad" 213117 213125 213519 213524) (-168 "CSTTOOLS.spad" 212360 212373 213107 213112) (-167 "CRFP.spad" 206064 206077 212350 212355) (-166 "CRAPACK.spad" 205107 205117 206054 206059) (-165 "CPMATCH.spad" 204607 204622 205032 205037) (-164 "CPIMA.spad" 204312 204331 204597 204602) (-163 "COORDSYS.spad" 199205 199215 204302 204307) (-162 "CONTOUR.spad" 198607 198615 199195 199200) (-161 "CONTFRAC.spad" 194219 194229 198509 198602) (-160 "COMRING.spad" 193893 193901 194157 194214) (-159 "COMPPROP.spad" 193407 193415 193883 193888) (-158 "COMPLPAT.spad" 193174 193189 193397 193402) (-157 "COMPLEX.spad" 187207 187217 187451 187712) (-156 "COMPLEX2.spad" 186920 186932 187197 187202) (-155 "COMPFACT.spad" 186522 186536 186910 186915) (-154 "COMPCAT.spad" 184578 184588 186244 186517) (-153 "COMPCAT.spad" 182341 182353 184009 184014) (-152 "COMMUPC.spad" 182087 182105 182331 182336) (-151 "COMMONOP.spad" 181620 181628 182077 182082) (-150 "COMM.spad" 181429 181437 181610 181615) (-149 "COMBOPC.spad" 180334 180342 181419 181424) (-148 "COMBINAT.spad" 179079 179089 180324 180329) (-147 "COMBF.spad" 176447 176463 179069 179074) (-146 "COLOR.spad" 175284 175292 176437 176442) (-145 "CMPLXRT.spad" 174993 175010 175274 175279) (-144 "CLIP.spad" 171085 171093 174983 174988) (-143 "CLIF.spad" 169724 169740 171041 171080) (-142 "CLAGG.spad" 166199 166209 169704 169719) (-141 "CLAGG.spad" 162555 162567 166062 166067) (-140 "CINTSLPE.spad" 161880 161893 162545 162550) (-139 "CHVAR.spad" 159958 159980 161870 161875) (-138 "CHARZ.spad" 159873 159881 159938 159953) (-137 "CHARPOL.spad" 159381 159391 159863 159868) (-136 "CHARNZ.spad" 159134 159142 159361 159376) (-135 "CHAR.spad" 157002 157010 159124 159129) (-134 "CFCAT.spad" 156318 156326 156992 156997) (-133 "CDEN.spad" 155476 155490 156308 156313) (-132 "CCLASS.spad" 153625 153633 154887 154926) (-131 "CATEGORY.spad" 153404 153412 153615 153620) (-130 "CARTEN.spad" 148507 148531 153394 153399) (-129 "CARTEN2.spad" 147893 147920 148497 148502) (-128 "CARD.spad" 145182 145190 147867 147888) (-127 "CACHSET.spad" 144804 144812 145172 145177) (-126 "CABMON.spad" 144357 144365 144794 144799) (-125 "BYTE.spad" 143751 143759 144347 144352) (-124 "BYTEARY.spad" 142826 142834 142920 142947) (-123 "BTREE.spad" 141895 141905 142433 142460) (-122 "BTOURN.spad" 140898 140908 141502 141529) (-121 "BTCAT.spad" 140274 140284 140854 140893) (-120 "BTCAT.spad" 139682 139694 140264 140269) (-119 "BTAGG.spad" 138698 138706 139638 139677) (-118 "BTAGG.spad" 137746 137756 138688 138693) (-117 "BSTREE.spad" 136481 136491 137353 137380) (-116 "BRILL.spad" 134676 134687 136471 136476) (-115 "BRAGG.spad" 133590 133600 134656 134671) (-114 "BRAGG.spad" 132478 132490 133546 133551) (-113 "BPADICRT.spad" 130462 130474 130717 130810) (-112 "BPADIC.spad" 130126 130138 130388 130457) (-111 "BOUNDZRO.spad" 129782 129799 130116 130121) (-110 "BOP.spad" 125246 125254 129772 129777) (-109 "BOP1.spad" 122632 122642 125202 125207) (-108 "BOOLEAN.spad" 121895 121903 122622 122627) (-107 "BMODULE.spad" 121607 121619 121863 121890) (-106 "BITS.spad" 121026 121034 121243 121270) (-105 "BINFILE.spad" 120369 120377 121016 121021) (-104 "BINDING.spad" 119788 119796 120359 120364) (-103 "BINARY.spad" 117681 117689 118258 118351) (-102 "BGAGG.spad" 116866 116876 117649 117676) (-101 "BGAGG.spad" 116071 116083 116856 116861) (-100 "BFUNCT.spad" 115635 115643 116051 116066) (-99 "BEZOUT.spad" 114770 114796 115585 115590) (-98 "BBTREE.spad" 111590 111599 114377 114404) (-97 "BASTYPE.spad" 111263 111270 111580 111585) (-96 "BASTYPE.spad" 110934 110943 111253 111258) (-95 "BALFACT.spad" 110374 110386 110924 110929) (-94 "AUTOMOR.spad" 109821 109830 110354 110369) (-93 "ATTREG.spad" 106540 106547 109573 109816) (-92 "ATTRBUT.spad" 102563 102570 106520 106535) (-91 "ATRIG.spad" 102033 102040 102553 102558) (-90 "ATRIG.spad" 101501 101510 102023 102028) (-89 "ASTACK.spad" 100834 100843 101108 101135) (-88 "ASSOCEQ.spad" 99634 99645 100790 100795) (-87 "ASP9.spad" 98715 98728 99624 99629) (-86 "ASP8.spad" 97758 97771 98705 98710) (-85 "ASP80.spad" 97080 97093 97748 97753) (-84 "ASP7.spad" 96240 96253 97070 97075) (-83 "ASP78.spad" 95691 95704 96230 96235) (-82 "ASP77.spad" 95060 95073 95681 95686) (-81 "ASP74.spad" 94152 94165 95050 95055) (-80 "ASP73.spad" 93423 93436 94142 94147) (-79 "ASP6.spad" 92055 92068 93413 93418) (-78 "ASP55.spad" 90564 90577 92045 92050) (-77 "ASP50.spad" 88381 88394 90554 90559) (-76 "ASP4.spad" 87676 87689 88371 88376) (-75 "ASP49.spad" 86675 86688 87666 87671) (-74 "ASP42.spad" 85082 85121 86665 86670) (-73 "ASP41.spad" 83661 83700 85072 85077) (-72 "ASP35.spad" 82649 82662 83651 83656) (-71 "ASP34.spad" 81950 81963 82639 82644) (-70 "ASP33.spad" 81510 81523 81940 81945) (-69 "ASP31.spad" 80650 80663 81500 81505) (-68 "ASP30.spad" 79542 79555 80640 80645) (-67 "ASP29.spad" 79008 79021 79532 79537) (-66 "ASP28.spad" 70281 70294 78998 79003) (-65 "ASP27.spad" 69178 69191 70271 70276) (-64 "ASP24.spad" 68265 68278 69168 69173) (-63 "ASP20.spad" 67481 67494 68255 68260) (-62 "ASP1.spad" 66862 66875 67471 67476) (-61 "ASP19.spad" 61548 61561 66852 66857) (-60 "ASP12.spad" 60962 60975 61538 61543) (-59 "ASP10.spad" 60233 60246 60952 60957) (-58 "ARRAY2.spad" 59593 59602 59840 59867) (-57 "ARRAY1.spad" 58428 58437 58776 58803) (-56 "ARRAY12.spad" 57097 57108 58418 58423) (-55 "ARR2CAT.spad" 52747 52768 57053 57092) (-54 "ARR2CAT.spad" 48429 48452 52737 52742) (-53 "APPRULE.spad" 47673 47695 48419 48424) (-52 "APPLYORE.spad" 47288 47301 47663 47668) (-51 "ANY.spad" 45630 45637 47278 47283) (-50 "ANY1.spad" 44701 44710 45620 45625) (-49 "ANTISYM.spad" 43140 43156 44681 44696) (-48 "ANON.spad" 42837 42844 43130 43135) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2241676 2241681 2241686 2241691) (-2 NIL 2241656 2241661 2241666 2241671) (-1 NIL 2241636 2241641 2241646 2241651) (0 NIL 2241616 2241621 2241626 2241631) (-1200 "ZMOD.spad" 2241425 2241438 2241554 2241611) (-1199 "ZLINDEP.spad" 2240469 2240480 2241415 2241420) (-1198 "ZDSOLVE.spad" 2230318 2230340 2240459 2240464) (-1197 "YSTREAM.spad" 2229811 2229822 2230308 2230313) (-1196 "XRPOLY.spad" 2229031 2229051 2229667 2229736) (-1195 "XPR.spad" 2226760 2226773 2228749 2228848) (-1194 "XPOLY.spad" 2226315 2226326 2226616 2226685) (-1193 "XPOLYC.spad" 2225632 2225648 2226241 2226310) (-1192 "XPBWPOLY.spad" 2224069 2224089 2225412 2225481) (-1191 "XF.spad" 2222530 2222545 2223971 2224064) (-1190 "XF.spad" 2220971 2220988 2222414 2222419) (-1189 "XFALG.spad" 2217995 2218011 2220897 2220966) (-1188 "XEXPPKG.spad" 2217246 2217272 2217985 2217990) (-1187 "XDPOLY.spad" 2216860 2216876 2217102 2217171) (-1186 "XALG.spad" 2216458 2216469 2216816 2216855) (-1185 "WUTSET.spad" 2212297 2212314 2216104 2216131) (-1184 "WP.spad" 2211311 2211355 2212155 2212222) (-1183 "WFFINTBS.spad" 2208874 2208896 2211301 2211306) (-1182 "WEIER.spad" 2207088 2207099 2208864 2208869) (-1181 "VSPACE.spad" 2206761 2206772 2207056 2207083) (-1180 "VSPACE.spad" 2206454 2206467 2206751 2206756) (-1179 "VOID.spad" 2206044 2206053 2206444 2206449) (-1178 "VIEW.spad" 2203666 2203675 2206034 2206039) (-1177 "VIEWDEF.spad" 2198863 2198872 2203656 2203661) (-1176 "VIEW3D.spad" 2182698 2182707 2198853 2198858) (-1175 "VIEW2D.spad" 2170435 2170444 2182688 2182693) (-1174 "VECTOR.spad" 2169112 2169123 2169363 2169390) (-1173 "VECTOR2.spad" 2167739 2167752 2169102 2169107) (-1172 "VECTCAT.spad" 2165627 2165638 2167695 2167734) (-1171 "VECTCAT.spad" 2163336 2163349 2165406 2165411) (-1170 "VARIABLE.spad" 2163116 2163131 2163326 2163331) (-1169 "UTYPE.spad" 2162750 2162759 2163096 2163111) (-1168 "UTSODETL.spad" 2162043 2162067 2162706 2162711) (-1167 "UTSODE.spad" 2160231 2160251 2162033 2162038) (-1166 "UTS.spad" 2155020 2155048 2158698 2158795) (-1165 "UTSCAT.spad" 2152471 2152487 2154918 2155015) (-1164 "UTSCAT.spad" 2149566 2149584 2152015 2152020) (-1163 "UTS2.spad" 2149159 2149194 2149556 2149561) (-1162 "URAGG.spad" 2143781 2143792 2149139 2149154) (-1161 "URAGG.spad" 2138377 2138390 2143737 2143742) (-1160 "UPXSSING.spad" 2136023 2136049 2137461 2137594) (-1159 "UPXS.spad" 2133050 2133078 2134155 2134304) (-1158 "UPXSCONS.spad" 2130807 2130827 2131182 2131331) (-1157 "UPXSCCA.spad" 2129265 2129285 2130653 2130802) (-1156 "UPXSCCA.spad" 2127865 2127887 2129255 2129260) (-1155 "UPXSCAT.spad" 2126446 2126462 2127711 2127860) (-1154 "UPXS2.spad" 2125987 2126040 2126436 2126441) (-1153 "UPSQFREE.spad" 2124399 2124413 2125977 2125982) (-1152 "UPSCAT.spad" 2121992 2122016 2124297 2124394) (-1151 "UPSCAT.spad" 2119291 2119317 2121598 2121603) (-1150 "UPOLYC.spad" 2114269 2114280 2119133 2119286) (-1149 "UPOLYC.spad" 2109139 2109152 2114005 2114010) (-1148 "UPOLYC2.spad" 2108608 2108627 2109129 2109134) (-1147 "UP.spad" 2105653 2105668 2106161 2106314) (-1146 "UPMP.spad" 2104543 2104556 2105643 2105648) (-1145 "UPDIVP.spad" 2104106 2104120 2104533 2104538) (-1144 "UPDECOMP.spad" 2102343 2102357 2104096 2104101) (-1143 "UPCDEN.spad" 2101550 2101566 2102333 2102338) (-1142 "UP2.spad" 2100912 2100933 2101540 2101545) (-1141 "UNISEG.spad" 2100265 2100276 2100831 2100836) (-1140 "UNISEG2.spad" 2099758 2099771 2100221 2100226) (-1139 "UNIFACT.spad" 2098859 2098871 2099748 2099753) (-1138 "ULS.spad" 2089418 2089446 2090511 2090940) (-1137 "ULSCONS.spad" 2083461 2083481 2083833 2083982) (-1136 "ULSCCAT.spad" 2081058 2081078 2083281 2083456) (-1135 "ULSCCAT.spad" 2078789 2078811 2081014 2081019) (-1134 "ULSCAT.spad" 2077005 2077021 2078635 2078784) (-1133 "ULS2.spad" 2076517 2076570 2076995 2077000) (-1132 "UFD.spad" 2075582 2075591 2076443 2076512) (-1131 "UFD.spad" 2074709 2074720 2075572 2075577) (-1130 "UDVO.spad" 2073556 2073565 2074699 2074704) (-1129 "UDPO.spad" 2070983 2070994 2073512 2073517) (-1128 "TYPE.spad" 2070905 2070914 2070963 2070978) (-1127 "TWOFACT.spad" 2069555 2069570 2070895 2070900) (-1126 "TUPLE.spad" 2068941 2068952 2069454 2069459) (-1125 "TUBETOOL.spad" 2065778 2065787 2068931 2068936) (-1124 "TUBE.spad" 2064419 2064436 2065768 2065773) (-1123 "TS.spad" 2063008 2063024 2063984 2064081) (-1122 "TSETCAT.spad" 2050123 2050140 2062964 2063003) (-1121 "TSETCAT.spad" 2037236 2037255 2050079 2050084) (-1120 "TRMANIP.spad" 2031602 2031619 2036942 2036947) (-1119 "TRIMAT.spad" 2030561 2030586 2031592 2031597) (-1118 "TRIGMNIP.spad" 2029078 2029095 2030551 2030556) (-1117 "TRIGCAT.spad" 2028590 2028599 2029068 2029073) (-1116 "TRIGCAT.spad" 2028100 2028111 2028580 2028585) (-1115 "TREE.spad" 2026671 2026682 2027707 2027734) (-1114 "TRANFUN.spad" 2026502 2026511 2026661 2026666) (-1113 "TRANFUN.spad" 2026331 2026342 2026492 2026497) (-1112 "TOPSP.spad" 2026005 2026014 2026321 2026326) (-1111 "TOOLSIGN.spad" 2025668 2025679 2025995 2026000) (-1110 "TEXTFILE.spad" 2024225 2024234 2025658 2025663) (-1109 "TEX.spad" 2021242 2021251 2024215 2024220) (-1108 "TEX1.spad" 2020798 2020809 2021232 2021237) (-1107 "TEMUTL.spad" 2020353 2020362 2020788 2020793) (-1106 "TBCMPPK.spad" 2018446 2018469 2020343 2020348) (-1105 "TBAGG.spad" 2017470 2017493 2018414 2018441) (-1104 "TBAGG.spad" 2016514 2016539 2017460 2017465) (-1103 "TANEXP.spad" 2015890 2015901 2016504 2016509) (-1102 "TABLE.spad" 2014301 2014324 2014571 2014598) (-1101 "TABLEAU.spad" 2013782 2013793 2014291 2014296) (-1100 "TABLBUMP.spad" 2010565 2010576 2013772 2013777) (-1099 "SYSTEM.spad" 2009839 2009848 2010555 2010560) (-1098 "SYSSOLP.spad" 2007312 2007323 2009829 2009834) (-1097 "SYNTAX.spad" 2003504 2003513 2007302 2007307) (-1096 "SYMTAB.spad" 2001560 2001569 2003494 2003499) (-1095 "SYMS.spad" 1997545 1997554 2001550 2001555) (-1094 "SYMPOLY.spad" 1996555 1996566 1996637 1996764) (-1093 "SYMFUNC.spad" 1996030 1996041 1996545 1996550) (-1092 "SYMBOL.spad" 1993366 1993375 1996020 1996025) (-1091 "SWITCH.spad" 1990123 1990132 1993356 1993361) (-1090 "SUTS.spad" 1987022 1987050 1988590 1988687) (-1089 "SUPXS.spad" 1984036 1984064 1985154 1985303) (-1088 "SUP.spad" 1980808 1980819 1981589 1981742) (-1087 "SUPFRACF.spad" 1979913 1979931 1980798 1980803) (-1086 "SUP2.spad" 1979303 1979316 1979903 1979908) (-1085 "SUMRF.spad" 1978269 1978280 1979293 1979298) (-1084 "SUMFS.spad" 1977902 1977919 1978259 1978264) (-1083 "SULS.spad" 1968448 1968476 1969554 1969983) (-1082 "SUCH.spad" 1968128 1968143 1968438 1968443) (-1081 "SUBSPACE.spad" 1960135 1960150 1968118 1968123) (-1080 "SUBRESP.spad" 1959295 1959309 1960091 1960096) (-1079 "STTF.spad" 1955394 1955410 1959285 1959290) (-1078 "STTFNC.spad" 1951862 1951878 1955384 1955389) (-1077 "STTAYLOR.spad" 1944260 1944271 1951743 1951748) (-1076 "STRTBL.spad" 1942765 1942782 1942914 1942941) (-1075 "STRING.spad" 1942174 1942183 1942188 1942215) (-1074 "STRICAT.spad" 1941950 1941959 1942130 1942169) (-1073 "STREAM.spad" 1938718 1938729 1941475 1941490) (-1072 "STREAM3.spad" 1938263 1938278 1938708 1938713) (-1071 "STREAM2.spad" 1937331 1937344 1938253 1938258) (-1070 "STREAM1.spad" 1937035 1937046 1937321 1937326) (-1069 "STINPROD.spad" 1935941 1935957 1937025 1937030) (-1068 "STEP.spad" 1935142 1935151 1935931 1935936) (-1067 "STBL.spad" 1933668 1933696 1933835 1933850) (-1066 "STAGG.spad" 1932733 1932744 1933648 1933663) (-1065 "STAGG.spad" 1931806 1931819 1932723 1932728) (-1064 "STACK.spad" 1931157 1931168 1931413 1931440) (-1063 "SREGSET.spad" 1928861 1928878 1930803 1930830) (-1062 "SRDCMPK.spad" 1927406 1927426 1928851 1928856) (-1061 "SRAGG.spad" 1922491 1922500 1927362 1927401) (-1060 "SRAGG.spad" 1917608 1917619 1922481 1922486) (-1059 "SQMATRIX.spad" 1915234 1915252 1916142 1916229) (-1058 "SPLTREE.spad" 1909786 1909799 1914670 1914697) (-1057 "SPLNODE.spad" 1906374 1906387 1909776 1909781) (-1056 "SPFCAT.spad" 1905151 1905160 1906364 1906369) (-1055 "SPECOUT.spad" 1903701 1903710 1905141 1905146) (-1054 "spad-parser.spad" 1903166 1903175 1903691 1903696) (-1053 "SPACEC.spad" 1887179 1887190 1903156 1903161) (-1052 "SPACE3.spad" 1886955 1886966 1887169 1887174) (-1051 "SORTPAK.spad" 1886500 1886513 1886911 1886916) (-1050 "SOLVETRA.spad" 1884257 1884268 1886490 1886495) (-1049 "SOLVESER.spad" 1882777 1882788 1884247 1884252) (-1048 "SOLVERAD.spad" 1878787 1878798 1882767 1882772) (-1047 "SOLVEFOR.spad" 1877207 1877225 1878777 1878782) (-1046 "SNTSCAT.spad" 1876795 1876812 1877163 1877202) (-1045 "SMTS.spad" 1875055 1875081 1876360 1876457) (-1044 "SMP.spad" 1872497 1872517 1872887 1873014) (-1043 "SMITH.spad" 1871340 1871365 1872487 1872492) (-1042 "SMATCAT.spad" 1869438 1869468 1871272 1871335) (-1041 "SMATCAT.spad" 1867480 1867512 1869316 1869321) (-1040 "SKAGG.spad" 1866429 1866440 1867436 1867475) (-1039 "SINT.spad" 1864737 1864746 1866295 1866424) (-1038 "SIMPAN.spad" 1864465 1864474 1864727 1864732) (-1037 "SIG.spad" 1864062 1864071 1864455 1864460) (-1036 "SIGNRF.spad" 1863170 1863181 1864052 1864057) (-1035 "SIGNEF.spad" 1862439 1862456 1863160 1863165) (-1034 "SHP.spad" 1860357 1860372 1862395 1862400) (-1033 "SHDP.spad" 1851393 1851420 1851902 1852031) (-1032 "SGROUP.spad" 1850859 1850868 1851383 1851388) (-1031 "SGROUP.spad" 1850323 1850334 1850849 1850854) (-1030 "SGCF.spad" 1843204 1843213 1850313 1850318) (-1029 "SFRTCAT.spad" 1842120 1842137 1843160 1843199) (-1028 "SFRGCD.spad" 1841183 1841203 1842110 1842115) (-1027 "SFQCMPK.spad" 1835820 1835840 1841173 1841178) (-1026 "SFORT.spad" 1835255 1835269 1835810 1835815) (-1025 "SEXOF.spad" 1835098 1835138 1835245 1835250) (-1024 "SEX.spad" 1834990 1834999 1835088 1835093) (-1023 "SEXCAT.spad" 1832094 1832134 1834980 1834985) (-1022 "SET.spad" 1830394 1830405 1831515 1831554) (-1021 "SETMN.spad" 1828828 1828845 1830384 1830389) (-1020 "SETCAT.spad" 1828313 1828322 1828818 1828823) (-1019 "SETCAT.spad" 1827796 1827807 1828303 1828308) (-1018 "SETAGG.spad" 1824305 1824316 1827764 1827791) (-1017 "SETAGG.spad" 1820834 1820847 1824295 1824300) (-1016 "SEGXCAT.spad" 1819946 1819959 1820814 1820829) (-1015 "SEG.spad" 1819759 1819770 1819865 1819870) (-1014 "SEGCAT.spad" 1818578 1818589 1819739 1819754) (-1013 "SEGBIND.spad" 1817650 1817661 1818533 1818538) (-1012 "SEGBIND2.spad" 1817346 1817359 1817640 1817645) (-1011 "SEG2.spad" 1816771 1816784 1817302 1817307) (-1010 "SDVAR.spad" 1816047 1816058 1816761 1816766) (-1009 "SDPOL.spad" 1813440 1813451 1813731 1813858) (-1008 "SCPKG.spad" 1811519 1811530 1813430 1813435) (-1007 "SCOPE.spad" 1810664 1810673 1811509 1811514) (-1006 "SCACHE.spad" 1809346 1809357 1810654 1810659) (-1005 "SAOS.spad" 1809218 1809227 1809336 1809341) (-1004 "SAERFFC.spad" 1808931 1808951 1809208 1809213) (-1003 "SAE.spad" 1807109 1807125 1807720 1807855) (-1002 "SAEFACT.spad" 1806810 1806830 1807099 1807104) (-1001 "RURPK.spad" 1804451 1804467 1806800 1806805) (-1000 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"NAGF04.spad" 1190930 1190938 1196688 1196693) (-698 "NAGF02.spad" 1184739 1184747 1190920 1190925) (-697 "NAGF01.spad" 1180342 1180350 1184729 1184734) (-696 "NAGE04.spad" 1173802 1173810 1180332 1180337) (-695 "NAGE02.spad" 1164144 1164152 1173792 1173797) (-694 "NAGE01.spad" 1160028 1160036 1164134 1164139) (-693 "NAGD03.spad" 1157948 1157956 1160018 1160023) (-692 "NAGD02.spad" 1150479 1150487 1157938 1157943) (-691 "NAGD01.spad" 1144592 1144600 1150469 1150474) (-690 "NAGC06.spad" 1140379 1140387 1144582 1144587) (-689 "NAGC05.spad" 1138848 1138856 1140369 1140374) (-688 "NAGC02.spad" 1138103 1138111 1138838 1138843) (-687 "NAALG.spad" 1137638 1137648 1138071 1138098) (-686 "NAALG.spad" 1137193 1137205 1137628 1137633) (-685 "MULTSQFR.spad" 1134151 1134168 1137183 1137188) (-684 "MULTFACT.spad" 1133534 1133551 1134141 1134146) (-683 "MTSCAT.spad" 1131568 1131589 1133432 1133529) (-682 "MTHING.spad" 1131225 1131235 1131558 1131563) (-681 "MSYSCMD.spad" 1130659 1130667 1131215 1131220) (-680 "MSET.spad" 1128601 1128611 1130365 1130404) (-679 "MSETAGG.spad" 1128434 1128444 1128557 1128596) (-678 "MRING.spad" 1125405 1125417 1128142 1128209) (-677 "MRF2.spad" 1124973 1124987 1125395 1125400) (-676 "MRATFAC.spad" 1124519 1124536 1124963 1124968) (-675 "MPRFF.spad" 1122549 1122568 1124509 1124514) (-674 "MPOLY.spad" 1119987 1120002 1120346 1120473) (-673 "MPCPF.spad" 1119251 1119270 1119977 1119982) (-672 "MPC3.spad" 1119066 1119106 1119241 1119246) (-671 "MPC2.spad" 1118708 1118741 1119056 1119061) (-670 "MONOTOOL.spad" 1117043 1117060 1118698 1118703) (-669 "MONOID.spad" 1116217 1116225 1117033 1117038) (-668 "MONOID.spad" 1115389 1115399 1116207 1116212) (-667 "MONOGEN.spad" 1114135 1114148 1115249 1115384) (-666 "MONOGEN.spad" 1112903 1112918 1114019 1114024) (-665 "MONADWU.spad" 1110917 1110925 1112893 1112898) (-664 "MONADWU.spad" 1108929 1108939 1110907 1110912) (-663 "MONAD.spad" 1108073 1108081 1108919 1108924) (-662 "MONAD.spad" 1107215 1107225 1108063 1108068) (-661 "MOEBIUS.spad" 1105901 1105915 1107195 1107210) (-660 "MODULE.spad" 1105771 1105781 1105869 1105896) (-659 "MODULE.spad" 1105661 1105673 1105761 1105766) (-658 "MODRING.spad" 1104992 1105031 1105641 1105656) (-657 "MODOP.spad" 1103651 1103663 1104814 1104881) (-656 "MODMONOM.spad" 1103183 1103201 1103641 1103646) (-655 "MODMON.spad" 1099888 1099904 1100664 1100817) (-654 "MODFIELD.spad" 1099246 1099285 1099790 1099883) (-653 "MMLFORM.spad" 1098106 1098114 1099236 1099241) (-652 "MMAP.spad" 1097846 1097880 1098096 1098101) (-651 "MLO.spad" 1096273 1096283 1097802 1097841) (-650 "MLIFT.spad" 1094845 1094862 1096263 1096268) (-649 "MKUCFUNC.spad" 1094378 1094396 1094835 1094840) (-648 "MKRECORD.spad" 1093980 1093993 1094368 1094373) (-647 "MKFUNC.spad" 1093361 1093371 1093970 1093975) (-646 "MKFLCFN.spad" 1092317 1092327 1093351 1093356) (-645 "MKCHSET.spad" 1092093 1092103 1092307 1092312) (-644 "MKBCFUNC.spad" 1091578 1091596 1092083 1092088) (-643 "MINT.spad" 1091017 1091025 1091480 1091573) (-642 "MHROWRED.spad" 1089518 1089528 1091007 1091012) (-641 "MFLOAT.spad" 1087963 1087971 1089408 1089513) (-640 "MFINFACT.spad" 1087363 1087385 1087953 1087958) (-639 "MESH.spad" 1085095 1085103 1087353 1087358) (-638 "MDDFACT.spad" 1083288 1083298 1085085 1085090) (-637 "MDAGG.spad" 1082563 1082573 1083256 1083283) (-636 "MCMPLX.spad" 1078543 1078551 1079157 1079358) (-635 "MCDEN.spad" 1077751 1077763 1078533 1078538) (-634 "MCALCFN.spad" 1074853 1074879 1077741 1077746) (-633 "MATSTOR.spad" 1072129 1072139 1074843 1074848) (-632 "MATRIX.spad" 1070833 1070843 1071317 1071344) (-631 "MATLIN.spad" 1068159 1068183 1070717 1070722) (-630 "MATCAT.spad" 1059732 1059754 1068115 1068154) (-629 "MATCAT.spad" 1051189 1051213 1059574 1059579) (-628 "MATCAT2.spad" 1050457 1050505 1051179 1051184) (-627 "MAPPKG3.spad" 1049356 1049370 1050447 1050452) (-626 "MAPPKG2.spad" 1048690 1048702 1049346 1049351) (-625 "MAPPKG1.spad" 1047508 1047518 1048680 1048685) (-624 "MAPHACK3.spad" 1047316 1047330 1047498 1047503) (-623 "MAPHACK2.spad" 1047081 1047093 1047306 1047311) (-622 "MAPHACK1.spad" 1046711 1046721 1047071 1047076) (-621 "MAGMA.spad" 1044501 1044518 1046701 1046706) (-620 "M3D.spad" 1042199 1042209 1043881 1043886) (-619 "LZSTAGG.spad" 1039417 1039427 1042179 1042194) (-618 "LZSTAGG.spad" 1036643 1036655 1039407 1039412) (-617 "LWORD.spad" 1033348 1033365 1036633 1036638) (-616 "LSQM.spad" 1031576 1031590 1031974 1032025) (-615 "LSPP.spad" 1031109 1031126 1031566 1031571) (-614 "LSMP.spad" 1029949 1029977 1031099 1031104) (-613 "LSMP1.spad" 1027753 1027767 1029939 1029944) (-612 "LSAGG.spad" 1027410 1027420 1027709 1027748) (-611 "LSAGG.spad" 1027099 1027111 1027400 1027405) (-610 "LPOLY.spad" 1026053 1026072 1026955 1027024) (-609 "LPEFRAC.spad" 1025310 1025320 1026043 1026048) (-608 "LO.spad" 1024711 1024725 1025244 1025271) (-607 "LOGIC.spad" 1024313 1024321 1024701 1024706) (-606 "LOGIC.spad" 1023913 1023923 1024303 1024308) (-605 "LODOOPS.spad" 1022831 1022843 1023903 1023908) (-604 "LODO.spad" 1022217 1022233 1022513 1022552) (-603 "LODOF.spad" 1021261 1021278 1022174 1022179) (-602 "LODOCAT.spad" 1019919 1019929 1021217 1021256) (-601 "LODOCAT.spad" 1018575 1018587 1019875 1019880) (-600 "LODO2.spad" 1017850 1017862 1018257 1018296) (-599 "LODO1.spad" 1017252 1017262 1017532 1017571) (-598 "LODEEF.spad" 1016024 1016042 1017242 1017247) (-597 "LNAGG.spad" 1011816 1011826 1016004 1016019) (-596 "LNAGG.spad" 1007582 1007594 1011772 1011777) (-595 "LMOPS.spad" 1004318 1004335 1007572 1007577) (-594 "LMODULE.spad" 1003960 1003970 1004308 1004313) (-593 "LMDICT.spad" 1003243 1003253 1003511 1003538) (-592 "LIST.spad" 1000961 1000971 1002390 1002417) (-591 "LIST3.spad" 1000252 1000266 1000951 1000956) (-590 "LIST2.spad" 998892 998904 1000242 1000247) (-589 "LIST2MAP.spad" 995769 995781 998882 998887) (-588 "LINEXP.spad" 995201 995211 995749 995764) (-587 "LINDEP.spad" 993978 993990 995113 995118) (-586 "LIMITRF.spad" 991892 991902 993968 993973) (-585 "LIMITPS.spad" 990775 990788 991882 991887) (-584 "LIE.spad" 988789 988801 990065 990210) (-583 "LIECAT.spad" 988265 988275 988715 988784) (-582 "LIECAT.spad" 987769 987781 988221 988226) (-581 "LIB.spad" 985817 985825 986428 986443) (-580 "LGROBP.spad" 983170 983189 985807 985812) (-579 "LF.spad" 982089 982105 983160 983165) (-578 "LFCAT.spad" 981108 981116 982079 982084) (-577 "LEXTRIPK.spad" 976611 976626 981098 981103) (-576 "LEXP.spad" 974614 974641 976591 976606) (-575 "LEADCDET.spad" 972998 973015 974604 974609) (-574 "LAZM3PK.spad" 971702 971724 972988 972993) (-573 "LAUPOL.spad" 970393 970406 971297 971366) (-572 "LAPLACE.spad" 969966 969982 970383 970388) (-571 "LA.spad" 969406 969420 969888 969927) (-570 "LALG.spad" 969182 969192 969386 969401) (-569 "LALG.spad" 968966 968978 969172 969177) (-568 "KOVACIC.spad" 967679 967696 968956 968961) (-567 "KONVERT.spad" 967401 967411 967669 967674) (-566 "KOERCE.spad" 967138 967148 967391 967396) (-565 "KERNEL.spad" 965673 965683 966922 966927) (-564 "KERNEL2.spad" 965376 965388 965663 965668) (-563 "KDAGG.spad" 964467 964489 965344 965371) (-562 "KDAGG.spad" 963578 963602 964457 964462) (-561 "KAFILE.spad" 962541 962557 962776 962803) (-560 "JORDAN.spad" 960368 960380 961831 961976) (-559 "JAVACODE.spad" 960134 960142 960358 960363) (-558 "IXAGG.spad" 958247 958271 960114 960129) (-557 "IXAGG.spad" 956225 956251 958094 958099) (-556 "IVECTOR.spad" 954998 955013 955153 955180) (-555 "ITUPLE.spad" 954143 954153 954988 954993) (-554 "ITRIGMNP.spad" 952954 952973 954133 954138) (-553 "ITFUN3.spad" 952448 952462 952944 952949) (-552 "ITFUN2.spad" 952178 952190 952438 952443) (-551 "ITAYLOR.spad" 949970 949985 952014 952139) (-550 "ISUPS.spad" 942381 942396 948944 949041) (-549 "ISUMP.spad" 941878 941894 942371 942376) (-548 "ISTRING.spad" 940881 940894 941047 941074) (-547 "IRURPK.spad" 939594 939613 940871 940876) (-546 "IRSN.spad" 937554 937562 939584 939589) (-545 "IRRF2F.spad" 936029 936039 937510 937515) (-544 "IRREDFFX.spad" 935630 935641 936019 936024) (-543 "IROOT.spad" 933961 933971 935620 935625) (-542 "IR.spad" 931751 931765 933817 933844) (-541 "IR2.spad" 930771 930787 931741 931746) (-540 "IR2F.spad" 929971 929987 930761 930766) (-539 "IPRNTPK.spad" 929731 929739 929961 929966) (-538 "IPF.spad" 929296 929308 929536 929629) (-537 "IPADIC.spad" 929057 929083 929222 929291) (-536 "INVLAPLA.spad" 928702 928718 929047 929052) (-535 "INTTR.spad" 921948 921965 928692 928697) (-534 "INTTOOLS.spad" 919660 919676 921523 921528) (-533 "INTSLPE.spad" 918966 918974 919650 919655) (-532 "INTRVL.spad" 918532 918542 918880 918961) (-531 "INTRF.spad" 916896 916910 918522 918527) (-530 "INTRET.spad" 916328 916338 916886 916891) (-529 "INTRAT.spad" 915003 915020 916318 916323) (-528 "INTPM.spad" 913366 913382 914646 914651) (-527 "INTPAF.spad" 911134 911152 913298 913303) (-526 "INTPACK.spad" 901444 901452 911124 911129) (-525 "INT.spad" 900805 900813 901298 901439) (-524 "INTHERTR.spad" 900071 900088 900795 900800) (-523 "INTHERAL.spad" 899737 899761 900061 900066) (-522 "INTHEORY.spad" 896150 896158 899727 899732) (-521 "INTG0.spad" 889613 889631 896082 896087) (-520 "INTFTBL.spad" 883642 883650 889603 889608) (-519 "INTFACT.spad" 882701 882711 883632 883637) (-518 "INTEF.spad" 881016 881032 882691 882696) (-517 "INTDOM.spad" 879631 879639 880942 881011) (-516 "INTDOM.spad" 878308 878318 879621 879626) (-515 "INTCAT.spad" 876561 876571 878222 878303) (-514 "INTBIT.spad" 876064 876072 876551 876556) (-513 "INTALG.spad" 875246 875273 876054 876059) (-512 "INTAF.spad" 874738 874754 875236 875241) (-511 "INTABL.spad" 873256 873287 873419 873446) (-510 "INS.spad" 870652 870660 873158 873251) (-509 "INS.spad" 868134 868144 870642 870647) (-508 "INPSIGN.spad" 867568 867581 868124 868129) (-507 "INPRODPF.spad" 866634 866653 867558 867563) (-506 "INPRODFF.spad" 865692 865716 866624 866629) (-505 "INNMFACT.spad" 864663 864680 865682 865687) (-504 "INMODGCD.spad" 864147 864177 864653 864658) (-503 "INFSP.spad" 862432 862454 864137 864142) (-502 "INFPROD0.spad" 861482 861501 862422 862427) (-501 "INFORM.spad" 858750 858758 861472 861477) (-500 "INFORM1.spad" 858375 858385 858740 858745) (-499 "INFINITY.spad" 857927 857935 858365 858370) (-498 "INEP.spad" 856459 856481 857917 857922) (-497 "INDE.spad" 856188 856205 856449 856454) (-496 "INCRMAPS.spad" 855609 855619 856178 856183) (-495 "INBFF.spad" 851379 851390 855599 855604) (-494 "IMATRIX.spad" 850324 850350 850836 850863) (-493 "IMATQF.spad" 849418 849462 850280 850285) (-492 "IMATLIN.spad" 848023 848047 849374 849379) (-491 "ILIST.spad" 846679 846694 847206 847233) (-490 "IIARRAY2.spad" 846067 846105 846286 846313) (-489 "IFF.spad" 845477 845493 845748 845841) (-488 "IFARRAY.spad" 842964 842979 844660 844687) (-487 "IFAMON.spad" 842826 842843 842920 842925) (-486 "IEVALAB.spad" 842215 842227 842816 842821) (-485 "IEVALAB.spad" 841602 841616 842205 842210) (-484 "IDPO.spad" 841400 841412 841592 841597) (-483 "IDPOAMS.spad" 841156 841168 841390 841395) (-482 "IDPOAM.spad" 840876 840888 841146 841151) (-481 "IDPC.spad" 839810 839822 840866 840871) (-480 "IDPAM.spad" 839555 839567 839800 839805) (-479 "IDPAG.spad" 839302 839314 839545 839550) (-478 "IDECOMP.spad" 836539 836557 839292 839297) (-477 "IDEAL.spad" 831462 831501 836474 836479) (-476 "ICDEN.spad" 830613 830629 831452 831457) (-475 "ICARD.spad" 829802 829810 830603 830608) (-474 "IBPTOOLS.spad" 828395 828412 829792 829797) (-473 "IBITS.spad" 827594 827607 828031 828058) (-472 "IBATOOL.spad" 824469 824488 827584 827589) (-471 "IBACHIN.spad" 822956 822971 824459 824464) (-470 "IARRAY2.spad" 821944 821970 822563 822590) (-469 "IARRAY1.spad" 820989 821004 821127 821154) (-468 "IAN.spad" 819204 819212 820807 820900) (-467 "IALGFACT.spad" 818805 818838 819194 819199) (-466 "HYPCAT.spad" 818229 818237 818795 818800) (-465 "HYPCAT.spad" 817651 817661 818219 818224) (-464 "HOAGG.spad" 814909 814919 817631 817646) (-463 "HOAGG.spad" 811952 811964 814676 814681) (-462 "HEXADEC.spad" 809824 809832 810422 810515) (-461 "HEUGCD.spad" 808839 808850 809814 809819) (-460 "HELLFDIV.spad" 808429 808453 808829 808834) (-459 "HEAP.spad" 807821 807831 808036 808063) (-458 "HDP.spad" 798989 799005 799366 799495) (-457 "HDMP.spad" 796168 796183 796786 796913) (-456 "HB.spad" 794405 794413 796158 796163) (-455 "HASHTBL.spad" 792875 792906 793086 793113) (-454 "HACKPI.spad" 792358 792366 792777 792870) (-453 "GTSET.spad" 791297 791313 792004 792031) (-452 "GSTBL.spad" 789816 789851 789990 790005) (-451 "GSERIES.spad" 786983 787010 787948 788097) (-450 "GROUP.spad" 786157 786165 786963 786978) (-449 "GROUP.spad" 785339 785349 786147 786152) (-448 "GROEBSOL.spad" 783827 783848 785329 785334) (-447 "GRMOD.spad" 782398 782410 783817 783822) (-446 "GRMOD.spad" 780967 780981 782388 782393) (-445 "GRIMAGE.spad" 773572 773580 780957 780962) (-444 "GRDEF.spad" 771951 771959 773562 773567) (-443 "GRAY.spad" 770410 770418 771941 771946) (-442 "GRALG.spad" 769457 769469 770400 770405) (-441 "GRALG.spad" 768502 768516 769447 769452) (-440 "GPOLSET.spad" 767956 767979 768184 768211) (-439 "GOSPER.spad" 767221 767239 767946 767951) (-438 "GMODPOL.spad" 766359 766386 767189 767216) (-437 "GHENSEL.spad" 765428 765442 766349 766354) (-436 "GENUPS.spad" 761529 761542 765418 765423) (-435 "GENUFACT.spad" 761106 761116 761519 761524) (-434 "GENPGCD.spad" 760690 760707 761096 761101) (-433 "GENMFACT.spad" 760142 760161 760680 760685) (-432 "GENEEZ.spad" 758081 758094 760132 760137) (-431 "GDMP.spad" 755102 755119 755878 756005) (-430 "GCNAALG.spad" 748997 749024 754896 754963) (-429 "GCDDOM.spad" 748169 748177 748923 748992) (-428 "GCDDOM.spad" 747403 747413 748159 748164) (-427 "GB.spad" 744921 744959 747359 747364) (-426 "GBINTERN.spad" 740941 740979 744911 744916) (-425 "GBF.spad" 736698 736736 740931 740936) (-424 "GBEUCLID.spad" 734572 734610 736688 736693) (-423 "GAUSSFAC.spad" 733869 733877 734562 734567) (-422 "GALUTIL.spad" 732191 732201 733825 733830) (-421 "GALPOLYU.spad" 730637 730650 732181 732186) (-420 "GALFACTU.spad" 728802 728821 730627 730632) (-419 "GALFACT.spad" 718935 718946 728792 728797) (-418 "FVFUN.spad" 715948 715956 718915 718930) (-417 "FVC.spad" 714990 714998 715928 715943) (-416 "FUNCTION.spad" 714839 714851 714980 714985) (-415 "FT.spad" 713051 713059 714829 714834) (-414 "FTEM.spad" 712214 712222 713041 713046) (-413 "FSUPFACT.spad" 711115 711134 712151 712156) (-412 "FST.spad" 709201 709209 711105 711110) (-411 "FSRED.spad" 708679 708695 709191 709196) (-410 "FSPRMELT.spad" 707503 707519 708636 708641) (-409 "FSPECF.spad" 705580 705596 707493 707498) (-408 "FS.spad" 699631 699641 705344 705575) (-407 "FS.spad" 693473 693485 699188 699193) (-406 "FSINT.spad" 693131 693147 693463 693468) (-405 "FSERIES.spad" 692318 692330 692951 693050) (-404 "FSCINT.spad" 691631 691647 692308 692313) (-403 "FSAGG.spad" 690736 690746 691575 691626) (-402 "FSAGG.spad" 689815 689827 690656 690661) (-401 "FSAGG2.spad" 688514 688530 689805 689810) (-400 "FS2UPS.spad" 682903 682937 688504 688509) (-399 "FS2.spad" 682548 682564 682893 682898) (-398 "FS2EXPXP.spad" 681671 681694 682538 682543) (-397 "FRUTIL.spad" 680613 680623 681661 681666) (-396 "FR.spad" 674310 674320 679640 679709) (-395 "FRNAALG.spad" 669397 669407 674252 674305) (-394 "FRNAALG.spad" 664496 664508 669353 669358) (-393 "FRNAAF2.spad" 663950 663968 664486 664491) (-392 "FRMOD.spad" 663345 663375 663882 663887) (-391 "FRIDEAL.spad" 662540 662561 663325 663340) (-390 "FRIDEAL2.spad" 662142 662174 662530 662535) (-389 "FRETRCT.spad" 661653 661663 662132 662137) (-388 "FRETRCT.spad" 661032 661044 661513 661518) (-387 "FRAMALG.spad" 659360 659373 660988 661027) (-386 "FRAMALG.spad" 657720 657735 659350 659355) (-385 "FRAC.spad" 654823 654833 655226 655399) (-384 "FRAC2.spad" 654426 654438 654813 654818) (-383 "FR2.spad" 653760 653772 654416 654421) (-382 "FPS.spad" 650569 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"FFCAT.spad" 527574 527596 534512 534668) (-319 "FFCAT.spad" 520554 520578 527494 527499) (-318 "FFCAT2.spad" 520299 520339 520544 520549) (-317 "FEXPR.spad" 512012 512058 520059 520098) (-316 "FEVALAB.spad" 511718 511728 512002 512007) (-315 "FEVALAB.spad" 511209 511221 511495 511500) (-314 "FDIV.spad" 510651 510675 511199 511204) (-313 "FDIVCAT.spad" 508693 508717 510641 510646) (-312 "FDIVCAT.spad" 506733 506759 508683 508688) (-311 "FDIV2.spad" 506387 506427 506723 506728) (-310 "FCPAK1.spad" 504940 504948 506377 506382) (-309 "FCOMP.spad" 504319 504329 504930 504935) (-308 "FC.spad" 494144 494152 504309 504314) (-307 "FAXF.spad" 487079 487093 494046 494139) (-306 "FAXF.spad" 480066 480082 487035 487040) (-305 "FARRAY.spad" 478212 478222 479249 479276) (-304 "FAMR.spad" 476332 476344 478110 478207) (-303 "FAMR.spad" 474436 474450 476216 476221) (-302 "FAMONOID.spad" 474086 474096 474390 474395) (-301 "FAMONC.spad" 472308 472320 474076 474081) (-300 "FAGROUP.spad" 471914 471924 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T) (($) -2067 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844)))) +((($) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((|#2|) -2067 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977)))) ((((-798)) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -189,25 +189,25 @@ ((((-798)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1|) . 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T)) (((|#1|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) -(((|#2|) . T) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3254 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-2067 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) @@ -218,11 +218,11 @@ (((|#2|) . T) (($) . T) (((-385 (-525))) . T)) (-12 (|has| |#1| (-1020)) (|has| |#2| (-1020))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . 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T)) -(((|#3| |#3|) -3254 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977))) (($ $) |has| |#3| (-160))) -(((|#4| |#4|) -3254 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977))) (($ $) |has| |#4| (-160))) +(((|#3| |#3|) -2067 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977))) (($ $) |has| |#3| (-160))) +(((|#4| |#4|) -2067 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977))) (($ $) |has| |#4| (-160))) (((|#1|) . T)) (((|#2|) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525))))) @@ -231,21 +231,21 @@ ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501))) (((-827 (-357))) |has| |#1| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#1| (-567 (-827 (-525))))) ((((-798)) . 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T) (((-205)) . T) (((-357)) . T) (((-827 (-357))) . T)) ((((-798)) . T)) -(-3254 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) +(-2067 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) (((|#1|) |has| |#1| (-160))) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-798)) . T)) @@ -256,15 +256,15 @@ (|has| |#1| (-789)) (|has| |#1| (-1020)) (((|#1|) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) ((((-125)) . 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T)) (((|#1| (-904)) . T)) (((#0=(-805 |#1|) $) |has| #0# (-265 #0# #0#))) @@ -273,7 +273,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1068)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) (|has| (-1160 |#1| |#2| |#3| |#4|) (-136)) (|has| (-1160 |#1| |#2| |#3| |#4|) (-138)) (|has| |#1| (-136)) @@ -290,20 +290,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-977))) ((((-798)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) #0#) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) #0#) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))))) (((|#1|) . 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T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -2067 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -3254 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-798)) . T)) ((((-798)) . T)) (|has| (-1159 |#2| |#3| |#4|) (-138)) @@ -314,16 +314,16 @@ ((((-798)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3254 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) +(-2067 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) (((|#1|) . T)) ((((-525) |#1|) . 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T)) ((((-525) (-125)) . T)) ((((-798)) . T)) @@ -660,22 +660,22 @@ (|has| |#1| (-1020)) (((|#2|) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525))))) -(((|#4|) -3254 (|has| |#4| (-160)) (|has| |#4| (-341)))) -(((|#3|) -3254 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#4|) -2067 (|has| |#4| (-160)) (|has| |#4| (-341)))) +(((|#3|) -2067 (|has| |#3| (-160)) (|has| |#3| (-341)))) ((((-798)) . T)) (((|#1|) . T)) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-844))) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-844))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-844))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) ((($ $) . T) ((#0=(-1092) $) |has| |#1| (-213)) ((#0# |#1|) |has| |#1| (-213)) ((#1=(-760 (-1092)) |#1|) . T) ((#1# $) . 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T)) (|has| (-385 |#2|) (-138)) (|has| (-385 |#2|) (-136)) @@ -688,22 +688,22 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-798)) . T)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-366) (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +((((-366) (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#2| (-1068)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (((|#1|) . T)) ((((-366) (-1075)) . T)) (|has| |#1| (-517)) ((((-112 |#1|)) . T)) ((((-125)) . T)) ((((-525) |#1|) . T)) -(-3254 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-2067 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T)) ((((-798)) . T)) ((((-761 |#1|)) . T)) @@ -716,7 +716,7 @@ (((|#1|) |has| |#1| (-160))) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -(-3254 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-2067 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#2|) |has| |#2| (-288 |#2|))) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -726,7 +726,7 @@ (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((($) . T) (((-525)) . T) (((-385 (-525))) . T)) (|has| |#2| (-346)) -(-3254 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-2067 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) @@ -737,9 +737,9 @@ ((((-1090 |#1| |#2| |#3|) $) -12 (|has| (-1090 |#1| |#2| |#3|) (-265 (-1090 |#1| |#2| |#3|) (-1090 |#1| |#2| |#3|))) (|has| |#1| (-341))) (($ $) . T)) ((((-798)) . T)) ((((-798)) . T)) -((($) . T) (((-385 (-525))) -3254 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -2067 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((($ $) . T)) ((($ $) . T)) ((((-798)) . T)) @@ -749,12 +749,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-385 (-525))) . 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T) (((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) (|has| |#1| (-770)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) (|has| |#1| (-1020)) @@ -819,8 +819,8 @@ (((|#3|) |has| |#3| (-1020))) (|has| |#3| (-346)) (((|#1|) . T) (((-798)) . T)) -((((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3254 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1166 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3254 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1166 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -2067 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((((-798)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) @@ -830,30 +830,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (((-525)) . 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T)) -(-3254 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-2067 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) (|has| $ (-138)) (|has| $ (-138)) (|has| |#1| (-1020)) ((((-798)) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) ((($ $) |has| |#1| (-265 $ $)) ((|#1| $) |has| |#1| (-265 |#1| |#1|))) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) ((((-1092)) . T)) (|has| |#1| (-517)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) @@ -864,7 +864,7 @@ (|has| |#1| (-138)) (|has| |#1| (-136)) (|has| |#4| (-787)) -(((|#2| (-220 (-3522 |#1|) (-713)) (-800 |#1|)) . T)) +(((|#2| (-220 (-2827 |#1|) (-713)) (-800 |#1|)) . T)) (|has| |#3| (-787)) (((|#1| (-497 |#3|) |#3|) . T)) (|has| |#1| (-138)) @@ -878,21 +878,21 @@ (|has| |#1| (-136)) ((((-385 (-525))) |has| |#2| (-341)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3254 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-2067 (|has| |#1| (-327)) (|has| |#1| (-346))) ((((-1059 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-160)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-213)) (|has| |#2| (-977))) -(((|#2|) . T) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) -(-3254 (|has| |#3| (-735)) (|has| |#3| (-787))) -(-3254 (|has| |#3| (-735)) (|has| |#3| (-787))) +(((|#2|) . T) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) +(-2067 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-2067 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-798)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-641)) . T)) -(-3254 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) (|has| |#1| (-517)) (((|#1|) . T)) (((|#1|) . T)) @@ -914,10 +914,10 @@ (((|#1| (-385 (-525))) . T)) (((|#3|) . T) (((-565 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((#0=(-1090 |#1| |#2| |#3|) #0#) -12 (|has| (-1090 |#1| |#2| |#3|) (-288 (-1090 |#1| |#2| |#3|))) (|has| |#1| (-341))) (((-1092) #0#) -12 (|has| (-1090 |#1| |#2| |#3|) (-486 (-1092) (-1090 |#1| |#2| |#3|))) (|has| |#1| (-341)))) @@ -925,8 +925,8 @@ ((((-798)) . T)) ((((-798)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))))) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) |has| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (-288 (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))))) +(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) |has| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (-288 (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))))) ((((-798)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -937,10 +937,10 @@ ((($ $) . T) ((#0=(-800 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-346)) @@ -1021,31 +1021,31 @@ (|has| |#1| (-346)) ((((-1092) $) |has| |#1| (-486 (-1092) $)) (($ $) |has| |#1| (-288 $)) ((|#1| |#1|) |has| |#1| (-288 |#1|)) (((-1092) |#1|) |has| |#1| (-486 (-1092) |#1|))) ((((-1092)) |has| |#1| (-835 (-1092)))) -(-3254 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) +(-2067 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) ((((-366) (-1039)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-366) |#1|) . T)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1020)) ((((-798)) . T)) ((((-798)) . T)) ((((-845 |#1|)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3254 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -2067 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-805 |#1|)) |has| #0# (-288 #0#))) (((|#1| |#2|) . T)) -(-3254 (|has| |#2| (-735)) (|has| |#2| (-787))) -(-3254 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-2067 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-2067 (|has| |#2| (-735)) (|has| |#2| (-787))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) (((|#1|) . T)) (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) -(-3254 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (|has| |#1| (-1114)) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((((-385 (-525))) . T) (($) . T)) @@ -1056,8 +1056,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (|has| |#1| (-341)) ((((-525)) . T) (((-385 (-525))) . T) (($) . T)) -((($ $) . T) ((#0=(-385 (-525)) #0#) -3254 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((($ $) . T) ((#0=(-385 (-525)) #0#) -2067 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -1072,14 +1072,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-787)) (|has| |#1| (-787)) -((($) . T) (((-385 (-525))) -3254 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) -(-3254 (|has| |#1| (-160)) (|has| |#1| (-517))) -(((#0=(-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) #0#) |has| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (-288 (-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))))) +((($) . T) (((-385 (-525))) -2067 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +(-2067 (|has| |#1| (-160)) (|has| |#1| (-517))) +(((#0=(-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) #0#) |has| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (-288 (-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))))) ((($) . T)) (|has| |#2| (-789)) ((($) . T)) (((|#2|) |has| |#2| (-1020))) -((((-798)) -3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1174 |#2|)) . T)) +((((-798)) -2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1174 |#2|)) . T)) (|has| |#1| (-789)) (|has| |#1| (-789)) ((((-1075) (-51)) . T)) @@ -1087,10 +1087,10 @@ ((((-798)) . T)) ((((-525)) |has| #0=(-385 |#2|) (-588 (-525))) ((#0#) . T)) ((((-525) (-135)) . T)) -((((-525) (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T) ((|#1| |#2|) . T)) ((((-385 (-525))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-798)) . T)) ((((-845 |#1|)) . T)) (|has| |#1| (-341)) @@ -1115,31 +1115,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-160))) -((((-525) (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#3|) . 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T)) (|has| |#2| (-787)) (-12 (|has| |#2| (-213)) (|has| |#2| (-977))) (|has| |#1| (-517)) (|has| |#1| (-1068)) ((((-1075) |#1|) . T)) -(-3254 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(((#0=(-385 (-525)) #0#) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) +(-2067 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(((#0=(-385 (-525)) #0#) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-525))) (((-525)) |has| |#1| (-968 (-525))) (((-1092)) |has| |#1| (-968 (-1092))) ((|#1|) . T)) ((((-525) |#2|) . T)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) ((((-525)) |has| |#1| (-821 (-525))) (((-357)) |has| |#1| (-821 (-357)))) -((((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) +((((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) (((|#1|) . T)) ((((-592 |#4|)) . T) (((-798)) . T)) ((((-501)) |has| |#4| (-567 (-501)))) @@ -1152,17 +1152,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1092)) |has| (-385 |#2|) (-835 (-1092)))) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) #0#) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) #0#) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-798)) -3254 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-566 (-798))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) (((-1174 |#3|)) . T)) +((((-798)) -2067 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-566 (-798))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) (((-1174 |#3|)) . T)) ((((-525) |#2|) . T)) -(-3254 (|has| |#1| (-789)) (|has| |#1| (-1020))) -(((|#2| |#2|) -3254 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($ $) |has| |#2| (-160))) +(-2067 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(((|#2| |#2|) -2067 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($ $) |has| |#2| (-160))) ((((-798)) . T)) ((((-798)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T) ((|#2|) . T)) ((((-798)) . T)) ((((-798)) . T)) ((((-1075) (-1092) (-525) (-205) (-798)) . T)) @@ -1197,8 +1197,8 @@ (|has| |#1| (-37 (-385 (-525)))) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -(((|#2|) -3254 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($) |has| |#2| (-160))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +(((|#2|) -2067 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-977))) (($) |has| |#2| (-160))) (|has| $ (-138)) ((((-385 |#2|)) . T)) ((((-385 (-525))) |has| #0=(-385 |#2|) (-968 (-385 (-525)))) (((-525)) |has| #0# (-968 (-525))) ((#0#) . T)) @@ -1209,11 +1209,11 @@ (((|#3|) |has| |#3| (-160))) (|has| |#1| (-138)) (|has| |#1| (-136)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) @@ -1244,7 +1244,7 @@ ((((-931 |#1|)) . T) ((|#1|) . T)) ((((-798)) . T)) ((((-798)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-385 (-525))) . T) (((-385 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1088 |#1|)) . T)) ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) @@ -1252,9 +1252,9 @@ (|has| |#1| (-789)) (((|#2|) . T)) ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) ((((-525) |#2|) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#2|) . T)) ((((-525) |#3|) . T)) (((|#2|) . T)) @@ -1269,7 +1269,7 @@ (((|#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1020)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) #0#) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) #0#) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-341)) (((|#2|) . T) (((-525)) |has| |#2| (-968 (-525))) (((-385 (-525))) |has| |#2| (-968 (-385 (-525))))) @@ -1299,19 +1299,19 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| |#2|) . T)) ((((-525) (-135)) . T)) -(((#0=(-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) #0#) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) -((($) -3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +(((#0=(-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) #0#) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) +((($) -2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#1| (-789)) (((|#2| (-713) (-1005)) . T)) (((|#1| |#2|) . T)) -(-3254 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-160)) (|has| |#1| (-517))) (|has| |#1| (-733)) (((|#1|) |has| |#1| (-160))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3254 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) -(-3254 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) +(-2067 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) +(-2067 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) (((|#4|) . T)) (|has| |#1| (-136)) ((((-1075) |#1|) . T)) @@ -1324,10 +1324,10 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#3|) . T)) ((((-1166 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3254 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-2067 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020))) (((-892 |#1|)) . T)) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020))) (((-892 |#1|)) . T)) (|has| |#1| (-787)) (|has| |#1| (-787)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) @@ -1340,8 +1340,8 @@ ((($) . T)) ((((-366) (-1075)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-798)) -3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1174 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3364 (-1075)) (|:| -4201 #0#))) . T)) +((((-798)) -2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-566 (-798))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((-1174 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1556 (-1075)) (|:| -3448 #0#))) . T)) (((|#1|) . T)) ((((-798)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) @@ -1349,7 +1349,7 @@ (|has| |#2| (-136)) (|has| |#2| (-138)) (|has| |#1| (-450)) -(-3254 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) +(-2067 (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) (|has| |#1| (-341)) ((((-798)) . T)) (|has| |#1| (-37 (-385 (-525)))) @@ -1358,8 +1358,8 @@ (|has| |#1| (-787)) (|has| |#1| (-787)) ((((-798)) . T)) -((((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3254 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1166 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3254 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1166 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -2067 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1092)) |has| |#1| (-835 (-1092)))) @@ -1367,7 +1367,7 @@ ((((-798)) . T)) ((((-798)) . T)) (|has| |#1| (-1020)) -(((|#2| (-458 (-3522 |#1|) (-713)) (-800 |#1|)) . T)) +(((|#2| (-458 (-2827 |#1|) (-713)) (-800 |#1|)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1| (-497 (-1092)) (-1092)) . T)) (((|#1|) . T)) @@ -1387,16 +1387,16 @@ (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) . T)) ((((-1090 |#1| |#2| |#3|)) |has| |#1| (-341))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-1092) (-51)) . T)) ((($ $) . T)) (((|#1| (-525)) . T)) ((((-845 |#1|)) . T)) -(((|#1|) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977))) (($) -3254 (|has| |#1| (-835 (-1092))) (|has| |#1| (-977)))) +(((|#1|) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977))) (($) -2067 (|has| |#1| (-835 (-1092))) (|has| |#1| (-977)))) (((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) |has| |#1| (-968 (-385 (-525))))) (|has| |#1| (-789)) (|has| |#1| (-789)) @@ -1411,13 +1411,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) (((|#1|) |has| |#1| (-160))) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) -(((|#3|) -3254 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -2067 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#2| (-789)) (|has| |#1| (-789)) -(-3254 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-844))) +(-2067 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-844))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-525) |#2|) . T)) -(((|#2|) -3254 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -2067 (|has| |#2| (-160)) (|has| |#2| (-341)))) (|has| |#1| (-327)) (((|#3| |#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1020)))) ((($) . T) (((-385 (-525))) . T)) @@ -1425,7 +1425,7 @@ (|has| |#1| (-762)) (|has| |#1| (-762)) (((|#1|) . T)) -(-3254 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-787)) (|has| |#1| (-787)) (|has| |#1| (-787)) @@ -1434,13 +1434,13 @@ ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-1092)) |has| |#1| (-835 (-1092))) (((-1005)) . T)) (((|#1|) . T)) (|has| |#1| (-787)) -(((#0=(-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) #0#) |has| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (-288 (-2 (|:| -3364 (-1075)) (|:| -4201 (-51)))))) +(((#0=(-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) #0#) |has| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (-288 (-2 (|:| -1556 (-1075)) (|:| -3448 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (|has| |#1| (-1020)) (((|#1|) . T)) @@ -1459,7 +1459,7 @@ (((|#1|) . T)) ((((-135)) . T)) (((|#2|) |has| |#2| (-160))) -(-3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((|#1|) . T)) (|has| |#1| (-136)) (|has| |#1| (-138)) @@ -1481,32 +1481,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) ((#0=(-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) #0#) |has| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (-288 (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))))) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-844))) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-844))) +(((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) ((#0=(-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) #0#) |has| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (-288 (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-844))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3254 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -2067 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#1| (-789)) (|has| |#1| (-517)) ((((-538 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3254 (-12 (|has| |#1| (-341)) (|has| |#2| (-762))) (-12 (|has| |#1| (-341)) (|has| |#2| (-789)))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (-12 (|has| |#1| (-341)) (|has| |#2| (-762))) (-12 (|has| |#1| (-341)) (|has| |#2| (-789)))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-845 |#1|)) . T)) (((|#1| (-469 |#1| |#3|) (-469 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-713)) . T)) ((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) |has| |#1| (-517))) -((((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3254 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1090 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3254 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1090 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -2067 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) . T)) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) . T)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) ((((-617 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1514,17 +1514,17 @@ ((((-798)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-798)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3254 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -2067 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) ((((-798)) . T)) ((((-798)) . T)) ((((-798)) . T)) (((|#2|) . 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T)) (|has| |#1| (-1114)) (|has| |#1| (-1114)) -(-3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (|has| |#1| (-1114)) (|has| |#1| (-1114)) (((|#3| |#3|) . T)) @@ -1537,43 +1537,43 @@ (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((((-1075) (-51)) . T)) (|has| |#1| (-1020)) -(-3254 (|has| |#2| (-762)) (|has| |#2| (-789))) +(-2067 (|has| |#2| (-762)) (|has| |#2| (-789))) (((|#1|) . T)) -((($) -3254 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3254 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . 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T)) (((|#1|) . T)) ((((-525)) . T)) ((((-108)) . T)) -(-3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-37 (-385 (-525)))) (((|#1| (-525)) . T)) ((($) . T)) @@ -1595,7 +1595,7 @@ (((|#1| (-1138 |#1| |#2| |#3|)) . T)) (((|#1| (-713)) . T)) (((|#1|) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-798)) . T)) (|has| |#1| (-1020)) ((((-1075) |#1|) . T)) @@ -1615,18 +1615,18 @@ (((|#1|) . T)) ((((-525)) . T)) ((((-798)) . T)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-798)) . T)) (((|#3|) . T)) -(-3254 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-2067 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((((-798)) . T)) ((((-1159 |#2| |#3| |#4|)) . T) (((-1160 |#1| |#2| |#3| |#4|)) . T)) ((((-798)) . T)) -((((-47)) -12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (((-565 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) -3254 (-12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (|has| |#1| (-968 (-385 (-525))))) (((-385 (-887 |#1|))) |has| |#1| (-517)) (((-887 |#1|)) |has| |#1| (-977)) (((-1092)) . T)) +((((-47)) -12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (((-565 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) -2067 (-12 (|has| |#1| (-517)) (|has| |#1| (-968 (-525)))) (|has| |#1| (-968 (-385 (-525))))) (((-385 (-887 |#1|))) |has| |#1| (-517)) (((-887 |#1|)) |has| |#1| (-977)) (((-1092)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-713)) . T)) -((($) -3254 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-288 |#1|))) ((((-1160 |#1| |#2| |#3| |#4|)) . T)) ((((-525)) |has| |#1| (-821 (-525))) (((-357)) |has| |#1| (-821 (-357)))) @@ -1634,14 +1634,14 @@ (|has| |#1| (-517)) (((|#1|) . T)) ((((-798)) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))))) (((|#1|) |has| |#1| (-160))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1020))) -(((|#2|) -3254 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -2067 (|has| |#2| (-160)) (|has| |#2| (-341)))) ((((-1159 |#2| |#3| |#4|)) . T)) ((((-108)) . T)) (|has| |#1| (-762)) @@ -1651,8 +1651,8 @@ (|has| |#1| (-787)) (|has| |#1| (-787)) (((|#1| (-525) (-1005)) . T)) -(-3254 (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +(-2067 (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (((|#1| (-385 (-525)) (-1005)) . T)) (((|#1| (-713) (-1005)) . T)) (|has| |#1| (-789)) @@ -1668,28 +1668,28 @@ (((|#1|) . T)) (|has| |#1| (-1020)) ((((-525)) -12 (|has| |#1| (-341)) (|has| |#2| (-588 (-525)))) ((|#2|) |has| |#1| (-341))) -(-3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((|#2|) |has| |#2| (-160))) (((|#1|) |has| |#1| (-160))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) ((((-798)) . T)) (|has| |#3| (-787)) ((((-798)) . T)) ((((-1159 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-798)) . T)) -(((|#1| |#1|) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) +(((|#1| |#1|) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) (((|#1|) . T)) ((((-525)) . T)) ((((-525)) . T)) -(((|#1|) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) +(((|#1|) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-977)))) (((|#2|) |has| |#2| (-341))) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-789)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) |has| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (-288 (-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))))) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-844))) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) |has| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (-288 (-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-844))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) ((((-798)) . T)) ((((-798)) . T)) @@ -1724,18 +1724,18 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (((|#1|) . T)) -(-3254 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-160)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-798)) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (|has| |#1| (-341)) (|has| |#1| (-341)) (|has| (-385 |#2|) (-213)) (|has| |#1| (-844)) (((|#2|) |has| |#2| (-977))) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))))) (|has| |#1| (-341)) (((|#1|) |has| |#1| (-160))) (((|#1| |#1|) . T)) @@ -1760,7 +1760,7 @@ (((|#1| (-385 (-525)) (-1005)) . T)) (((|#1| (-713) (-1005)) . T)) (((#0=(-385 |#2|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-525)) -3254 (|has| (-385 (-525)) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) . T)) +(((|#1|) . T) (((-525)) -2067 (|has| (-385 (-525)) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) . T)) (((|#1| (-556 |#1| |#3|) (-556 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) @@ -1779,24 +1779,24 @@ ((((-641)) . T)) (((|#2|) |has| |#2| (-160))) (|has| |#2| (-787)) -((((-108)) |has| |#1| (-1020)) (((-798)) -3254 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020)))) +((((-108)) |has| |#1| (-1020)) (((-798)) -2067 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 (-51)))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 (-51)))) . T)) ((((-798)) . T)) ((((-525) |#1|) . T)) ((((-641)) . T) (((-385 (-525))) . T) (((-525)) . T)) (((|#1| |#1|) |has| |#1| (-160))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))))) ((((-357)) . T)) ((((-641)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1|) |has| |#1| (-160))) ((((-385 (-887 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T)) (|has| |#2| (-789)) (((|#3|) |has| |#3| (-977))) @@ -1806,14 +1806,14 @@ (|has| |#1| (-789)) ((((-1092)) |has| |#2| (-835 (-1092)))) ((((-798)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-385 (-525))) . T) (($) . T)) (|has| |#1| (-450)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-341)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-977)) (|has| |#1| (-1032))) (|has| |#1| (-37 (-385 (-525)))) ((((-112 |#1|)) . T)) ((((-112 |#1|)) . T)) @@ -1834,11 +1834,11 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-789)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)))) ((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)))) ((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#2|) . T)) (((|#3|) . T)) ((((-112 |#1|)) . T)) @@ -1856,11 +1856,11 @@ ((((-501)) |has| |#1| (-567 (-501))) (((-827 (-525))) |has| |#1| (-567 (-827 (-525)))) (((-827 (-357))) |has| |#1| (-567 (-827 (-357)))) (((-357)) . #0=(|has| |#1| (-953))) (((-205)) . #0#)) (((|#1|) |has| |#1| (-341))) ((((-798)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((($ $) . T) (((-565 $) $) . T)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) ((($) . T) (((-1160 |#1| |#2| |#3| |#4|)) . T) (((-385 (-525))) . T)) -((($) -3254 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-517))) +((($) -2067 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-517))) (|has| |#1| (-341)) (|has| |#1| (-341)) (|has| |#1| (-341)) @@ -1871,11 +1871,11 @@ ((((-357)) . T)) (((|#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1020)))) ((((-798)) . T)) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-844))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-844))) (((|#1|) . T)) (|has| |#1| (-789)) (|has| |#1| (-789)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (|has| |#1| (-1020)) @@ -1884,13 +1884,13 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) ((((-525)) . T)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (((#0=(-1159 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525)))) (($) . T)) ((((-525)) . T)) (|has| |#1| (-341)) -(-3254 (-12 (|has| (-1166 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3254 (-12 (|has| (-1166 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-2067 (-12 (|has| (-1166 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-2067 (-12 (|has| (-1166 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) (|has| |#1| (-341)) (|has| |#1| (-136)) (|has| |#1| (-138)) @@ -1907,18 +1907,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) (((|#3|) |has| |#3| (-160))) -(-3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) ((((-525)) . T)) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-385 (-525))) . T) (($) . T) (((-385 |#1|)) . T) ((|#1|) . T)) ((((-798)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3254 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -2067 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) . T)) ((($) . T)) ((((-525) |#1|) . T)) ((((-1092)) |has| (-385 |#2|) (-835 (-1092)))) -(((|#1|) . T) (($) -3254 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) +(((|#1|) . T) (($) -2067 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) ((((-501)) |has| |#2| (-567 (-501)))) ((((-632 |#2|)) . T) (((-798)) . T)) (((|#1|) . T)) @@ -1926,8 +1926,8 @@ (((|#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) ((((-805 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3254 (|has| |#4| (-735)) (|has| |#4| (-787))) -(-3254 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-2067 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-2067 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-798)) . T)) ((((-798)) . T)) (((|#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) @@ -1943,17 +1943,17 @@ ((((-385 (-525))) . T) (($) . T)) ((((-385 (-525))) . T) (($) . T)) ((((-385 (-525))) . T) (($) . T)) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-1132))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-1132))) ((($) . T)) ((((-385 (-525))) |has| #0=(-385 |#2|) (-968 (-385 (-525)))) (((-525)) |has| #0# (-968 (-525))) ((#0#) . T)) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) (((|#1| (-713)) . T)) (|has| |#1| (-789)) (((|#1|) . T) (((-525)) |has| |#1| (-588 (-525)))) -((($) -3254 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3254 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -2067 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -2067 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-525)) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -3364 (-1075)) (|:| -4201 (-51)))) |has| (-2 (|:| -3364 (-1075)) (|:| -4201 (-51))) (-288 (-2 (|:| -3364 (-1075)) (|:| -4201 (-51)))))) +((((-2 (|:| -1556 (-1075)) (|:| -3448 (-51)))) |has| (-2 (|:| -1556 (-1075)) (|:| -3448 (-51))) (-288 (-2 (|:| -1556 (-1075)) (|:| -3448 (-51)))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (|has| |#1| (-787)) (|has| |#1| (-37 (-385 (-525)))) @@ -1978,24 +1978,24 @@ (((|#1| |#2|) . T)) ((((-135)) . T)) ((((-722 |#1| (-800 |#2|))) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (|has| |#1| (-1114)) (((|#1|) . T)) -(-3254 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) +(-2067 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-669)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977)) (|has| |#3| (-1020))) ((((-1092) |#1|) |has| |#1| (-486 (-1092) |#1|))) (((|#2|) . T)) -((($ $) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($ $) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-845 |#1|)) . T)) ((($) . T)) ((((-385 (-887 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-501)) |has| |#4| (-567 (-501)))) ((((-798)) . T) (((-592 |#4|)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-787)) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) |has| (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|)) (-288 (-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))))) +(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020))) (((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) |has| (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|)) (-288 (-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))))) (|has| |#1| (-1020)) (|has| |#1| (-341)) (|has| |#1| (-789)) @@ -2003,16 +2003,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-385 (-525))) . T)) -((($) -3254 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (|has| |#1| (-136)) (|has| |#1| (-138)) -(-3254 (-12 (|has| (-1090 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3254 (-12 (|has| (-1090 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-2067 (-12 (|has| (-1090 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-2067 (-12 (|has| (-1090 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-1166 |#1| |#2| |#3|)) |has| |#1| (-341))) (|has| |#1| (-787)) (((|#1| |#2|) . T)) @@ -2035,9 +2035,9 @@ ((((-798)) . T)) ((((-798)) . T)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-1092) |#1|) |has| |#1| (-486 (-1092) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) -(((|#1|) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)))) +(((|#1|) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)))) ((((-294 |#1|)) . T)) (((|#2|) |has| |#2| (-341))) (((|#2|) . T)) @@ -2058,13 +2058,13 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) ((($ $) . T)) -(-3254 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) +(-2067 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) (|has| |#1| (-517)) (((|#2|) . T)) ((((-525)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (((|#1|) . T)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) ((((-538 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2073,7 +2073,7 @@ ((($) . T)) (((|#1|) . T)) ((((-798)) . T)) -(((|#2|) |has| |#2| (-6 (-4260 "*")))) +(((|#2|) |has| |#2| (-6 (-4261 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2090,12 +2090,12 @@ (((|#1| |#2|) . T)) ((((-1092) |#1|) . T)) (((|#4|) . T)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-327))) ((((-1092) (-51)) . T)) ((((-1159 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-385 (-525))) |has| |#1| (-968 (-385 (-525)))) (((-525)) |has| |#1| (-968 (-525))) ((|#1|) . T)) ((((-798)) . T)) -(-3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) +(-2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-669)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977)) (|has| |#2| (-1020))) (((#0=(-1160 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-160)) ((#0=(-385 (-525)) #0#) |has| |#1| (-517)) (($ $) |has| |#1| (-517))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) @@ -2114,14 +2114,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((|#2| |#3|) . T)) -(-3254 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-2067 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) (((|#1| (-497 |#2|)) . T)) (((|#1| (-713)) . T)) (((|#1| (-497 (-1010 (-1092)))) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (|has| |#2| (-844)) -(-3254 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-2067 (|has| |#2| (-735)) (|has| |#2| (-787))) ((((-798)) . T)) ((($ $) . T) ((#0=(-1159 |#2| |#3| |#4|) #0#) . T) ((#1=(-385 (-525)) #1#) |has| #0# (-37 (-385 (-525))))) ((((-845 |#1|)) . T)) @@ -2130,13 +2130,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-341)) -(-3254 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (|has| |#1| (-341)) ((($) . T) ((#0=(-1159 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1090 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3254 (-12 (|has| |#1| (-286)) (|has| |#1| (-844))) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3254 (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) +(-2067 (-12 (|has| |#1| (-286)) (|has| |#1| (-844))) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-835 (-1092))) (|has| |#1| (-977))) ((((-525)) |has| |#1| (-588 (-525))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-798)) . T)) @@ -2168,27 +2168,27 @@ (((|#1|) |has| |#1| (-160))) ((((-798)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) -(((|#2|) -3254 (|has| |#2| (-6 (-4260 "*"))) (|has| |#2| (-160)))) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(((|#2|) -2067 (|has| |#2| (-6 (-4261 "*"))) (|has| |#2| (-160)))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#1| (-844)) (((|#2|) |has| |#2| (-160))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-1166 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-798)) . T)) ((((-798)) . T)) ((((-501)) . T) (((-525)) . T) (((-827 (-525))) . T) (((-357)) . T) (((-205)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 (-51)))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 (-51)))) . T)) (((|#1|) . T)) ((((-798)) . T)) (((|#1| |#2|) . T)) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) -(-3254 (|has| |#1| (-269)) (|has| |#1| (-341))) +(-2067 (|has| |#1| (-269)) (|has| |#1| (-341))) ((((-135)) . T)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) (|has| |#1| (-787)) @@ -2203,7 +2203,7 @@ ((((-385 (-525))) . T) (($) . T)) ((((-798)) . T)) ((((-798)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -2214,7 +2214,7 @@ (((|#1|) . T)) ((((-592 (-135))) . T) (((-1075)) . T)) ((((-798)) . T)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) ((((-1092) |#1|) |has| |#1| (-486 (-1092) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-789)) ((((-798)) . T)) @@ -2226,16 +2226,16 @@ ((((-798)) . T) (((-592 |#4|)) . T)) (((|#2|) . T)) ((((-845 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3254 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) -(-3254 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-2067 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) +(-2067 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((((-1092) (-51)) . T)) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3254 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#2|) . T)) @@ -2250,12 +2250,12 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (|has| |#1| (-762)) (((#0=(-845 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((((-385 |#2|)) . T)) (|has| |#1| (-787)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) ((#1=(-525) #1#) . T) (($ $) . T)) ((((-845 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) (((|#2|) |has| |#2| (-977)) (((-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-977)))) @@ -2265,25 +2265,25 @@ (|has| |#1| (-136)) (((|#2|) . T)) ((((-798)) . T)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3364 (-1092)) (|:| -4201 #0#))) . T)) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1556 (-1092)) (|:| -3448 #0#))) . T)) (|has| |#1| (-327)) ((((-525)) . T)) ((((-798)) . T)) (((#0=(-1160 |#1| |#2| |#3| |#4|) $) |has| #0# (-265 #0# #0#))) (|has| |#1| (-341)) (((#0=(-1005) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-327))) (((#0=(-385 (-525)) #0#) . T) ((#1=(-641) #1#) . T) (($ $) . T)) ((((-294 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-1020)) (((|#1|) . T)) -(((|#1|) -3254 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) -(((|#1|) -3254 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -2067 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -2067 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) (((|#2|) . T)) ((((-385 (-525))) . T) (((-641)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2302,7 +2302,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-525)) . T)) -(-3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) (((|#2|) . T) (((-525)) |has| |#2| (-588 (-525)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2339,7 +2339,7 @@ (|has| |#2| (-953)) ((($) . T)) (|has| |#1| (-844)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2347,24 +2347,24 @@ ((($) . T)) (|has| |#1| (-341)) ((((-845 |#1|)) . T)) -((($) -3254 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) -(-3254 (|has| |#1| (-346)) (|has| |#1| (-789))) +(-2067 (|has| |#1| (-346)) (|has| |#1| (-789))) (((|#1|) . T)) ((((-798)) . T)) ((((-1092)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-835 (-1092))))) ((((-385 |#2|) |#3|) . T)) ((($) . T) (((-385 (-525))) . T)) ((((-713) |#1|) . T)) -(((|#2| (-220 (-3522 |#1|) (-713))) . T)) +(((|#2| (-220 (-2827 |#1|) (-713))) . T)) (((|#1| (-497 |#3|)) . T)) ((((-385 (-525))) . T)) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((((-798)) . T)) -(((#0=(-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) #0#) |has| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (-288 (-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))))) +(((#0=(-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) #0#) |has| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (-288 (-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))))) (|has| |#1| (-844)) (|has| |#2| (-341)) -(-3254 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-798)) . T)) (((|#1|) . T)) @@ -2381,11 +2381,11 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3254 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) (-12 (|has| |#1| (-510)) (|has| |#1| (-770))) ((((-798)) . T)) -((((-1092)) -3254 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1092)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-835 (-1092)))))) +((((-1092)) -2067 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1092)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-835 (-1092)))))) (|has| |#1| (-341)) ((((-1092)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-835 (-1092))))) (|has| |#1| (-341)) @@ -2395,7 +2395,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-341))) (((|#2|) |has| |#1| (-341))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) @@ -2418,31 +2418,31 @@ (((|#2|) |has| |#1| (-341))) ((((-357)) -12 (|has| |#1| (-341)) (|has| |#2| (-821 (-357)))) (((-525)) -12 (|has| |#1| (-341)) (|has| |#2| (-821 (-525))))) (|has| |#1| (-341)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (|has| |#1| (-517)) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1020)))) (((|#3|) . T)) (((|#1|) . T)) -(-3254 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#2|) . T)) (((|#2|) . T)) -(-3254 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +(-2067 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-385 (-525)))) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-1075) |#1|) . T)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-538 |#1|)) . T)) ((($) . T)) @@ -2450,7 +2450,7 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-798)) . T)) ((($) . T)) @@ -2475,7 +2475,7 @@ (|has| |#1| (-733)) (|has| |#1| (-733)) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-110)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2496,7 +2496,7 @@ ((((-525)) . T)) ((((-798)) . T)) ((((-525)) . T)) -(-3254 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-2067 (|has| |#2| (-735)) (|has| |#2| (-787))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-798)) . T)) ((((-798)) . T)) @@ -2508,9 +2508,9 @@ (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) (|has| |#1| (-341)) (|has| |#1| (-341)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) -(-3254 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +(-2067 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-669)) (|has| |#1| (-835 (-1092))) (|has| |#1| (-977)) (|has| |#1| (-1032)) (|has| |#1| (-1020))) (|has| |#1| (-1068)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -2528,8 +2528,8 @@ (((|#1|) . T)) (|has| |#1| (-517)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-357)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2538,7 +2538,7 @@ (|has| |#1| (-517)) (|has| |#1| (-1020)) ((((-722 |#1| (-800 |#2|))) |has| (-722 |#1| (-800 |#2|)) (-288 (-722 |#1| (-800 |#2|))))) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-844)) @@ -2548,12 +2548,12 @@ (|has| |#1| (-213)) (((|#1| (-497 (-1010 (-1092)))) . T)) (|has| |#2| (-341)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 (-51)))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) ((((-798)) . T)) ((((-798)) . T)) -(-3254 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-2067 (|has| |#3| (-735)) (|has| |#3| (-787))) ((((-798)) . T)) ((((-798)) . T)) (((|#1|) . T)) @@ -2562,8 +2562,8 @@ ((((-525)) . T)) (((|#3|) . T)) ((((-798)) . T)) -(-3254 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3254 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) +(-2067 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-977))) (((#0=(-538 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (((|#1|) |has| |#1| (-160))) @@ -2571,12 +2571,12 @@ ((((-538 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) ((($) . T) (((-385 (-525))) . T)) ((($) . T) (((-385 (-525))) . T)) -(((|#2|) |has| |#2| (-6 (-4260 "*")))) +(((|#2|) |has| |#2| (-6 (-4261 "*")))) (((|#1|) . T)) (((|#1|) . T)) ((((-798)) |has| |#1| (-566 (-798)))) ((((-273 |#3|)) . T)) -(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3254 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -2067 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T)) @@ -2584,20 +2584,20 @@ (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) -((($ $) -3254 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($ $) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -2067 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T) (($) -3254 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T) (($) -2067 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844)))) (((|#2|) . T) ((|#6|) . T)) -((($ $) -3254 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($ $) -2067 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) ((((-798)) . T)) -((($) -3254 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((($) -3254 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-844)) (|has| |#1| (-844)) -((($) -3254 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) . T)) -((((-2 (|:| -3364 (-1075)) (|:| -4201 |#1|))) . T)) +((((-2 (|:| -1556 (-1075)) (|:| -3448 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2611,10 +2611,10 @@ (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020)))) (((#0=(-385 (-525)) #0#) . T)) ((((-385 (-525))) . T)) -(-3254 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) (((|#1|) . T)) (((|#1|) . T)) -(-3254 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-501)) . T)) ((((-798)) . T)) ((((-1092)) |has| |#2| (-835 (-1092))) (((-1005)) . T)) @@ -2629,12 +2629,12 @@ ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-1092)) |has| |#1| (-835 (-1092)))) ((((-845 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -((($) . T) (((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) -(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -3254 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((($) . T) (((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -2067 (|has| |#1| (-160)) (|has| |#1| (-517)))) ((($) . T) (((-385 (-525))) . T)) (((|#1|) . T) (((-385 (-525))) . T) (((-525)) . T) (($) . T)) (((|#2|) |has| |#2| (-977)) (((-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-977)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3254 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -2067 (|has| |#1| (-160)) (|has| |#1| (-517)))) (|has| |#1| (-517)) (((|#1|) |has| |#1| (-341))) ((((-525)) . T)) @@ -2653,8 +2653,8 @@ ((((-798)) . T)) (|has| |#2| (-762)) (|has| |#2| (-762)) -((((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-385 (-525))) -3254 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) +((((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-385 (-525))) -2067 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1|) . T) (((-525)) |has| |#1| (-968 (-525))) (((-385 (-525))) |has| |#1| (-968 (-385 (-525))))) ((((-525)) |has| |#1| (-821 (-525))) (((-357)) |has| |#1| (-821 (-357)))) @@ -2680,12 +2680,12 @@ (((|#2| (-713)) . T)) ((((-1092)) . T)) ((((-805 |#1|)) . T)) -(-3254 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977))) -(-3254 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-2067 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-735)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-2067 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((((-798)) . T)) (((|#1|) . T)) -(-3254 (|has| |#2| (-735)) (|has| |#2| (-787))) -(-3254 (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) +(-2067 (|has| |#2| (-735)) (|has| |#2| (-787))) +(-2067 (-12 (|has| |#1| (-735)) (|has| |#2| (-735))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) ((((-805 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-346)) @@ -2711,7 +2711,7 @@ (((|#1|) . T)) ((((-798)) . T)) (|has| |#2| (-844)) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) . T)) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525))))) ((((-798)) . T)) ((((-798)) . T)) @@ -2744,11 +2744,11 @@ ((((-385 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1020)) -(((|#2| (-458 (-3522 |#1|) (-713))) . T)) +(((|#2| (-458 (-2827 |#1|) (-713))) . T)) ((((-525) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-497 (-1092))) . T)) -(-3254 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-525)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2758,9 +2758,9 @@ ((($) . T) (((-385 (-525))) . T)) ((($) . T)) ((($) . T)) -(-3254 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-2067 (|has| |#1| (-789)) (|has| |#1| (-1020))) (((|#1|) . 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T)) @@ -2859,25 +2859,25 @@ (((|#1|) |has| |#2| (-395 |#1|))) (((|#1|) |has| |#2| (-395 |#1|))) ((((-845 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) ((((-798)) . T)) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) |has| (-2 (|:| -3364 (-1092)) (|:| -4201 (-51))) (-288 (-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))))) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) |has| (-2 (|:| -1556 (-1092)) (|:| -3448 (-51))) (-288 (-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) ((((-525) |#1|) . T)) ((((-525) |#1|) . T)) ((((-525) |#1|) . 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T)) -((($) -3254 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T)) ((($) . T)) -((($) -3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-844)) (|has| |#1| (-844)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-160))) ((((-641)) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (($) . T)) (((|#1| (-525)) . T)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-341)) (|has| |#1| (-341)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3254 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-160)) (|has| |#1| (-517))) (((|#1| (-525)) . T)) (((|#1| (-385 (-525))) . T)) (((|#1| (-713)) . T)) @@ -3029,16 +3029,16 @@ ((((-827 (-357))) . T) (((-827 (-525))) . T) (((-1092)) . T) (((-501)) . T)) (((|#1|) . T)) ((((-798)) . T)) -(-3254 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) -(-3254 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) +(-2067 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-735)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-735)) (|has| |#2| (-735)))) ((((-525)) . T)) ((((-525)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3254 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) +(-2067 (|has| |#2| (-160)) (|has| |#2| (-669)) (|has| |#2| (-787)) (|has| |#2| (-977))) ((((-1092)) -12 (|has| |#2| (-835 (-1092))) (|has| |#2| (-977)))) -(-3254 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-669)) (|has| |#2| (-669)))) +(-2067 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-669)) (|has| |#2| (-669)))) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-341)) @@ -3062,7 +3062,7 @@ ((((-1075) (-1092) (-525) (-205) (-798)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-3254 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-2067 (|has| |#1| (-327)) (|has| |#1| (-346))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-798)) . T)) @@ -3070,7 +3070,7 @@ ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) |has| |#2| (-1020)) (((-525)) -12 (|has| |#2| (-968 (-525))) (|has| |#2| (-1020))) (((-385 (-525))) -12 (|has| |#2| (-968 (-385 (-525)))) (|has| |#2| (-1020)))) ((((-501)) |has| |#1| (-567 (-501)))) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-789)) (|has| |#1| (-1020)))) ((($) . T) (((-385 (-525))) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) @@ -3079,14 +3079,14 @@ ((((-798)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-160))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3254 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-2067 (|has| |#1| (-21)) (|has| |#1| (-787))) (((|#2|) . T)) -(-3254 (|has| |#1| (-21)) (|has| |#1| (-787))) +(-2067 (|has| |#1| (-21)) (|has| |#1| (-787))) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (((|#1|) . T)) -((((-798)) -3254 (-12 (|has| |#1| (-566 (-798))) (|has| |#2| (-566 (-798)))) (-12 (|has| |#1| (-1020)) (|has| |#2| (-1020))))) +((((-798)) -2067 (-12 (|has| |#1| (-566 (-798))) (|has| |#2| (-566 (-798)))) (-12 (|has| |#1| (-1020)) (|has| |#2| (-1020))))) ((((-385 |#2|) |#3|) . T)) ((((-385 (-525))) . T) (($) . T)) (|has| |#1| (-37 (-385 (-525)))) @@ -3098,17 +3098,17 @@ (((|#1|) . T) (((-385 (-525))) . T) (((-525)) . T) (($) . T)) (((#0=(-525) #0#) . T)) ((($) . T) (((-385 (-525))) . T)) -(-3254 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) -(-3254 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) +(-2067 (|has| |#4| (-160)) (|has| |#4| (-669)) (|has| |#4| (-787)) (|has| |#4| (-977))) +(-2067 (|has| |#3| (-160)) (|has| |#3| (-669)) (|has| |#3| (-787)) (|has| |#3| (-977))) (|has| |#4| (-735)) -(-3254 (|has| |#4| (-735)) (|has| |#4| (-787))) +(-2067 (|has| |#4| (-735)) (|has| |#4| (-787))) (|has| |#4| (-787)) (|has| |#3| (-735)) -(-3254 (|has| |#3| (-735)) (|has| |#3| (-787))) +(-2067 (|has| |#3| (-735)) (|has| |#3| (-787))) (|has| |#3| (-787)) ((((-525)) . T)) (((|#2|) . T)) -((((-1092)) -3254 (-12 (|has| (-1090 |#1| |#2| |#3|) (-835 (-1092))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1092)))))) +((((-1092)) -2067 (-12 (|has| (-1090 |#1| |#2| |#3|) (-835 (-1092))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-835 (-1092)))))) ((((-1092)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-835 (-1092))))) ((((-1092)) -12 (|has| |#1| (-15 * (|#1| (-713) |#1|))) (|has| |#1| (-835 (-1092))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3123,11 +3123,11 @@ ((((-1090 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1057 |#1| |#2|)) . T)) ((((-1090 |#1| |#2| |#3|)) |has| |#1| (-341))) -(((|#2|) . T) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) . T)) ((($) . T)) (|has| |#1| (-953)) -(((|#2|) . T) (((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) ((((-798)) . T)) ((((-501)) |has| |#2| (-567 (-501))) (((-827 (-525))) |has| |#2| (-567 (-827 (-525)))) (((-827 (-357))) |has| |#2| (-567 (-827 (-357)))) (((-357)) . #0=(|has| |#2| (-953))) (((-205)) . #0#)) ((((-1092) (-51)) . T)) @@ -3139,15 +3139,15 @@ ((((-1090 |#1| |#2| |#3|)) . T)) ((((-1090 |#1| |#2| |#3|)) . T) (((-1083 |#1| |#2| |#3|)) . T)) ((((-798)) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-525) |#1|) . T)) ((((-1090 |#1| |#2| |#3|)) |has| |#1| (-341))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-341)) -(((|#3|) . T) ((|#2|) . T) (($) -3254 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-977))) ((|#4|) -3254 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977)))) -(((|#2|) . T) (($) -3254 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((|#3|) -3254 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977)))) +(((|#3|) . T) ((|#2|) . T) (($) -2067 (|has| |#4| (-160)) (|has| |#4| (-787)) (|has| |#4| (-977))) ((|#4|) -2067 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-977)))) +(((|#2|) . T) (($) -2067 (|has| |#3| (-160)) (|has| |#3| (-787)) (|has| |#3| (-977))) ((|#3|) -2067 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-977)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-341)) @@ -3159,7 +3159,7 @@ ((((-798)) . T)) ((((-798)) . T)) (((|#1|) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) ((((-125)) . T) (((-798)) . T)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -3167,30 +3167,30 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-341)) (|has| |#2| (-265 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) -(-3254 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-844))) +(-2067 (|has| |#1| (-789)) (|has| |#1| (-1020))) ((((-798)) . T)) ((((-798)) . T)) ((((-798)) . T)) (((|#1| (-497 |#2|)) . T)) -((((-2 (|:| -3364 (-1092)) (|:| -4201 (-51)))) . T)) +((((-2 (|:| -1556 (-1092)) (|:| -3448 (-51)))) . T)) (((|#1| (-525)) . T)) (((|#1| (-385 (-525))) . T)) (((|#1| (-713)) . T)) ((((-112 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) -(-3254 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) -(-3254 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) +(-2067 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-844))) +(-2067 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-844))) ((($) . T)) (((|#2| (-497 (-800 |#1|))) . T)) ((((-525) |#1|) . T)) (((|#2|) . T)) (((|#2| (-713)) . T)) -((((-798)) -3254 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) +((((-798)) -2067 (|has| |#1| (-566 (-798))) (|has| |#1| (-1020)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1075) |#1|) . T)) ((((-385 |#2|)) . T)) -((((-2 (|:| -3364 |#1|) (|:| -4201 |#2|))) . T)) +((((-2 (|:| -1556 |#1|) (|:| -3448 |#2|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) ((($) . T) ((|#2|) . T)) @@ -3198,12 +3198,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-265 |#2| |#2|))) (((|#1| (-592 |#1|)) |has| |#1| (-787))) -(-3254 (|has| |#1| (-213)) (|has| |#1| (-327))) -(-3254 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-213)) (|has| |#1| (-327))) +(-2067 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1020)) (((|#1|) . T)) ((((-385 (-525))) . T) (($) . T)) -((((-931 |#1|)) . T) ((|#1|) . T) (((-525)) -3254 (|has| (-931 |#1|) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) -3254 (|has| (-931 |#1|) (-968 (-385 (-525)))) (|has| |#1| (-968 (-385 (-525)))))) +((((-931 |#1|)) . T) ((|#1|) . T) (((-525)) -2067 (|has| (-931 |#1|) (-968 (-525))) (|has| |#1| (-968 (-525)))) (((-385 (-525))) -2067 (|has| (-931 |#1|) (-968 (-385 (-525)))) (|has| |#1| (-968 (-385 (-525)))))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1020)))) @@ -3214,9 +3214,9 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1057 |#1| |#2|) #0#) |has| (-1057 |#1| |#2|) (-288 (-1057 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) #0#) |has| (-2 (|:| -3364 |#1|) (|:| -4201 |#2|)) (-288 (-2 (|:| -3364 |#1|) (|:| -4201 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((#0=(-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) #0#) |has| (-2 (|:| -1556 |#1|) (|:| -3448 |#2|)) (-288 (-2 (|:| -1556 |#1|) (|:| -3448 |#2|))))) (((#0=(-112 |#1|)) |has| #0# (-288 #0#))) -(-3254 (|has| |#1| (-789)) (|has| |#1| (-1020))) +(-2067 (|has| |#1| (-789)) (|has| |#1| (-1020))) ((($ $) . T)) ((($ $) . T) ((#0=(-800 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-213)) ((|#2| |#1|) |has| |#1| (-213)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 59e1c30f..3fc88430 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3425075210) -(4261 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3427192336) +(4262 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -460,647 +460,645 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |position!| |integrate| |roughEqualIdeals?| - |complexEigenvalues| |zero?| |OMencodingBinary| |leftFactor| - |monomial?| |error| |f02agf| |colorFunction| |mdeg| |coerce| - |associative?| |pushuconst| |insertRoot!| |algebraicVariables| - |positive?| |cot2trig| |showClipRegion| |assert| |constant?| - |absolutelyIrreducible?| |normInvertible?| |preprocess| |construct| - |realRoots| |unrankImproperPartitions1| |exprToGenUPS| |maxint| - |hasTopPredicate?| |cothIfCan| |minColIndex| |simplifyExp| - |genericRightTrace| |UpTriBddDenomInv| |rootProduct| - |linearPolynomials| |factorials| |pmComplexintegrate| |frobenius| - |gcdPrimitive| |closedCurve| |csch2sinh| |controlPanel| - |dihedralGroup| |removeSquaresIfCan| |commutative?| |unexpand| - |ramified?| |findCycle| |iidprod| |d02bhf| |in?| |transcendent?| - |split| |closed?| |insert!| |startTable!| |cAcot| |semicolonSeparate| - |fortranReal| |exactQuotient!| |numerators| |lift| |f02bbf| |real?| - |normalizeAtInfinity| |normalElement| |orbits| |incrementKthElement| - |mirror| |forLoop| |setVariableOrder| |cotIfCan| |ode| |s18aef| - |leftDivide| |linearAssociatedOrder| |reduce| |power!| - |squareFreePart| |f07aef| |internalInfRittWu?| |supRittWu?| - |evenlambert| |startPolynomial| |reflect| |polyPart| |gcdprim| - |palgLODE| |pquo| |width| |lexico| |nor| |cyclotomic| |ScanRoman| - |cAsinh| |f02aaf| |characteristicPolynomial| |symbol?| |OMputObject| - |arguments| |returnTypeOf| |palginfieldint| |copy!| - |getMultiplicationTable| |leftTrace| |tubePoints| |getIdentifier| - |wronskianMatrix| |void| |nextLatticePermutation| |setchildren!| - |prepareDecompose| |collectQuasiMonic| |debug3D| |cot2tan| - |graphStates| |OMconnInDevice| |OMputError| |setRealSteps| - |modularGcdPrimitive| |cAcsch| |internalDecompose| |readable?| - |d01anf| |makeSUP| |linearlyDependentOverZ?| |isTimes| |localUnquote| - |cyclicSubmodule| |univcase| |printInfo!| |cRationalPower| |center| - |distdfact| |varselect| |d01aqf| |OMsupportsCD?| |makeUnit| - |overlabel| |variable?| |permutationRepresentation| - |indiceSubResultantEuclidean| |rewriteIdealWithQuasiMonicGenerators| - |pdf2ef| |ref| |probablyZeroDim?| |cycleSplit!| |binaryTree| |delete!| - |e02akf| |countRealRoots| |useEisensteinCriterion| |solveInField| - |movedPoints| |selectNonFiniteRoutines| |outputAsScript| |read!| - |legendreP| |btwFact| |groebnerIdeal| |optional| |stFunc1| - |powerAssociative?| |tubeRadiusDefault| |OMputEndObject| |reset| - |palgRDE| |clipSurface| |makeSeries| |choosemon| |f02aef| |d01alf| - |splitNodeOf!| |box| |OMputEndBind| |fglmIfCan| |augment| - |checkForZero| |s20adf| |complexExpand| |OMwrite| |nthExponent| - |separateFactors| |topPredicate| |primPartElseUnitCanonical| |unary?| - |completeHermite| |linearPart| |one?| |numberOfImproperPartitions| - |hostPlatform| |integers| |removeCosSq| |bitLength| |adaptive3D?| - |realZeros| |write| |nil| |OMopenFile| |back| |symmetricTensors| - |integral?| |factorset| |algintegrate| |binaryFunction| |edf2df| - |integralRepresents| |reorder| |saturate| |branchIfCan| |cycles| - |generalizedInverse| |fill!| |groebgen| |mainCoefficients| |domainOf| - |binaryTournament| |collectUnder| |airyBi| |outputGeneral| |simpson| - |tanh2trigh| |setelt| |ellipticCylindrical| |conditionsForIdempotents| - |save| |null?| |invmultisect| |nextPartition| |expPot| |f02akf| - |postfix| |smith| |nary?| |contractSolve| |oneDimensionalArray| |red| - |completeEval| |parametersOf| |csc| |squareFreePolynomial| - |curveColor| |heap| |cAcos| |reducedDiscriminant| |overlap| - |approximate| |exponential1| |RemainderList| |sparsityIF| |prologue| - |resize| |mapCoef| |rightLcm| |copy| - |zeroSetSplitIntoTriangularSystems| |integralAtInfinity?| |asin| - |complex| |infiniteProduct| |internalZeroSetSplit| |rightRemainder| - |getConstant| |inverseLaplace| |useSingleFactorBound?| |redPol| |qPot| - |palgint| |cCos| |nextColeman| |numberOfComputedEntries| |acos| - |graphState| |typeList| |enterPointData| |increase| |setMinPoints| - |hdmpToP| |list?| |minus!| |e01bgf| |complete| |sqfree| |autoCoerce| - |atan| |minPoints| |c06ecf| |univariatePolynomials| |monomRDE| - |reducedContinuedFraction| |coshIfCan| 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|hitherPlane| |conditionP| |expIfCan| - |quatern| |tanIfCan| |lazyIntegrate| |s13acf| |f01maf| |tanintegrate| - |ParCond| |exteriorDifferential| |rightAlternative?| |f02bjf| - |polarCoordinates| |simplifyLog| |eigenvalues| |quasiAlgebraicSet| - |bag| |rotatex| |constantIfCan| |genericLeftNorm| |belong?| |reduced?| - |associatorDependence| |dimensionsOf| |primintegrate| |npcoef| - |noLinearFactor?| |LyndonCoordinates| |complexEigenvectors| |f2df| - |linearlyDependent?| |s17acf| |radix| |approximants| |option| - |discriminant| |OMputInteger| |characteristicSet| |twist| |rk4qc| - |orbit| |iitanh| |lllip| |find| |exponentialOrder| |tracePowMod| - |constDsolve| |gcdcofact| |groebner| |scalarMatrix| |commutator| - |subResultantsChain| |shuffle| |infLex?| |reducedSystem| |prem| - |inHallBasis?| |bumptab| |indicialEquation| |move| |leftExtendedGcd| - |isPlus| |rootSplit| |expenseOfEvaluationIF| |member?| |showSummary| - |directSum| |diagonal?| |mapBivariate| |sinhIfCan| |s17dlf| |equation| - |lhs| |edf2fi| |setPoly| |s17agf| |OMunhandledSymbol| |optimize| - |semiResultantEuclideannaif| |radicalEigenvector| |stirling1| - |HermiteIntegrate| D |bipolarCylindrical| |extractBottom!| |rhs| - |noncommutativeJordanAlgebra?| |sumSquares| |symmetricRemainder| - |mathieu23| |bezoutDiscriminant| |showAttributes| |f04arf| |prefix| - |shrinkable| |imagI| |e02aef| |twoFactor| |concat| |prinshINFO| - |normFactors| |splitLinear| |aLinear| |rightGcd| |space| - |deleteRoutine!| |primitivePart!| |dot| |numericalOptimization| - |e02bbf| |setsubMatrix!| |noKaratsuba| |finite?| - |balancedFactorisation| |linearDependence| |bezoutResultant| |isMult| - |curry| |OMParseError?| |operators| |leftUnit| |expandPower| - |backOldPos| |kroneckerDelta| |represents| |coercePreimagesImages| - |multiplyCoefficients| |acscIfCan| |drawStyle| |nullary?| - |lieAlgebra?| |flexibleArray| |PollardSmallFactor| |vertConcat| - |leadingTerm| |LyndonWordsList1| |byte| |OMputBVar| |listBranches| - |minPol| |functionIsOscillatory| |algebraic?| |prindINFO| |OMgetError| - |mainValue| |LyndonWordsList| |hasoln| |expt| |numberOfHues| - |yCoordinates| |isOp| |horizConcat| |equiv?| |hash| |normDeriv2| - |balancedBinaryTree| |semiIndiceSubResultantEuclidean| |harmonic| - |printStatement| |intersect| |xn| |subNodeOf?| |tanNa| - |algSplitSimple| |point?| |swapRows!| |approxNthRoot| |s01eaf| - |s17aef| |lazyGintegrate| |count| |exprHasWeightCosWXorSinWX| - |nonSingularModel| |fortranLiteral| |toseInvertibleSet| |ksec| - |purelyAlgebraic?| |lazyResidueClass| |clikeUniv| |getZechTable| - |f02awf| |isExpt| |dim| |triangularSystems| |screenResolution3D| - UTS2UP |minimalPolynomial| |charpol| |clip| |identification| - |extractProperty| |makeViewport2D| |c06fqf| |term| |sequences| - |selectPolynomials| |mathieu22| |monomialIntPoly| |epilogue| |rotatez| - |stoseLastSubResultant| |fortranTypeOf| |eulerPhi| |primlimintfrac| - |bernoulli| |divisorCascade| |whileLoop| |lazyPseudoQuotient| - |baseRDEsys| |Si| |solid| |buildSyntax| |modulus| |intensity| |f04adf| - |constantKernel| |vspace| |nsqfree| |schema| |f02wef| |doubleDisc| - |showScalarValues| |numberOfOperations| |diophantineSystem| - |partialFraction| |sort!| |mapExpon| |entry?| |principalIdeal| - |sample| |cyclotomicFactorization| |nthRoot| |mapExponents| - |divideExponents| |jacobian| |expint| |charClass| - |constantToUnaryFunction| |delta| |bezoutMatrix| |coord| |separate| - |positiveSolve| |multiple| |karatsuba| |tablePow| |repSq| |trigs| - |pomopo!| |untab| |mkIntegral| |pointLists| |skewSFunction| - |sizeLess?| |applyQuote| |variationOfParameters| |interpret| - |leastPower| |createLowComplexityNormalBasis| |subMatrix| |exQuo| - |infinite?| |lowerCase?| |stiffnessAndStabilityFactor| - |primPartElseUnitCanonical!| |tanhIfCan| |internalSubPolSet?| - |realEigenvalues| FG2F |exptMod| |OMgetType| |compound?| |recolor| - |deriv| |changeWeightLevel| |doubleResultant| - |generalizedContinuumHypothesisAssumed| |f04jgf| - |leadingCoefficientRicDE| |number?| |jordanAlgebra?| |e01saf| |qelt| - |rangePascalTriangle| |lyndonIfCan| |bitCoef| |monomialIntegrate| - |ruleset| |fixedPoints| |e01daf| |seed| |module| |gcdcofactprim| - |shade| |insertMatch| |low| |Lazard2| |lfextlimint| |primlimitedint| - |key?| |leftExactQuotient| |weakBiRank| |simplify| |basisOfNucleus| - |createPrimitiveElement| |xRange| |newSubProgram| |zoom| - |viewDefaults| |pmintegrate| |reverseLex| |rk4f| |minrank| |initial| - |createNormalElement| |complementaryBasis| |leftAlternative?| |lambda| - |yRange| |powers| |tan2cot| |primaryDecomp| |mainPrimitivePart| - |suchThat| |uniform01| |nativeModuleExtension| |equality| |subset?| - |cap| |rightMinimalPolynomial| |pushdterm| |zRange| - |continuedFraction| |mapmult| GE |notelem| |tableau| |extractPoint| - |mapDown!| |laurentRep| |seriesSolve| |distFact| |properties| - |writable?| |map!| |d01ajf| GT |semiResultantEuclidean1| |tab| |open?| - |problemPoints| |cAsec| |cosSinInfo| |lexTriangular| |match?| |init| - |iExquo| |polyRDE| |makeSketch| |rootKerSimp| |simpleBounds?| - |qsetelt!| |zeroMatrix| |string?| |cAcsc| LE |upperCase!| |redmat| - |rombergo| |enumerate| |alphanumeric?| |setClipValue| |bandedJacobian| - |nullity| LT |vectorise| |rename!| |makeGraphImage| |OMread| - |nullSpace| |mesh| |conjugates| |viewport3D| |objectOf| - |linearAssociatedExp| |stop| |OMgetAttr| |listConjugateBases| - |wordsForStrongGenerators| |divisors| |mkPrim| |flagFactor| |iiatanh| - |multiEuclideanTree| |extractTop!| |iibinom| |diagonalProduct| - |factorSquareFreeByRecursion| |infRittWu?| |atanIfCan| |mpsode| - |OMUnknownCD?| |rdHack1| |degree| |denominators| |ignore?| - |changeName| |multiple?| |updatD| |d02ejf| GF2FG |curve| |printCode| - |possiblyInfinite?| |iilog| |integralCoordinates| |keys| - |factorGroebnerBasis| |nextsubResultant2| |acsch| |leadingIndex| - |rowEchelon| |numberOfPrimitivePoly| |csubst| |cross| |cAcosh| - |OMsupportsSymbol?| |numFunEvals3D| |repeatUntilLoop| |leftRank| - |lastSubResultant| |s17adf| |generalLambert| |nextPrimitivePoly| - |rule| |pop!| |e02ddf| |rischDEsys| |optpair| - |leftCharacteristicPolynomial| |BumInSepFFE| |algint| |norm| - |leftTraceMatrix| |zeroDim?| |totalfract| |subresultantSequence| - |coordinates| |points| |solveLinearlyOverQ| |ratDsolve| |minRowIndex| - |increment| |next| |s13adf| |symbol| |rangeIsFinite| |finiteBound| - |pole?| |radicalSolve| |nlde| |mkAnswer| |Beta| |makeSin| |nand| - |sortConstraints| |deepExpand| |dark| |basisOfMiddleNucleus| |se2rfi| - |dflist| |integer| |hue| |monicModulo| |insertionSort!| |linear?| - |rules| |front| |monicDivide| |setMaxPoints3D| |lazyPseudoDivide| - |hyperelliptic| |cAcoth| |initiallyReduce| |bindings| |reducedQPowers| - |bivariate?| |doublyTransitive?| |OMputAttr| |generalInfiniteProduct| - |sinIfCan| |mainVariable| |phiCoord| |coleman| |replace| |htrigs| - |leftRankPolynomial| |trivialIdeal?| |testDim| |coefChoose| |Lazard| - |stoseInternalLastSubResultant| |maxPoints3D| |writeLine!| |cAtan| - |d01gbf| |rootDirectory| |bsolve| |selectSumOfSquaresRoutines| - |clearTable!| |rightZero| |head| |inrootof| |FormatRoman| |fractRadix| - |lfunc| |coerceL| |eval| |sort| |function| |s19aaf| |setAdaptive| - |basisOfCentroid| |repeating?| |sylvesterSequence| |expr| - |numberOfDivisors| |aspFilename| |plusInfinity| - |internalSubQuasiComponent?| |sorted?| |dmpToHdmp| |innerEigenvectors| - |createThreeSpace| |symbolIfCan| |doubleComplex?| |invmod| - |minusInfinity| |fortranCarriageReturn| |getOperator| |roughSubIdeal?| - |eigenMatrix| |implies?| |character?| |s14baf| |generators| - |characteristicSerie| |floor| |aCubic| |true| |polygon?| |lifting1| - |supDimElseRittWu?| |printInfo| |assign| |stronglyReduce| - |integralDerivationMatrix| |integralMatrixAtInfinity| |regime| - |variable| |OMconnOutDevice| |OMputEndApp| |random| |branchPoint?| - |scaleRoots| |OMconnectTCP| |nonQsign| |decomposeFunc| |lprop| - |rightCharacteristicPolynomial| |messagePrint| |moebiusMu| |empty| - |palgextint0| |viewZoomDefault| |systemCommand| |reduceLODE| - |chebyshevU| |janko2| |stoseInvertible?| |obj| |karatsubaOnce| |type| - |cAsin| |mainMonomials| |chvar| |weighted| |mapGen| |radicalSimplify| - |cache| |sts2stst| |insert| |setprevious!| |s18aff| |lflimitedint| - |OMgetEndObject| |maxrank| |deepestInitial| |predicate| - |sumOfKthPowerDivisors| |alternatingGroup| |minPoly| |block| - |setPosition| |semiDiscriminantEuclidean| |lazy?| - |removeRoughlyRedundantFactorsInPols| |subscript| - |inverseIntegralMatrixAtInfinity| |singularAtInfinity?| - |complexIntegrate| |iisec| |printTypes| |meshPar2Var| |linears| - |loopPoints| |lcm| |explogs2trigs| |color| |numberOfComposites| - |oblateSpheroidal| |clearTheFTable| |getlo| |tower| |leader| |s21bdf| - |coordinate| |useSingleFactorBound| |point| |resultantReduit| |llprop| - |OMgetEndApp| |plotPolar| |normalDeriv| |primitiveElement| |ode1| ** - |linearAssociatedLog| |selectsecond| |rquo| |pointColor| |order| - |unitNormal| |iiacsc| |outputMeasure| |inRadical?| |flatten| - |dAndcExp| |chebyshevT| |gcd| |perspective| |search| |printingInfo?| - |lyndon?| |getCode| |e04dgf| |e02bdf| |antiCommutator| |series| - |startTableInvSet!| |union| |cos2sec| |idealiserMatrix| |setlast!| EQ - |dom| |f01qdf| |OMgetBVar| |basisOfRightNucleus| |zero| |false| - |alternating| |functionIsFracPolynomial?| |trapezoidalo| |eq?| - |createRandomElement| |sumOfSquares| |symFunc| |callForm?| |latex| - |closeComponent| |var2StepsDefault| |universe| |equivOperands| - |fortranLinkerArgs| |ridHack1| |pdf2df| |And| |indices| |showAll?| - |lifting| |row| |ptree| |normalized?| |identity| |factorSquareFree| - |dn| |Or| |min| |merge!| |digamma| |integralBasis| |quickSort| - |splitConstant| |e02ahf| |middle| |Not| |lepol| |intPatternMatch| - |root| |deepestTail| |d03faf| |routines| |OMmakeConn| |atanhIfCan| - |title| |setAttributeButtonStep| |mulmod| |subQuasiComponent?| - |empty?| |escape| |addMatchRestricted| |freeOf?| |diagonalMatrix| - |modularGcd| |kmax| |subCase?| |resetVariableOrder| |setMinPoints3D| - |squareFree| |extension| |invertIfCan| |resetAttributeButtons| |sub| - |genericRightMinimalPolynomial| |trueEqual| |rightTrim| |limitPlus| - |e| |f02xef| |setTex!| |completeHensel| |qinterval| |symmetricProduct| - |imagE| |OMopenString| |initiallyReduced?| |normal| |checkRur| - |leftTrim| |safeCeiling| |contours| |reduction| |getProperty| - |members| |algebraicSort| |headReduced?| |fixedPoint| |c06fpf| |log2| - |reverse!| |createIrreduciblePoly| |d02raf| |inGroundField?| |s14abf| - |resetBadValues| |complexRoots| |tryFunctionalDecomposition| - |squareMatrix| |constant| |showFortranOutputStack| - |mapUnivariateIfCan| |rewriteSetWithReduction| |hexDigit?| |diagonals| - |irreducibleFactor| |outputArgs| |complexNumeric| |maximumExponent| - |close| |c06gcf| |removeIrreducibleRedundantFactors| |toScale| - |upperCase| |combineFeatureCompatibility| |derivationCoordinates| - |varList| |OMgetBind| |dmp2rfi| |binarySearchTree| |cCoth| |acosIfCan| - |cyclicParents| |erf| |kernels| |leadingIdeal| |display| - |mainDefiningPolynomial| |halfExtendedSubResultantGcd2| |setStatus| - |maxrow| |vedf2vef| |getSyntaxFormsFromFile| |rischDE| |univariate| - |leviCivitaSymbol| |intcompBasis| |e02baf| |fracPart| - |modifyPointData| |triangular?| |systemSizeIF| |leftQuotient| |Ei| - |commutativeEquality| |terms| |definingPolynomial| |quasiRegular?| - |df2fi| |OMputApp| |showArrayValues| |paraboloidal| |compdegd| - |outputAsTex| |rightMult| |att2Result| |xCoord| |datalist| |dilog| - |rightTrace| |factor| |argument| |thetaCoord| |compiledFunction| - |normalizedAssociate| |setCondition!| |countRealRootsMultiple| |nthr| - |scale| |input| |sin| |powmod| |sqrt| |mathieu11| |coth2trigh| - |derivative| |normalDenom| |OMputFloat| |categoryFrame| |pack!| - |e01sbf| |cyclicGroup| |mindegTerm| |output| |cos| |library| |real| - |changeBase| |tail| |separateDegrees| |radicalEigenvectors| - |changeThreshhold| |abs| |leaves| |tan| |Aleph| |imag| |compBound| - |cSec| |randomR| |findBinding| |inverseColeman| |laplace| |e04mbf| - |pseudoQuotient| |cot| |directProduct| |leftPower| |divide| - |convergents| |numFunEvals| |polygamma| |makeVariable| - |perfectSquare?| |e02agf| |setPredicates| |fortranDouble| - |lfintegrate| |leftMult| |quotient| |tab1| |rightFactorIfCan| - |setProperties| |appendPoint| |reduceByQuasiMonic| - |halfExtendedSubResultantGcd1| |sec| |rightPower| |destruct| |set| - |shufflein| |unit| |e01bff| |sPol| |multinomial| |makeTerm| |f07adf| - |resultantReduitEuclidean| |d03eef| |presuper| - |nextPrimitiveNormalPoly| |s18adf| |firstDenom| |plus| |f04asf| - |OMputAtp| |setMaxPoints| |changeMeasure| |extensionDegree| |enqueue!| - |baseRDE| |jordanAdmissible?| |quadraticForm| |extractIfCan| - |nthFractionalTerm| |weights| |differentialVariables| |addiag| - |localIntegralBasis| |splitSquarefree| |minimumDegree| |pleskenSplit| - |s17dcf| |extractIndex| |eigenvectors| |lowerPolynomial| |monomial| - |pattern| |listRepresentation| |pointData| |addPoint| |setErrorBound| - |GospersMethod| |dimensionOfIrreducibleRepresentation| |delay| - |alphanumeric| |critBonD| |multivariate| |gradient| - |listYoungTableaus| |prinpolINFO| |badNum| |setButtonValue| - |highCommonTerms| |initializeGroupForWordProblem| |factorOfDegree| - |increasePrecision| |variables| |times| |anticoord| |e01bhf| - |swapColumns!| |nthRootIfCan| |critM| |rotate| |cyclic?| - |changeNameToObjf| |LyndonBasis| |diag| |multisect| |gethi| |s15adf| - |less?| |wrregime| |viewPhiDefault| |ldf2vmf| |parabolic| - |listOfMonoms| |firstUncouplingMatrix| |currentScope| |csc2sin| - |randomLC| |scripted?| |getGraph| |triangSolve| |rationalFunction| - |ipow| |LiePoly| |OMencodingXML| |readLineIfCan!| |show| |makeMulti| - |e02ajf| |integralBasisAtInfinity| |SturmHabicht| |edf2ef| - |brillhartTrials| |polynomialZeros| |monom| |leftScalarTimes!| |push!| - |unaryFunction| |s17def| |physicalLength| |recur| |decrease| - |zeroDimensional?| |musserTrials| |meshPar1Var| |and?| |taylor| - |float?| |trace| |hdmpToDmp| |createGenericMatrix| |evaluateInverse| - |minordet| |createPrimitivePoly| |OMsend| |seriesToOutputForm| - |fortran| |halfExtendedResultant1| |laurent| |completeEchelonBasis| - |rootOf| |mergeDifference| |mainCharacterization| |rightQuotient| - |prefixRagits| |solveLinearPolynomialEquation| |separant| - |tableForDiscreteLogarithm| |fortranLogical| |puiseux| - |minimumExponent| |subHeight| |f02adf| |s20acf| |index?| |bright| - |shiftRight| |showTypeInOutput| |computeCycleEntry| |call| |iiGamma| - |vark| |string| |pdct| |f04mbf| |patternMatch| |presub| |monomRDEsys| - |inspect| |clipBoolean| |iiexp| |lintgcd| |zeroDimPrimary?| |inv| - |c05pbf| |ODESolve| |li| |iteratedInitials| |debug| |polar| - |cycleTail| |lookup| |numberOfIrreduciblePoly| |ground?| |elColumn2!| - |setref| |rectangularMatrix| |compose| |zag| |permanent| |arity| - |computeInt| |elRow1!| |coerceP| |leftDiscriminant| |ground| - |ScanArabic| |tubePointsDefault| |errorKind| - |selectMultiDimensionalRoutines| |typeLists| |eq| |cartesian| - |midpoints| |setRow!| |any?| |rename| |leadingMonomial| - |internalLastSubResultant| |besselJ| |e01sef| |OMencodingSGML| |iter| - |cardinality| |delete| |d02gbf| |swap| |adjoint| |stoseInvertible?reg| - |leadingCoefficient| |extendIfCan| |failed?| |initTable!| |power| - |condition| |iroot| |OMgetEndBind| |lyndon| |primitiveMonomials| - |sec2cos| |monicRightFactorIfCan| |makeCos| |torsion?| - |representationType| |prinb| |say| |rightTraceMatrix| |setProperty!| - |dfRange| |reductum| |leadingSupport| |standardBasisOfCyclicSubmodule| - |torsionIfCan| |complexForm| |dec| |selectIntegrationRoutines| - |invertible?| |bombieriNorm| |critMTonD1| |approxSqrt| |ceiling| - |unrankImproperPartitions0| |factorSquareFreePolynomial| - |retractIfCan| |direction| |complexNormalize| |atom?| |reify| - |rightRankPolynomial| |bubbleSort!| |nthExpon| |mapdiv| - |extendedIntegrate| |bat1| |selectfirst| |script| |currentEnv| - |ranges| |f02abf| |yCoord| |basis| |expintfldpoly| |exp| - |lineColorDefault| |transcendenceDegree| |rischNormalize| - |useEisensteinCriterion?| |pol| |outputList| |linkToFortran| |polygon| - |iisin| |lSpaceBasis| |primeFactor| |print| |translate| |cExp| - |cosh2sech| |cCsc| |s17ajf| |numer| |edf2efi| |besselI| - |trigs2explogs| |tex| |iiabs| |lazyPseudoRemainder| |setright!| - |rightDivide| |denom| |cons| |sizeMultiplication| |e04ycf| |Frobenius| - |mapUp!| |virtualDegree| |e01baf| |is?| |iisinh| |log10| - |LazardQuotient| |constantOperator| |antiCommutative?| - |recoverAfterFail| |cyclicCopy| |magnitude| |pi| |bitand| - |jacobiIdentity?| |symmetricPower| |nonLinearPart| |relerror| - |elRow2!| |distribute| |quadraticNorm| |infinity| |bitior| |pastel| - |youngGroup| |mvar| |s21baf| |minPoints3D| |contains?| |mainForm| - |generalPosition| |initials| |f01bsf| |stopMusserTrials| - |algebraicCoefficients?| |binomial| |selectODEIVPRoutines| |map| - |cSinh| |sup| |pToDmp| 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|setScreenResolution3D| |sin?| - |copyInto!| |factorPolynomial| LODO2FUN |reducedForm| |normalizeIfCan| - |associatedEquations| |myDegree| |wreath| |leftRecip| - |isAbsolutelyIrreducible?| |qqq| |chineseRemainder| |arrayStack| - |rightExactQuotient| |getStream| |duplicates| |arg1| |romberg| - |upperCase?| |usingTable?| |newReduc| |cAtanh| |ran| - |fractionFreeGauss!| |useNagFunctions| |factorFraction| |irreducible?| - |explimitedint| |removeCoshSq| |extract!| |arg2| |makingStats?| - |cyclePartition| |crest| |stopTable!| |orthonormalBasis| |compile| - |iiasech| |perfectSqrt| |constantLeft| |expandLog| |rightExtendedGcd| - |trace2PowMod| |innerint| |doubleFloatFormat| |denominator| - |monomials| |setfirst!| |rationalPoints| |nthCoef| |expintegrate| - |fixPredicate| |extendedResultant| |listOfLists| |divisor| |pushucoef| - |pade| |conditions| |rootOfIrreduciblePoly| |factorList| |submod| - |failed| |areEquivalent?| |elements| |pair?| |hexDigit| |rowEchLocal| - |match| |toseLastSubResultant| |cycleEntry| |bernoulliB| |mix| - |setEpilogue!| |lazyPremWithDefault| |mindeg| - |createLowComplexityTable| |iicsc| |e02zaf| |algDsolve| - |rationalPower| |length| |integralMatrix| |critB| |firstSubsetGray| - |OMgetApp| |f02ajf| |coerceListOfPairs| |fullPartialFraction| - |binding| |rotatey| |op| |getBadValues| |graphs| |scripts| |scan| - |exponent| |solid?| |OMreceive| |poisson| |symmetric?| |infix| - |hypergeometric0F1| |setnext!| |entry| |iifact| |var1Steps| - |algebraicDecompose| |genericLeftDiscriminant| |hex| |aromberg| - |setValue!| |taylorIfCan| |univariatePolynomial| |resultantEuclidean| - |clearTheIFTable| |totalLex| |identityMatrix| |OMReadError?| - |aQuadratic| |exp1| |unitCanonical| |ptFunc| |mathieu24| |rroot| - |semiSubResultantGcdEuclidean2| |modularFactor| |quoByVar| |viewpoint| - |copies| |nextsousResultant2| |tanSum| |s18dcf| |euler| - |extractSplittingLeaf| |randnum| |viewport2D| |critT| |test| ~= - |imagK| |split!| |nil| |infinite| |arbitraryExponent| |approximate| + |Record| |Union| |cAsec| |irreducibleFactors| |e02ajf| |stFunc2| + |functionIsFracPolynomial?| |gcdcofact| |exprToGenUPS| |drawToScale| + |companionBlocks| |node| |extendedint| |cosSinInfo| + |partialDenominators| |integralBasisAtInfinity| |groebner| |maxint| + |zero| |trapezoidalo| |coHeight| |clipWithRanges| |lquo| |dequeue| + |UP2ifCan| |lexTriangular| |SturmHabicht| |destruct| |eq?| + |scalarMatrix| |setelt| |f01brf| |hasTopPredicate?| |setAdaptive3D| + |parabolicCylindrical| |iExquo| |e02dff| |accuracyIF| |edf2ef| + |commutator| |And| |createRandomElement| |antisymmetric?| + |rootNormalize| |createNormalPrimitivePoly| |polyRDE| |setStatus!| + |brillhartTrials| |f04qaf| |Or| |homogeneous?| |sumOfSquares| |f07aef| + |startTableGcd!| |measure| |makeSketch| |rootBound| |polynomialZeros| + |numberOfCycles| |cyclicEqual?| |Not| |showTheIFTable| |symFunc| + |internalInfRittWu?| |nodeOf?| |rootKerSimp| |leftScalarTimes!| + |particularSolution| |tRange| |monomial| |computePowers| |callForm?| + |fintegrate| |semiSubResultantGcdEuclidean1| |supRittWu?| + |ReduceOrder| |simpleBounds?| |minGbasis| |compile| |push!| + |superscript| |multivariate| |tower| |next| |airyAi| + |functionIsContinuousAtEndPoints| |latex| |showIntensityFunctions| + |evenlambert| |difference| |comp| |unaryFunction| |weierstrass| + |variables| |solveLinearPolynomialEquationByFractions| + |indicialEquationAtInfinity| |closeComponent| |OMputBind| |signAround| + |fTable| |nthRoot| |biRank| |s17def| |d01gaf| |startPolynomial| |top!| + |var2StepsDefault| |processTemplate| |exquo| |showSummary| |f2st| + |mapExponents| |rarrow| |elementary| |physicalLength| |getDatabase| + |reflect| |universe| |e04ucf| |div| |dimensions| |c06eaf| + |patternVariable| |divideExponents| |iiasinh| |recur| |quasiComponent| + |realElementary| |polyPart| |quo| |showAttributes| |jacobian| + |acschIfCan| |decrease| |OMputString| |B1solve| |primeFrobenius| + |floor| |gcdprim| |declare| |bitTruth| ** |leadingBasisTerm| |expint| + |setOfMinN| |linearMatrix| |zeroDimensional?| |taylor| |bat| + |innerSolve1| |aCubic| |summation| |palgLODE| |rem| |charClass| + |removeRedundantFactorsInContents| |musserTrials| |resultantnaif| + |laurent| |inR?| |d02cjf| |polygon?| |completeSmith| + |constantToUnaryFunction| |rational| |puiseux| EQ |LiePolyIfCan| + |lifting1| |fractionPart| |bits| |pquo| |bezoutMatrix| |OMgetInteger| + |setelt!| |setPredicates| |gcdPolynomial| |supDimElseRittWu?| + |quasiRegular| |octon| |coord| |besselK| |fortranDouble| |operator| + |inv| |iisqrt2| |BasicMethod| |assign| |nextSubsetGray| |lfintegrate| + SEGMENT |tree| |padicallyExpand| |separate| |extend| |keys| |ground?| + |infinityNorm| |ef2edf| |stronglyReduce| |calcRanges| |positiveSolve| + |comparison| |leftMult| |ground| |radicalOfLeftTraceForm| |imaginary| + |integralDerivationMatrix| |collectQuasiMonic| |minPoints3D| |imagK| + |pascalTriangle| |karatsuba| |quotient| |rational?| |leadingMonomial| + |integralMatrixAtInfinity| |safetyMargin| |cCosh| |debug3D| |center| + |contains?| |split!| |tablePow| |expandTrigProducts| |singular?| + |tab1| |leadingCoefficient| |complexNumeric| |cCsch| |hclf| |regime| + |cot2tan| |mainForm| |beauzamyBound| |repSq| |toseInvertible?| + |rightFactorIfCan| |primitiveMonomials| |rootRadius| + |wordInGenerators| |OMconnOutDevice| |graphStates| |generalPosition| + |intermediateResultsIF| |trigs| |setProperties| + |lastSubResultantEuclidean| |reductum| |monicRightDivide| + |positiveRemainder| |OMputEndApp| |initials| |nil| |pomopo!| + |sinh2csch| |appendPoint| |getCurve| |branchPoint?| |dequeue!| + |charthRoot| |OMconnInDevice| |f01bsf| |id| |cAsech| |untab| + |reduceByQuasiMonic| |hasHi| |internalIntegrate0| |scaleRoots| + |largest| |OMputError| |stopMusserTrials| |mkIntegral| |child| + |perfectNthPower?| |halfExtendedSubResultantGcd1| |setRealSteps| + |unprotectedRemoveRedundantFactors| |OMconnectTCP| |squareFreeFactors| + |algebraicCoefficients?| |approximate| |pointLists| |po| |rightPower| + |wordInStrongGenerators| |goto| |stopTableInvSet!| + |modularGcdPrimitive| |nonQsign| |binomial| |property| |complex| + |skewSFunction| |removeZeroes| Y |partialQuotients| |shufflein| |blue| + |rationalApproximation| |cAcsch| |decomposeFunc| + |selectODEIVPRoutines| |sizeLess?| |heapSort| |unit| + |radicalEigenvalues| |frst| |lprop| |internalAugment| |cSinh| |search| + |variationOfParameters| |subspace| |every?| |e01bff| |iflist2Result| + |rightCharacteristicPolynomial| |list| |definingInequation| + |internalDecompose| |sup| |units| |gbasis| |leastPower| |sPol| + |newTypeLists| |rationalPoint?| |OMreadStr| |car| |op| |messagePrint| + |pToDmp| |eq| |createLowComplexityNormalBasis| |flexible?| + |multinomial| |powerSum| |arg1| |asecIfCan| |cdr| |moebiusMu| |e01sff| + |computeBasis| |iter| |factor1| |subMatrix| |makeTerm| |asinhIfCan| + |setDifference| |arg2| |clearTheSymbolTable| |key| + |removeConstantTerm| |empty| |monicDecomposeIfCan| |morphism| |exQuo| + |f07adf| |userOrdered?| |innerSolve| |setIntersection| |palgextint0| + |makeResult| |unit?| |antiAssociative?| |external?| |associates?| + |infinite?| |resultantReduitEuclidean| |reset| |filename| |conditions| + |setUnion| |rewriteSetByReducingWithParticularGenerators| |c06ebf| + |viewZoomDefault| |relativeApprox| |code| |degreeSubResultant| + |lowerCase?| |multiplyExponents| |d03eef| |stronglyReduced?| + |regularRepresentation| |match| |apply| |not?| |Ci| |reduceLODE| + |OMgetEndAttr| |sech2cosh| |stiffnessAndStabilityFactor| |makeCrit| + |presuper| |antisymmetricTensors| |components| |parse| |gcdPrimitive| + |e04naf| |chebyshevU| |addPointLast| |factorial| |coerceS| + |primPartElseUnitCanonical!| |max| |nextPrimitiveNormalPoly| + |generalSqFr| |simplifyPower| |size| |closedCurve| |cup| |janko2| + |component| |exp| |clipParametric| |f01rcf| |tanhIfCan| |rightTrim| + |s18adf| |write| |specialTrigs| |csch2sinh| |stoseInvertible?| + |argscript| |OMgetString| |reduceBasisAtInfinity| |atrapezoidal| + |internalSubPolSet?| |leftTrim| |firstDenom| |numberOfComponents| |sn| + |surface| |karatsubaOnce| |resultantEuclideannaif| |e04fdf| |fortran| + |stiffnessAndStabilityOfODEIF| |realEigenvalues| |factorAndSplit| + |f04asf| |matrixConcat3D| |first| |controlPanel| |cAsin| |e02bef| + |iiasec| |reverse| |wholePart| FG2F |rewriteIdealWithHeadRemainder| + |trapezoidal| |OMputAtp| |logGamma| |rest| |dihedralGroup| |content| + |mainMonomials| |getMeasure| |maxPoints| |exptMod| |multiset| + |rdregime| |setMaxPoints| |failed| |substitute| |psolve| + |removeSquaresIfCan| |chvar| |sizePascalTriangle| |sqfrFactor| + |subResultantGcdEuclidean| |c02agf| |OMgetType| |iidsum| + |changeMeasure| |removeDuplicates| |commutative?| |medialSet| |pushup| + |weighted| |complexLimit| |quoted?| |compound?| |fortranComplex| + |extensionDegree| |cSin| |unexpand| |mapGen| |e02bcf| |diagonal| |lex| + |recolor| |roughBase?| |enqueue!| |mainContent| |arguments| |iiatan| + |LowTriBddDenomInv| |radicalSimplify| |union| |oddintegers| |distance| + |deriv| |generateIrredPoly| |baseRDE| |totalDifferential| |ramified?| + |constantCoefficientRicDE| |sts2stst| |flatten| |getPickedPoints| + |entries| |changeWeightLevel| |jordanAdmissible?| |stFuncN| |push| + |index| |upDateBranches| |setprevious!| |movedPoints| |iicsch| + |doubleResultant| |rk4a| |quadraticForm| |transpose| |cSech| + |minIndex| |s18aff| |selectNonFiniteRoutines| |c05nbf| + |generalizedContinuumHypothesisAssumed| |sinhcosh| |argumentList!| + |extractIfCan| |lflimitedint| |mantissa| |bumptab1| |outputAsScript| + |readLine!| |style| |ramifiedAtInfinity?| |f04jgf| |acot| |leftGcd| + |nthFractionalTerm| |mainKernel| |fi2df| |pair| |read!| + |OMgetEndObject| |common| |squareFreePrim| |leadingCoefficientRicDE| + |hcrf| |asec| |weights| |OMserve| |blankSeparate| |padicFraction| + |maxrank| |super| |number?| |script| |credPol| |acsc| + |differentialVariables| |intChoose| |setColumn!| |explicitEntries?| + |legendreP| |deepestInitial| |range| |radPoly| |inverseIntegralMatrix| + |jordanAlgebra?| |sinh| |simpsono| |addiag| |sayLength| |btwFact| + |sumOfKthPowerDivisors| |f04faf| |critpOrder| |d01fcf| |e01saf| + |child?| |cosh| |removeDuplicates!| |localIntegralBasis| + |groebnerIdeal| |determinant| |alternatingGroup| |prime?| + |numberOfChildren| |rangePascalTriangle| |f02agf| |tex| |tanh| + |eyeDistance| |high| |splitSquarefree| |degreeSubResultantEuclidean| + |minPoly| |hermite| |hasSolution?| |stFunc1| |zeroSquareMatrix| + |colorFunction| |lyndonIfCan| |OMencodingUnknown| |coth| + |laurentIfCan| |leftZero| |minimumDegree| |insertTop!| |block| + |powerAssociative?| |c06gbf| |limitedint| |outerProduct| |bitCoef| + |mdeg| |sech| |viewDeltaXDefault| |conjug| |pleskenSplit| + |integralLastSubResultant| |decreasePrecision| F |setPosition| + |laguerre| |vconcat| |cycleElt| |associative?| |monomialIntegrate| + |csch| |sort| |trailingCoefficient| |s17dcf| |unvectorise| + |semiDiscriminantEuclidean| |setClosed| |tubeRadiusDefault| + |karatsubaDivide| |pushuconst| |setTopPredicate| |fixedPoints| |asinh| + |currentSubProgram| |Vectorise| |extractIndex| |KrullNumber| + |mapMatrixIfCan| |lazy?| |withPredicates| |insertRoot!| |result| + |iprint| |cLog| |e01daf| |acosh| |eigenvectors| |shallowExpand| + |inverseLaplace| |pr2dmp| |removeRoughlyRedundantFactorsInPols| + |integral| |toroidal| |algebraicVariables| |seed| |atanh| + |create3Space| |lowerPolynomial| |opeval| |stack| |column| + |useSingleFactorBound?| |rotate!| |subscript| |univariateSolve| + |alternative?| |erf| |module| |positive?| |normal?| |acoth| |d02kef| + |listRepresentation| |e01bef| |redPol| + |inverseIntegralMatrixAtInfinity| |totalGroebner| |isList| + |gcdcofactprim| |cot2trig| |toseSquareFreePart| |asech| |random| + |lowerCase| |putColorInfo| |pointData| |cn| |mapSolve| |qPot| + |singularAtInfinity?| |shiftLeft| |asinIfCan| |showClipRegion| + |associatedSystem| |addPoint| |topFortranOutputStack| + |complexIntegrate| |cCot| |inf| |toseInvertibleSet| |inverse| + |permutation| |setErrorBound| |OMgetObject| |palgint| |iisec| + |euclideanSize| |totalDegree| |ksec| |constant?| |goodPoint| + |GospersMethod| |fprindINFO| |retractIfCan| |cCos| |printTypes| + |removeSinSq| |genericPosition| |e| |absolutelyIrreducible?| + |purelyAlgebraic?| |binary| |dimensionOfIrreducibleRepresentation| + |identitySquareMatrix| |divergence| |nextColeman| |setvalue!| + |normInvertible?| |lazyResidueClass| |elliptic?| |delay| |bindings| + |times!| |purelyTranscendental?| |numberOfComputedEntries| + |OMputEndBVar| |tryFunctionalDecomposition?| |clikeUniv| |preprocess| + |alphanumeric| |d01asf| |reducedQPowers| |complex?| |graphState| + |OMgetEndAtp| |OMopenFile| |addBadValue| |f01qcf| |getZechTable| + |realRoots| |decimal| |critBonD| |solve1| |logpart| |imagi| + |bivariate?| |back| |contract| |f02awf| |doublyTransitive?| |typeList| + |cfirst| |atoms| |symmetricTensors| |or?| |isExpt| + |unrankImproperPartitions1| |minimize| |Ei| |save| |integral?| |light| + |OMputAttr| |uniform| |clearFortranOutputStack| |triangularSystems| + |commutativeEquality| |headReduce| |curve?| |d01amf| + |generalInfiniteProduct| |HenselLift| |screenResolution3D| + |numberOfFactors| |terms| |symbolTableOf| |factorset| |sinIfCan| + |subNode?| |leaves| UTS2UP |graeffe| |definingPolynomial| + |mergeFactors| |duplicates?| |map| |algintegrate| |mainVariable| + |e02zaf| |nthExpon| |minimalPolynomial| |getGoodPrime| |quasiRegular?| + |binaryFunction| |removeRedundantFactorsInPols| ~ |moduloP| |phiCoord| + |algDsolve| |mapdiv| |charpol| |df2fi| |whatInfinity| |edf2df| + |concat| |lagrange| |lazyVariations| |coleman| |extendedIntegrate| + |rationalPower| |dim| |clip| |discreteLog| |OMputApp| + |integralRepresents| |open| |crushedSet| |tanAn| |htrigs| + |integralMatrix| |bat1| |identification| |showArrayValues| |maxdeg| + NOT |leftRankPolynomial| |sincos| |replace| |divideIfCan| |critB| + |selectfirst| |extractProperty| |paraboloidal| |f01rdf| + |setLegalFortranSourceExtensions| |reorder| OR |tanh2coth| |convert| + |bright| |trivialIdeal?| |firstSubsetGray| |ranges| |compdegd| + |makeViewport2D| |SturmHabichtCoefficients| |status| AND |cyclic| + |testDim| |fractRagits| |f02abf| |OMgetApp| |checkPrecision| |test| + |c06fqf| |unparse| |outputAsTex| |obj| |iicoth| |principal?| + |coefChoose| |prefix| |f02ajf| |yCoord| |term| |rightMult| |rCoord| + |cache| |compactFraction| |createZechTable| |Lazard| |basis| + |coerceListOfPairs| |sequences| |att2Result| |c05adf| |label| |refine| + |figureUnits| |stoseInternalLastSubResultant| |fullPartialFraction| + |expintfldpoly| |primintfldpoly| |selectPolynomials| + |fortranLiteralLine| |xCoord| |removeRoughlyRedundantFactorsInPol| + |ffactor| |maxPoints3D| |binding| |lineColorDefault| |properties| + |shanksDiscLogAlgorithm| |mathieu22| |rightTrace| |clipPointsDefault| + |normalise| |iiasin| |writeLine!| |rotatey| |transcendenceDegree| + |translate| |monomialIntPoly| |groebner?| |argument| + |partialNumerators| |cAtan| |delete| |coerceImages| |rischNormalize| + |getBadValues| |cosIfCan| |epilogue| |dioSolve| |thetaCoord| + |var2Steps| |d01gbf| |pseudoRemainder| |useEisensteinCriterion?| + |graphs| |rotatez| |multMonom| |compiledFunction| |imagJ| + |plenaryPower| |rootDirectory| |pol| |scan| |stoseLastSubResultant| + |d02bbf| |normalizedAssociate| * |subPolSet?| |OMgetVariable| |bsolve| + |linkToFortran| |exponent| |currentEnv| |fortranTypeOf| |monic?| + |setCondition!| |genus| |s21bbf| |parts| |selectSumOfSquaresRoutines| + |solid?| |polygon| |eulerPhi| |brace| |singRicDE| + |countRealRootsMultiple| |expressIdealMember| |indicialEquations| + |clearTable!| |iisin| |OMreceive| |error| |primlimintfrac| + |mapUnivariate| |nthr| |iiacos| |enterPointData| |rightZero| + |possiblyNewVariety?| |lSpaceBasis| |poisson| |bernoulli| |assert| + |acotIfCan| |scale| |increase| |plot| |d03edf| |head| |primeFactor| + |symmetric?| |divisorCascade| |powmod| |gramschmidt| |option| + |infieldIntegrate| |setMinPoints| |inrootof| |double?| |cExp| |infix| + |whileLoop| |value| |reopen!| |mathieu11| |leftRegularRepresentation| + |hdmpToP| |FormatRoman| |chainSubResultants| |hypergeometric0F1| + |cosh2sech| |lazyPseudoQuotient| |endOfFile?| |coth2trigh| |maxIndex| + |list?| |fractRadix| |oddlambert| |setnext!| |cCsc| |second| |expPot| + |box| |baseRDEsys| |derivative| |fortranInteger| |log10| |lfunc| + |printHeader| |f02aff| |constant| |iifact| |s17ajf| |third| + |prolateSpheroidal| |outputList| |Si| |f02akf| |normalDenom| + |completeHermite| |bitand| |minus!| |nil?| |coerceL| |meatAxe| + |var1Steps| |edf2efi| |solid| |linearPart| |postfix| |OMputFloat| + |removeZero| |bitior| |partitions| |bottom!| |s19aaf| |besselI| + |algebraicDecompose| |categoryFrame| |smith| |buildSyntax| |one?| + |sechIfCan| |permutations| |setAdaptive| |leastMonomial| + |genericLeftDiscriminant| |trigs2explogs| |predicate| |pack!| + |modulus| |numberOfImproperPartitions| |repeating| |zeroDimPrime?| + |basisOfCentroid| |s17dhf| |iiabs| |hex| |nary?| |cothIfCan| + |intensity| |iisqrt3| |e01sbf| |palglimint| |triangulate| |repeating?| + |lazyPseudoRemainder| |aromberg| |fibonacci| |f04adf| |minColIndex| + |contractSolve| |cyclicGroup| |hostPlatform| |UnVectorise| |generic| + |sylvesterSequence| |setright!| |setValue!| |oneDimensionalArray| + |brillhartIrreducible?| |constantKernel| |simplifyExp| |integers| + |mindegTerm| |halfExtendedResultant2| |numberOfDivisors| + |normalizedDivide| |rightDivide| |taylorIfCan| |red| + |genericRightTrace| |vspace| |changeBase| |algebraicOf| |removeCosSq| + |sizeMultiplication| |matrixDimensions| |aspFilename| + |screenResolution| |level| |univariatePolynomial| |separateDegrees| + |completeEval| |nsqfree| |bitLength| |An| |basisOfCenter| + |incrementBy| |invertibleSet| |internalSubQuasiComponent?| |e04ycf| + |resultantEuclidean| |position!| |systemCommand| |UpTriBddDenomInv| + |schema| |numericalIntegration| |adaptive3D?| |radicalEigenvectors| + |leftMinimalPolynomial| |sorted?| |pattern| |clearDenominator| + |expand| |clearTheIFTable| |Frobenius| |rootProduct| |f02wef| + |parametersOf| |integrate| |ocf2ocdf| |changeThreshhold| |mapUp!| + |interval| |has?| |dmpToHdmp| |filterWhile| |totalLex| |parameters| + |linearPolynomials| |doubleDisc| |realZeros| |abs| |lambert| + |virtualDegree| |parametric?| |innerEigenvectors| |startStats!| + |identityMatrix| |filterUntil| |debug| |factorials| + |roughEqualIdeals?| |showScalarValues| |normal| |Aleph| |rightUnit| + |e01baf| |nextPrime| |restorePrecision| |createThreeSpace| |select| + |OMReadError?| D |numberOfOperations| |pmComplexintegrate| + |complexEigenvalues| |compBound| |region| |irreducibleRepresentation| + |message| |returnType!| |symbolIfCan| |name| |is?| |aQuadratic| + |zero?| |diophantineSystem| |cSec| |showTheRoutinesTable| |body| + |fortranCompilerName| |nthFlag| |doubleComplex?| |iisinh| |exp1| + |frobenius| |OMencodingBinary| |squareFreePolynomial| + |partialFraction| |randomR| |subresultantVector| |denomLODE| + |matrixGcd| |invmod| |unitCanonical| |LazardQuotient| |curveColor| + |sort!| |leftFactor| |isobaric?| |findBinding| |corrPoly| + |fortranCarriageReturn| |lazyPrem| |constantOperator| |ptFunc| |rules| + |heap| |mapExpon| |characteristic| |inverseColeman| |externalList| + |relationsIdeal| |getOperator| |antiCommutative?| |mathieu24| |cAcos| + |entry?| |monomial?| |laplace| |laguerreL| |totolex| |makeRecord| + |roughSubIdeal?| |rroot| |recoverAfterFail| |reducedDiscriminant| + |principalIdeal| |e04mbf| |mainVariable?| |deleteProperty!| + |eigenMatrix| |connect| |semiSubResultantGcdEuclidean2| |cyclicCopy| + |overlap| |sample| |explicitlyFinite?| |pseudoQuotient| |redpps| + |implies?| |outlineRender| |modularFactor| |magnitude| + |cyclotomicFactorization| |exponential1| |euclideanGroebner| + |leftPower| |basisOfCommutingElements| |character?| |exponential| + |jacobiIdentity?| |quoByVar| |print| |RemainderList| |divide| |delta| + |solve| |prime| |s14baf| |mathieu12| |symmetricPower| |viewpoint| + |isMult| |copy| |sparsityIF| |convergents| |slash| + |numberOfNormalPoly| |logical?| |generators| |copies| |nonLinearPart| + |curry| |implies| |prologue| |numFunEvals| |more?| |birth| |const| + |characteristicSerie| |relerror| |nextsousResultant2| |OMParseError?| + |autoCoerce| |precision| |resize| |groebSolve| |polygamma| |normalize| + |elRow2!| |tanSum| |operators| |xor| |log| |mapCoef| |makeVariable| + |extendedSubResultantGcd| |enterInCache| |asechIfCan| |csubst| + |distribute| |s18dcf| |leftUnit| |perfectSquare?| |leftRemainder| + |symbolTable| |outputSpacing| |subSet| |cross| |quadraticNorm| |euler| + |clearCache| |expandPower| |rightLcm| |e02agf| |trim| |palglimint0| + |iitan| |cAcosh| |pastel| |extractSplittingLeaf| |backOldPos| + |zeroSetSplitIntoTriangularSystems| |pushFortranOutputStack| + |OMcloseConn| |OMsupportsSymbol?| |quote| |youngGroup| |randnum| + |kroneckerDelta| |integralAtInfinity?| |checkRur| |OMgetAtp| + |popFortranOutputStack| |permutationGroup| |numFunEvals3D| + |showRegion| |mvar| BY |viewport2D| |represents| |safeCeiling| + |setFieldInfo| |infiniteProduct| |outputAsFortran| |doubleRank| + |repeatUntilLoop| |setFormula!| |critT| |s21baf| |over| + |coercePreimagesImages| |contours| |internalZeroSetSplit| |insert| + |d01bbf| |leftRank| |showTheFTable| |multiplyCoefficients| + |schwerpunkt| |reduction| |d02gaf| |lastSubResultant| |moreAlgebraic?| + |elRow1!| |duplicates| |getProperty| |acscIfCan| + |SturmHabichtMultiple| |rightRemainder| |ScanFloatIgnoreSpaces| + |s17adf| |ode2| |coerceP| |romberg| |numeric| |drawStyle| |members| + |commonDenominator| |ord| |lowerCase!| |generalLambert| |upperCase?| + |leftDiscriminant| |nullary?| |radical| |function| |partition| + |algebraicSort| |cylindrical| |nextPrimitivePoly| |rk4| |ScanArabic| + |usingTable?| |lieAlgebra?| |headReduced?| |pointColorDefault| + |dictionary| |anfactor| |pop!| |newReduc| |tubePointsDefault| |any| + |flexibleArray| |fixedPoint| |f04maf| |iiacoth| |e02ddf| + |symmetricGroup| |cAtanh| |errorKind| |PollardSmallFactor| + |genericLeftMinimalPolynomial| |c06fpf| |ideal| |OMlistSymbols| + |rischDEsys| |ran| |selectMultiDimensionalRoutines| |vertConcat| + |log2| |leftUnits| |makeObject| |setleaves!| |sncndn| |optpair| + |fractionFreeGauss!| |typeLists| |varList| |leadingTerm| |reverse!| + |defineProperty| |mainMonomial| |leftCharacteristicPolynomial| + |interpretString| |cartesian| |useNagFunctions| + |createIrreduciblePoly| |LyndonWordsList1| |formula| |fixedDivisor| + |coef| |close| |graphImage| |BumInSepFFE| |fixedPointExquo| + |midpoints| |factorFraction| |byte| |d02raf| |impliesOperands| + |vector| |transform| |algint| |check| |setRow!| |irreducible?| + |OMputBVar| |remove| |yellow| |inGroundField?| |display| + |differentiate| |lfinfieldint| |norm| |bumprow| |any?| |explimitedint| + |listBranches| |exprToXXP| |s14abf| |drawCurves| |leftOne| + |leftTraceMatrix| |rename| |removeCoshSq| |minPol| |resetBadValues| + |last| |indiceSubResultant| |nrows| |square?| |tubeRadius| |zeroDim?| + |extract!| |internalLastSubResultant| |substring?| |assoc| + |functionIsOscillatory| |complexRoots| |truncate| |ncols| |ricDsolve| + |totalfract| |sh| |besselJ| |makingStats?| + |tryFunctionalDecomposition| |algebraic?| |lcm| |resetNew| + |extendedEuclidean| |pToHdmp| |subresultantSequence| |e01sef| + |cyclePartition| |suffix?| |prindINFO| |qfactor| |squareMatrix| + |input| |pdf2ef| |powern| |roughBasicSet| |coordinates| + |OMencodingSGML| |crest| |showFortranOutputStack| |OMgetError| + |append| |monicLeftDivide| |library| |countable?| |cardinality| + |points| |makeViewport3D| |ref| |stopTable!| |prefix?| + |mapUnivariateIfCan| |mainValue| |wholeRagits| |gcd| |write!| |pile| = + |d02gbf| |solveLinearlyOverQ| |probablyZeroDim?| |orthonormalBasis| + |false| |LyndonWordsList| |computeCycleLength| + |rewriteSetWithReduction| |iicot| |iiasech| |ratDsolve| + |definingEquations| |swap| |cycleSplit!| |hexDigit?| |hasoln| + |getConstant| |c06gqf| |primextintfrac| < |pureLex| |minRowIndex| + |perfectSqrt| |adjoint| |plus| |expt| |lazyEvaluate| |diagonals| + |binaryTree| |set| |iisech| > |increment| |e04jaf| |constantLeft| + |stoseInvertible?reg| |numberOfHues| |irreducibleFactor| |wholeRadix| + |Nul| |validExponential| <= |delete!| |s13adf| |expandLog| + |extendIfCan| |call| |yCoordinates| |outputArgs| |eval| |subTriSet?| + |#| |rangeIsFinite| |pointColorPalette| >= |complexSolve| |e02akf| + |rightExtendedGcd| |failed?| |infix?| |isOp| |getButtonValue| + |maximumExponent| |trace2PowMod| |quotientByP| |finiteBound| + |showTheSymbolTable| |countRealRoots| |initTable!| |mask| |times| + |horizConcat| |c06gcf| |integer?| |innerint| |froot| |OMgetSymbol| + |pole?| |useEisensteinCriterion| |power| |equiv?| + |removeIrreducibleRedundantFactors| |removeSuperfluousQuasiComponents| + |notOperand| + |radicalSolve| |internal?| |iroot| |doubleFloatFormat| + |say| |normDeriv2| |toScale| |factors| |uncouplingMatrices| + |generalizedEigenvector| - |OMgetEndBind| |nlde| |denominator| + |solveInField| |balancedBinaryTree| |upperCase| |nextItem| + |lazyIrreducibleFactors| / |branchPointAtInfinity?| |mkAnswer| + |lyndon| |monomials| |monom| |semiIndiceSubResultantEuclidean| + |combineFeatureCompatibility| |expextendedint| |isQuotient| |aQuartic| + |normalForm| |Beta| |sec2cos| |setfirst!| |depth| |harmonic| + |derivationCoordinates| |outputForm| |groebnerFactorize| |makeSin| + |s19adf| |rationalPoints| |monicRightFactorIfCan| |printStatement| + |OMgetBind| |putGraph| |show| |conical| |nand| |outputFloating| + |nthCoef| |makeCos| |intersect| |dmp2rfi| |int| |packageCall| + |sortConstraints| |quasiMonic?| |expintegrate| |torsion?| |xn| + |binarySearchTree| |monicCompleteDecompose| |trace| |rowEchelonLocal| + |tanQ| |deepExpand| |representationType| |fixPredicate| |readable?| + |subNodeOf?| |localReal?| |cCoth| |height| |s17akf| |lieAdmissible?| + |dark| |prinb| |extendedResultant| |d01anf| |tanNa| |realEigenvectors| + |acosIfCan| |basisOfMiddleNucleus| |measure2Result| |rightTraceMatrix| + |optional?| |init| |listOfLists| |makeSUP| |algSplitSimple| + |cyclicParents| |listLoops| |unmakeSUP| |genericRightDiscriminant| + |se2rfi| |setProperty!| |divisor| |linearlyDependentOverZ?| |point?| + |stirling2| |leadingIdeal| |reseed| |dflist| |hconcat| |dfRange| + |pushucoef| |swapRows!| |optimize| |mainDefiningPolynomial| |sign| + |socf2socdf| |hspace| |hue| |leadingSupport| |pade| |isTimes| + |approxNthRoot| |makeFloatFunction| |halfExtendedSubResultantGcd2| + |elliptic| |nextSublist| |monicModulo| |rootOfIrreduciblePoly| + |standardBasisOfCyclicSubmodule| |localUnquote| |dom| |s01eaf| + |semiDegreeSubResultantEuclidean| |setStatus| |headRemainder| + |OMgetEndError| |insertionSort!| |factorList| |torsionIfCan| |series| + |cyclicSubmodule| |s17aef| |numerator| |maxrow| |jacobi| |linear?| + |deepCopy| |submod| |complexForm| |univcase| |lazyGintegrate| + |vedf2vef| |plus!| |front| |getOrder| |areEquivalent?| + |selectIntegrationRoutines| |printInfo!| |droot| + |exprHasWeightCosWXorSinWX| |qelt| |getSyntaxFormsFromFile| + |mightHaveRoots| |singleFactorBound| |monicDivide| |invertible?| + |elements| |nonSingularModel| |lp| |iiperm| |rischDE| |odd?| |e02dcf| + |setMaxPoints3D| |bombieriNorm| |pair?| |min| |leviCivitaSymbol| + |cRationalPower| |fortranLiteral| |title| |s21bcf| |xRange| |makeprod| + |condition| |pointPlot| |lazyPseudoDivide| |hexDigit| |critMTonD1| + |coshIfCan| |intcompBasis| |yRange| |tan2trig| |select!| + |hyperelliptic| |updateStatus!| |approxSqrt| |rowEchLocal| |conjugate| + |subResultantsChain| |unravel| |e02baf| |primes| |zRange| |parent| + |cAcoth| |chiSquare1| |ceiling| |toseLastSubResultant| + |generalTwoFactor| |shuffle| |fracPart| |map!| |composite| |quadratic| + |sturmVariationsOf| |genericLeftTraceForm| |li| + |unrankImproperPartitions0| |initiallyReduce| |cycleEntry| |lexico| + |getProperties| |infLex?| |qsetelt!| |traverse| |stoseInvertibleSet| + |modifyPointData| |rank| |qroot| |nor| |bernoulliB| + |factorSquareFreePolynomial| |reducedSystem| |basisOfRightAnnihilator| + |c06fuf| |triangular?| |e02adf| |zeroMatrix| |s18acf| |mix| + |direction| |cyclotomic| |build| |prem| |systemSizeIF| |c06frf| + |exactQuotient| |currentCategoryFrame| |paren| |string?| + |setEpilogue!| |complexNormalize| |ScanRoman| |inHallBasis?| |s17dgf| + |critMonD1| |leftQuotient| |mainSquareFreePart| |stop| + |selectOrPolynomials| |cAcsc| |bracket| |lazyPremWithDefault| |atom?| + |create| |bumptab| |univariatePolynomialsGcds| |product| + |RittWuCompare| |upperCase!| |reify| |cAsinh| |mindeg| |hasPredicate?| + |indicialEquation| |associator| |equivOperands| |acsch| |coefficient| + |coefficients| |getMatch| |redmat| |createLowComplexityTable| + |rightRankPolynomial| |f02aaf| |acoshIfCan| |move| |fortranLinkerArgs| + |rspace| |setImagSteps| |lists| |insertBottom!| |rombergo| + |printStats!| |iicsc| |characteristicPolynomial| |bubbleSort!| + |leftExtendedGcd| |eulerE| |ridHack1| |createPrimitiveNormalPoly| + |isPower| |genericLeftTrace| |enumerate| |symbol?| |sdf2lst| |shift| + |isPlus| |pdf2df| |FormatArabic| |scalarTypeOf| |bivariatePolynomials| + |findCycle| |alphanumeric?| |viewDeltaYDefault| |palgint0| + |meshPar1Var| |OMputObject| |rootSplit| |indices| |numericIfCan| + |lllp| |iidprod| |SFunction| |setClipValue| |fortranCharacter| + |bivariateSLPEBR| |and?| |expenseOfEvaluationIF| |showAll?| |colorDef| + |complement| |d02bhf| |cons| |realSolve| |bandedJacobian| + |maxRowIndex| |rubiksGroup| |float?| |returnTypeOf| |member?| + |localAbs| |lifting| |primitivePart| |in?| |radicalRoots| |nullity| + |shallowCopy| |hdmpToDmp| |univariate?| |directSum| |row| + |maxColIndex| |lambda| |merge| |allRootsOf| |transcendent?| |generic?| + |vectorise| |curryRight| |createGenericMatrix| |diagonal?| |digit| + |normalized?| |subtractIfCan| |revert| |split| |makeFR| |rename!| + |evaluateInverse| |orOperands| |mapBivariate| |identity| |iiacsch| + |sturmSequence| |makeGraphImage| |OMgetFloat| |closed?| + |strongGenerators| |equation| |zeroOf| |minordet| |sinhIfCan| |cycle| + F2FG |factorSquareFree| |eisensteinIrreducible?| |polCase| |insert!| + |elem?| |OMread| |createPrimitivePoly| |solveLinear| |s17dlf| |t| + |gderiv| |dn| |discriminantEuclidean| |OMlistCDs| + |stoseSquareFreePart| |source| |options| |startTable!| |nullSpace| + |modifyPoint| |squareTop| |OMsend| |iiacot| |edf2fi| |close!| |lhs| + |merge!| |argumentListOf| |palginfieldint| |not| |nilFactor| |cAcot| + |modTree| |mesh| |seriesToOutputForm| |retractable?| |exprToUPS| |inc| + |setPoly| |f04mcf| |rhs| |digamma| |leftFactorIfCan| |copy!| + |loadNativeModule| |ScanFloatIgnoreSpacesIfCan| |swap!| |conjugates| + |green| |halfExtendedResultant1| |s17agf| |df2ef| |integralBasis| + |getMultiplicationTable| |nullary| |string| RF2UTS |recip| + |viewport3D| |completeEchelonBasis| |endSubProgram| |quickSort| + |OMunhandledSymbol| |rationalIfCan| |or| |rewriteIdealWithRemainder| + |leftTrace| |constantRight| |table| |objectOf| |exprex| |adaptive| + |purelyAlgebraicLeadingMonomial?| |ptree| |rootOf| + |semiResultantEuclideannaif| |stopTableGcd!| |rootPower| + |splitConstant| |rightRecip| |linearAssociatedExp| |new| |shiftRoots| + |target| |width| |ParCondList| |mergeDifference| + |selectAndPolynomials| |radicalEigenvector| |makeEq| |e02ahf| + |tubePoints| |palgLODE0| |pushdown| |OMgetAttr| |complexElementary| + |mainCharacterization| |viewSizeDefault| |null| |stirling1| |initial| + |shellSort| |middle| |getIdentifier| |zeroSetSplit| |f01ref| + |tubePlot| |listConjugateBases| |rightQuotient| |geometric| |case| + |HermiteIntegrate| |createNormalPoly| |lepol| |hMonic| + |wronskianMatrix| |rur| |wordsForStrongGenerators| + |setScreenResolution| |cycleRagits| |prefixRagits| |Zero| + |bipolarCylindrical| |intPatternMatch| |linSolve| |c06gsf| + |nextLatticePermutation| |e02def| |reciprocalPolynomial| |divisors| + |solveLinearPolynomialEquation| |stripCommentsAndBlanks| |One| + |extractBottom!| |df2mf| |root| |setchildren!| |closedCurve?| + |axesColorDefault| |infieldint| |mkPrim| |alphabetic| |separant| + |datalist| |noncommutativeJordanAlgebra?| |nextNormalPrimitivePoly| + |deepestTail| |primextendedint| |generalizedEigenvectors| |flagFactor| + |listexp| |optional| |tableForDiscreteLogarithm| + |numberOfFractionalTerms| |saturate| |sumSquares| |d03faf| |quartic| + |f01qef| |prepareDecompose| |outputFixed| |iiatanh| |leftLcm| + |fortranLogical| |cscIfCan| |void| |branchIfCan| |symmetricRemainder| + |rightDiscriminant| |routines| |overbar| |lexGroebner| + |multiEuclideanTree| |raisePolynomial| |minimumExponent| |graphCurves| + |cycles| |mathieu23| |OMmakeConn| |prepareSubResAlgo| |expr| + |supersub| |linGenPos| |extractTop!| |divideIfCan!| |rightRank| + |subHeight| |generalizedInverse| |elt| |bezoutDiscriminant| + |fillPascalTriangle| |atanhIfCan| |mainVariables| |left| |firstNumer| + |iibinom| |OMputEndAttr| |setProperty| |f02adf| |f04arf| + |setAttributeButtonStep| |digits| |alphabetic?| |right| |rightNorm| + |entry| |replaceKthElement| |diagonalProduct| |s20acf| + |showAllElements| |fill!| |shrinkable| |mulmod| + |stosePrepareSubResAlgo| |sumOfDivisors| |f04atf| |s19abf| + |factorSquareFreeByRecursion| |index?| |removeSinhSq| |distdfact| + |groebgen| |imagI| |f01mcf| |subQuasiComponent?| |consnewpol| + |variable| |diff| |OMputVariable| |infRittWu?| |unitVector| + |shiftRight| |varselect| |mainCoefficients| |e02aef| |zCoord| |empty?| + |basisOfLeftAnnihilator| |leader| |ListOfTerms| + |quasiMonicPolynomials| |atanIfCan| |showTypeInOutput| |overset?| + |domainOf| |d01aqf| |escape| |top| |twoFactor| |lift| |char| + |taylorRep| |idealSimplify| |Gamma| |mpsode| |rootSimp| + |computeCycleEntry| |OMsupportsCD?| |binaryTournament| |continue| + |prinshINFO| |reduce| |addMatchRestricted| |leaf?| + |viewWriteAvailable| |bringDown| |OMUnknownCD?| |iiGamma| |acothIfCan| + |normFactors| |freeOf?| |tensorProduct| |f02axf| |match?| |rdHack1| + |coth2tanh| |fortranDoubleComplex| |vark| |makeUnit| |collectUnder| + |splitLinear| |comment| |diagonalMatrix| |pointSizeDefault| + |commaSeparate| |leastAffineMultiple| |degree| |legendre| |pdct| + |overlabel| |spherical| |aLinear| |modularGcd| |float| |denominators| + |nthFactor| |f04mbf| |setEmpty!| |airyBi| |roughUnitIdeal?| + |variable?| |linear| |rightGcd| |kmax| |rightScalarTimes!| |ignore?| + |interReduce| |outputGeneral| |structuralConstants| |patternMatch| + |besselY| |permutationRepresentation| |space| |integerBound| + |subCase?| |dihedral| |iFTable| |cyclotomicDecomposition| |changeName| + |simpson| |presub| |indiceSubResultantEuclidean| |polynomial| + |deleteRoutine!| |exprHasLogarithmicWeights| |resetVariableOrder| + |node?| |multiple?| |boundOfCauchy| |cTan| |monomRDEsys| + |primitivePart!| |setMinPoints3D| |children| |inspect| |OMputEndAtp| + |updatD| |invertibleElseSplit?| |tanh2trigh| |inconsistent?| + |rewriteIdealWithQuasiMonicGenerators| |dot| |updatF| |squareFree| + |ellipticCylindrical| |transcendentalDecompose| |c02aff| |d02ejf| + |clipBoolean| |equiv| |numericalOptimization| |extension| |omError| + |iiexp| |safeFloor| GF2FG |makeop| |conditionsForIdempotents| UP2UTS + |e02bbf| |invertIfCan| |unitsColorDefault| |augment| |ratPoly| + |makeYoungTableau| |lintgcd| |curve| |null?| |setScreenResolution3D| + |resetAttributeButtons| |bfEntry| |setsubMatrix!| |dilog| GE + |checkForZero| |curveColorPalette| |printCode| |sin?| |sin2csc| + |zeroDimPrimary?| |invmultisect| |multiEuclidean| |noKaratsuba| |sub| + GT |s20adf| |stoseInvertible?sqfreg| |tValues| |possiblyInfinite?| + |copyInto!| |c05pbf| |genericRightMinimalPolynomial| |finite?| + |badValues| LE |sin| |complexExpand| |iilog| |solveid| |nextPartition| + |ODESolve| |factorPolynomial| |ratDenom| |balancedFactorisation| + |trueEqual| LT |cos| |rule| |someBasis| |integralCoordinates| |fmecg| + |iteratedInitials| LODO2FUN |linearDependence| |minset| |limitPlus| + |tan| |OMwrite| |integerIfCan| |symbol| |factorGroebnerBasis| |roman| + |reducedForm| |polar| |bezoutResultant| |redPo| |f02xef| |nthExponent| + |s19acf| |createMultiplicationTable| |nextsubResultant2| + |normalizeIfCan| |cycleTail| |c06ekf| |setTex!| |cot| + |separateFactors| |integer| |remainder| |leadingIndex| + |subResultantChain| |associatedEquations| |lookup| |fullDisplay| + |completeHensel| |PDESolve| |topPredicate| |lighting| + |semiLastSubResultantEuclidean| |rowEchelon| |numberOfIrreduciblePoly| + |myDegree| |addmod| |qinterval| |midpoint| |sec| + |primPartElseUnitCanonical| |scanOneDimSubspaces| |wreath| |subst| + |numberOfPrimitivePoly| |setOrder| |elColumn2!| ^ |limit| + |symmetricProduct| |composites| |setProperties!| |leftRecip| |setref| + |optAttributes| |leftNorm| |imagE| |unary?| |LagrangeInterpolation| + |shade| |secIfCan| |isAbsolutelyIrreducible?| |rectangularMatrix| + |d01apf| |createMultiplicationMatrix| |OMopenString| + |basisOfLeftNucloid| |insertMatch| |viewWriteDefault| |compose| |qqq| + |hitherPlane| |complexNumericIfCan| |initiallyReduced?| |ravel| + |rightUnits| |leadingExponent| |low| |chineseRemainder| |zag| + |conditionP| |subscriptedVariables| |reshape| |Lazard2| |slex| + |arrayStack| |permanent| |digit?| |expIfCan| |meshPar2Var| |e04gcf| + |pow| |lfextlimint| |OMUnknownSymbol?| |arity| |rightExactQuotient| + |quatern| |linears| |normal01| |primlimitedint| |deref| |curryLeft| + |objects| |computeInt| |getStream| |sum| |tanIfCan| |queue| + |loopPoints| |df2st| |asimpson| |key?| |base| |OMputEndObject| + |lazyIntegrate| |genericRightTraceForm| |explogs2trigs| |setrest!| + |leftExactQuotient| |LazardQuotient2| |size?| |gradient| |double| + |printInfo| |palgRDE| |s13acf| |color| |solveRetract| |weakBiRank| + |f02fjf| |iicosh| |update| |e02daf| |listYoungTableaus| |directory| + |f01maf| |clipSurface| |numberOfComposites| |axes| |csc| |basicSet| + |simplify| |resultant| |prinpolINFO| |viewThetaDefault| |tanintegrate| + |makeSeries| |oblateSpheroidal| |palgRDE0| |asin| |rootPoly| + |basisOfNucleus| |getRef| |badNum| + |removeRoughlyRedundantFactorsInContents| |ParCond| |clearTheFTable| + |viewPosDefault| |generator| |chiSquare| |setButtonValue| |acos| + |cond| |rowEch| |createPrimitiveElement| |polyRicDE| |iCompose| |/\\| + |exteriorDifferential| |choosemon| |getlo| |pseudoDivide| + |getExplanations| |sylvesterMatrix| |highCommonTerms| + |oddInfiniteProduct| |newSubProgram| |\\/| |OMsetEncoding| + |rightAlternative?| |f02aef| |s21bdf| |errorInfo| |complexZeros| + |ldf2lst| |pushNewContour| |zoom| |newLine| + |initializeGroupForWordProblem| |d01alf| |f02bjf| |coordinate| + |selectPDERoutines| |finiteBasis| |atan| |drawComplexVectorField| + |traceMatrix| |position| |viewDefaults| |factorOfDegree| + |explicitlyEmpty?| |declare!| |polarCoordinates| |splitNodeOf!| + |useSingleFactorBound| |even?| |semicolonSeparate| |patternMatchTimes| + |OMbindTCP| |pmintegrate| |round| |increasePrecision| |OMclose| + |OMputEndBind| |simplifyLog| |adaptive?| |resultantReduit| + |fortranReal| |removeSuperfluousCases| |palgextint| + |basisOfRightNucloid| |reverseLex| |anticoord| |subResultantGcd| + |eigenvalues| |OMgetEndBVar| |llprop| |euclideanNormalForm| + |exactQuotient!| |applyRules| |OMputEndError| |previous| |rk4f| + |e01bhf| |OMputSymbol| |fglmIfCan| |quasiAlgebraicSet| |OMgetEndApp| + |tube| |numerators| |kovacic| |dominantTerm| + |factorsOfCyclicGroupSize| |minrank| |exprHasAlgebraicWeight| + |swapColumns!| |bag| |plotPolar| |symmetricDifference| |knownInfBasis| + |lo| |reindex| |createNormalElement| |e01bgf| |stoseInvertibleSetreg| + |s17ahf| |nthRootIfCan| |interpret| + |generalizedContinuumHypothesisAssumed?| |rotatex| |normalDeriv| + |primitive?| |f02bbf| |incr| |mkcomm| |complementaryBasis| |Hausdorff| + |complete| |critM| |extractClosed| |true| |nextIrreduciblePoly| + |constantIfCan| |primitiveElement| |dimension| |real?| |hi| |central?| + |physicalLength!| |leftAlternative?| |sqfree| |imagj| |rotate| + |genericLeftNorm| |perfectNthRoot| |and| |ode1| |normalizeAtInfinity| + |removeRedundantFactors| |bandedHessian| |powers| + |stoseInvertibleSetsqfreg| |minPoints| |iiacosh| |cyclic?| |belong?| + |linearAssociatedLog| |e02gaf| |normalElement| |cschIfCan| |f04axf| + |numberOfVariables| |tan2cot| |changeNameToObjf| |collect| |reduced?| + |taylorQuoByVar| |selectsecond| |moduleSum| |orbits| |unitNormalize| + |exists?| |primaryDecomp| |option?| |LyndonBasis| + |associatorDependence| |zerosOf| |rquo| |OMreadFile| |c06ecf| |tail| + |denomRicDE| |palgintegrate| |mainPrimitivePart| |diag| |padecf| + |pointColor| |dimensionsOf| |factorsOfDegree| + |semiResultantReduitEuclidean| |incrementKthElement| |output| + |ratpart| |univariatePolynomials| |hash| |nodes| |uniform01| + |prevPrime| |multisect| |primintegrate| |splitDenominator| |order| + |degreePartition| |count| |monomRDE| |factorSFBRlcUnit| |imagk| + |nativeModuleExtension| |singularitiesOf| |gethi| |segment| |npcoef| + |unitNormal| |readIfCan!| |genericRightNorm| |meshFun2Var| |equality| + |weight| |setLabelValue| |s15adf| |noLinearFactor?| |iiacsc| + |superHeight| |iomode| |reducedContinuedFraction| |f07fef| + |numberOfMonomials| |subset?| |zeroVector| |less?| |operation| + |LyndonCoordinates| |multiple| |drawComplex| |outputMeasure| |rst| + |s14aaf| |cap| |SturmHabichtSequence| |changeVar| |wrregime| + |applyQuote| |complexEigenvectors| |binomThmExpt| |inRadical?| + |goodnessOfFit| |selectOptimizationRoutines| |eigenvector| + |rightMinimalPolynomial| |viewPhiDefault| |var1StepsDefault| |f2df| + |dAndcExp| |linearDependenceOverZ| |logIfCan| |matrix| |interpolate| + |moebius| |pushdterm| |ldf2vmf| |evenInfiniteProduct| + |limitedIntegrate| |linearlyDependent?| |chebyshevT| |abelianGroup| + |mirror| |generate| |numer| |constructorName| |neglist| |scopes| + |continuedFraction| |parabolic| |d01akf| |mr| |s17acf| |ruleset| + |evaluate| |perspective| |forLoop| |negative?| |denom| |idealiser| + |cycleLength| |plusInfinity| |mapmult| |listOfMonoms| |hermiteH| ~= + |radix| |setleft!| |printingInfo?| |setVariableOrder| + |getVariableOrder| |iipow| |notelem| |minusInfinity| |henselFact| + |iicos| |firstUncouplingMatrix| |approximants| |coerce| |lyndon?| + |ddFact| |cotIfCan| |lazyPquo| |retract| |pi| |trunc| |mat| |tableau| + |solveLinearPolynomialEquationByRecursion| |currentScope| |point| + |suchThat| |construct| |discriminant| |getCode| + |semiResultantEuclidean2| |term?| |infinity| |rightOne| + |symmetricSquare| |extractPoint| |exponents| |csc2sin| |e04dgf| + |OMputInteger| |satisfy?| |length| |decompose| |ode| |s13aaf| + |mapDown!| |rightFactorCandidate| |quadratic?| |randomLC| |e02bdf| + |characteristicSet| |prod| |scripts| |laplacian| |s18aef| + |constantOpIfCan| |Is| |laurentRep| |returns| |scripted?| |twist| + |antiCommutator| |getOperands| |leftDivide| |collectUpper| |kernel| + |kernels| |addPoint2| |seriesSolve| |mesh?| |nextNormalPoly| + |getGraph| |rk4qc| |startTableInvSet!| |root?| |linearAssociatedOrder| + |internalIntegrate| |draw| |type| |distFact| |s15aef| + |selectFiniteRoutines| |univariate| |autoReduced?| |triangSolve| + |orbit| |stoseIntegralLastSubResultant| |cos2sec| |power!| |dmpToP| + |cubic| |rootsOf| |writable?| |lastSubResultantElseSplit| + |rationalFunction| |iitanh| |idealiserMatrix| |lfextendedint| |s17aff| + |testModulus| |rightRegularRepresentation| |d01ajf| |ipow| |concat!| + |lllip| |bipolar| |setlast!| |bfKeys| |squareFreePart| + |expenseOfEvaluation| |squareFreeLexTriangular| + |getMultiplicationMatrix| |semiResultantEuclidean1| |LiePoly| |factor| + |find| |f01qdf| |setPrologue!| |remove!| |element?| |part?| |addMatch| + |factorByRecursion| |tab| |sqrt| |OMencodingXML| |exponentialOrder| + |bit?| |OMgetBVar| |andOperands| |f07fdf| |certainlySubVariety?| + |open?| |real| |polyred| |readLineIfCan!| |dec| |tracePowMod| + |basisOfRightNucleus| |hessian| |quotedOperators| |problemPoints| + |s18def| |cTanh| |cPower| |makeMulti| |imag| |constDsolve| + |basisOfLeftNucleus| |alternating| |predicates| |directProduct| + |cyclicEntries| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 6cb601e7..a8e34635 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4920 +1,4920 @@ -(3148834 . 3425075231) -((-2470 (((-108) (-1 (-108) |#2| |#2|) $) 63) (((-108) $) NIL)) (-2165 (($ (-1 (-108) |#2| |#2|) $) 18) (($ $) NIL)) (-1430 ((|#2| $ (-525) |#2|) NIL) ((|#2| $ (-1141 (-525)) |#2|) 34)) (-2700 (($ $) 59)) (-1284 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| 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T) ((-23) . T) ((-25) . T) ((-37 #0=(-385 (-525))) -2067 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-37 |#1|) . T) ((-37 $) -2067 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-34) |has| |#1| (-1114)) ((-91) |has| |#1| (-1114)) ((-97) . T) ((-107 #0# #0#) -2067 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-126) . T) ((-136) -2067 (|has| |#1| (-327)) (|has| |#1| (-136))) ((-138) |has| |#1| (-138)) ((-566 (-798)) . T) ((-160) . T) ((-567 (-157 (-205))) |has| |#1| (-953)) ((-567 (-157 (-357))) |has| |#1| (-953)) ((-567 (-501)) |has| |#1| (-567 (-501))) ((-567 (-827 (-357))) |has| |#1| (-567 (-827 (-357)))) ((-567 (-827 (-525))) |has| |#1| (-567 (-827 (-525)))) ((-567 #1=(-1088 |#1|)) . T) ((-211 |#1|) . 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(|has| |#2| (-735)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-33) . 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T) ((-37 |#2|) |has| |#2| (-160)) ((-97) -2067 (|has| |#2| (-1020)) (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-669)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-107 |#2| |#2|) -2067 (|has| |#2| (-977)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-107 $ $) |has| |#2| (-160)) ((-126) -2067 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126))) ((-566 (-798)) -2067 (|has| |#2| (-1020)) (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-669)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-566 (-798))) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-566 (-1174 |#2|)) . T) ((-160) |has| |#2| (-160)) ((-211 |#2|) |has| |#2| (-977)) ((-213) -12 (|has| |#2| (-213)) (|has| |#2| (-977))) ((-265 #0=(-525) |#2|) . T) ((-267 #0# |#2|) . T) ((-288 |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((-346) |has| |#2| (-346)) ((-355 |#2|) |has| |#2| (-977)) ((-389 |#2|) |has| |#2| (-1020)) ((-464 |#2|) . T) ((-558 #0# |#2|) . T) ((-486 |#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1020))) ((-594 |#2|) -2067 (|has| |#2| (-977)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-594 $) -2067 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-588 (-525)) -12 (|has| |#2| (-588 (-525))) (|has| |#2| (-977))) ((-588 |#2|) |has| |#2| (-977)) ((-660 |#2|) -2067 (|has| |#2| (-341)) (|has| |#2| (-160))) ((-669) -2067 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-669)) (|has| |#2| (-160))) ((-733) |has| |#2| (-787)) ((-734) -2067 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-735) |has| |#2| (-735)) ((-736) -2067 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-737) -2067 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-787) |has| |#2| (-787)) ((-789) -2067 (|has| |#2| (-787)) (|has| |#2| (-735))) ((-835 (-1092)) -12 (|has| |#2| (-835 (-1092))) (|has| |#2| (-977))) ((-968 (-385 (-525))) -12 (|has| |#2| (-968 (-385 (-525)))) (|has| |#2| (-1020))) ((-968 (-525)) -12 (|has| |#2| (-968 (-525))) (|has| |#2| (-1020))) ((-968 |#2|) |has| |#2| (-1020)) ((-983 |#2|) -2067 (|has| |#2| (-977)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-983 $) |has| |#2| (-160)) ((-977) -2067 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-984) -2067 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-160))) ((-1032) -2067 (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-669)) (|has| |#2| (-160))) ((-1020) -2067 (|has| |#2| (-1020)) (|has| |#2| (-977)) (|has| |#2| (-787)) (|has| |#2| (-735)) (|has| |#2| (-669)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-1128) . T) ((-1181 |#2|) |has| |#2| (-341))) +((-2159 (((-220 |#1| |#3|) (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|) 21)) (-3504 ((|#3| (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|) 23)) (-2016 (((-220 |#1| |#3|) (-1 |#3| |#2|) (-220 |#1| |#2|)) 18))) +(((-219 |#1| |#2| |#3|) (-10 -7 (-15 -2159 ((-220 |#1| |#3|) (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|)) (-15 -3504 (|#3| (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|)) (-15 -2016 ((-220 |#1| |#3|) (-1 |#3| |#2|) (-220 |#1| |#2|)))) (-713) (-1128) (-1128)) (T -219)) +((-2016 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-220 *5 *6)) (-14 *5 (-713)) (-4 *6 (-1128)) (-4 *7 (-1128)) (-5 *2 (-220 *5 *7)) (-5 *1 (-219 *5 *6 *7)))) (-3504 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-220 *5 *6)) (-14 *5 (-713)) (-4 *6 (-1128)) (-4 *2 (-1128)) (-5 *1 (-219 *5 *6 *2)))) (-2159 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-220 *6 *7)) (-14 *6 (-713)) (-4 *7 (-1128)) (-4 *5 (-1128)) (-5 *2 (-220 *6 *5)) (-5 *1 (-219 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-46 |#1| #0=(-713)) . T) ((-25) . T) ((-37 #1=(-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((-37 |#1|) |has| |#1| (-160)) ((-37 $) -2067 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341))) ((-97) . T) ((-107 #1# #1#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -2067 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-126) . T) ((-136) |has| |#1| (-136)) ((-138) |has| |#1| (-138)) ((-566 (-798)) . T) ((-160) -2067 (|has| |#1| (-844)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-567 (-501)) -12 (|has| (-1005) (-567 (-501))) (|has| |#1| (-567 (-501)))) ((-567 (-827 (-357))) -12 (|has| (-1005) (-567 (-827 (-357)))) (|has| |#1| (-567 (-827 (-357))))) ((-567 (-827 (-525))) -12 (|has| (-1005) (-567 (-827 (-525)))) (|has| |#1| (-567 (-827 (-525))))) ((-211 |#1|) . T) ((-213) . 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3131806 "XPR" 3132897 NIL XPR (NIL T T) -8 NIL NIL) (-1194 3127609 3129230 3129433 "XPOLY" 3129726 NIL XPOLY (NIL T) -8 NIL NIL) (-1193 3125423 3126801 3126855 "XPOLYC" 3127140 NIL XPOLYC (NIL T T) -9 NIL 3127253) (-1192 3121795 3123940 3124328 "XPBWPOLY" 3125081 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1191 3117723 3120036 3120078 "XF" 3120699 NIL XF (NIL T) -9 NIL 3121098) (-1190 3117344 3117432 3117601 "XF-" 3117606 NIL XF- (NIL T T) -8 NIL NIL) (-1189 3112724 3114023 3114077 "XFALG" 3116225 NIL XFALG (NIL T T) -9 NIL 3117012) (-1188 3111861 3111965 3112169 "XEXPPKG" 3112616 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1187 3109960 3111712 3111807 "XDPOLY" 3111812 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1186 3108839 3109449 3109491 "XALG" 3109553 NIL XALG (NIL T) -9 NIL 3109672) (-1185 3102315 3106823 3107316 "WUTSET" 3108431 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1184 3100127 3100934 3101285 "WP" 3102097 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1183 3099013 3099211 3099506 "WFFINTBS" 3099924 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1182 3096917 3097344 3097806 "WEIER" 3098585 NIL WEIER (NIL T) -7 NIL NIL) (-1181 3096066 3096490 3096532 "VSPACE" 3096668 NIL VSPACE (NIL T) -9 NIL 3096742) (-1180 3095904 3095931 3096022 "VSPACE-" 3096027 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1179 3095650 3095693 3095764 "VOID" 3095855 T VOID (NIL) -8 NIL NIL) (-1178 3093786 3094145 3094551 "VIEW" 3095266 T VIEW (NIL) -7 NIL NIL) (-1177 3090211 3090849 3091586 "VIEWDEF" 3093071 T VIEWDEF (NIL) -7 NIL NIL) (-1176 3079549 3081759 3083932 "VIEW3D" 3088060 T VIEW3D (NIL) -8 NIL NIL) (-1175 3071831 3073460 3075039 "VIEW2D" 3077992 T VIEW2D (NIL) -8 NIL NIL) (-1174 3067240 3071601 3071693 "VECTOR" 3071774 NIL VECTOR (NIL T) -8 NIL NIL) (-1173 3065817 3066076 3066394 "VECTOR2" 3066970 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1172 3059357 3063609 3063652 "VECTCAT" 3064640 NIL VECTCAT (NIL T) -9 NIL 3065224) (-1171 3058371 3058625 3059015 "VECTCAT-" 3059020 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1170 3057852 3058022 3058142 "VARIABLE" 3058286 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1169 3057785 3057790 3057820 "UTYPE" 3057825 T UTYPE (NIL) -9 NIL NIL) (-1168 3056620 3056774 3057035 "UTSODETL" 3057611 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1167 3054060 3054520 3055044 "UTSODE" 3056161 NIL UTSODE (NIL T T) -7 NIL NIL) (-1166 3045904 3051700 3052188 "UTS" 3053629 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1165 3037249 3042614 3042656 "UTSCAT" 3043757 NIL UTSCAT (NIL T) -9 NIL 3044514) (-1164 3034604 3035320 3036308 "UTSCAT-" 3036313 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1163 3034235 3034278 3034409 "UTS2" 3034555 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1162 3028511 3031076 3031119 "URAGG" 3033189 NIL URAGG (NIL T) -9 NIL 3033911) (-1161 3025450 3026313 3027436 "URAGG-" 3027441 NIL URAGG- (NIL T T) -8 NIL NIL) (-1160 3021136 3024067 3024538 "UPXSSING" 3025114 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1159 3013027 3020257 3020537 "UPXS" 3020913 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1158 3006056 3012932 3013003 "UPXSCONS" 3013008 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1157 2996345 3003175 3003236 "UPXSCCA" 3003885 NIL UPXSCCA (NIL T T) -9 NIL 3004126) (-1156 2995984 2996069 2996242 "UPXSCCA-" 2996247 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1155 2986195 2992798 2992840 "UPXSCAT" 2993483 NIL UPXSCAT (NIL T) -9 NIL 2994091) (-1154 2985629 2985708 2985885 "UPXS2" 2986110 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1153 2984283 2984536 2984887 "UPSQFREE" 2985372 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1152 2978174 2981229 2981283 "UPSCAT" 2982432 NIL UPSCAT (NIL T T) -9 NIL 2983206) (-1151 2977379 2977586 2977912 "UPSCAT-" 2977917 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1150 2963465 2971502 2971544 "UPOLYC" 2973622 NIL UPOLYC (NIL T) -9 NIL 2974843) (-1149 2954795 2957220 2960366 "UPOLYC-" 2960371 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1148 2954426 2954469 2954600 "UPOLYC2" 2954746 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1147 2945845 2953995 2954132 "UP" 2954336 NIL UP (NIL NIL T) -8 NIL NIL) (-1146 2945188 2945295 2945458 "UPMP" 2945734 NIL UPMP (NIL T T) -7 NIL NIL) (-1145 2944741 2944822 2944961 "UPDIVP" 2945101 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1144 2943309 2943558 2943874 "UPDECOMP" 2944490 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1143 2942544 2942656 2942841 "UPCDEN" 2943193 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1142 2942067 2942136 2942283 "UP2" 2942469 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1141 2940584 2941271 2941548 "UNISEG" 2941825 NIL UNISEG (NIL T) -8 NIL NIL) (-1140 2939799 2939926 2940131 "UNISEG2" 2940427 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1139 2938859 2939039 2939265 "UNIFACT" 2939615 NIL UNIFACT (NIL T) -7 NIL NIL) (-1138 2922755 2938040 2938290 "ULS" 2938666 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1137 2910720 2922660 2922731 "ULSCONS" 2922736 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1136 2893470 2905483 2905544 "ULSCCAT" 2906256 NIL ULSCCAT (NIL T T) -9 NIL 2906552) (-1135 2892521 2892766 2893153 "ULSCCAT-" 2893158 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1134 2882511 2889028 2889070 "ULSCAT" 2889926 NIL ULSCAT (NIL T) -9 NIL 2890656) (-1133 2881945 2882024 2882201 "ULS2" 2882426 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1132 2880343 2881310 2881340 "UFD" 2881552 T UFD (NIL) -9 NIL 2881666) (-1131 2880137 2880183 2880278 "UFD-" 2880283 NIL UFD- (NIL T) -8 NIL NIL) (-1130 2879219 2879402 2879618 "UDVO" 2879943 T UDVO (NIL) -7 NIL NIL) (-1129 2877035 2877444 2877915 "UDPO" 2878783 NIL UDPO (NIL T) -7 NIL NIL) (-1128 2876968 2876973 2877003 "TYPE" 2877008 T TYPE (NIL) -9 NIL NIL) (-1127 2875939 2876141 2876381 "TWOFACT" 2876762 NIL TWOFACT (NIL T) -7 NIL NIL) (-1126 2874877 2875214 2875477 "TUPLE" 2875711 NIL TUPLE (NIL T) -8 NIL NIL) (-1125 2872568 2873087 2873626 "TUBETOOL" 2874360 T TUBETOOL (NIL) -7 NIL NIL) (-1124 2871417 2871622 2871863 "TUBE" 2872361 NIL TUBE (NIL T) -8 NIL NIL) (-1123 2866141 2870395 2870677 "TS" 2871169 NIL TS (NIL T) -8 NIL NIL) (-1122 2854845 2858937 2859033 "TSETCAT" 2864267 NIL TSETCAT (NIL T T T T) -9 NIL 2865798) (-1121 2849580 2851178 2853068 "TSETCAT-" 2853073 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1120 2843843 2844689 2845631 "TRMANIP" 2848716 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1119 2843284 2843347 2843510 "TRIMAT" 2843775 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1118 2841090 2841327 2841690 "TRIGMNIP" 2843033 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1117 2840610 2840723 2840753 "TRIGCAT" 2840966 T TRIGCAT (NIL) -9 NIL NIL) (-1116 2840279 2840358 2840499 "TRIGCAT-" 2840504 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1115 2837178 2839139 2839419 "TREE" 2840034 NIL TREE (NIL T) -8 NIL NIL) (-1114 2836452 2836980 2837010 "TRANFUN" 2837045 T TRANFUN (NIL) -9 NIL 2837111) (-1113 2835731 2835922 2836202 "TRANFUN-" 2836207 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1112 2835535 2835567 2835628 "TOPSP" 2835692 T TOPSP (NIL) -7 NIL NIL) (-1111 2834887 2835002 2835155 "TOOLSIGN" 2835416 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1110 2833548 2834064 2834303 "TEXTFILE" 2834670 T TEXTFILE (NIL) -8 NIL NIL) (-1109 2831413 2831927 2832365 "TEX" 2833132 T TEX (NIL) -8 NIL NIL) (-1108 2831194 2831225 2831297 "TEX1" 2831376 NIL TEX1 (NIL T) -7 NIL NIL) (-1107 2830842 2830905 2830995 "TEMUTL" 2831126 T TEMUTL (NIL) -7 NIL NIL) (-1106 2828996 2829276 2829601 "TBCMPPK" 2830565 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1105 2820885 2827157 2827213 "TBAGG" 2827613 NIL TBAGG (NIL T T) -9 NIL 2827824) (-1104 2815955 2817443 2819197 "TBAGG-" 2819202 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1103 2815339 2815446 2815591 "TANEXP" 2815844 NIL TANEXP (NIL T) -7 NIL NIL) (-1102 2808840 2815196 2815289 "TABLE" 2815294 NIL TABLE (NIL T T) -8 NIL NIL) (-1101 2808252 2808351 2808489 "TABLEAU" 2808737 NIL TABLEAU (NIL T) -8 NIL NIL) (-1100 2802860 2804080 2805328 "TABLBUMP" 2807038 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1099 2802288 2802388 2802516 "SYSTEM" 2802754 T SYSTEM (NIL) -7 NIL NIL) (-1098 2798751 2799446 2800229 "SYSSOLP" 2801539 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1097 2795042 2795750 2796484 "SYNTAX" 2798039 T SYNTAX (NIL) -8 NIL NIL) (-1096 2792176 2792784 2793422 "SYMTAB" 2794426 T SYMTAB (NIL) -8 NIL NIL) (-1095 2787425 2788327 2789310 "SYMS" 2791215 T SYMS (NIL) -8 NIL NIL) (-1094 2784658 2786885 2787114 "SYMPOLY" 2787230 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1093 2784178 2784253 2784375 "SYMFUNC" 2784570 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1092 2780155 2781415 2782237 "SYMBOL" 2783378 T SYMBOL (NIL) -8 NIL NIL) (-1091 2773694 2775383 2777103 "SWITCH" 2778457 T SWITCH (NIL) -8 NIL NIL) (-1090 2766924 2772521 2772823 "SUTS" 2773449 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1089 2758814 2766045 2766325 "SUPXS" 2766701 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1088 2750306 2758435 2758560 "SUP" 2758723 NIL SUP (NIL T) -8 NIL NIL) (-1087 2749465 2749592 2749809 "SUPFRACF" 2750174 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1086 2749090 2749149 2749260 "SUP2" 2749400 NIL SUP2 (NIL T T) -7 NIL NIL) (-1085 2747508 2747782 2748144 "SUMRF" 2748789 NIL SUMRF (NIL T) -7 NIL NIL) (-1084 2746825 2746891 2747089 "SUMFS" 2747429 NIL SUMFS (NIL T T) -7 NIL NIL) (-1083 2730761 2746006 2746256 "SULS" 2746632 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1082 2730083 2730286 2730426 "SUCH" 2730669 NIL SUCH (NIL T T) -8 NIL NIL) (-1081 2724010 2725022 2725980 "SUBSPACE" 2729171 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1080 2723440 2723530 2723694 "SUBRESP" 2723898 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1079 2716809 2718105 2719416 "STTF" 2722176 NIL STTF (NIL T) -7 NIL NIL) (-1078 2710982 2712102 2713249 "STTFNC" 2715709 NIL STTFNC (NIL T) -7 NIL NIL) (-1077 2702333 2704200 2705993 "STTAYLOR" 2709223 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1076 2695577 2702197 2702280 "STRTBL" 2702285 NIL STRTBL (NIL T) -8 NIL NIL) (-1075 2690968 2695532 2695563 "STRING" 2695568 T STRING (NIL) -8 NIL NIL) (-1074 2685857 2690342 2690372 "STRICAT" 2690431 T STRICAT (NIL) -9 NIL 2690493) (-1073 2678571 2683380 2684000 "STREAM" 2685272 NIL STREAM (NIL T) -8 NIL NIL) (-1072 2678081 2678158 2678302 "STREAM3" 2678488 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1071 2677063 2677246 2677481 "STREAM2" 2677894 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1070 2676751 2676803 2676896 "STREAM1" 2677005 NIL STREAM1 (NIL T) -7 NIL NIL) (-1069 2675767 2675948 2676179 "STINPROD" 2676567 NIL STINPROD (NIL T) -7 NIL NIL) (-1068 2675346 2675530 2675560 "STEP" 2675640 T STEP (NIL) -9 NIL 2675718) (-1067 2668889 2675245 2675322 "STBL" 2675327 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1066 2664065 2668112 2668155 "STAGG" 2668308 NIL STAGG (NIL T) -9 NIL 2668397) (-1065 2661767 2662369 2663241 "STAGG-" 2663246 NIL STAGG- (NIL T T) -8 NIL NIL) (-1064 2659962 2661537 2661629 "STACK" 2661710 NIL STACK (NIL T) -8 NIL NIL) (-1063 2652693 2658109 2658564 "SREGSET" 2659592 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1062 2645133 2646501 2648013 "SRDCMPK" 2651299 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1061 2638101 2642574 2642604 "SRAGG" 2643907 T SRAGG (NIL) -9 NIL 2644515) (-1060 2637118 2637373 2637752 "SRAGG-" 2637757 NIL SRAGG- (NIL T) -8 NIL NIL) (-1059 2631567 2636037 2636464 "SQMATRIX" 2636737 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1058 2625319 2628287 2629013 "SPLTREE" 2630913 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1057 2621309 2621975 2622621 "SPLNODE" 2624745 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1056 2620356 2620589 2620619 "SPFCAT" 2621063 T SPFCAT (NIL) -9 NIL NIL) (-1055 2619093 2619303 2619567 "SPECOUT" 2620114 T SPECOUT (NIL) -7 NIL NIL) (-1054 2618854 2618894 2618963 "SPADPRSR" 2619046 T SPADPRSR (NIL) -7 NIL NIL) (-1053 2610877 2612624 2612666 "SPACEC" 2616989 NIL SPACEC (NIL T) -9 NIL 2618805) (-1052 2609048 2610810 2610858 "SPACE3" 2610863 NIL SPACE3 (NIL T) -8 NIL NIL) (-1051 2607800 2607971 2608262 "SORTPAK" 2608853 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1050 2605856 2606159 2606577 "SOLVETRA" 2607464 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1049 2604867 2605089 2605363 "SOLVESER" 2605629 NIL SOLVESER (NIL T) -7 NIL NIL) (-1048 2600087 2600968 2601970 "SOLVERAD" 2603919 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1047 2595902 2596511 2597240 "SOLVEFOR" 2599454 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1046 2590202 2595254 2595350 "SNTSCAT" 2595355 NIL SNTSCAT (NIL T T T T) -9 NIL 2595425) (-1045 2584306 2588533 2588923 "SMTS" 2589892 NIL SMTS (NIL T T T) -8 NIL NIL) (-1044 2578716 2584195 2584271 "SMP" 2584276 NIL SMP (NIL T T) -8 NIL NIL) (-1043 2576875 2577176 2577574 "SMITH" 2578413 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1042 2569840 2574036 2574138 "SMATCAT" 2575478 NIL SMATCAT (NIL NIL T T T) -9 NIL 2576027) (-1041 2566781 2567604 2568781 "SMATCAT-" 2568786 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1040 2564495 2566018 2566061 "SKAGG" 2566322 NIL SKAGG (NIL T) -9 NIL 2566457) (-1039 2560553 2563599 2563877 "SINT" 2564239 T SINT (NIL) -8 NIL NIL) (-1038 2560325 2560363 2560429 "SIMPAN" 2560509 T SIMPAN (NIL) -7 NIL NIL) (-1037 2559841 2560027 2560126 "SIG" 2560248 T SIG (NIL) -8 NIL NIL) (-1036 2558679 2558900 2559175 "SIGNRF" 2559600 NIL SIGNRF (NIL T) -7 NIL NIL) (-1035 2557488 2557639 2557929 "SIGNEF" 2558508 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1034 2555178 2555632 2556138 "SHP" 2557029 NIL SHP (NIL T NIL) -7 NIL NIL) (-1033 2549031 2555079 2555155 "SHDP" 2555160 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1032 2548521 2548713 2548743 "SGROUP" 2548895 T SGROUP (NIL) -9 NIL 2548982) (-1031 2548291 2548343 2548447 "SGROUP-" 2548452 NIL SGROUP- (NIL T) -8 NIL NIL) (-1030 2545127 2545824 2546547 "SGCF" 2547590 T SGCF (NIL) -7 NIL NIL) (-1029 2539526 2544578 2544674 "SFRTCAT" 2544679 NIL SFRTCAT (NIL T T T T) -9 NIL 2544717) (-1028 2532986 2534001 2535135 "SFRGCD" 2538509 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1027 2526152 2527223 2528407 "SFQCMPK" 2531919 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1026 2525774 2525863 2525973 "SFORT" 2526093 NIL SFORT (NIL T T) -8 NIL NIL) (-1025 2524919 2525614 2525735 "SEXOF" 2525740 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1024 2524053 2524800 2524868 "SEX" 2524873 T SEX (NIL) -8 NIL NIL) (-1023 2518830 2519519 2519614 "SEXCAT" 2523385 NIL SEXCAT (NIL T T T T T) -9 NIL 2524004) (-1022 2516010 2518764 2518812 "SET" 2518817 NIL SET (NIL T) -8 NIL NIL) (-1021 2514261 2514723 2515028 "SETMN" 2515751 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1020 2513869 2513995 2514025 "SETCAT" 2514142 T SETCAT (NIL) -9 NIL 2514226) (-1019 2513649 2513701 2513800 "SETCAT-" 2513805 NIL SETCAT- (NIL T) -8 NIL NIL) (-1018 2510037 2512111 2512154 "SETAGG" 2513024 NIL SETAGG (NIL T) -9 NIL 2513364) (-1017 2509495 2509611 2509848 "SETAGG-" 2509853 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1016 2508699 2508992 2509053 "SEGXCAT" 2509339 NIL SEGXCAT (NIL T T) -9 NIL 2509459) (-1015 2507755 2508365 2508547 "SEG" 2508552 NIL SEG (NIL T) -8 NIL NIL) (-1014 2506662 2506875 2506918 "SEGCAT" 2507500 NIL SEGCAT (NIL T) -9 NIL 2507738) (-1013 2505711 2506041 2506241 "SEGBIND" 2506497 NIL SEGBIND (NIL T) -8 NIL NIL) (-1012 2505332 2505391 2505504 "SEGBIND2" 2505646 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1011 2504551 2504677 2504881 "SEG2" 2505176 NIL SEG2 (NIL T T) -7 NIL NIL) (-1010 2503988 2504486 2504533 "SDVAR" 2504538 NIL SDVAR (NIL T) -8 NIL NIL) (-1009 2496240 2503761 2503889 "SDPOL" 2503894 NIL SDPOL (NIL T) -8 NIL NIL) (-1008 2494833 2495099 2495418 "SCPKG" 2495955 NIL SCPKG (NIL T) -7 NIL NIL) (-1007 2493969 2494149 2494349 "SCOPE" 2494655 T SCOPE (NIL) -8 NIL NIL) (-1006 2493190 2493323 2493502 "SCACHE" 2493824 NIL SCACHE (NIL T) -7 NIL NIL) (-1005 2492629 2492950 2493035 "SAOS" 2493127 T SAOS (NIL) -8 NIL NIL) (-1004 2492194 2492229 2492402 "SAERFFC" 2492588 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1003 2486088 2492091 2492171 "SAE" 2492176 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1002 2485681 2485716 2485875 "SAEFACT" 2486047 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1001 2484002 2484316 2484717 "RURPK" 2485347 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1000 2482650 2482927 2483236 "RULESET" 2483838 NIL RULESET (NIL T T T) -8 NIL NIL) (-999 2479858 2480361 2480822 "RULE" 2482332 NIL RULE (NIL T T T) -8 NIL NIL) (-998 2479500 2479655 2479736 "RULECOLD" 2479810 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-997 2474392 2475186 2476102 "RSETGCD" 2478699 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-996 2463707 2468759 2468853 "RSETCAT" 2472918 NIL RSETCAT (NIL T T T T) -9 NIL 2474015) (-995 2461638 2462177 2462997 "RSETCAT-" 2463002 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-994 2454068 2455443 2456959 "RSDCMPK" 2460237 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-993 2452086 2452527 2452599 "RRCC" 2453675 NIL RRCC (NIL T T) -9 NIL 2454019) (-992 2451440 2451614 2451890 "RRCC-" 2451895 NIL RRCC- (NIL T T T) -8 NIL NIL) (-991 2425807 2435432 2435496 "RPOLCAT" 2445998 NIL RPOLCAT (NIL T T T) -9 NIL 2449156) (-990 2417311 2419649 2422767 "RPOLCAT-" 2422772 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-989 2408377 2415541 2416021 "ROUTINE" 2416851 T ROUTINE (NIL) -8 NIL NIL) (-988 2405082 2407933 2408080 "ROMAN" 2408250 T ROMAN (NIL) -8 NIL NIL) (-987 2403368 2403953 2404210 "ROIRC" 2404888 NIL ROIRC (NIL T T) -8 NIL NIL) (-986 2399773 2402077 2402105 "RNS" 2402401 T RNS (NIL) -9 NIL 2402671) (-985 2398287 2398670 2399201 "RNS-" 2399274 NIL RNS- (NIL T) -8 NIL NIL) (-984 2397713 2398121 2398149 "RNG" 2398154 T RNG (NIL) -9 NIL 2398175) (-983 2397111 2397473 2397513 "RMODULE" 2397573 NIL RMODULE (NIL T) -9 NIL 2397615) (-982 2395963 2396057 2396387 "RMCAT2" 2397012 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-981 2392677 2395146 2395467 "RMATRIX" 2395698 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-980 2385674 2387908 2388020 "RMATCAT" 2391329 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2392311) (-979 2385053 2385200 2385503 "RMATCAT-" 2385508 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-978 2384623 2384698 2384824 "RINTERP" 2384972 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-977 2383674 2384238 2384266 "RING" 2384376 T RING (NIL) -9 NIL 2384470) (-976 2383469 2383513 2383607 "RING-" 2383612 NIL RING- (NIL T) -8 NIL NIL) (-975 2382317 2382554 2382810 "RIDIST" 2383233 T RIDIST (NIL) -7 NIL NIL) (-974 2373639 2381791 2381994 "RGCHAIN" 2382166 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-973 2370644 2371258 2371926 "RF" 2373003 NIL RF (NIL T) -7 NIL NIL) (-972 2370293 2370356 2370457 "RFFACTOR" 2370575 NIL RFFACTOR (NIL T) -7 NIL NIL) (-971 2370021 2370056 2370151 "RFFACT" 2370252 NIL RFFACT (NIL T) -7 NIL NIL) (-970 2368151 2368515 2368895 "RFDIST" 2369661 T RFDIST (NIL) -7 NIL NIL) (-969 2367609 2367701 2367861 "RETSOL" 2368053 NIL RETSOL (NIL T T) -7 NIL NIL) (-968 2367202 2367282 2367323 "RETRACT" 2367513 NIL RETRACT (NIL T) -9 NIL NIL) (-967 2367054 2367079 2367163 "RETRACT-" 2367168 NIL RETRACT- (NIL T T) -8 NIL NIL) (-966 2359912 2366711 2366836 "RESULT" 2366949 T RESULT (NIL) -8 NIL NIL) (-965 2358497 2359186 2359383 "RESRING" 2359815 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-964 2358137 2358186 2358282 "RESLATC" 2358434 NIL RESLATC (NIL T) -7 NIL NIL) (-963 2357846 2357880 2357985 "REPSQ" 2358096 NIL REPSQ (NIL T) -7 NIL NIL) (-962 2355277 2355857 2356457 "REP" 2357266 T REP (NIL) -7 NIL NIL) (-961 2354978 2355012 2355121 "REPDB" 2355236 NIL REPDB (NIL T) -7 NIL NIL) (-960 2348923 2350302 2351522 "REP2" 2353790 NIL REP2 (NIL T) -7 NIL NIL) (-959 2345329 2346010 2346815 "REP1" 2348150 NIL REP1 (NIL T) -7 NIL NIL) (-958 2338075 2343490 2343942 "REGSET" 2344960 NIL REGSET (NIL T T T T) -8 NIL NIL) (-957 2336896 2337231 2337479 "REF" 2337860 NIL REF (NIL T) -8 NIL NIL) (-956 2336277 2336380 2336545 "REDORDER" 2336780 NIL REDORDER (NIL T T) -7 NIL NIL) (-955 2332246 2335511 2335732 "RECLOS" 2336108 NIL RECLOS (NIL T) -8 NIL NIL) (-954 2331303 2331484 2331697 "REALSOLV" 2332053 T REALSOLV (NIL) -7 NIL NIL) (-953 2331151 2331192 2331220 "REAL" 2331225 T REAL (NIL) -9 NIL 2331260) (-952 2327642 2328444 2329326 "REAL0Q" 2330316 NIL REAL0Q (NIL T) -7 NIL NIL) (-951 2323253 2324241 2325300 "REAL0" 2326623 NIL REAL0 (NIL T) -7 NIL NIL) (-950 2322661 2322733 2322938 "RDIV" 2323175 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-949 2321734 2321908 2322119 "RDIST" 2322483 NIL RDIST (NIL T) -7 NIL NIL) (-948 2320338 2320625 2320994 "RDETRS" 2321442 NIL RDETRS (NIL T T) -7 NIL NIL) (-947 2318159 2318613 2319148 "RDETR" 2319880 NIL RDETR (NIL T T) -7 NIL NIL) (-946 2316775 2317053 2317454 "RDEEFS" 2317875 NIL RDEEFS (NIL T T) -7 NIL NIL) (-945 2315275 2315581 2316010 "RDEEF" 2316463 NIL RDEEF (NIL T T) -7 NIL NIL) (-944 2309560 2312492 2312520 "RCFIELD" 2313797 T RCFIELD (NIL) -9 NIL 2314527) (-943 2307629 2308133 2308826 "RCFIELD-" 2308899 NIL RCFIELD- (NIL T) -8 NIL NIL) (-942 2303961 2305746 2305787 "RCAGG" 2306858 NIL RCAGG (NIL T) -9 NIL 2307323) (-941 2303592 2303686 2303846 "RCAGG-" 2303851 NIL RCAGG- (NIL T T) -8 NIL NIL) (-940 2302936 2303048 2303210 "RATRET" 2303476 NIL RATRET (NIL T) -7 NIL NIL) (-939 2302493 2302560 2302679 "RATFACT" 2302864 NIL RATFACT (NIL T) -7 NIL NIL) (-938 2301808 2301928 2302078 "RANDSRC" 2302363 T RANDSRC (NIL) -7 NIL NIL) (-937 2301545 2301589 2301660 "RADUTIL" 2301757 T RADUTIL (NIL) -7 NIL NIL) (-936 2294552 2300288 2300605 "RADIX" 2301260 NIL RADIX (NIL NIL) -8 NIL NIL) (-935 2286122 2294396 2294524 "RADFF" 2294529 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-934 2285774 2285849 2285877 "RADCAT" 2286034 T RADCAT (NIL) -9 NIL NIL) (-933 2285559 2285607 2285704 "RADCAT-" 2285709 NIL RADCAT- (NIL T) -8 NIL NIL) (-932 2283710 2285334 2285423 "QUEUE" 2285503 NIL QUEUE (NIL T) -8 NIL NIL) (-931 2280207 2283647 2283692 "QUAT" 2283697 NIL QUAT (NIL T) -8 NIL NIL) (-930 2279845 2279888 2280015 "QUATCT2" 2280158 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-929 2273639 2277019 2277059 "QUATCAT" 2277838 NIL QUATCAT (NIL T) -9 NIL 2278603) (-928 2269783 2270820 2272207 "QUATCAT-" 2272301 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-927 2267304 2268868 2268909 "QUAGG" 2269284 NIL QUAGG (NIL T) -9 NIL 2269459) (-926 2266229 2266702 2266874 "QFORM" 2267176 NIL QFORM (NIL NIL T) -8 NIL NIL) (-925 2257526 2262784 2262824 "QFCAT" 2263482 NIL QFCAT (NIL T) -9 NIL 2264475) (-924 2253098 2254299 2255890 "QFCAT-" 2255984 NIL QFCAT- (NIL T T) -8 NIL NIL) (-923 2252736 2252779 2252906 "QFCAT2" 2253049 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-922 2252196 2252306 2252436 "QEQUAT" 2252626 T QEQUAT (NIL) -8 NIL NIL) (-921 2245382 2246453 2247635 "QCMPACK" 2251129 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-920 2242958 2243379 2243807 "QALGSET" 2245037 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-919 2242203 2242377 2242609 "QALGSET2" 2242778 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-918 2240894 2241117 2241434 "PWFFINTB" 2241976 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-917 2239082 2239250 2239603 "PUSHVAR" 2240708 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-916 2235000 2236054 2236095 "PTRANFN" 2237979 NIL PTRANFN (NIL T) -9 NIL NIL) (-915 2233412 2233703 2234024 "PTPACK" 2234711 NIL PTPACK (NIL T) -7 NIL NIL) (-914 2233048 2233105 2233212 "PTFUNC2" 2233349 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-913 2227525 2231866 2231906 "PTCAT" 2232274 NIL PTCAT (NIL T) -9 NIL 2232436) (-912 2227183 2227218 2227342 "PSQFR" 2227484 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-911 2225778 2226076 2226410 "PSEUDLIN" 2226881 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-910 2212585 2214950 2217273 "PSETPK" 2223538 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-909 2205672 2208386 2208480 "PSETCAT" 2211461 NIL PSETCAT (NIL T T T T) -9 NIL 2212275) (-908 2203510 2204144 2204963 "PSETCAT-" 2204968 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-907 2202859 2203024 2203052 "PSCURVE" 2203320 T PSCURVE (NIL) -9 NIL 2203487) (-906 2199311 2200837 2200901 "PSCAT" 2201737 NIL PSCAT (NIL T T T) -9 NIL 2201977) (-905 2198375 2198591 2198990 "PSCAT-" 2198995 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-904 2197027 2197660 2197874 "PRTITION" 2198181 T PRTITION (NIL) -8 NIL NIL) (-903 2186125 2188331 2190519 "PRS" 2194889 NIL PRS (NIL T T) -7 NIL NIL) (-902 2183984 2185476 2185516 "PRQAGG" 2185699 NIL PRQAGG (NIL T) -9 NIL 2185801) (-901 2183555 2183657 2183685 "PROPLOG" 2183870 T PROPLOG (NIL) -9 NIL NIL) (-900 2180678 2181243 2181770 "PROPFRML" 2183060 NIL PROPFRML (NIL T) -8 NIL NIL) (-899 2180138 2180248 2180378 "PROPERTY" 2180568 T PROPERTY (NIL) -8 NIL NIL) (-898 2173912 2178304 2179124 "PRODUCT" 2179364 NIL PRODUCT (NIL T T) -8 NIL NIL) (-897 2171188 2173372 2173605 "PR" 2173723 NIL PR (NIL T T) -8 NIL NIL) (-896 2170984 2171016 2171075 "PRINT" 2171149 T PRINT (NIL) -7 NIL NIL) (-895 2170324 2170441 2170593 "PRIMES" 2170864 NIL PRIMES (NIL T) -7 NIL NIL) (-894 2168389 2168790 2169256 "PRIMELT" 2169903 NIL PRIMELT (NIL T) -7 NIL NIL) (-893 2168118 2168167 2168195 "PRIMCAT" 2168319 T PRIMCAT (NIL) -9 NIL NIL) (-892 2164279 2168056 2168101 "PRIMARR" 2168106 NIL PRIMARR (NIL T) -8 NIL NIL) (-891 2163286 2163464 2163692 "PRIMARR2" 2164097 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-890 2162929 2162985 2163096 "PREASSOC" 2163224 NIL PREASSOC (NIL T T) -7 NIL NIL) (-889 2162404 2162537 2162565 "PPCURVE" 2162770 T PPCURVE (NIL) -9 NIL 2162906) (-888 2159763 2160162 2160754 "POLYROOT" 2161985 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-887 2153669 2159369 2159528 "POLY" 2159636 NIL POLY (NIL T) -8 NIL NIL) (-886 2153054 2153112 2153345 "POLYLIFT" 2153605 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-885 2149339 2149788 2150416 "POLYCATQ" 2152599 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-884 2136380 2141777 2141841 "POLYCAT" 2145326 NIL POLYCAT (NIL T T T) -9 NIL 2147253) (-883 2129831 2131692 2134075 "POLYCAT-" 2134080 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-882 2129420 2129488 2129607 "POLY2UP" 2129757 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-881 2129056 2129113 2129220 "POLY2" 2129357 NIL POLY2 (NIL T T) -7 NIL NIL) (-880 2127741 2127980 2128256 "POLUTIL" 2128830 NIL POLUTIL (NIL T T) -7 NIL NIL) (-879 2126103 2126380 2126710 "POLTOPOL" 2127463 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-878 2121626 2126040 2126085 "POINT" 2126090 NIL POINT (NIL T) -8 NIL NIL) (-877 2119813 2120170 2120545 "PNTHEORY" 2121271 T PNTHEORY (NIL) -7 NIL NIL) (-876 2118241 2118538 2118947 "PMTOOLS" 2119511 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-875 2117834 2117912 2118029 "PMSYM" 2118157 NIL PMSYM (NIL T) -7 NIL NIL) (-874 2117344 2117413 2117587 "PMQFCAT" 2117759 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-873 2116699 2116809 2116965 "PMPRED" 2117221 NIL PMPRED (NIL T) -7 NIL NIL) (-872 2116095 2116181 2116342 "PMPREDFS" 2116600 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-871 2114741 2114949 2115333 "PMPLCAT" 2115857 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-870 2114273 2114352 2114504 "PMLSAGG" 2114656 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-869 2113750 2113826 2114006 "PMKERNEL" 2114191 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-868 2113367 2113442 2113555 "PMINS" 2113669 NIL PMINS (NIL T) -7 NIL NIL) (-867 2112797 2112866 2113081 "PMFS" 2113292 NIL PMFS (NIL T T T) -7 NIL NIL) (-866 2112028 2112146 2112350 "PMDOWN" 2112674 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-865 2111191 2111350 2111532 "PMASS" 2111866 T PMASS (NIL) -7 NIL NIL) (-864 2110465 2110576 2110739 "PMASSFS" 2111077 NIL PMASSFS (NIL T T) -7 NIL NIL) (-863 2110120 2110188 2110282 "PLOTTOOL" 2110391 T PLOTTOOL (NIL) -7 NIL NIL) (-862 2104742 2105931 2107079 "PLOT" 2108992 T PLOT (NIL) -8 NIL NIL) (-861 2100556 2101590 2102511 "PLOT3D" 2103841 T PLOT3D (NIL) -8 NIL NIL) (-860 2099468 2099645 2099880 "PLOT1" 2100360 NIL PLOT1 (NIL T) -7 NIL NIL) (-859 2074862 2079534 2084385 "PLEQN" 2094734 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-858 2074180 2074302 2074482 "PINTERP" 2074727 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-857 2073873 2073920 2074023 "PINTERPA" 2074127 NIL PINTERPA (NIL T T) -7 NIL NIL) (-856 2073112 2073679 2073766 "PI" 2073806 T PI (NIL) -8 NIL NIL) (-855 2071504 2072489 2072517 "PID" 2072699 T PID (NIL) -9 NIL 2072833) (-854 2071229 2071266 2071354 "PICOERCE" 2071461 NIL PICOERCE (NIL T) -7 NIL NIL) (-853 2070549 2070688 2070864 "PGROEB" 2071085 NIL PGROEB (NIL T) -7 NIL NIL) (-852 2066136 2066950 2067855 "PGE" 2069664 T PGE (NIL) -7 NIL NIL) (-851 2064260 2064506 2064872 "PGCD" 2065853 NIL PGCD (NIL T T T T) -7 NIL NIL) (-850 2063598 2063701 2063862 "PFRPAC" 2064144 NIL PFRPAC (NIL T) -7 NIL NIL) (-849 2060213 2062146 2062499 "PFR" 2063277 NIL PFR (NIL T) -8 NIL NIL) (-848 2058602 2058846 2059171 "PFOTOOLS" 2059960 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-847 2057135 2057374 2057725 "PFOQ" 2058359 NIL PFOQ (NIL T T T) -7 NIL NIL) (-846 2055612 2055824 2056186 "PFO" 2056919 NIL PFO (NIL T T T T T) -7 NIL NIL) (-845 2052135 2055501 2055570 "PF" 2055575 NIL PF (NIL NIL) -8 NIL NIL) (-844 2049564 2050845 2050873 "PFECAT" 2051458 T PFECAT (NIL) -9 NIL 2051842) (-843 2049009 2049163 2049377 "PFECAT-" 2049382 NIL PFECAT- (NIL T) -8 NIL NIL) (-842 2047613 2047864 2048165 "PFBRU" 2048758 NIL PFBRU (NIL T T) -7 NIL NIL) (-841 2045480 2045831 2046263 "PFBR" 2047264 NIL PFBR (NIL T T T T) -7 NIL NIL) (-840 2041331 2042856 2043532 "PERM" 2044837 NIL PERM (NIL T) -8 NIL NIL) (-839 2036596 2037538 2038408 "PERMGRP" 2040494 NIL PERMGRP (NIL T) -8 NIL NIL) (-838 2034667 2035660 2035701 "PERMCAT" 2036147 NIL PERMCAT (NIL T) -9 NIL 2036452) (-837 2034322 2034363 2034486 "PERMAN" 2034620 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-836 2031762 2033891 2034022 "PENDTREE" 2034224 NIL PENDTREE (NIL T) -8 NIL NIL) (-835 2029835 2030613 2030654 "PDRING" 2031311 NIL PDRING (NIL T) -9 NIL 2031596) (-834 2028938 2029156 2029518 "PDRING-" 2029523 NIL PDRING- (NIL T T) -8 NIL NIL) (-833 2026079 2026830 2027521 "PDEPROB" 2028267 T PDEPROB (NIL) -8 NIL NIL) (-832 2023650 2024146 2024695 "PDEPACK" 2025550 T PDEPACK (NIL) -7 NIL NIL) (-831 2022562 2022752 2023003 "PDECOMP" 2023449 NIL PDECOMP (NIL T T) -7 NIL NIL) (-830 2020174 2020989 2021017 "PDECAT" 2021802 T PDECAT (NIL) -9 NIL 2022513) (-829 2019927 2019960 2020049 "PCOMP" 2020135 NIL PCOMP (NIL T T) -7 NIL NIL) (-828 2018134 2018730 2019026 "PBWLB" 2019657 NIL PBWLB (NIL T) -8 NIL NIL) (-827 2010642 2012211 2013547 "PATTERN" 2016819 NIL PATTERN (NIL T) -8 NIL NIL) (-826 2010274 2010331 2010440 "PATTERN2" 2010579 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-825 2008031 2008419 2008876 "PATTERN1" 2009863 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-824 2005426 2005980 2006461 "PATRES" 2007596 NIL PATRES (NIL T T) -8 NIL NIL) (-823 2004990 2005057 2005189 "PATRES2" 2005353 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-822 2002887 2003287 2003692 "PATMATCH" 2004659 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-821 2002424 2002607 2002648 "PATMAB" 2002755 NIL PATMAB (NIL T) -9 NIL 2002838) (-820 2000969 2001278 2001536 "PATLRES" 2002229 NIL PATLRES (NIL T T T) -8 NIL NIL) (-819 2000515 2000638 2000679 "PATAB" 2000684 NIL PATAB (NIL T) -9 NIL 2000856) (-818 1997996 1998528 1999101 "PARTPERM" 1999962 T PARTPERM (NIL) -7 NIL NIL) (-817 1997617 1997680 1997782 "PARSURF" 1997927 NIL PARSURF (NIL T) -8 NIL NIL) (-816 1997249 1997306 1997415 "PARSU2" 1997554 NIL PARSU2 (NIL T T) -7 NIL NIL) (-815 1997013 1997053 1997120 "PARSER" 1997202 T PARSER (NIL) -7 NIL NIL) (-814 1996634 1996697 1996799 "PARSCURV" 1996944 NIL PARSCURV (NIL T) -8 NIL NIL) (-813 1996266 1996323 1996432 "PARSC2" 1996571 NIL PARSC2 (NIL T T) -7 NIL NIL) (-812 1995905 1995963 1996060 "PARPCURV" 1996202 NIL PARPCURV (NIL T) -8 NIL NIL) (-811 1995537 1995594 1995703 "PARPC2" 1995842 NIL PARPC2 (NIL T T) -7 NIL NIL) (-810 1995057 1995143 1995262 "PAN2EXPR" 1995438 T PAN2EXPR (NIL) -7 NIL NIL) (-809 1993863 1994178 1994406 "PALETTE" 1994849 T PALETTE (NIL) -8 NIL NIL) (-808 1992331 1992868 1993228 "PAIR" 1993549 NIL PAIR (NIL T T) -8 NIL NIL) (-807 1986181 1991590 1991784 "PADICRC" 1992186 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-806 1979389 1985527 1985711 "PADICRAT" 1986029 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-805 1977693 1979326 1979371 "PADIC" 1979376 NIL PADIC (NIL NIL) -8 NIL NIL) (-804 1974898 1976472 1976512 "PADICCT" 1977093 NIL PADICCT (NIL NIL) -9 NIL 1977375) (-803 1973855 1974055 1974323 "PADEPAC" 1974685 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-802 1973067 1973200 1973406 "PADE" 1973717 NIL PADE (NIL T T T) -7 NIL NIL) (-801 1971078 1971910 1972225 "OWP" 1972835 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-800 1970187 1970683 1970855 "OVAR" 1970946 NIL OVAR (NIL NIL) -8 NIL NIL) (-799 1969451 1969572 1969733 "OUT" 1970046 T OUT (NIL) -7 NIL NIL) (-798 1958505 1960676 1962846 "OUTFORM" 1967301 T OUTFORM (NIL) -8 NIL NIL) (-797 1957913 1958234 1958323 "OSI" 1958436 T OSI (NIL) -8 NIL NIL) (-796 1957444 1957782 1957810 "OSGROUP" 1957815 T OSGROUP (NIL) -9 NIL 1957837) (-795 1956189 1956416 1956701 "ORTHPOL" 1957191 NIL ORTHPOL (NIL T) -7 NIL NIL) (-794 1953560 1955850 1955988 "OREUP" 1956132 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-793 1950956 1953253 1953379 "ORESUP" 1953502 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-792 1948491 1948991 1949551 "OREPCTO" 1950445 NIL OREPCTO (NIL T T) -7 NIL NIL) (-791 1942401 1944607 1944647 "OREPCAT" 1946968 NIL OREPCAT (NIL T) -9 NIL 1948071) (-790 1939549 1940331 1941388 "OREPCAT-" 1941393 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-789 1938727 1938999 1939027 "ORDSET" 1939336 T ORDSET (NIL) -9 NIL 1939500) (-788 1938246 1938368 1938561 "ORDSET-" 1938566 NIL ORDSET- (NIL T) -8 NIL NIL) (-787 1936860 1937661 1937689 "ORDRING" 1937891 T ORDRING (NIL) -9 NIL 1938015) (-786 1936505 1936599 1936743 "ORDRING-" 1936748 NIL ORDRING- (NIL T) -8 NIL NIL) (-785 1935868 1936349 1936377 "ORDMON" 1936382 T ORDMON (NIL) -9 NIL 1936403) (-784 1935030 1935177 1935372 "ORDFUNS" 1935717 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-783 1934542 1934901 1934929 "ORDFIN" 1934934 T ORDFIN (NIL) -9 NIL 1934955) (-782 1931054 1933128 1933537 "ORDCOMP" 1934166 NIL ORDCOMP (NIL T) -8 NIL NIL) (-781 1930320 1930447 1930633 "ORDCOMP2" 1930914 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-780 1926827 1927710 1928547 "OPTPROB" 1929503 T OPTPROB (NIL) -8 NIL NIL) (-779 1923669 1924298 1924992 "OPTPACK" 1926153 T OPTPACK (NIL) -7 NIL NIL) (-778 1921395 1922131 1922159 "OPTCAT" 1922974 T OPTCAT (NIL) -9 NIL 1923620) (-777 1921163 1921202 1921268 "OPQUERY" 1921349 T OPQUERY (NIL) -7 NIL NIL) (-776 1918299 1919490 1919990 "OP" 1920695 NIL OP (NIL T) -8 NIL NIL) (-775 1915064 1917096 1917465 "ONECOMP" 1917963 NIL ONECOMP (NIL T) -8 NIL NIL) (-774 1914369 1914484 1914658 "ONECOMP2" 1914936 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-773 1913788 1913894 1914024 "OMSERVER" 1914259 T OMSERVER (NIL) -7 NIL NIL) (-772 1910677 1913229 1913269 "OMSAGG" 1913330 NIL OMSAGG (NIL T) -9 NIL 1913394) (-771 1909300 1909563 1909845 "OMPKG" 1910415 T OMPKG (NIL) -7 NIL NIL) (-770 1908730 1908833 1908861 "OM" 1909160 T OM (NIL) -9 NIL NIL) (-769 1907269 1908282 1908450 "OMLO" 1908611 NIL OMLO (NIL T T) -8 NIL NIL) (-768 1906199 1906346 1906572 "OMEXPR" 1907095 NIL OMEXPR (NIL T) -7 NIL NIL) (-767 1905517 1905745 1905881 "OMERR" 1906083 T OMERR (NIL) -8 NIL NIL) (-766 1904695 1904938 1905098 "OMERRK" 1905377 T OMERRK (NIL) -8 NIL NIL) (-765 1904173 1904372 1904480 "OMENC" 1904607 T OMENC (NIL) -8 NIL NIL) (-764 1898068 1899253 1900424 "OMDEV" 1903022 T OMDEV (NIL) -8 NIL NIL) (-763 1897137 1897308 1897502 "OMCONN" 1897894 T OMCONN (NIL) -8 NIL NIL) (-762 1895753 1896739 1896767 "OINTDOM" 1896772 T OINTDOM (NIL) -9 NIL 1896793) (-761 1891515 1892745 1893460 "OFMONOID" 1895070 NIL OFMONOID (NIL T) -8 NIL NIL) (-760 1890953 1891452 1891497 "ODVAR" 1891502 NIL ODVAR (NIL T) -8 NIL NIL) (-759 1888078 1890450 1890635 "ODR" 1890828 NIL ODR (NIL T T NIL) -8 NIL NIL) (-758 1880384 1887857 1887981 "ODPOL" 1887986 NIL ODPOL (NIL T) -8 NIL NIL) (-757 1874207 1880256 1880361 "ODP" 1880366 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-756 1872973 1873188 1873463 "ODETOOLS" 1873981 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-755 1869942 1870598 1871314 "ODESYS" 1872306 NIL ODESYS (NIL T T) -7 NIL NIL) (-754 1864846 1865754 1866777 "ODERTRIC" 1869017 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-753 1864272 1864354 1864548 "ODERED" 1864758 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-752 1861174 1861722 1862397 "ODERAT" 1863695 NIL ODERAT (NIL T T) -7 NIL NIL) (-751 1858142 1858606 1859202 "ODEPRRIC" 1860703 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-750 1856011 1856580 1857089 "ODEPROB" 1857653 T ODEPROB (NIL) -8 NIL NIL) (-749 1852543 1853026 1853672 "ODEPRIM" 1855490 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-748 1851796 1851898 1852156 "ODEPAL" 1852435 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-747 1847998 1848779 1849633 "ODEPACK" 1850962 T ODEPACK (NIL) -7 NIL NIL) (-746 1847035 1847142 1847370 "ODEINT" 1847887 NIL ODEINT (NIL T T) -7 NIL NIL) (-745 1841136 1842561 1844008 "ODEIFTBL" 1845608 T ODEIFTBL (NIL) -8 NIL NIL) (-744 1836480 1837266 1838224 "ODEEF" 1840295 NIL ODEEF (NIL T T) -7 NIL NIL) (-743 1835817 1835906 1836135 "ODECONST" 1836385 NIL ODECONST (NIL T T T) -7 NIL NIL) (-742 1833975 1834608 1834636 "ODECAT" 1835239 T ODECAT (NIL) -9 NIL 1835768) (-741 1830847 1833687 1833806 "OCT" 1833888 NIL OCT (NIL T) -8 NIL NIL) (-740 1830485 1830528 1830655 "OCTCT2" 1830798 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-739 1825319 1827757 1827797 "OC" 1828893 NIL OC (NIL T) -9 NIL 1829750) (-738 1822546 1823294 1824284 "OC-" 1824378 NIL OC- (NIL T T) -8 NIL NIL) (-737 1821925 1822367 1822395 "OCAMON" 1822400 T OCAMON (NIL) -9 NIL 1822421) (-736 1821483 1821798 1821826 "OASGP" 1821831 T OASGP (NIL) -9 NIL 1821851) (-735 1820771 1821234 1821262 "OAMONS" 1821302 T OAMONS (NIL) -9 NIL 1821345) (-734 1820212 1820619 1820647 "OAMON" 1820652 T OAMON (NIL) -9 NIL 1820672) (-733 1819517 1820009 1820037 "OAGROUP" 1820042 T OAGROUP (NIL) -9 NIL 1820062) (-732 1819207 1819257 1819345 "NUMTUBE" 1819461 NIL NUMTUBE (NIL T) -7 NIL NIL) (-731 1812780 1814298 1815834 "NUMQUAD" 1817691 T NUMQUAD (NIL) -7 NIL NIL) (-730 1808536 1809524 1810549 "NUMODE" 1811775 T NUMODE (NIL) -7 NIL NIL) (-729 1805940 1806786 1806814 "NUMINT" 1807731 T NUMINT (NIL) -9 NIL 1808487) (-728 1804888 1805085 1805303 "NUMFMT" 1805742 T NUMFMT (NIL) -7 NIL NIL) (-727 1791267 1794204 1796734 "NUMERIC" 1802397 NIL NUMERIC (NIL T) -7 NIL NIL) (-726 1785668 1790720 1790814 "NTSCAT" 1790819 NIL NTSCAT (NIL T T T T) -9 NIL 1790857) (-725 1784862 1785027 1785220 "NTPOLFN" 1785507 NIL NTPOLFN (NIL T) -7 NIL NIL) (-724 1772678 1781704 1782514 "NSUP" 1784084 NIL NSUP (NIL T) -8 NIL NIL) (-723 1772314 1772371 1772478 "NSUP2" 1772615 NIL NSUP2 (NIL T T) -7 NIL NIL) (-722 1762276 1772093 1772223 "NSMP" 1772228 NIL NSMP (NIL T T) -8 NIL NIL) (-721 1760708 1761009 1761366 "NREP" 1761964 NIL NREP (NIL T) -7 NIL NIL) (-720 1759299 1759551 1759909 "NPCOEF" 1760451 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-719 1758365 1758480 1758696 "NORMRETR" 1759180 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-718 1756418 1756708 1757115 "NORMPK" 1758073 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-717 1756103 1756131 1756255 "NORMMA" 1756384 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-716 1755930 1756060 1756089 "NONE" 1756094 T NONE (NIL) -8 NIL NIL) (-715 1755719 1755748 1755817 "NONE1" 1755894 NIL NONE1 (NIL T) -7 NIL NIL) (-714 1755204 1755266 1755451 "NODE1" 1755651 NIL NODE1 (NIL T T) -7 NIL NIL) (-713 1753498 1754367 1754622 "NNI" 1754969 T NNI (NIL) -8 NIL NIL) (-712 1751918 1752231 1752595 "NLINSOL" 1753166 NIL NLINSOL (NIL T) -7 NIL NIL) (-711 1748085 1749053 1749975 "NIPROB" 1751016 T NIPROB (NIL) -8 NIL NIL) (-710 1746842 1747076 1747378 "NFINTBAS" 1747847 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-709 1745550 1745781 1746062 "NCODIV" 1746610 NIL NCODIV (NIL T T) -7 NIL NIL) (-708 1745312 1745349 1745424 "NCNTFRAC" 1745507 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-707 1743492 1743856 1744276 "NCEP" 1744937 NIL NCEP (NIL T) -7 NIL NIL) (-706 1742404 1743143 1743171 "NASRING" 1743281 T NASRING (NIL) -9 NIL 1743355) (-705 1742199 1742243 1742337 "NASRING-" 1742342 NIL NASRING- (NIL T) -8 NIL NIL) (-704 1741353 1741852 1741880 "NARNG" 1741997 T NARNG (NIL) -9 NIL 1742088) (-703 1741045 1741112 1741246 "NARNG-" 1741251 NIL NARNG- (NIL T) -8 NIL NIL) (-702 1739924 1740131 1740366 "NAGSP" 1740830 T NAGSP (NIL) -7 NIL NIL) (-701 1731348 1732994 1734629 "NAGS" 1738309 T NAGS (NIL) -7 NIL NIL) (-700 1729912 1730216 1730543 "NAGF07" 1731041 T NAGF07 (NIL) -7 NIL NIL) (-699 1724494 1725774 1727070 "NAGF04" 1728636 T NAGF04 (NIL) -7 NIL NIL) (-698 1717526 1719124 1720741 "NAGF02" 1722897 T NAGF02 (NIL) -7 NIL NIL) (-697 1712790 1713880 1714987 "NAGF01" 1716439 T NAGF01 (NIL) -7 NIL NIL) (-696 1706450 1708008 1709585 "NAGE04" 1711233 T NAGE04 (NIL) -7 NIL NIL) (-695 1697691 1699794 1701906 "NAGE02" 1704358 T NAGE02 (NIL) -7 NIL NIL) (-694 1693684 1694621 1695575 "NAGE01" 1696757 T NAGE01 (NIL) -7 NIL NIL) (-693 1691491 1692022 1692577 "NAGD03" 1693149 T NAGD03 (NIL) -7 NIL NIL) (-692 1683277 1685196 1687141 "NAGD02" 1689566 T NAGD02 (NIL) -7 NIL NIL) (-691 1677136 1678549 1679977 "NAGD01" 1681869 T NAGD01 (NIL) -7 NIL NIL) (-690 1673393 1674203 1675028 "NAGC06" 1676331 T NAGC06 (NIL) -7 NIL NIL) (-689 1671870 1672199 1672552 "NAGC05" 1673060 T NAGC05 (NIL) -7 NIL NIL) (-688 1671254 1671371 1671513 "NAGC02" 1671748 T NAGC02 (NIL) -7 NIL NIL) (-687 1670316 1670873 1670913 "NAALG" 1670992 NIL NAALG (NIL T) -9 NIL 1671053) (-686 1670151 1670180 1670270 "NAALG-" 1670275 NIL NAALG- (NIL T T) -8 NIL NIL) (-685 1664101 1665209 1666396 "MULTSQFR" 1669047 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-684 1663420 1663495 1663679 "MULTFACT" 1664013 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-683 1656614 1660525 1660577 "MTSCAT" 1661637 NIL MTSCAT (NIL T T) -9 NIL 1662151) (-682 1656326 1656380 1656472 "MTHING" 1656554 NIL MTHING (NIL T) -7 NIL NIL) (-681 1656118 1656151 1656211 "MSYSCMD" 1656286 T MSYSCMD (NIL) -7 NIL NIL) (-680 1652230 1654873 1655193 "MSET" 1655831 NIL MSET (NIL T) -8 NIL NIL) (-679 1649326 1651792 1651833 "MSETAGG" 1651838 NIL MSETAGG (NIL T) -9 NIL 1651872) (-678 1645182 1646724 1647465 "MRING" 1648629 NIL MRING (NIL T T) -8 NIL NIL) (-677 1644752 1644819 1644948 "MRF2" 1645109 NIL MRF2 (NIL T T T) -7 NIL NIL) (-676 1644370 1644405 1644549 "MRATFAC" 1644711 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-675 1641982 1642277 1642708 "MPRFF" 1644075 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-674 1636002 1641837 1641933 "MPOLY" 1641938 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-673 1635492 1635527 1635735 "MPCPF" 1635961 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-672 1635008 1635051 1635234 "MPC3" 1635443 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-671 1634209 1634290 1634509 "MPC2" 1634923 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-670 1632510 1632847 1633237 "MONOTOOL" 1633869 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-669 1631635 1631970 1631998 "MONOID" 1632275 T MONOID (NIL) -9 NIL 1632447) (-668 1631013 1631176 1631419 "MONOID-" 1631424 NIL MONOID- (NIL T) -8 NIL NIL) (-667 1621994 1627980 1628039 "MONOGEN" 1628713 NIL MONOGEN (NIL T T) -9 NIL 1629169) (-666 1619212 1619947 1620947 "MONOGEN-" 1621066 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-665 1618072 1618492 1618520 "MONADWU" 1618912 T MONADWU (NIL) -9 NIL 1619150) (-664 1617444 1617603 1617851 "MONADWU-" 1617856 NIL MONADWU- (NIL T) -8 NIL NIL) (-663 1616830 1617048 1617076 "MONAD" 1617283 T MONAD (NIL) -9 NIL 1617395) (-662 1616515 1616593 1616725 "MONAD-" 1616730 NIL MONAD- (NIL T) -8 NIL NIL) (-661 1614766 1615428 1615707 "MOEBIUS" 1616268 NIL MOEBIUS (NIL T) -8 NIL NIL) (-660 1614160 1614538 1614578 "MODULE" 1614583 NIL MODULE (NIL T) -9 NIL 1614609) (-659 1613728 1613824 1614014 "MODULE-" 1614019 NIL MODULE- (NIL T T) -8 NIL NIL) (-658 1611399 1612094 1612420 "MODRING" 1613553 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-657 1608355 1609520 1610037 "MODOP" 1610931 NIL MODOP (NIL T T) -8 NIL NIL) (-656 1606542 1606994 1607335 "MODMONOM" 1608154 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-655 1596221 1604746 1605168 "MODMON" 1606170 NIL MODMON (NIL T T) -8 NIL NIL) (-654 1593347 1595065 1595341 "MODFIELD" 1596096 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-653 1592351 1592628 1592818 "MMLFORM" 1593177 T MMLFORM (NIL) -8 NIL NIL) (-652 1591877 1591920 1592099 "MMAP" 1592302 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-651 1590114 1590891 1590931 "MLO" 1591348 NIL MLO (NIL T) -9 NIL 1591589) (-650 1587481 1587996 1588598 "MLIFT" 1589595 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-649 1586872 1586956 1587110 "MKUCFUNC" 1587392 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-648 1586471 1586541 1586664 "MKRECORD" 1586795 NIL MKRECORD (NIL T T) -7 NIL NIL) (-647 1585519 1585680 1585908 "MKFUNC" 1586282 NIL MKFUNC (NIL T) -7 NIL NIL) (-646 1584907 1585011 1585167 "MKFLCFN" 1585402 NIL MKFLCFN (NIL T) -7 NIL NIL) (-645 1584333 1584700 1584789 "MKCHSET" 1584851 NIL MKCHSET (NIL T) -8 NIL NIL) (-644 1583610 1583712 1583897 "MKBCFUNC" 1584226 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-643 1580294 1583164 1583300 "MINT" 1583494 T MINT (NIL) -8 NIL NIL) (-642 1579106 1579349 1579626 "MHROWRED" 1580049 NIL MHROWRED (NIL T) -7 NIL NIL) (-641 1574377 1577551 1577975 "MFLOAT" 1578702 T MFLOAT (NIL) -8 NIL NIL) (-640 1573734 1573810 1573981 "MFINFACT" 1574289 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-639 1570049 1570897 1571781 "MESH" 1572870 T MESH (NIL) -7 NIL NIL) (-638 1568439 1568751 1569104 "MDDFACT" 1569736 NIL MDDFACT (NIL T) -7 NIL NIL) (-637 1565282 1567599 1567640 "MDAGG" 1567895 NIL MDAGG (NIL T) -9 NIL 1568038) (-636 1554980 1564575 1564782 "MCMPLX" 1565095 T MCMPLX (NIL) -8 NIL NIL) (-635 1554121 1554267 1554467 "MCDEN" 1554829 NIL MCDEN (NIL T T) -7 NIL NIL) (-634 1552011 1552281 1552661 "MCALCFN" 1553851 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-633 1549633 1550156 1550717 "MATSTOR" 1551482 NIL MATSTOR (NIL T) -7 NIL NIL) (-632 1545642 1549008 1549255 "MATRIX" 1549418 NIL MATRIX (NIL T) -8 NIL NIL) (-631 1541411 1542115 1542851 "MATLIN" 1544999 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-630 1531609 1534747 1534823 "MATCAT" 1539661 NIL MATCAT (NIL T T T) -9 NIL 1541078) (-629 1527974 1528987 1530342 "MATCAT-" 1530347 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-628 1526576 1526729 1527060 "MATCAT2" 1527809 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-627 1524688 1525012 1525396 "MAPPKG3" 1526251 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-626 1523669 1523842 1524064 "MAPPKG2" 1524512 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-625 1522168 1522452 1522779 "MAPPKG1" 1523375 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-624 1521779 1521837 1521960 "MAPHACK3" 1522104 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-623 1521371 1521432 1521546 "MAPHACK2" 1521711 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-622 1520809 1520912 1521054 "MAPHACK1" 1521262 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-621 1518917 1519511 1519814 "MAGMA" 1520538 NIL MAGMA (NIL T) -8 NIL NIL) (-620 1515391 1517161 1517621 "M3D" 1518490 NIL M3D (NIL T) -8 NIL NIL) (-619 1509547 1513762 1513803 "LZSTAGG" 1514585 NIL LZSTAGG (NIL T) -9 NIL 1514880) (-618 1505520 1506678 1508135 "LZSTAGG-" 1508140 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-617 1502636 1503413 1503899 "LWORD" 1505066 NIL LWORD (NIL T) -8 NIL NIL) (-616 1495796 1502407 1502541 "LSQM" 1502546 NIL LSQM (NIL NIL T) -8 NIL NIL) (-615 1495020 1495159 1495387 "LSPP" 1495651 NIL LSPP (NIL T T T T) -7 NIL NIL) (-614 1492832 1493133 1493589 "LSMP" 1494709 NIL LSMP (NIL T T T T) -7 NIL NIL) (-613 1489611 1490285 1491015 "LSMP1" 1492134 NIL LSMP1 (NIL T) -7 NIL NIL) (-612 1483538 1488780 1488821 "LSAGG" 1488883 NIL LSAGG (NIL T) -9 NIL 1488961) (-611 1480233 1481157 1482370 "LSAGG-" 1482375 NIL LSAGG- (NIL T T) -8 NIL NIL) (-610 1477859 1479377 1479626 "LPOLY" 1480028 NIL LPOLY (NIL T T) -8 NIL NIL) (-609 1477441 1477526 1477649 "LPEFRAC" 1477768 NIL LPEFRAC (NIL T) -7 NIL NIL) (-608 1475788 1476535 1476788 "LO" 1477273 NIL LO (NIL T T T) -8 NIL NIL) (-607 1475442 1475554 1475582 "LOGIC" 1475693 T LOGIC (NIL) -9 NIL 1475773) (-606 1475304 1475327 1475398 "LOGIC-" 1475403 NIL LOGIC- (NIL T) -8 NIL NIL) (-605 1474497 1474637 1474830 "LODOOPS" 1475160 NIL LODOOPS (NIL T T) -7 NIL NIL) (-604 1471915 1474414 1474479 "LODO" 1474484 NIL LODO (NIL T NIL) -8 NIL NIL) (-603 1470461 1470696 1471047 "LODOF" 1471662 NIL LODOF (NIL T T) -7 NIL NIL) (-602 1466881 1469317 1469357 "LODOCAT" 1469789 NIL LODOCAT (NIL T) -9 NIL 1470000) (-601 1466615 1466673 1466799 "LODOCAT-" 1466804 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-600 1463929 1466456 1466574 "LODO2" 1466579 NIL LODO2 (NIL T T) -8 NIL NIL) (-599 1461358 1463866 1463911 "LODO1" 1463916 NIL LODO1 (NIL T) -8 NIL NIL) (-598 1460221 1460386 1460697 "LODEEF" 1461181 NIL LODEEF (NIL T T T) -7 NIL NIL) (-597 1455508 1458352 1458393 "LNAGG" 1459340 NIL LNAGG (NIL T) -9 NIL 1459784) (-596 1454655 1454869 1455211 "LNAGG-" 1455216 NIL LNAGG- (NIL T T) -8 NIL NIL) (-595 1450820 1451582 1452220 "LMOPS" 1454071 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-594 1450218 1450580 1450620 "LMODULE" 1450680 NIL LMODULE (NIL T) -9 NIL 1450722) (-593 1447464 1449863 1449986 "LMDICT" 1450128 NIL LMDICT (NIL T) -8 NIL NIL) (-592 1440691 1446410 1446708 "LIST" 1447199 NIL LIST (NIL T) -8 NIL NIL) (-591 1440216 1440290 1440429 "LIST3" 1440611 NIL LIST3 (NIL T T T) -7 NIL NIL) (-590 1439223 1439401 1439629 "LIST2" 1440034 NIL LIST2 (NIL T T) -7 NIL NIL) (-589 1437357 1437669 1438068 "LIST2MAP" 1438870 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-588 1436070 1436750 1436790 "LINEXP" 1437043 NIL LINEXP (NIL T) -9 NIL 1437191) (-587 1434717 1434977 1435274 "LINDEP" 1435822 NIL LINDEP (NIL T T) -7 NIL NIL) (-586 1431484 1432203 1432980 "LIMITRF" 1433972 NIL LIMITRF (NIL T) -7 NIL NIL) (-585 1429764 1430059 1430474 "LIMITPS" 1431179 NIL LIMITPS (NIL T T) -7 NIL NIL) (-584 1424219 1429275 1429503 "LIE" 1429585 NIL LIE (NIL T T) -8 NIL NIL) (-583 1423270 1423713 1423753 "LIECAT" 1423893 NIL LIECAT (NIL T) -9 NIL 1424044) (-582 1423111 1423138 1423226 "LIECAT-" 1423231 NIL LIECAT- (NIL T T) -8 NIL NIL) (-581 1415723 1422560 1422725 "LIB" 1422966 T LIB (NIL) -8 NIL NIL) (-580 1411360 1412241 1413176 "LGROBP" 1414840 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-579 1409226 1409500 1409862 "LF" 1411081 NIL LF (NIL T T) -7 NIL NIL) (-578 1408066 1408758 1408786 "LFCAT" 1408993 T LFCAT (NIL) -9 NIL 1409132) (-577 1404978 1405604 1406290 "LEXTRIPK" 1407432 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-576 1401684 1402548 1403051 "LEXP" 1404558 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-575 1400082 1400395 1400796 "LEADCDET" 1401366 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-574 1399278 1399352 1399579 "LAZM3PK" 1400003 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-573 1394195 1397357 1397894 "LAUPOL" 1398791 NIL LAUPOL (NIL T T) -8 NIL NIL) (-572 1393762 1393806 1393973 "LAPLACE" 1394145 NIL LAPLACE (NIL T T) -7 NIL NIL) (-571 1391690 1392863 1393114 "LA" 1393595 NIL LA (NIL T T T) -8 NIL NIL) (-570 1390753 1391347 1391387 "LALG" 1391448 NIL LALG (NIL T) -9 NIL 1391506) (-569 1390468 1390527 1390662 "LALG-" 1390667 NIL LALG- (NIL T T) -8 NIL NIL) (-568 1389378 1389565 1389862 "KOVACIC" 1390268 NIL KOVACIC (NIL T T) -7 NIL NIL) (-567 1389213 1389237 1389278 "KONVERT" 1389340 NIL KONVERT (NIL T) -9 NIL NIL) (-566 1389048 1389072 1389113 "KOERCE" 1389175 NIL KOERCE (NIL T) -9 NIL NIL) (-565 1386782 1387542 1387935 "KERNEL" 1388687 NIL KERNEL (NIL T) -8 NIL NIL) (-564 1386284 1386365 1386495 "KERNEL2" 1386696 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-563 1380136 1384824 1384878 "KDAGG" 1385255 NIL KDAGG (NIL T T) -9 NIL 1385461) (-562 1379665 1379789 1379994 "KDAGG-" 1379999 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-561 1372840 1379326 1379481 "KAFILE" 1379543 NIL KAFILE (NIL T) -8 NIL NIL) (-560 1367295 1372351 1372579 "JORDAN" 1372661 NIL JORDAN (NIL T T) -8 NIL NIL) (-559 1367024 1367083 1367170 "JAVACODE" 1367228 T JAVACODE (NIL) -8 NIL NIL) (-558 1363324 1365230 1365284 "IXAGG" 1366213 NIL IXAGG (NIL T T) -9 NIL 1366672) (-557 1362243 1362549 1362968 "IXAGG-" 1362973 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-556 1357828 1362165 1362224 "IVECTOR" 1362229 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-555 1356594 1356831 1357097 "ITUPLE" 1357595 NIL ITUPLE (NIL T) -8 NIL NIL) (-554 1355030 1355207 1355513 "ITRIGMNP" 1356416 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-553 1353775 1353979 1354262 "ITFUN3" 1354806 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-552 1353407 1353464 1353573 "ITFUN2" 1353712 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-551 1351209 1352280 1352577 "ITAYLOR" 1353142 NIL ITAYLOR (NIL T) -8 NIL NIL) (-550 1340197 1345395 1346554 "ISUPS" 1350082 NIL ISUPS (NIL T) -8 NIL NIL) (-549 1339301 1339441 1339677 "ISUMP" 1340044 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-548 1334565 1339102 1339181 "ISTRING" 1339254 NIL ISTRING (NIL NIL) -8 NIL NIL) (-547 1333778 1333859 1334074 "IRURPK" 1334479 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-546 1332714 1332915 1333155 "IRSN" 1333558 T IRSN (NIL) -7 NIL NIL) (-545 1330749 1331104 1331539 "IRRF2F" 1332352 NIL IRRF2F (NIL T) -7 NIL NIL) (-544 1330496 1330534 1330610 "IRREDFFX" 1330705 NIL IRREDFFX (NIL T) -7 NIL NIL) (-543 1329111 1329370 1329669 "IROOT" 1330229 NIL IROOT (NIL T) -7 NIL NIL) (-542 1325749 1326800 1327490 "IR" 1328453 NIL IR (NIL T) -8 NIL NIL) (-541 1323362 1323857 1324423 "IR2" 1325227 NIL IR2 (NIL T T) -7 NIL NIL) (-540 1322438 1322551 1322771 "IR2F" 1323245 NIL IR2F (NIL T T) -7 NIL NIL) (-539 1322229 1322263 1322323 "IPRNTPK" 1322398 T IPRNTPK (NIL) -7 NIL NIL) (-538 1318783 1322118 1322187 "IPF" 1322192 NIL IPF (NIL NIL) -8 NIL NIL) (-537 1317100 1318708 1318765 "IPADIC" 1318770 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-536 1316599 1316657 1316846 "INVLAPLA" 1317036 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-535 1306248 1308601 1310987 "INTTR" 1314263 NIL INTTR (NIL T T) -7 NIL NIL) (-534 1302596 1303337 1304200 "INTTOOLS" 1305434 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-533 1302182 1302273 1302390 "INTSLPE" 1302499 T INTSLPE (NIL) -7 NIL NIL) (-532 1300132 1302105 1302164 "INTRVL" 1302169 NIL INTRVL (NIL T) -8 NIL NIL) (-531 1297739 1298251 1298825 "INTRF" 1299617 NIL INTRF (NIL T) -7 NIL NIL) (-530 1297154 1297251 1297392 "INTRET" 1297637 NIL INTRET (NIL T) -7 NIL NIL) (-529 1295156 1295545 1296014 "INTRAT" 1296762 NIL INTRAT (NIL T T) -7 NIL NIL) (-528 1292389 1292972 1293597 "INTPM" 1294641 NIL INTPM (NIL T T) -7 NIL NIL) (-527 1289098 1289697 1290441 "INTPAF" 1291775 NIL INTPAF (NIL T T T) -7 NIL NIL) (-526 1284341 1285287 1286322 "INTPACK" 1288083 T INTPACK (NIL) -7 NIL NIL) (-525 1281195 1284070 1284197 "INT" 1284234 T INT (NIL) -8 NIL NIL) (-524 1280447 1280599 1280807 "INTHERTR" 1281037 NIL INTHERTR (NIL T T) -7 NIL NIL) (-523 1279886 1279966 1280154 "INTHERAL" 1280361 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-522 1277732 1278175 1278632 "INTHEORY" 1279449 T INTHEORY (NIL) -7 NIL NIL) (-521 1269054 1270675 1272453 "INTG0" 1276084 NIL INTG0 (NIL T T T) -7 NIL NIL) (-520 1249627 1254417 1259227 "INTFTBL" 1264264 T INTFTBL (NIL) -8 NIL NIL) (-519 1248876 1249014 1249187 "INTFACT" 1249486 NIL INTFACT (NIL T) -7 NIL NIL) (-518 1246267 1246713 1247276 "INTEF" 1248430 NIL INTEF (NIL T T) -7 NIL NIL) (-517 1244729 1245478 1245506 "INTDOM" 1245807 T INTDOM (NIL) -9 NIL 1246014) (-516 1244098 1244272 1244514 "INTDOM-" 1244519 NIL INTDOM- (NIL T) -8 NIL NIL) (-515 1240591 1242523 1242577 "INTCAT" 1243376 NIL INTCAT (NIL T) -9 NIL 1243695) (-514 1240064 1240166 1240294 "INTBIT" 1240483 T INTBIT (NIL) -7 NIL NIL) (-513 1238739 1238893 1239206 "INTALG" 1239909 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-512 1238196 1238286 1238456 "INTAF" 1238643 NIL INTAF (NIL T T) -7 NIL NIL) (-511 1231650 1238006 1238146 "INTABL" 1238151 NIL INTABL (NIL T T T) -8 NIL NIL) (-510 1226601 1229330 1229358 "INS" 1230326 T INS (NIL) -9 NIL 1231007) (-509 1223841 1224612 1225586 "INS-" 1225659 NIL INS- (NIL T) -8 NIL NIL) (-508 1222620 1222847 1223144 "INPSIGN" 1223594 NIL INPSIGN (NIL T T) -7 NIL NIL) (-507 1221738 1221855 1222052 "INPRODPF" 1222500 NIL INPRODPF (NIL T T) -7 NIL NIL) (-506 1220632 1220749 1220986 "INPRODFF" 1221618 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-505 1219632 1219784 1220044 "INNMFACT" 1220468 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-504 1218829 1218926 1219114 "INMODGCD" 1219531 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-503 1217338 1217582 1217906 "INFSP" 1218574 NIL INFSP (NIL T T T) -7 NIL NIL) (-502 1216522 1216639 1216822 "INFPROD0" 1217218 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-501 1213533 1214691 1215182 "INFORM" 1216039 T INFORM (NIL) -8 NIL NIL) (-500 1213143 1213203 1213301 "INFORM1" 1213468 NIL INFORM1 (NIL T) -7 NIL NIL) (-499 1212666 1212755 1212869 "INFINITY" 1213049 T INFINITY (NIL) -7 NIL NIL) (-498 1211283 1211532 1211853 "INEP" 1212414 NIL INEP (NIL T T T) -7 NIL NIL) (-497 1210559 1211180 1211245 "INDE" 1211250 NIL INDE (NIL T) -8 NIL NIL) (-496 1210123 1210191 1210308 "INCRMAPS" 1210486 NIL INCRMAPS (NIL T) -7 NIL NIL) (-495 1205434 1206359 1207303 "INBFF" 1209211 NIL INBFF (NIL T) -7 NIL NIL) (-494 1201929 1205279 1205382 "IMATRIX" 1205387 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-493 1200641 1200764 1201079 "IMATQF" 1201785 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-492 1198861 1199088 1199425 "IMATLIN" 1200397 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-491 1193487 1198785 1198843 "ILIST" 1198848 NIL ILIST (NIL T NIL) -8 NIL NIL) (-490 1191440 1193347 1193460 "IIARRAY2" 1193465 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-489 1186808 1191351 1191415 "IFF" 1191420 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-488 1181851 1186100 1186288 "IFARRAY" 1186665 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-487 1181058 1181755 1181828 "IFAMON" 1181833 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-486 1180642 1180707 1180761 "IEVALAB" 1180968 NIL IEVALAB (NIL T T) -9 NIL NIL) (-485 1180317 1180385 1180545 "IEVALAB-" 1180550 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-484 1179975 1180231 1180294 "IDPO" 1180299 NIL IDPO (NIL T T) -8 NIL NIL) (-483 1179252 1179864 1179939 "IDPOAMS" 1179944 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-482 1178586 1179141 1179216 "IDPOAM" 1179221 NIL IDPOAM (NIL T T) -8 NIL NIL) (-481 1177672 1177922 1177975 "IDPC" 1178388 NIL IDPC (NIL T T) -9 NIL 1178537) (-480 1177168 1177564 1177637 "IDPAM" 1177642 NIL IDPAM (NIL T T) -8 NIL NIL) (-479 1176571 1177060 1177133 "IDPAG" 1177138 NIL IDPAG (NIL T T) -8 NIL NIL) (-478 1172826 1173674 1174569 "IDECOMP" 1175728 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-477 1165699 1166749 1167796 "IDEAL" 1171862 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-476 1164863 1164975 1165174 "ICDEN" 1165583 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-475 1163962 1164343 1164490 "ICARD" 1164736 T ICARD (NIL) -8 NIL NIL) (-474 1162034 1162347 1162750 "IBPTOOLS" 1163639 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-473 1157648 1161654 1161767 "IBITS" 1161953 NIL IBITS (NIL NIL) -8 NIL NIL) (-472 1154371 1154947 1155642 "IBATOOL" 1157065 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-471 1152151 1152612 1153145 "IBACHIN" 1153906 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-470 1150028 1151997 1152100 "IARRAY2" 1152105 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-469 1146181 1149954 1150011 "IARRAY1" 1150016 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-468 1140119 1144599 1145077 "IAN" 1145723 T IAN (NIL) -8 NIL NIL) (-467 1139630 1139687 1139860 "IALGFACT" 1140056 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-466 1139158 1139271 1139299 "HYPCAT" 1139506 T HYPCAT (NIL) -9 NIL NIL) (-465 1138696 1138813 1138999 "HYPCAT-" 1139004 NIL HYPCAT- (NIL T) -8 NIL NIL) (-464 1135376 1136707 1136748 "HOAGG" 1137729 NIL HOAGG (NIL T) -9 NIL 1138408) (-463 1133970 1134369 1134895 "HOAGG-" 1134900 NIL HOAGG- (NIL T T) -8 NIL NIL) (-462 1127800 1133411 1133577 "HEXADEC" 1133824 T HEXADEC (NIL) -8 NIL NIL) (-461 1126548 1126770 1127033 "HEUGCD" 1127577 NIL HEUGCD (NIL T) -7 NIL NIL) (-460 1125651 1126385 1126515 "HELLFDIV" 1126520 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-459 1123879 1125428 1125516 "HEAP" 1125595 NIL HEAP (NIL T) -8 NIL NIL) (-458 1117746 1123794 1123856 "HDP" 1123861 NIL HDP (NIL NIL T) -8 NIL NIL) (-457 1111458 1117383 1117534 "HDMP" 1117647 NIL HDMP (NIL NIL T) -8 NIL NIL) (-456 1110783 1110922 1111086 "HB" 1111314 T HB (NIL) -7 NIL NIL) (-455 1104280 1110629 1110733 "HASHTBL" 1110738 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-454 1102033 1103908 1104087 "HACKPI" 1104121 T HACKPI (NIL) -8 NIL NIL) (-453 1097729 1101887 1101999 "GTSET" 1102004 NIL GTSET (NIL T T T T) -8 NIL NIL) (-452 1091255 1097607 1097705 "GSTBL" 1097710 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-451 1083488 1090291 1090555 "GSERIES" 1091046 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-450 1082511 1082964 1082992 "GROUP" 1083253 T GROUP (NIL) -9 NIL 1083412) (-449 1081627 1081850 1082194 "GROUP-" 1082199 NIL GROUP- (NIL T) -8 NIL NIL) (-448 1079996 1080315 1080702 "GROEBSOL" 1081304 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-447 1078937 1079199 1079250 "GRMOD" 1079779 NIL GRMOD (NIL T T) -9 NIL 1079947) (-446 1078705 1078741 1078869 "GRMOD-" 1078874 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-445 1074031 1075059 1076059 "GRIMAGE" 1077725 T GRIMAGE (NIL) -8 NIL NIL) (-444 1072498 1072758 1073082 "GRDEF" 1073727 T GRDEF (NIL) -7 NIL NIL) (-443 1071942 1072058 1072199 "GRAY" 1072377 T GRAY (NIL) -7 NIL NIL) (-442 1071176 1071556 1071607 "GRALG" 1071760 NIL GRALG (NIL T T) -9 NIL 1071852) (-441 1070837 1070910 1071073 "GRALG-" 1071078 NIL GRALG- (NIL T T T) -8 NIL NIL) (-440 1067645 1070426 1070602 "GPOLSET" 1070744 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-439 1067001 1067058 1067315 "GOSPER" 1067582 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-438 1062760 1063439 1063965 "GMODPOL" 1066700 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-437 1061765 1061949 1062187 "GHENSEL" 1062572 NIL GHENSEL (NIL T T) -7 NIL NIL) (-436 1055831 1056674 1057700 "GENUPS" 1060849 NIL GENUPS (NIL T T) -7 NIL NIL) (-435 1055528 1055579 1055668 "GENUFACT" 1055774 NIL GENUFACT (NIL T) -7 NIL NIL) (-434 1054940 1055017 1055182 "GENPGCD" 1055446 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-433 1054414 1054449 1054662 "GENMFACT" 1054899 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-432 1052982 1053237 1053544 "GENEEZ" 1054157 NIL GENEEZ (NIL T T) -7 NIL NIL) (-431 1046856 1052595 1052756 "GDMP" 1052905 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-430 1036233 1040627 1041733 "GCNAALG" 1045839 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-429 1034655 1035527 1035555 "GCDDOM" 1035810 T GCDDOM (NIL) -9 NIL 1035967) (-428 1034125 1034252 1034467 "GCDDOM-" 1034472 NIL GCDDOM- (NIL T) -8 NIL NIL) (-427 1032797 1032982 1033286 "GB" 1033904 NIL GB (NIL T T T T) -7 NIL NIL) (-426 1021417 1023743 1026135 "GBINTERN" 1030488 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-425 1019254 1019546 1019967 "GBF" 1021092 NIL GBF (NIL T T T T) -7 NIL NIL) (-424 1018035 1018200 1018467 "GBEUCLID" 1019070 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-423 1017384 1017509 1017658 "GAUSSFAC" 1017906 T GAUSSFAC (NIL) -7 NIL NIL) (-422 1015761 1016063 1016376 "GALUTIL" 1017103 NIL GALUTIL (NIL T) -7 NIL NIL) (-421 1014078 1014352 1014675 "GALPOLYU" 1015488 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-420 1011467 1011757 1012162 "GALFACTU" 1013775 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-419 1003273 1004772 1006380 "GALFACT" 1009899 NIL GALFACT (NIL T) -7 NIL NIL) (-418 1000661 1001319 1001347 "FVFUN" 1002503 T FVFUN (NIL) -9 NIL 1003223) (-417 999927 1000109 1000137 "FVC" 1000428 T FVC (NIL) -9 NIL 1000611) (-416 999569 999724 999805 "FUNCTION" 999879 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-415 997239 997790 998279 "FT" 999100 T FT (NIL) -8 NIL NIL) (-414 996057 996540 996743 "FTEM" 997056 T FTEM (NIL) -8 NIL NIL) (-413 994322 994610 995012 "FSUPFACT" 995749 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-412 992719 993008 993340 "FST" 994010 T FST (NIL) -8 NIL NIL) (-411 991894 992000 992194 "FSRED" 992601 NIL FSRED (NIL T T) -7 NIL NIL) (-410 990573 990828 991182 "FSPRMELT" 991609 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-409 987658 988096 988595 "FSPECF" 990136 NIL FSPECF (NIL T T) -7 NIL NIL) (-408 970032 978589 978629 "FS" 982467 NIL FS (NIL T) -9 NIL 984749) (-407 958682 961672 965728 "FS-" 966025 NIL FS- (NIL T T) -8 NIL NIL) (-406 958198 958252 958428 "FSINT" 958623 NIL FSINT (NIL T T) -7 NIL NIL) (-405 956479 957191 957494 "FSERIES" 957977 NIL FSERIES (NIL T T) -8 NIL NIL) (-404 955497 955613 955843 "FSCINT" 956359 NIL FSCINT (NIL T T) -7 NIL NIL) (-403 951732 954442 954483 "FSAGG" 954853 NIL FSAGG (NIL T) -9 NIL 955112) (-402 949494 950095 950891 "FSAGG-" 950986 NIL FSAGG- (NIL T T) -8 NIL NIL) (-401 948536 948679 948906 "FSAGG2" 949347 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-400 946195 946474 947027 "FS2UPS" 948254 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-399 945781 945824 945977 "FS2" 946146 NIL FS2 (NIL T T T T) -7 NIL NIL) (-398 944641 944812 945120 "FS2EXPXP" 945606 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-397 944067 944182 944334 "FRUTIL" 944521 NIL FRUTIL (NIL T) -7 NIL NIL) (-396 935487 939566 940922 "FR" 942743 NIL FR (NIL T) -8 NIL NIL) (-395 930564 933207 933247 "FRNAALG" 934643 NIL FRNAALG (NIL T) -9 NIL 935250) (-394 926242 927313 928588 "FRNAALG-" 929338 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-393 925880 925923 926050 "FRNAAF2" 926193 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-392 924245 924737 925031 "FRMOD" 925693 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-391 921967 922636 922952 "FRIDEAL" 924036 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-390 921166 921253 921540 "FRIDEAL2" 921874 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-389 920424 920832 920873 "FRETRCT" 920878 NIL FRETRCT (NIL T) -9 NIL 921049) (-388 919536 919767 920118 "FRETRCT-" 920123 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-387 916746 917966 918025 "FRAMALG" 918907 NIL FRAMALG (NIL T T) -9 NIL 919199) (-386 914879 915335 915965 "FRAMALG-" 916188 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-385 908781 914354 914630 "FRAC" 914635 NIL FRAC (NIL T) -8 NIL NIL) (-384 908417 908474 908581 "FRAC2" 908718 NIL FRAC2 (NIL T T) -7 NIL NIL) (-383 908053 908110 908217 "FR2" 908354 NIL FR2 (NIL T T) -7 NIL NIL) (-382 902727 905640 905668 "FPS" 906787 T FPS (NIL) -9 NIL 907343) (-381 902176 902285 902449 "FPS-" 902595 NIL FPS- (NIL T) -8 NIL NIL) (-380 899625 901322 901350 "FPC" 901575 T FPC (NIL) -9 NIL 901717) (-379 899418 899458 899555 "FPC-" 899560 NIL FPC- (NIL T) -8 NIL NIL) (-378 898297 898907 898948 "FPATMAB" 898953 NIL FPATMAB (NIL T) -9 NIL 899105) (-377 895997 896473 896899 "FPARFRAC" 897934 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-376 891390 891889 892571 "FORTRAN" 895429 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-375 889106 889606 890145 "FORT" 890871 T FORT (NIL) -7 NIL NIL) (-374 886782 887344 887372 "FORTFN" 888432 T FORTFN (NIL) -9 NIL 889056) (-373 886546 886596 886624 "FORTCAT" 886683 T FORTCAT (NIL) -9 NIL 886745) (-372 884606 885089 885488 "FORMULA" 886167 T FORMULA (NIL) -8 NIL NIL) (-371 884394 884424 884493 "FORMULA1" 884570 NIL FORMULA1 (NIL T) -7 NIL NIL) (-370 883917 883969 884142 "FORDER" 884336 NIL FORDER (NIL T T T T) -7 NIL NIL) (-369 883013 883177 883370 "FOP" 883744 T FOP (NIL) -7 NIL NIL) (-368 881621 882293 882467 "FNLA" 882895 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-367 880290 880679 880707 "FNCAT" 881279 T FNCAT (NIL) -9 NIL 881572) (-366 879856 880249 880277 "FNAME" 880282 T FNAME (NIL) -8 NIL NIL) (-365 878516 879489 879517 "FMTC" 879522 T FMTC (NIL) -9 NIL 879557) (-364 874834 876041 876669 "FMONOID" 877921 NIL FMONOID (NIL T) -8 NIL NIL) (-363 874054 874577 874725 "FM" 874730 NIL FM (NIL T T) -8 NIL NIL) (-362 871478 872124 872152 "FMFUN" 873296 T FMFUN (NIL) -9 NIL 874004) (-361 870747 870928 870956 "FMC" 871246 T FMC (NIL) -9 NIL 871428) (-360 867977 868811 868864 "FMCAT" 870046 NIL FMCAT (NIL T T) -9 NIL 870540) (-359 866872 867745 867844 "FM1" 867922 NIL FM1 (NIL T T) -8 NIL NIL) (-358 864646 865062 865556 "FLOATRP" 866423 NIL FLOATRP (NIL T) -7 NIL NIL) (-357 858132 862302 862932 "FLOAT" 864036 T FLOAT (NIL) -8 NIL NIL) (-356 855570 856070 856648 "FLOATCP" 857599 NIL FLOATCP (NIL T) -7 NIL NIL) (-355 854359 855207 855247 "FLINEXP" 855252 NIL FLINEXP (NIL T) -9 NIL 855345) (-354 853514 853749 854076 "FLINEXP-" 854081 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-353 852590 852734 852958 "FLASORT" 853366 NIL FLASORT (NIL T T) -7 NIL NIL) (-352 849809 850651 850703 "FLALG" 851930 NIL FLALG (NIL T T) -9 NIL 852397) (-351 843594 847296 847337 "FLAGG" 848599 NIL FLAGG (NIL T) -9 NIL 849251) (-350 842320 842659 843149 "FLAGG-" 843154 NIL FLAGG- (NIL T T) -8 NIL NIL) (-349 841362 841505 841732 "FLAGG2" 842173 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-348 838335 839353 839412 "FINRALG" 840540 NIL FINRALG (NIL T T) -9 NIL 841048) (-347 837495 837724 838063 "FINRALG-" 838068 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-346 836902 837115 837143 "FINITE" 837339 T FINITE (NIL) -9 NIL 837446) (-345 829362 831523 831563 "FINAALG" 835230 NIL FINAALG (NIL T) -9 NIL 836683) (-344 824703 825744 826888 "FINAALG-" 828267 NIL FINAALG- (NIL T T) -8 NIL NIL) (-343 824098 824458 824561 "FILE" 824633 NIL FILE (NIL T) -8 NIL NIL) (-342 822783 823095 823149 "FILECAT" 823833 NIL FILECAT (NIL T T) -9 NIL 824049) (-341 820646 822202 822230 "FIELD" 822270 T FIELD (NIL) -9 NIL 822350) (-340 819266 819651 820162 "FIELD-" 820167 NIL FIELD- (NIL T) -8 NIL NIL) (-339 817081 817903 818249 "FGROUP" 818953 NIL FGROUP (NIL T) -8 NIL NIL) (-338 816171 816335 816555 "FGLMICPK" 816913 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-337 811973 816096 816153 "FFX" 816158 NIL FFX (NIL T NIL) -8 NIL NIL) (-336 811574 811635 811770 "FFSLPE" 811906 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-335 807567 808346 809142 "FFPOLY" 810810 NIL FFPOLY (NIL T) -7 NIL NIL) (-334 807071 807107 807316 "FFPOLY2" 807525 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-333 802892 806990 807053 "FFP" 807058 NIL FFP (NIL T NIL) -8 NIL NIL) (-332 798260 802803 802867 "FF" 802872 NIL FF (NIL NIL NIL) -8 NIL NIL) (-331 793356 797603 797793 "FFNBX" 798114 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-330 788265 792491 792749 "FFNBP" 793210 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-329 782868 787549 787760 "FFNB" 788098 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-328 781700 781898 782213 "FFINTBAS" 782665 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-327 777924 780164 780192 "FFIELDC" 780812 T FFIELDC (NIL) -9 NIL 781188) (-326 776587 776957 777454 "FFIELDC-" 777459 NIL FFIELDC- (NIL T) -8 NIL NIL) (-325 776157 776202 776326 "FFHOM" 776529 NIL FFHOM (NIL T T T) -7 NIL NIL) (-324 773855 774339 774856 "FFF" 775672 NIL FFF (NIL T) -7 NIL NIL) (-323 769443 773597 773698 "FFCGX" 773798 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-322 765045 769175 769282 "FFCGP" 769386 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-321 760198 764772 764880 "FFCG" 764981 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-320 742144 751267 751353 "FFCAT" 756518 NIL FFCAT (NIL T T T) -9 NIL 758005) (-319 737342 738389 739703 "FFCAT-" 740933 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-318 736753 736796 737031 "FFCAT2" 737293 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-317 725953 729743 730960 "FEXPR" 735608 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-316 724953 725388 725429 "FEVALAB" 725513 NIL FEVALAB (NIL T) -9 NIL 725774) (-315 724112 724322 724660 "FEVALAB-" 724665 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-314 722705 723495 723698 "FDIV" 724011 NIL FDIV (NIL T T T T) -8 NIL NIL) (-313 719772 720487 720602 "FDIVCAT" 722170 NIL FDIVCAT (NIL T T T T) -9 NIL 722607) (-312 719534 719561 719731 "FDIVCAT-" 719736 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-311 718754 718841 719118 "FDIV2" 719441 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-310 717440 717699 717988 "FCPAK1" 718485 T FCPAK1 (NIL) -7 NIL NIL) (-309 716568 716940 717081 "FCOMP" 717331 NIL FCOMP (NIL T) -8 NIL NIL) (-308 700203 703617 707178 "FC" 713027 T FC (NIL) -8 NIL NIL) (-307 692799 696845 696885 "FAXF" 698687 NIL FAXF (NIL T) -9 NIL 699378) (-306 690078 690733 691558 "FAXF-" 692023 NIL FAXF- (NIL T T) -8 NIL NIL) (-305 685178 689454 689630 "FARRAY" 689935 NIL FARRAY (NIL T) -8 NIL NIL) (-304 680569 682640 682692 "FAMR" 683704 NIL FAMR (NIL T T) -9 NIL 684164) (-303 679460 679762 680196 "FAMR-" 680201 NIL FAMR- (NIL T T T) -8 NIL NIL) (-302 678656 679382 679435 "FAMONOID" 679440 NIL FAMONOID (NIL T) -8 NIL NIL) (-301 676489 677173 677226 "FAMONC" 678167 NIL FAMONC (NIL T T) -9 NIL 678552) (-300 675181 676243 676380 "FAGROUP" 676385 NIL FAGROUP (NIL T) -8 NIL NIL) (-299 672984 673303 673705 "FACUTIL" 674862 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-298 672083 672268 672490 "FACTFUNC" 672794 NIL FACTFUNC (NIL T) -7 NIL NIL) (-297 664403 671334 671546 "EXPUPXS" 671939 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-296 661886 662426 663012 "EXPRTUBE" 663837 T EXPRTUBE (NIL) -7 NIL NIL) (-295 658080 658672 659409 "EXPRODE" 661225 NIL EXPRODE (NIL T T) -7 NIL NIL) (-294 643239 656739 657165 "EXPR" 657686 NIL EXPR (NIL T) -8 NIL NIL) (-293 637667 638254 639066 "EXPR2UPS" 642537 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-292 637303 637360 637467 "EXPR2" 637604 NIL EXPR2 (NIL T T) -7 NIL NIL) (-291 628657 636440 636735 "EXPEXPAN" 637141 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-290 628484 628614 628643 "EXIT" 628648 T EXIT (NIL) -8 NIL NIL) (-289 628111 628173 628286 "EVALCYC" 628416 NIL EVALCYC (NIL T) -7 NIL NIL) (-288 627652 627770 627811 "EVALAB" 627981 NIL EVALAB (NIL T) -9 NIL 628085) (-287 627133 627255 627476 "EVALAB-" 627481 NIL EVALAB- (NIL T T) -8 NIL NIL) (-286 624596 625908 625936 "EUCDOM" 626491 T EUCDOM (NIL) -9 NIL 626841) (-285 623001 623443 624033 "EUCDOM-" 624038 NIL EUCDOM- (NIL T) -8 NIL NIL) (-284 610579 613327 616067 "ESTOOLS" 620281 T ESTOOLS (NIL) -7 NIL NIL) (-283 610215 610272 610379 "ESTOOLS2" 610516 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-282 609966 610008 610088 "ESTOOLS1" 610167 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-281 603904 605628 605656 "ES" 608420 T ES (NIL) -9 NIL 609826) (-280 598851 600138 601955 "ES-" 602119 NIL ES- (NIL T) -8 NIL NIL) (-279 595226 595986 596766 "ESCONT" 598091 T ESCONT (NIL) -7 NIL NIL) (-278 594971 595003 595085 "ESCONT1" 595188 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-277 594646 594696 594796 "ES2" 594915 NIL ES2 (NIL T T) -7 NIL NIL) (-276 594276 594334 594443 "ES1" 594582 NIL ES1 (NIL T T) -7 NIL NIL) (-275 593492 593621 593797 "ERROR" 594120 T ERROR (NIL) -7 NIL NIL) (-274 586995 593351 593442 "EQTBL" 593447 NIL EQTBL (NIL T T) -8 NIL NIL) (-273 579432 582313 583760 "EQ" 585581 NIL -2604 (NIL T) -8 NIL NIL) (-272 579064 579121 579230 "EQ2" 579369 NIL EQ2 (NIL T T) -7 NIL NIL) (-271 574356 575402 576495 "EP" 578003 NIL EP (NIL T) -7 NIL NIL) (-270 572938 573239 573556 "ENV" 574059 T ENV (NIL) -8 NIL NIL) (-269 572098 572662 572690 "ENTIRER" 572695 T ENTIRER (NIL) -9 NIL 572740) (-268 568554 570053 570423 "EMR" 571897 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-267 567698 567883 567937 "ELTAGG" 568317 NIL ELTAGG (NIL T T) -9 NIL 568528) (-266 567417 567479 567620 "ELTAGG-" 567625 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-265 567206 567235 567289 "ELTAB" 567373 NIL ELTAB (NIL T T) -9 NIL NIL) (-264 566332 566478 566677 "ELFUTS" 567057 NIL ELFUTS (NIL T T) -7 NIL NIL) (-263 566074 566130 566158 "ELEMFUN" 566263 T ELEMFUN (NIL) -9 NIL NIL) (-262 565944 565965 566033 "ELEMFUN-" 566038 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-261 560836 564045 564086 "ELAGG" 565026 NIL ELAGG (NIL T) -9 NIL 565489) (-260 559121 559555 560218 "ELAGG-" 560223 NIL ELAGG- (NIL T T) -8 NIL NIL) (-259 557778 558058 558353 "ELABEXPR" 558846 T ELABEXPR (NIL) -8 NIL NIL) (-258 550646 552445 553272 "EFUPXS" 557054 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-257 544096 545897 546707 "EFULS" 549922 NIL EFULS (NIL T T T) -8 NIL NIL) (-256 541527 541885 542363 "EFSTRUC" 543728 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-255 530599 532164 533724 "EF" 540042 NIL EF (NIL T T) -7 NIL NIL) (-254 529700 530084 530233 "EAB" 530470 T EAB (NIL) -8 NIL NIL) (-253 528913 529659 529687 "E04UCFA" 529692 T E04UCFA (NIL) -8 NIL NIL) (-252 528126 528872 528900 "E04NAFA" 528905 T E04NAFA (NIL) -8 NIL NIL) (-251 527339 528085 528113 "E04MBFA" 528118 T E04MBFA (NIL) -8 NIL NIL) (-250 526552 527298 527326 "E04JAFA" 527331 T E04JAFA (NIL) -8 NIL NIL) (-249 525767 526511 526539 "E04GCFA" 526544 T E04GCFA (NIL) -8 NIL NIL) (-248 524982 525726 525754 "E04FDFA" 525759 T E04FDFA (NIL) -8 NIL NIL) (-247 524195 524941 524969 "E04DGFA" 524974 T E04DGFA (NIL) -8 NIL NIL) (-246 518380 519725 521087 "E04AGNT" 522853 T E04AGNT (NIL) -7 NIL NIL) (-245 517107 517587 517627 "DVARCAT" 518102 NIL DVARCAT (NIL T) -9 NIL 518300) (-244 516311 516523 516837 "DVARCAT-" 516842 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-243 509173 516113 516240 "DSMP" 516245 NIL DSMP (NIL T T T) -8 NIL NIL) (-242 503983 505118 506186 "DROPT" 508125 T DROPT (NIL) -8 NIL NIL) (-241 503648 503707 503805 "DROPT1" 503918 NIL DROPT1 (NIL T) -7 NIL NIL) (-240 498763 499889 501026 "DROPT0" 502531 T DROPT0 (NIL) -7 NIL NIL) (-239 497108 497433 497819 "DRAWPT" 498397 T DRAWPT (NIL) -7 NIL NIL) (-238 491695 492618 493697 "DRAW" 496082 NIL DRAW (NIL T) -7 NIL NIL) (-237 491328 491381 491499 "DRAWHACK" 491636 NIL DRAWHACK (NIL T) -7 NIL NIL) (-236 490059 490328 490619 "DRAWCX" 491057 T DRAWCX (NIL) -7 NIL NIL) (-235 489577 489645 489795 "DRAWCURV" 489985 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-234 480048 482007 484122 "DRAWCFUN" 487482 T DRAWCFUN (NIL) -7 NIL NIL) (-233 476862 478744 478785 "DQAGG" 479414 NIL DQAGG (NIL T) -9 NIL 479687) (-232 465369 472107 472189 "DPOLCAT" 474027 NIL DPOLCAT (NIL T T T T) -9 NIL 474571) (-231 460209 461555 463512 "DPOLCAT-" 463517 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-230 453005 460071 460168 "DPMO" 460173 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-229 445704 452786 452952 "DPMM" 452957 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-228 445124 445327 445441 "DOMAIN" 445610 T DOMAIN (NIL) -8 NIL NIL) (-227 438836 444761 444912 "DMP" 445025 NIL DMP (NIL NIL T) -8 NIL NIL) (-226 438436 438492 438636 "DLP" 438774 NIL DLP (NIL T) -7 NIL NIL) (-225 432080 437537 437764 "DLIST" 438241 NIL DLIST (NIL T) -8 NIL NIL) (-224 428927 430936 430977 "DLAGG" 431527 NIL DLAGG (NIL T) -9 NIL 431756) (-223 427637 428329 428357 "DIVRING" 428507 T DIVRING (NIL) -9 NIL 428615) (-222 426625 426878 427271 "DIVRING-" 427276 NIL DIVRING- (NIL T) -8 NIL NIL) (-221 424727 425084 425490 "DISPLAY" 426239 T DISPLAY (NIL) -7 NIL NIL) (-220 418616 424641 424704 "DIRPROD" 424709 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-219 417464 417667 417932 "DIRPROD2" 418409 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-218 406983 412988 413041 "DIRPCAT" 413449 NIL DIRPCAT (NIL NIL T) -9 NIL 414288) (-217 404309 404951 405832 "DIRPCAT-" 406169 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-216 403596 403756 403942 "DIOSP" 404143 T DIOSP (NIL) -7 NIL NIL) (-215 400299 402509 402550 "DIOPS" 402984 NIL DIOPS (NIL T) -9 NIL 403213) (-214 399848 399962 400153 "DIOPS-" 400158 NIL DIOPS- (NIL T T) -8 NIL NIL) (-213 398720 399358 399386 "DIFRING" 399573 T DIFRING (NIL) -9 NIL 399682) (-212 398366 398443 398595 "DIFRING-" 398600 NIL DIFRING- (NIL T) -8 NIL NIL) (-211 396156 397438 397478 "DIFEXT" 397837 NIL DIFEXT (NIL T) -9 NIL 398130) (-210 394442 394870 395535 "DIFEXT-" 395540 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-209 391765 393975 394016 "DIAGG" 394021 NIL DIAGG (NIL T) -9 NIL 394041) (-208 391149 391306 391558 "DIAGG-" 391563 NIL DIAGG- (NIL T T) -8 NIL NIL) (-207 386614 390108 390385 "DHMATRIX" 390918 NIL DHMATRIX (NIL T) -8 NIL NIL) (-206 382226 383135 384145 "DFSFUN" 385624 T DFSFUN (NIL) -7 NIL NIL) (-205 377012 380940 381305 "DFLOAT" 381881 T DFLOAT (NIL) -8 NIL NIL) (-204 375245 375526 375921 "DFINTTLS" 376720 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-203 372278 373280 373678 "DERHAM" 374912 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-202 370127 372053 372142 "DEQUEUE" 372222 NIL DEQUEUE (NIL T) -8 NIL NIL) (-201 369345 369478 369673 "DEGRED" 369989 NIL DEGRED (NIL T T) -7 NIL NIL) (-200 365745 366490 367342 "DEFINTRF" 368573 NIL DEFINTRF (NIL T) -7 NIL NIL) (-199 363276 363745 364343 "DEFINTEF" 365264 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-198 357106 362717 362883 "DECIMAL" 363130 T DECIMAL (NIL) -8 NIL NIL) (-197 354618 355076 355582 "DDFACT" 356650 NIL DDFACT (NIL T T) -7 NIL NIL) (-196 354214 354257 354408 "DBLRESP" 354569 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-195 351924 352258 352627 "DBASE" 353972 NIL DBASE (NIL T) -8 NIL NIL) (-194 351059 351883 351911 "D03FAFA" 351916 T D03FAFA (NIL) -8 NIL NIL) (-193 350195 351018 351046 "D03EEFA" 351051 T D03EEFA (NIL) -8 NIL NIL) (-192 348145 348611 349100 "D03AGNT" 349726 T D03AGNT (NIL) -7 NIL NIL) (-191 347463 348104 348132 "D02EJFA" 348137 T D02EJFA (NIL) -8 NIL NIL) (-190 346781 347422 347450 "D02CJFA" 347455 T D02CJFA (NIL) -8 NIL NIL) (-189 346099 346740 346768 "D02BHFA" 346773 T D02BHFA (NIL) -8 NIL NIL) (-188 345417 346058 346086 "D02BBFA" 346091 T D02BBFA (NIL) -8 NIL NIL) (-187 338615 340203 341809 "D02AGNT" 343831 T D02AGNT (NIL) -7 NIL NIL) (-186 336384 336906 337452 "D01WGTS" 338089 T D01WGTS (NIL) -7 NIL NIL) (-185 335487 336343 336371 "D01TRNS" 336376 T D01TRNS (NIL) -8 NIL NIL) (-184 334590 335446 335474 "D01GBFA" 335479 T D01GBFA (NIL) -8 NIL NIL) (-183 333693 334549 334577 "D01FCFA" 334582 T D01FCFA (NIL) -8 NIL NIL) (-182 332796 333652 333680 "D01ASFA" 333685 T D01ASFA (NIL) -8 NIL NIL) (-181 331899 332755 332783 "D01AQFA" 332788 T D01AQFA (NIL) -8 NIL NIL) (-180 331002 331858 331886 "D01APFA" 331891 T D01APFA (NIL) -8 NIL NIL) (-179 330105 330961 330989 "D01ANFA" 330994 T D01ANFA (NIL) -8 NIL NIL) (-178 329208 330064 330092 "D01AMFA" 330097 T D01AMFA (NIL) -8 NIL NIL) (-177 328311 329167 329195 "D01ALFA" 329200 T D01ALFA (NIL) -8 NIL NIL) (-176 327414 328270 328298 "D01AKFA" 328303 T D01AKFA (NIL) -8 NIL NIL) (-175 326517 327373 327401 "D01AJFA" 327406 T D01AJFA (NIL) -8 NIL NIL) (-174 319821 321370 322929 "D01AGNT" 324978 T D01AGNT (NIL) -7 NIL NIL) (-173 319158 319286 319438 "CYCLOTOM" 319689 T CYCLOTOM (NIL) -7 NIL NIL) (-172 315893 316606 317333 "CYCLES" 318451 T CYCLES (NIL) -7 NIL NIL) (-171 315205 315339 315510 "CVMP" 315754 NIL CVMP (NIL T) -7 NIL NIL) (-170 312986 313244 313619 "CTRIGMNP" 314933 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-169 312497 312686 312785 "CTORCALL" 312907 T CTORCALL (NIL) -8 NIL NIL) (-168 311871 311970 312123 "CSTTOOLS" 312394 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-167 307670 308327 309085 "CRFP" 311183 NIL CRFP (NIL T T) -7 NIL NIL) (-166 306717 306902 307130 "CRAPACK" 307474 NIL CRAPACK (NIL T) -7 NIL NIL) (-165 306101 306202 306406 "CPMATCH" 306593 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-164 305826 305854 305960 "CPIMA" 306067 NIL CPIMA (NIL T T T) -7 NIL NIL) (-163 302190 302862 303580 "COORDSYS" 305161 NIL COORDSYS (NIL T) -7 NIL NIL) (-162 301574 301703 301853 "CONTOUR" 302060 T CONTOUR (NIL) -8 NIL NIL) (-161 297435 299577 300069 "CONTFRAC" 301114 NIL CONTFRAC (NIL T) -8 NIL NIL) (-160 296589 297153 297181 "COMRING" 297186 T COMRING (NIL) -9 NIL 297237) (-159 295670 295947 296131 "COMPPROP" 296425 T COMPPROP (NIL) -8 NIL NIL) (-158 295331 295366 295494 "COMPLPAT" 295629 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-157 285312 295140 295249 "COMPLEX" 295254 NIL COMPLEX (NIL T) -8 NIL NIL) (-156 284948 285005 285112 "COMPLEX2" 285249 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-155 284666 284701 284799 "COMPFACT" 284907 NIL COMPFACT (NIL T T) -7 NIL NIL) (-154 269001 279295 279335 "COMPCAT" 280337 NIL COMPCAT (NIL T) -9 NIL 281730) (-153 258516 261440 265067 "COMPCAT-" 265423 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-152 258247 258275 258377 "COMMUPC" 258482 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-151 258042 258075 258134 "COMMONOP" 258208 T COMMONOP (NIL) -7 NIL NIL) (-150 257625 257793 257880 "COMM" 257975 T COMM (NIL) -8 NIL NIL) (-149 256874 257068 257096 "COMBOPC" 257434 T COMBOPC (NIL) -9 NIL 257609) (-148 255770 255980 256222 "COMBINAT" 256664 NIL COMBINAT (NIL T) -7 NIL NIL) (-147 251968 252541 253181 "COMBF" 255192 NIL COMBF (NIL T T) -7 NIL NIL) (-146 250754 251084 251319 "COLOR" 251753 T COLOR (NIL) -8 NIL NIL) (-145 250394 250441 250566 "CMPLXRT" 250701 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-144 245896 246924 248004 "CLIP" 249334 T CLIP (NIL) -7 NIL NIL) (-143 244234 245004 245242 "CLIF" 245724 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-142 240457 242381 242422 "CLAGG" 243351 NIL CLAGG (NIL T) -9 NIL 243887) (-141 238879 239336 239919 "CLAGG-" 239924 NIL CLAGG- (NIL T T) -8 NIL NIL) (-140 238423 238508 238648 "CINTSLPE" 238788 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-139 235924 236395 236943 "CHVAR" 237951 NIL CHVAR (NIL T T T) -7 NIL NIL) (-138 235147 235711 235739 "CHARZ" 235744 T CHARZ (NIL) -9 NIL 235758) (-137 234901 234941 235019 "CHARPOL" 235101 NIL CHARPOL (NIL T) -7 NIL NIL) (-136 234008 234605 234633 "CHARNZ" 234680 T CHARNZ (NIL) -9 NIL 234735) (-135 232033 232698 233033 "CHAR" 233693 T CHAR (NIL) -8 NIL NIL) (-134 231759 231820 231848 "CFCAT" 231959 T CFCAT (NIL) -9 NIL NIL) (-133 231004 231115 231297 "CDEN" 231643 NIL CDEN (NIL T T T) -7 NIL NIL) (-132 226996 230157 230437 "CCLASS" 230744 T CCLASS (NIL) -8 NIL NIL) (-131 226915 226941 226976 "CATEGORY" 226981 T -10 (NIL) -8 NIL NIL) (-130 221967 222944 223697 "CARTEN" 226218 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-129 221075 221223 221444 "CARTEN2" 221814 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-128 219373 220227 220483 "CARD" 220839 T CARD (NIL) -8 NIL NIL) (-127 218746 219074 219102 "CACHSET" 219234 T CACHSET (NIL) -9 NIL 219311) (-126 218243 218539 218567 "CABMON" 218617 T CABMON (NIL) -9 NIL 218673) (-125 217411 217790 217933 "BYTE" 218120 T BYTE (NIL) -8 NIL NIL) (-124 213359 217358 217392 "BYTEARY" 217397 T BYTEARY (NIL) -8 NIL NIL) (-123 210916 213051 213158 "BTREE" 213285 NIL BTREE (NIL T) -8 NIL NIL) (-122 208414 210564 210686 "BTOURN" 210826 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205833 207886 207927 "BTCAT" 207995 NIL BTCAT (NIL T) -9 NIL 208072) (-120 205500 205580 205729 "BTCAT-" 205734 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200721 204592 204620 "BTAGG" 204876 T BTAGG (NIL) -9 NIL 205055) (-118 200144 200288 200518 "BTAGG-" 200523 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197188 199422 199637 "BSTREE" 199961 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196326 196452 196636 "BRILL" 197044 NIL BRILL (NIL T) -7 NIL NIL) (-115 193028 195055 195096 "BRAGG" 195745 NIL BRAGG (NIL T) -9 NIL 196002) (-114 191557 191963 192518 "BRAGG-" 192523 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184765 190903 191087 "BPADICRT" 191405 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183069 184702 184747 "BPADIC" 184752 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182769 182799 182912 "BOUNDZRO" 183033 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178284 179375 180242 "BOP" 181922 T BOP (NIL) -8 NIL NIL) (-109 175905 176349 176869 "BOP1" 177797 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174540 175245 175463 "BOOLEAN" 175707 T BOOLEAN (NIL) -8 NIL NIL) (-107 173907 174285 174337 "BMODULE" 174342 NIL BMODULE (NIL T T) -9 NIL 174406) (-106 169717 173705 173778 "BITS" 173854 T BITS (NIL) -8 NIL NIL) (-105 168814 169249 169401 "BINFILE" 169585 T BINFILE (NIL) -8 NIL NIL) (-104 168226 168348 168490 "BINDING" 168692 T BINDING (NIL) -8 NIL NIL) (-103 162060 167670 167835 "BINARY" 168081 T BINARY (NIL) -8 NIL NIL) (-102 159888 161316 161357 "BGAGG" 161617 NIL BGAGG (NIL T) -9 NIL 161754) (-101 159719 159751 159842 "BGAGG-" 159847 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158817 159103 159308 "BFUNCT" 159534 T BFUNCT (NIL) -8 NIL NIL) (-99 157518 157696 157981 "BEZOUT" 158641 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154043 156378 156706 "BBTREE" 157221 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153781 153834 153860 "BASTYPE" 153977 T BASTYPE (NIL) -9 NIL NIL) (-96 153636 153665 153735 "BASTYPE-" 153740 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153074 153150 153300 "BALFACT" 153547 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151896 152493 152678 "AUTOMOR" 152919 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151622 151627 151653 "ATTREG" 151658 T ATTREG (NIL) -9 NIL NIL) (-92 149901 150319 150671 "ATTRBUT" 151288 T ATTRBUT (NIL) -8 NIL NIL) (-91 149437 149550 149576 "ATRIG" 149777 T ATRIG (NIL) -9 NIL NIL) (-90 149246 149287 149374 "ATRIG-" 149379 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147443 149022 149110 "ASTACK" 149189 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145948 146245 146610 "ASSOCEQ" 147125 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144980 145607 145731 "ASP9" 145855 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144744 144928 144967 "ASP8" 144972 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143613 144349 144491 "ASP80" 144633 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142512 143248 143380 "ASP7" 143512 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141466 142189 142307 "ASP78" 142425 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140435 141146 141263 "ASP77" 141380 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139347 140073 140204 "ASP74" 140335 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138247 138982 139114 "ASP73" 139246 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137202 137924 138042 "ASP6" 138160 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136150 136879 136997 "ASP55" 137115 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135100 135824 135943 "ASP50" 136062 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134188 134801 134911 "ASP4" 135021 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133276 133889 133999 "ASP49" 134109 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132061 132815 132983 "ASP42" 133165 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130838 131594 131764 "ASP41" 131948 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129788 130515 130633 "ASP35" 130751 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129553 129736 129775 "ASP34" 129780 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129290 129357 129433 "ASP33" 129508 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128185 128925 129057 "ASP31" 129189 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127950 128133 128172 "ASP30" 128177 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127685 127754 127830 "ASP29" 127905 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127450 127633 127672 "ASP28" 127677 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127215 127398 127437 "ASP27" 127442 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126299 126913 127024 "ASP24" 127135 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125215 125940 126070 "ASP20" 126200 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124303 124916 125026 "ASP1" 125136 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123247 123977 124096 "ASP19" 124215 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122984 123051 123127 "ASP12" 123202 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121836 122583 122727 "ASP10" 122871 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119735 121680 121771 "ARRAY2" 121776 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115551 119383 119497 "ARRAY1" 119652 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114583 114756 114977 "ARRAY12" 115374 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108943 110814 110889 "ARR2CAT" 113519 NIL ARR2CAT (NIL T T T) -9 NIL 114277) (-54 106377 107121 108075 "ARR2CAT-" 108080 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105137 105287 105590 "APPRULE" 106215 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104790 104838 104956 "APPLYORE" 105083 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103764 104055 104250 "ANY" 104613 T ANY (NIL) -8 NIL NIL) (-50 103042 103165 103322 "ANY1" 103638 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100574 101492 101817 "ANTISYM" 102767 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100089 100278 100375 "ANON" 100495 T ANON (NIL) -8 NIL NIL) (-47 94166 98634 99085 "AN" 99656 T AN (NIL) -8 NIL NIL) (-46 90520 91918 91968 "AMR" 92707 NIL AMR (NIL T T) -9 NIL 93306) (-45 89633 89854 90216 "AMR-" 90221 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74183 89550 89611 "ALIST" 89616 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71020 73777 73946 "ALGSC" 74101 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67576 68130 68737 "ALGPKG" 70460 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66853 66954 67138 "ALGMFACT" 67462 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63283 63937 "ALGMANIP" 66377 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-3 3148819 3148824 3148829 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3148804 3148809 3148814 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3148789 3148794 3148799 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3148774 3148779 3148784 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1200 3147904 3148649 3148726 "ZMOD" 3148731 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1199 3147014 3147178 3147387 "ZLINDEP" 3147736 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1198 3136418 3138163 3140115 "ZDSOLVE" 3145163 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1197 3135664 3135805 3135994 "YSTREAM" 3136264 NIL YSTREAM (NIL T) -7 NIL NIL) (-1196 3133433 3134969 3135172 "XRPOLY" 3135507 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1195 3129895 3131224 3131806 "XPR" 3132897 NIL XPR (NIL T T) -8 NIL NIL) (-1194 3127609 3129230 3129433 "XPOLY" 3129726 NIL XPOLY (NIL T) -8 NIL NIL) (-1193 3125423 3126801 3126855 "XPOLYC" 3127140 NIL XPOLYC (NIL T T) -9 NIL 3127253) (-1192 3121795 3123940 3124328 "XPBWPOLY" 3125081 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1191 3117723 3120036 3120078 "XF" 3120699 NIL XF (NIL T) -9 NIL 3121098) (-1190 3117344 3117432 3117601 "XF-" 3117606 NIL XF- (NIL T T) -8 NIL NIL) (-1189 3112724 3114023 3114077 "XFALG" 3116225 NIL XFALG (NIL T T) -9 NIL 3117012) (-1188 3111861 3111965 3112169 "XEXPPKG" 3112616 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1187 3109960 3111712 3111807 "XDPOLY" 3111812 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1186 3108839 3109449 3109491 "XALG" 3109553 NIL XALG (NIL T) -9 NIL 3109672) (-1185 3102315 3106823 3107316 "WUTSET" 3108431 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1184 3100127 3100934 3101285 "WP" 3102097 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1183 3099013 3099211 3099506 "WFFINTBS" 3099924 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1182 3096917 3097344 3097806 "WEIER" 3098585 NIL WEIER (NIL T) -7 NIL NIL) (-1181 3096066 3096490 3096532 "VSPACE" 3096668 NIL VSPACE (NIL T) -9 NIL 3096742) (-1180 3095904 3095931 3096022 "VSPACE-" 3096027 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1179 3095650 3095693 3095764 "VOID" 3095855 T VOID (NIL) -8 NIL NIL) (-1178 3093786 3094145 3094551 "VIEW" 3095266 T VIEW (NIL) -7 NIL NIL) (-1177 3090211 3090849 3091586 "VIEWDEF" 3093071 T VIEWDEF (NIL) -7 NIL NIL) (-1176 3079549 3081759 3083932 "VIEW3D" 3088060 T VIEW3D (NIL) -8 NIL NIL) (-1175 3071831 3073460 3075039 "VIEW2D" 3077992 T VIEW2D (NIL) -8 NIL NIL) (-1174 3067240 3071601 3071693 "VECTOR" 3071774 NIL VECTOR (NIL T) -8 NIL NIL) (-1173 3065817 3066076 3066394 "VECTOR2" 3066970 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1172 3059357 3063609 3063652 "VECTCAT" 3064640 NIL VECTCAT (NIL T) -9 NIL 3065224) (-1171 3058371 3058625 3059015 "VECTCAT-" 3059020 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1170 3057852 3058022 3058142 "VARIABLE" 3058286 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1169 3057785 3057790 3057820 "UTYPE" 3057825 T UTYPE (NIL) -9 NIL NIL) (-1168 3056620 3056774 3057035 "UTSODETL" 3057611 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1167 3054060 3054520 3055044 "UTSODE" 3056161 NIL UTSODE (NIL T T) -7 NIL NIL) (-1166 3045904 3051700 3052188 "UTS" 3053629 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1165 3037249 3042614 3042656 "UTSCAT" 3043757 NIL UTSCAT (NIL T) -9 NIL 3044514) (-1164 3034604 3035320 3036308 "UTSCAT-" 3036313 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1163 3034235 3034278 3034409 "UTS2" 3034555 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1162 3028511 3031076 3031119 "URAGG" 3033189 NIL URAGG (NIL T) -9 NIL 3033911) (-1161 3025450 3026313 3027436 "URAGG-" 3027441 NIL URAGG- (NIL T T) -8 NIL NIL) (-1160 3021136 3024067 3024538 "UPXSSING" 3025114 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1159 3013027 3020257 3020537 "UPXS" 3020913 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1158 3006056 3012932 3013003 "UPXSCONS" 3013008 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1157 2996345 3003175 3003236 "UPXSCCA" 3003885 NIL UPXSCCA (NIL T T) -9 NIL 3004126) (-1156 2995984 2996069 2996242 "UPXSCCA-" 2996247 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1155 2986195 2992798 2992840 "UPXSCAT" 2993483 NIL UPXSCAT (NIL T) -9 NIL 2994091) (-1154 2985629 2985708 2985885 "UPXS2" 2986110 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1153 2984283 2984536 2984887 "UPSQFREE" 2985372 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1152 2978174 2981229 2981283 "UPSCAT" 2982432 NIL UPSCAT (NIL T T) -9 NIL 2983206) (-1151 2977379 2977586 2977912 "UPSCAT-" 2977917 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1150 2963465 2971502 2971544 "UPOLYC" 2973622 NIL UPOLYC (NIL T) -9 NIL 2974843) (-1149 2954795 2957220 2960366 "UPOLYC-" 2960371 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1148 2954426 2954469 2954600 "UPOLYC2" 2954746 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1147 2945845 2953995 2954132 "UP" 2954336 NIL UP (NIL NIL T) -8 NIL NIL) (-1146 2945188 2945295 2945458 "UPMP" 2945734 NIL UPMP (NIL T T) -7 NIL NIL) (-1145 2944741 2944822 2944961 "UPDIVP" 2945101 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1144 2943309 2943558 2943874 "UPDECOMP" 2944490 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1143 2942544 2942656 2942841 "UPCDEN" 2943193 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1142 2942067 2942136 2942283 "UP2" 2942469 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1141 2940584 2941271 2941548 "UNISEG" 2941825 NIL UNISEG (NIL T) -8 NIL NIL) (-1140 2939799 2939926 2940131 "UNISEG2" 2940427 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1139 2938859 2939039 2939265 "UNIFACT" 2939615 NIL UNIFACT (NIL T) -7 NIL NIL) (-1138 2922755 2938040 2938290 "ULS" 2938666 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1137 2910720 2922660 2922731 "ULSCONS" 2922736 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1136 2893470 2905483 2905544 "ULSCCAT" 2906256 NIL ULSCCAT (NIL T T) -9 NIL 2906552) (-1135 2892521 2892766 2893153 "ULSCCAT-" 2893158 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1134 2882511 2889028 2889070 "ULSCAT" 2889926 NIL ULSCAT (NIL T) -9 NIL 2890656) (-1133 2881945 2882024 2882201 "ULS2" 2882426 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1132 2880343 2881310 2881340 "UFD" 2881552 T UFD (NIL) -9 NIL 2881666) (-1131 2880137 2880183 2880278 "UFD-" 2880283 NIL UFD- (NIL T) -8 NIL NIL) (-1130 2879219 2879402 2879618 "UDVO" 2879943 T UDVO (NIL) -7 NIL NIL) (-1129 2877035 2877444 2877915 "UDPO" 2878783 NIL UDPO (NIL T) -7 NIL NIL) (-1128 2876968 2876973 2877003 "TYPE" 2877008 T TYPE (NIL) -9 NIL NIL) (-1127 2875939 2876141 2876381 "TWOFACT" 2876762 NIL TWOFACT (NIL T) -7 NIL NIL) (-1126 2874877 2875214 2875477 "TUPLE" 2875711 NIL TUPLE (NIL T) -8 NIL NIL) (-1125 2872568 2873087 2873626 "TUBETOOL" 2874360 T TUBETOOL (NIL) -7 NIL NIL) (-1124 2871417 2871622 2871863 "TUBE" 2872361 NIL TUBE (NIL T) -8 NIL NIL) (-1123 2866141 2870395 2870677 "TS" 2871169 NIL TS (NIL T) -8 NIL NIL) (-1122 2854845 2858937 2859033 "TSETCAT" 2864267 NIL TSETCAT (NIL T T T T) -9 NIL 2865798) (-1121 2849580 2851178 2853068 "TSETCAT-" 2853073 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1120 2843843 2844689 2845631 "TRMANIP" 2848716 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1119 2843284 2843347 2843510 "TRIMAT" 2843775 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1118 2841090 2841327 2841690 "TRIGMNIP" 2843033 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1117 2840610 2840723 2840753 "TRIGCAT" 2840966 T TRIGCAT (NIL) -9 NIL NIL) (-1116 2840279 2840358 2840499 "TRIGCAT-" 2840504 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1115 2837178 2839139 2839419 "TREE" 2840034 NIL TREE (NIL T) -8 NIL NIL) (-1114 2836452 2836980 2837010 "TRANFUN" 2837045 T TRANFUN (NIL) -9 NIL 2837111) (-1113 2835731 2835922 2836202 "TRANFUN-" 2836207 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1112 2835535 2835567 2835628 "TOPSP" 2835692 T TOPSP (NIL) -7 NIL NIL) (-1111 2834887 2835002 2835155 "TOOLSIGN" 2835416 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1110 2833548 2834064 2834303 "TEXTFILE" 2834670 T TEXTFILE (NIL) -8 NIL NIL) (-1109 2831413 2831927 2832365 "TEX" 2833132 T TEX (NIL) -8 NIL NIL) (-1108 2831194 2831225 2831297 "TEX1" 2831376 NIL TEX1 (NIL T) -7 NIL NIL) (-1107 2830842 2830905 2830995 "TEMUTL" 2831126 T TEMUTL (NIL) -7 NIL NIL) (-1106 2828996 2829276 2829601 "TBCMPPK" 2830565 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1105 2820885 2827157 2827213 "TBAGG" 2827613 NIL TBAGG (NIL T T) -9 NIL 2827824) (-1104 2815955 2817443 2819197 "TBAGG-" 2819202 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1103 2815339 2815446 2815591 "TANEXP" 2815844 NIL TANEXP (NIL T) -7 NIL NIL) (-1102 2808840 2815196 2815289 "TABLE" 2815294 NIL TABLE (NIL T T) -8 NIL NIL) (-1101 2808252 2808351 2808489 "TABLEAU" 2808737 NIL TABLEAU (NIL T) -8 NIL NIL) (-1100 2802860 2804080 2805328 "TABLBUMP" 2807038 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1099 2802288 2802388 2802516 "SYSTEM" 2802754 T SYSTEM (NIL) -7 NIL NIL) (-1098 2798751 2799446 2800229 "SYSSOLP" 2801539 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1097 2795042 2795750 2796484 "SYNTAX" 2798039 T SYNTAX (NIL) -8 NIL NIL) (-1096 2792176 2792784 2793422 "SYMTAB" 2794426 T SYMTAB (NIL) -8 NIL NIL) (-1095 2787425 2788327 2789310 "SYMS" 2791215 T SYMS (NIL) -8 NIL NIL) (-1094 2784658 2786885 2787114 "SYMPOLY" 2787230 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1093 2784178 2784253 2784375 "SYMFUNC" 2784570 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1092 2780155 2781415 2782237 "SYMBOL" 2783378 T SYMBOL (NIL) -8 NIL NIL) (-1091 2773694 2775383 2777103 "SWITCH" 2778457 T SWITCH (NIL) -8 NIL NIL) (-1090 2766924 2772521 2772823 "SUTS" 2773449 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1089 2758814 2766045 2766325 "SUPXS" 2766701 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1088 2750306 2758435 2758560 "SUP" 2758723 NIL SUP (NIL T) -8 NIL NIL) (-1087 2749465 2749592 2749809 "SUPFRACF" 2750174 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1086 2749090 2749149 2749260 "SUP2" 2749400 NIL SUP2 (NIL T T) -7 NIL NIL) (-1085 2747508 2747782 2748144 "SUMRF" 2748789 NIL SUMRF (NIL T) -7 NIL NIL) (-1084 2746825 2746891 2747089 "SUMFS" 2747429 NIL SUMFS (NIL T T) -7 NIL NIL) (-1083 2730761 2746006 2746256 "SULS" 2746632 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1082 2730083 2730286 2730426 "SUCH" 2730669 NIL SUCH (NIL T T) -8 NIL NIL) (-1081 2724010 2725022 2725980 "SUBSPACE" 2729171 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1080 2723440 2723530 2723694 "SUBRESP" 2723898 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1079 2716809 2718105 2719416 "STTF" 2722176 NIL STTF (NIL T) -7 NIL NIL) (-1078 2710982 2712102 2713249 "STTFNC" 2715709 NIL STTFNC (NIL T) -7 NIL NIL) (-1077 2702333 2704200 2705993 "STTAYLOR" 2709223 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1076 2695577 2702197 2702280 "STRTBL" 2702285 NIL STRTBL (NIL T) -8 NIL NIL) (-1075 2690968 2695532 2695563 "STRING" 2695568 T STRING (NIL) -8 NIL NIL) (-1074 2685857 2690342 2690372 "STRICAT" 2690431 T STRICAT (NIL) -9 NIL 2690493) (-1073 2678571 2683380 2684000 "STREAM" 2685272 NIL STREAM (NIL T) -8 NIL NIL) (-1072 2678081 2678158 2678302 "STREAM3" 2678488 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1071 2677063 2677246 2677481 "STREAM2" 2677894 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1070 2676751 2676803 2676896 "STREAM1" 2677005 NIL STREAM1 (NIL T) -7 NIL NIL) (-1069 2675767 2675948 2676179 "STINPROD" 2676567 NIL STINPROD (NIL T) -7 NIL NIL) (-1068 2675346 2675530 2675560 "STEP" 2675640 T STEP (NIL) -9 NIL 2675718) (-1067 2668889 2675245 2675322 "STBL" 2675327 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1066 2664065 2668112 2668155 "STAGG" 2668308 NIL STAGG (NIL T) -9 NIL 2668397) (-1065 2661767 2662369 2663241 "STAGG-" 2663246 NIL STAGG- (NIL T T) -8 NIL NIL) (-1064 2659962 2661537 2661629 "STACK" 2661710 NIL STACK (NIL T) -8 NIL NIL) (-1063 2652693 2658109 2658564 "SREGSET" 2659592 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1062 2645133 2646501 2648013 "SRDCMPK" 2651299 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1061 2638101 2642574 2642604 "SRAGG" 2643907 T SRAGG (NIL) -9 NIL 2644515) (-1060 2637118 2637373 2637752 "SRAGG-" 2637757 NIL SRAGG- (NIL T) -8 NIL NIL) (-1059 2631567 2636037 2636464 "SQMATRIX" 2636737 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1058 2625319 2628287 2629013 "SPLTREE" 2630913 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1057 2621309 2621975 2622621 "SPLNODE" 2624745 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1056 2620356 2620589 2620619 "SPFCAT" 2621063 T SPFCAT (NIL) -9 NIL NIL) (-1055 2619093 2619303 2619567 "SPECOUT" 2620114 T SPECOUT (NIL) -7 NIL NIL) (-1054 2618854 2618894 2618963 "SPADPRSR" 2619046 T SPADPRSR (NIL) -7 NIL NIL) (-1053 2610877 2612624 2612666 "SPACEC" 2616989 NIL SPACEC (NIL T) -9 NIL 2618805) (-1052 2609048 2610810 2610858 "SPACE3" 2610863 NIL SPACE3 (NIL T) -8 NIL NIL) (-1051 2607800 2607971 2608262 "SORTPAK" 2608853 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1050 2605856 2606159 2606577 "SOLVETRA" 2607464 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1049 2604867 2605089 2605363 "SOLVESER" 2605629 NIL SOLVESER (NIL T) -7 NIL NIL) (-1048 2600087 2600968 2601970 "SOLVERAD" 2603919 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1047 2595902 2596511 2597240 "SOLVEFOR" 2599454 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1046 2590202 2595254 2595350 "SNTSCAT" 2595355 NIL SNTSCAT (NIL T T T T) -9 NIL 2595425) (-1045 2584306 2588533 2588923 "SMTS" 2589892 NIL SMTS (NIL T T T) -8 NIL NIL) (-1044 2578716 2584195 2584271 "SMP" 2584276 NIL SMP (NIL T T) -8 NIL NIL) (-1043 2576875 2577176 2577574 "SMITH" 2578413 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1042 2569840 2574036 2574138 "SMATCAT" 2575478 NIL SMATCAT (NIL NIL T T T) -9 NIL 2576027) (-1041 2566781 2567604 2568781 "SMATCAT-" 2568786 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1040 2564495 2566018 2566061 "SKAGG" 2566322 NIL SKAGG (NIL T) -9 NIL 2566457) (-1039 2560553 2563599 2563877 "SINT" 2564239 T SINT (NIL) -8 NIL NIL) (-1038 2560325 2560363 2560429 "SIMPAN" 2560509 T SIMPAN (NIL) -7 NIL NIL) (-1037 2559841 2560027 2560126 "SIG" 2560248 T SIG (NIL) -8 NIL NIL) (-1036 2558679 2558900 2559175 "SIGNRF" 2559600 NIL SIGNRF (NIL T) -7 NIL NIL) (-1035 2557488 2557639 2557929 "SIGNEF" 2558508 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1034 2555178 2555632 2556138 "SHP" 2557029 NIL SHP (NIL T NIL) -7 NIL NIL) (-1033 2549031 2555079 2555155 "SHDP" 2555160 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1032 2548521 2548713 2548743 "SGROUP" 2548895 T SGROUP (NIL) -9 NIL 2548982) (-1031 2548291 2548343 2548447 "SGROUP-" 2548452 NIL SGROUP- (NIL T) -8 NIL NIL) (-1030 2545127 2545824 2546547 "SGCF" 2547590 T SGCF (NIL) -7 NIL NIL) (-1029 2539526 2544578 2544674 "SFRTCAT" 2544679 NIL SFRTCAT (NIL T T T T) -9 NIL 2544717) (-1028 2532986 2534001 2535135 "SFRGCD" 2538509 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1027 2526152 2527223 2528407 "SFQCMPK" 2531919 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1026 2525774 2525863 2525973 "SFORT" 2526093 NIL SFORT (NIL T T) -8 NIL NIL) (-1025 2524919 2525614 2525735 "SEXOF" 2525740 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1024 2524053 2524800 2524868 "SEX" 2524873 T SEX (NIL) -8 NIL NIL) (-1023 2518830 2519519 2519614 "SEXCAT" 2523385 NIL SEXCAT (NIL T T T T T) -9 NIL 2524004) (-1022 2516010 2518764 2518812 "SET" 2518817 NIL SET (NIL T) -8 NIL NIL) (-1021 2514261 2514723 2515028 "SETMN" 2515751 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1020 2513869 2513995 2514025 "SETCAT" 2514142 T SETCAT (NIL) -9 NIL 2514226) (-1019 2513649 2513701 2513800 "SETCAT-" 2513805 NIL SETCAT- (NIL T) -8 NIL NIL) (-1018 2510037 2512111 2512154 "SETAGG" 2513024 NIL SETAGG (NIL T) -9 NIL 2513364) (-1017 2509495 2509611 2509848 "SETAGG-" 2509853 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1016 2508699 2508992 2509053 "SEGXCAT" 2509339 NIL SEGXCAT (NIL T T) -9 NIL 2509459) (-1015 2507755 2508365 2508547 "SEG" 2508552 NIL SEG (NIL T) -8 NIL NIL) (-1014 2506662 2506875 2506918 "SEGCAT" 2507500 NIL SEGCAT (NIL T) -9 NIL 2507738) (-1013 2505711 2506041 2506241 "SEGBIND" 2506497 NIL SEGBIND (NIL T) -8 NIL NIL) (-1012 2505332 2505391 2505504 "SEGBIND2" 2505646 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1011 2504551 2504677 2504881 "SEG2" 2505176 NIL SEG2 (NIL T T) -7 NIL NIL) (-1010 2503988 2504486 2504533 "SDVAR" 2504538 NIL SDVAR (NIL T) -8 NIL NIL) (-1009 2496240 2503761 2503889 "SDPOL" 2503894 NIL SDPOL (NIL T) -8 NIL NIL) (-1008 2494833 2495099 2495418 "SCPKG" 2495955 NIL SCPKG (NIL T) -7 NIL NIL) (-1007 2493969 2494149 2494349 "SCOPE" 2494655 T SCOPE (NIL) -8 NIL NIL) (-1006 2493190 2493323 2493502 "SCACHE" 2493824 NIL SCACHE (NIL T) -7 NIL NIL) (-1005 2492629 2492950 2493035 "SAOS" 2493127 T SAOS (NIL) -8 NIL NIL) (-1004 2492194 2492229 2492402 "SAERFFC" 2492588 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1003 2486088 2492091 2492171 "SAE" 2492176 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1002 2485681 2485716 2485875 "SAEFACT" 2486047 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1001 2484002 2484316 2484717 "RURPK" 2485347 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1000 2482650 2482927 2483236 "RULESET" 2483838 NIL RULESET (NIL T T T) -8 NIL NIL) (-999 2479858 2480361 2480822 "RULE" 2482332 NIL RULE (NIL T T T) -8 NIL NIL) (-998 2479500 2479655 2479736 "RULECOLD" 2479810 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-997 2474392 2475186 2476102 "RSETGCD" 2478699 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-996 2463707 2468759 2468853 "RSETCAT" 2472918 NIL RSETCAT (NIL T T T T) -9 NIL 2474015) (-995 2461638 2462177 2462997 "RSETCAT-" 2463002 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-994 2454068 2455443 2456959 "RSDCMPK" 2460237 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-993 2452086 2452527 2452599 "RRCC" 2453675 NIL RRCC (NIL T T) -9 NIL 2454019) (-992 2451440 2451614 2451890 "RRCC-" 2451895 NIL RRCC- (NIL T T T) -8 NIL NIL) (-991 2425807 2435432 2435496 "RPOLCAT" 2445998 NIL RPOLCAT (NIL T T T) -9 NIL 2449156) (-990 2417311 2419649 2422767 "RPOLCAT-" 2422772 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-989 2408377 2415541 2416021 "ROUTINE" 2416851 T ROUTINE (NIL) -8 NIL NIL) (-988 2405082 2407933 2408080 "ROMAN" 2408250 T ROMAN (NIL) -8 NIL NIL) (-987 2403368 2403953 2404210 "ROIRC" 2404888 NIL ROIRC (NIL T T) -8 NIL NIL) (-986 2399773 2402077 2402105 "RNS" 2402401 T RNS (NIL) -9 NIL 2402671) (-985 2398287 2398670 2399201 "RNS-" 2399274 NIL RNS- (NIL T) -8 NIL NIL) (-984 2397713 2398121 2398149 "RNG" 2398154 T RNG (NIL) -9 NIL 2398175) (-983 2397111 2397473 2397513 "RMODULE" 2397573 NIL RMODULE (NIL T) -9 NIL 2397615) (-982 2395963 2396057 2396387 "RMCAT2" 2397012 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-981 2392677 2395146 2395467 "RMATRIX" 2395698 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-980 2385674 2387908 2388020 "RMATCAT" 2391329 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2392311) (-979 2385053 2385200 2385503 "RMATCAT-" 2385508 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-978 2384623 2384698 2384824 "RINTERP" 2384972 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-977 2383674 2384238 2384266 "RING" 2384376 T RING (NIL) -9 NIL 2384470) (-976 2383469 2383513 2383607 "RING-" 2383612 NIL RING- (NIL T) -8 NIL NIL) (-975 2382317 2382554 2382810 "RIDIST" 2383233 T RIDIST (NIL) -7 NIL NIL) (-974 2373639 2381791 2381994 "RGCHAIN" 2382166 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-973 2370644 2371258 2371926 "RF" 2373003 NIL RF (NIL T) -7 NIL NIL) (-972 2370293 2370356 2370457 "RFFACTOR" 2370575 NIL RFFACTOR (NIL T) -7 NIL NIL) (-971 2370021 2370056 2370151 "RFFACT" 2370252 NIL RFFACT (NIL T) -7 NIL NIL) (-970 2368151 2368515 2368895 "RFDIST" 2369661 T RFDIST (NIL) -7 NIL NIL) (-969 2367609 2367701 2367861 "RETSOL" 2368053 NIL RETSOL (NIL T T) -7 NIL NIL) (-968 2367202 2367282 2367323 "RETRACT" 2367513 NIL RETRACT (NIL T) -9 NIL NIL) (-967 2367054 2367079 2367163 "RETRACT-" 2367168 NIL RETRACT- (NIL T T) -8 NIL NIL) (-966 2359912 2366711 2366836 "RESULT" 2366949 T RESULT (NIL) -8 NIL NIL) (-965 2358497 2359186 2359383 "RESRING" 2359815 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-964 2358137 2358186 2358282 "RESLATC" 2358434 NIL RESLATC (NIL T) -7 NIL NIL) (-963 2357846 2357880 2357985 "REPSQ" 2358096 NIL REPSQ (NIL T) -7 NIL NIL) (-962 2355277 2355857 2356457 "REP" 2357266 T REP (NIL) -7 NIL NIL) (-961 2354978 2355012 2355121 "REPDB" 2355236 NIL REPDB (NIL T) -7 NIL NIL) (-960 2348923 2350302 2351522 "REP2" 2353790 NIL REP2 (NIL T) -7 NIL NIL) (-959 2345329 2346010 2346815 "REP1" 2348150 NIL REP1 (NIL T) -7 NIL NIL) (-958 2338075 2343490 2343942 "REGSET" 2344960 NIL REGSET (NIL T T T T) -8 NIL NIL) (-957 2336896 2337231 2337479 "REF" 2337860 NIL REF (NIL T) -8 NIL NIL) (-956 2336277 2336380 2336545 "REDORDER" 2336780 NIL REDORDER (NIL T T) -7 NIL NIL) (-955 2332246 2335511 2335732 "RECLOS" 2336108 NIL RECLOS (NIL T) -8 NIL NIL) (-954 2331303 2331484 2331697 "REALSOLV" 2332053 T REALSOLV (NIL) -7 NIL NIL) (-953 2331151 2331192 2331220 "REAL" 2331225 T REAL (NIL) -9 NIL 2331260) (-952 2327642 2328444 2329326 "REAL0Q" 2330316 NIL REAL0Q (NIL T) -7 NIL NIL) (-951 2323253 2324241 2325300 "REAL0" 2326623 NIL REAL0 (NIL T) -7 NIL NIL) (-950 2322661 2322733 2322938 "RDIV" 2323175 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-949 2321734 2321908 2322119 "RDIST" 2322483 NIL RDIST (NIL T) -7 NIL NIL) (-948 2320338 2320625 2320994 "RDETRS" 2321442 NIL RDETRS (NIL T T) -7 NIL NIL) (-947 2318159 2318613 2319148 "RDETR" 2319880 NIL RDETR (NIL T T) -7 NIL NIL) (-946 2316775 2317053 2317454 "RDEEFS" 2317875 NIL RDEEFS (NIL T T) -7 NIL NIL) (-945 2315275 2315581 2316010 "RDEEF" 2316463 NIL RDEEF (NIL T T) -7 NIL NIL) (-944 2309560 2312492 2312520 "RCFIELD" 2313797 T RCFIELD (NIL) -9 NIL 2314527) (-943 2307629 2308133 2308826 "RCFIELD-" 2308899 NIL RCFIELD- (NIL T) -8 NIL NIL) (-942 2303961 2305746 2305787 "RCAGG" 2306858 NIL RCAGG (NIL T) -9 NIL 2307323) (-941 2303592 2303686 2303846 "RCAGG-" 2303851 NIL RCAGG- (NIL T T) -8 NIL NIL) (-940 2302936 2303048 2303210 "RATRET" 2303476 NIL RATRET (NIL T) -7 NIL NIL) (-939 2302493 2302560 2302679 "RATFACT" 2302864 NIL RATFACT (NIL T) -7 NIL NIL) (-938 2301808 2301928 2302078 "RANDSRC" 2302363 T RANDSRC (NIL) -7 NIL NIL) (-937 2301545 2301589 2301660 "RADUTIL" 2301757 T RADUTIL (NIL) -7 NIL NIL) (-936 2294552 2300288 2300605 "RADIX" 2301260 NIL RADIX (NIL NIL) -8 NIL NIL) (-935 2286122 2294396 2294524 "RADFF" 2294529 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-934 2285774 2285849 2285877 "RADCAT" 2286034 T RADCAT (NIL) -9 NIL NIL) (-933 2285559 2285607 2285704 "RADCAT-" 2285709 NIL RADCAT- (NIL T) -8 NIL NIL) (-932 2283710 2285334 2285423 "QUEUE" 2285503 NIL QUEUE (NIL T) -8 NIL NIL) (-931 2280207 2283647 2283692 "QUAT" 2283697 NIL QUAT (NIL T) -8 NIL NIL) (-930 2279845 2279888 2280015 "QUATCT2" 2280158 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-929 2273639 2277019 2277059 "QUATCAT" 2277838 NIL QUATCAT (NIL T) -9 NIL 2278603) (-928 2269783 2270820 2272207 "QUATCAT-" 2272301 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-927 2267304 2268868 2268909 "QUAGG" 2269284 NIL QUAGG (NIL T) -9 NIL 2269459) (-926 2266229 2266702 2266874 "QFORM" 2267176 NIL QFORM (NIL NIL T) -8 NIL NIL) (-925 2257526 2262784 2262824 "QFCAT" 2263482 NIL QFCAT (NIL T) -9 NIL 2264475) (-924 2253098 2254299 2255890 "QFCAT-" 2255984 NIL QFCAT- (NIL T T) -8 NIL NIL) (-923 2252736 2252779 2252906 "QFCAT2" 2253049 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-922 2252196 2252306 2252436 "QEQUAT" 2252626 T QEQUAT (NIL) -8 NIL NIL) (-921 2245382 2246453 2247635 "QCMPACK" 2251129 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-920 2242958 2243379 2243807 "QALGSET" 2245037 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-919 2242203 2242377 2242609 "QALGSET2" 2242778 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-918 2240894 2241117 2241434 "PWFFINTB" 2241976 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-917 2239082 2239250 2239603 "PUSHVAR" 2240708 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-916 2235000 2236054 2236095 "PTRANFN" 2237979 NIL PTRANFN (NIL T) -9 NIL NIL) (-915 2233412 2233703 2234024 "PTPACK" 2234711 NIL PTPACK (NIL T) -7 NIL NIL) (-914 2233048 2233105 2233212 "PTFUNC2" 2233349 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-913 2227525 2231866 2231906 "PTCAT" 2232274 NIL PTCAT (NIL T) -9 NIL 2232436) (-912 2227183 2227218 2227342 "PSQFR" 2227484 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-911 2225778 2226076 2226410 "PSEUDLIN" 2226881 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-910 2212585 2214950 2217273 "PSETPK" 2223538 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-909 2205672 2208386 2208480 "PSETCAT" 2211461 NIL PSETCAT (NIL T T T T) -9 NIL 2212275) (-908 2203510 2204144 2204963 "PSETCAT-" 2204968 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-907 2202859 2203024 2203052 "PSCURVE" 2203320 T PSCURVE (NIL) -9 NIL 2203487) (-906 2199311 2200837 2200901 "PSCAT" 2201737 NIL PSCAT (NIL T T T) -9 NIL 2201977) (-905 2198375 2198591 2198990 "PSCAT-" 2198995 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-904 2197027 2197660 2197874 "PRTITION" 2198181 T PRTITION (NIL) -8 NIL NIL) (-903 2186125 2188331 2190519 "PRS" 2194889 NIL PRS (NIL T T) -7 NIL NIL) (-902 2183984 2185476 2185516 "PRQAGG" 2185699 NIL PRQAGG (NIL T) -9 NIL 2185801) (-901 2183555 2183657 2183685 "PROPLOG" 2183870 T PROPLOG (NIL) -9 NIL NIL) (-900 2180678 2181243 2181770 "PROPFRML" 2183060 NIL PROPFRML (NIL T) -8 NIL NIL) (-899 2180138 2180248 2180378 "PROPERTY" 2180568 T PROPERTY (NIL) -8 NIL NIL) (-898 2173912 2178304 2179124 "PRODUCT" 2179364 NIL PRODUCT (NIL T T) -8 NIL NIL) (-897 2171188 2173372 2173605 "PR" 2173723 NIL PR (NIL T T) -8 NIL NIL) (-896 2170984 2171016 2171075 "PRINT" 2171149 T PRINT (NIL) -7 NIL NIL) (-895 2170324 2170441 2170593 "PRIMES" 2170864 NIL PRIMES (NIL T) -7 NIL NIL) (-894 2168389 2168790 2169256 "PRIMELT" 2169903 NIL PRIMELT (NIL T) -7 NIL NIL) (-893 2168118 2168167 2168195 "PRIMCAT" 2168319 T PRIMCAT (NIL) -9 NIL NIL) (-892 2164279 2168056 2168101 "PRIMARR" 2168106 NIL PRIMARR (NIL T) -8 NIL NIL) (-891 2163286 2163464 2163692 "PRIMARR2" 2164097 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-890 2162929 2162985 2163096 "PREASSOC" 2163224 NIL PREASSOC (NIL T T) -7 NIL NIL) (-889 2162404 2162537 2162565 "PPCURVE" 2162770 T PPCURVE (NIL) -9 NIL 2162906) (-888 2159763 2160162 2160754 "POLYROOT" 2161985 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-887 2153669 2159369 2159528 "POLY" 2159636 NIL POLY (NIL T) -8 NIL NIL) (-886 2153054 2153112 2153345 "POLYLIFT" 2153605 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-885 2149339 2149788 2150416 "POLYCATQ" 2152599 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-884 2136380 2141777 2141841 "POLYCAT" 2145326 NIL POLYCAT (NIL T T T) -9 NIL 2147253) (-883 2129831 2131692 2134075 "POLYCAT-" 2134080 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-882 2129420 2129488 2129607 "POLY2UP" 2129757 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-881 2129056 2129113 2129220 "POLY2" 2129357 NIL POLY2 (NIL T T) -7 NIL NIL) (-880 2127741 2127980 2128256 "POLUTIL" 2128830 NIL POLUTIL (NIL T T) -7 NIL NIL) (-879 2126103 2126380 2126710 "POLTOPOL" 2127463 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-878 2121626 2126040 2126085 "POINT" 2126090 NIL POINT (NIL T) -8 NIL NIL) (-877 2119813 2120170 2120545 "PNTHEORY" 2121271 T PNTHEORY (NIL) -7 NIL NIL) (-876 2118241 2118538 2118947 "PMTOOLS" 2119511 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-875 2117834 2117912 2118029 "PMSYM" 2118157 NIL PMSYM (NIL T) -7 NIL NIL) (-874 2117344 2117413 2117587 "PMQFCAT" 2117759 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-873 2116699 2116809 2116965 "PMPRED" 2117221 NIL PMPRED (NIL T) -7 NIL NIL) (-872 2116095 2116181 2116342 "PMPREDFS" 2116600 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-871 2114741 2114949 2115333 "PMPLCAT" 2115857 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-870 2114273 2114352 2114504 "PMLSAGG" 2114656 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-869 2113750 2113826 2114006 "PMKERNEL" 2114191 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-868 2113367 2113442 2113555 "PMINS" 2113669 NIL PMINS (NIL T) -7 NIL NIL) (-867 2112797 2112866 2113081 "PMFS" 2113292 NIL PMFS (NIL T T T) -7 NIL NIL) (-866 2112028 2112146 2112350 "PMDOWN" 2112674 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-865 2111191 2111350 2111532 "PMASS" 2111866 T PMASS (NIL) -7 NIL NIL) (-864 2110465 2110576 2110739 "PMASSFS" 2111077 NIL PMASSFS (NIL T T) -7 NIL NIL) (-863 2110120 2110188 2110282 "PLOTTOOL" 2110391 T PLOTTOOL (NIL) -7 NIL NIL) (-862 2104742 2105931 2107079 "PLOT" 2108992 T PLOT (NIL) -8 NIL NIL) (-861 2100556 2101590 2102511 "PLOT3D" 2103841 T PLOT3D (NIL) -8 NIL NIL) (-860 2099468 2099645 2099880 "PLOT1" 2100360 NIL PLOT1 (NIL T) -7 NIL NIL) (-859 2074862 2079534 2084385 "PLEQN" 2094734 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-858 2074180 2074302 2074482 "PINTERP" 2074727 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-857 2073873 2073920 2074023 "PINTERPA" 2074127 NIL PINTERPA (NIL T T) -7 NIL NIL) (-856 2073112 2073679 2073766 "PI" 2073806 T PI (NIL) -8 NIL NIL) (-855 2071504 2072489 2072517 "PID" 2072699 T PID (NIL) -9 NIL 2072833) (-854 2071229 2071266 2071354 "PICOERCE" 2071461 NIL PICOERCE (NIL T) -7 NIL NIL) (-853 2070549 2070688 2070864 "PGROEB" 2071085 NIL PGROEB (NIL T) -7 NIL NIL) (-852 2066136 2066950 2067855 "PGE" 2069664 T PGE (NIL) -7 NIL NIL) (-851 2064260 2064506 2064872 "PGCD" 2065853 NIL PGCD (NIL T T T T) -7 NIL NIL) (-850 2063598 2063701 2063862 "PFRPAC" 2064144 NIL PFRPAC (NIL T) -7 NIL NIL) (-849 2060213 2062146 2062499 "PFR" 2063277 NIL PFR (NIL T) -8 NIL NIL) (-848 2058602 2058846 2059171 "PFOTOOLS" 2059960 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-847 2057135 2057374 2057725 "PFOQ" 2058359 NIL PFOQ (NIL T T T) -7 NIL NIL) (-846 2055612 2055824 2056186 "PFO" 2056919 NIL PFO (NIL T T T T T) -7 NIL NIL) (-845 2052135 2055501 2055570 "PF" 2055575 NIL PF (NIL NIL) -8 NIL NIL) (-844 2049564 2050845 2050873 "PFECAT" 2051458 T PFECAT (NIL) -9 NIL 2051842) (-843 2049009 2049163 2049377 "PFECAT-" 2049382 NIL PFECAT- (NIL T) -8 NIL NIL) (-842 2047613 2047864 2048165 "PFBRU" 2048758 NIL PFBRU (NIL T T) -7 NIL NIL) (-841 2045480 2045831 2046263 "PFBR" 2047264 NIL PFBR (NIL T T T T) -7 NIL NIL) (-840 2041331 2042856 2043532 "PERM" 2044837 NIL PERM (NIL T) -8 NIL NIL) (-839 2036596 2037538 2038408 "PERMGRP" 2040494 NIL PERMGRP (NIL T) -8 NIL NIL) (-838 2034667 2035660 2035701 "PERMCAT" 2036147 NIL PERMCAT (NIL T) -9 NIL 2036452) (-837 2034322 2034363 2034486 "PERMAN" 2034620 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-836 2031762 2033891 2034022 "PENDTREE" 2034224 NIL PENDTREE (NIL T) -8 NIL NIL) (-835 2029835 2030613 2030654 "PDRING" 2031311 NIL PDRING (NIL T) -9 NIL 2031596) (-834 2028938 2029156 2029518 "PDRING-" 2029523 NIL PDRING- (NIL T T) -8 NIL NIL) (-833 2026079 2026830 2027521 "PDEPROB" 2028267 T PDEPROB (NIL) -8 NIL NIL) (-832 2023650 2024146 2024695 "PDEPACK" 2025550 T PDEPACK (NIL) -7 NIL NIL) (-831 2022562 2022752 2023003 "PDECOMP" 2023449 NIL PDECOMP (NIL T T) -7 NIL NIL) (-830 2020174 2020989 2021017 "PDECAT" 2021802 T PDECAT (NIL) -9 NIL 2022513) (-829 2019927 2019960 2020049 "PCOMP" 2020135 NIL PCOMP (NIL T T) -7 NIL NIL) (-828 2018134 2018730 2019026 "PBWLB" 2019657 NIL PBWLB (NIL T) -8 NIL NIL) (-827 2010642 2012211 2013547 "PATTERN" 2016819 NIL PATTERN (NIL T) -8 NIL NIL) (-826 2010274 2010331 2010440 "PATTERN2" 2010579 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-825 2008031 2008419 2008876 "PATTERN1" 2009863 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-824 2005426 2005980 2006461 "PATRES" 2007596 NIL PATRES (NIL T T) -8 NIL NIL) (-823 2004990 2005057 2005189 "PATRES2" 2005353 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-822 2002887 2003287 2003692 "PATMATCH" 2004659 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-821 2002424 2002607 2002648 "PATMAB" 2002755 NIL PATMAB (NIL T) -9 NIL 2002838) (-820 2000969 2001278 2001536 "PATLRES" 2002229 NIL PATLRES (NIL T T T) -8 NIL NIL) (-819 2000515 2000638 2000679 "PATAB" 2000684 NIL PATAB (NIL T) -9 NIL 2000856) (-818 1997996 1998528 1999101 "PARTPERM" 1999962 T PARTPERM (NIL) -7 NIL NIL) (-817 1997617 1997680 1997782 "PARSURF" 1997927 NIL PARSURF (NIL T) -8 NIL NIL) (-816 1997249 1997306 1997415 "PARSU2" 1997554 NIL PARSU2 (NIL T T) -7 NIL NIL) (-815 1997013 1997053 1997120 "PARSER" 1997202 T PARSER (NIL) -7 NIL NIL) (-814 1996634 1996697 1996799 "PARSCURV" 1996944 NIL PARSCURV (NIL T) -8 NIL NIL) (-813 1996266 1996323 1996432 "PARSC2" 1996571 NIL PARSC2 (NIL T T) -7 NIL NIL) (-812 1995905 1995963 1996060 "PARPCURV" 1996202 NIL PARPCURV (NIL T) -8 NIL NIL) (-811 1995537 1995594 1995703 "PARPC2" 1995842 NIL PARPC2 (NIL T T) -7 NIL NIL) (-810 1995057 1995143 1995262 "PAN2EXPR" 1995438 T PAN2EXPR (NIL) -7 NIL NIL) (-809 1993863 1994178 1994406 "PALETTE" 1994849 T PALETTE (NIL) -8 NIL NIL) (-808 1992331 1992868 1993228 "PAIR" 1993549 NIL PAIR (NIL T T) -8 NIL NIL) (-807 1986181 1991590 1991784 "PADICRC" 1992186 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-806 1979389 1985527 1985711 "PADICRAT" 1986029 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-805 1977693 1979326 1979371 "PADIC" 1979376 NIL PADIC (NIL NIL) -8 NIL NIL) (-804 1974898 1976472 1976512 "PADICCT" 1977093 NIL PADICCT (NIL NIL) -9 NIL 1977375) (-803 1973855 1974055 1974323 "PADEPAC" 1974685 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-802 1973067 1973200 1973406 "PADE" 1973717 NIL PADE (NIL T T T) -7 NIL NIL) (-801 1971078 1971910 1972225 "OWP" 1972835 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-800 1970187 1970683 1970855 "OVAR" 1970946 NIL OVAR (NIL NIL) -8 NIL NIL) (-799 1969451 1969572 1969733 "OUT" 1970046 T OUT (NIL) -7 NIL NIL) (-798 1958505 1960676 1962846 "OUTFORM" 1967301 T OUTFORM (NIL) -8 NIL NIL) (-797 1957913 1958234 1958323 "OSI" 1958436 T OSI (NIL) -8 NIL NIL) (-796 1957444 1957782 1957810 "OSGROUP" 1957815 T OSGROUP (NIL) -9 NIL 1957837) (-795 1956189 1956416 1956701 "ORTHPOL" 1957191 NIL ORTHPOL (NIL T) -7 NIL NIL) (-794 1953560 1955850 1955988 "OREUP" 1956132 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-793 1950956 1953253 1953379 "ORESUP" 1953502 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-792 1948491 1948991 1949551 "OREPCTO" 1950445 NIL OREPCTO (NIL T T) -7 NIL NIL) (-791 1942401 1944607 1944647 "OREPCAT" 1946968 NIL OREPCAT (NIL T) -9 NIL 1948071) (-790 1939549 1940331 1941388 "OREPCAT-" 1941393 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-789 1938727 1938999 1939027 "ORDSET" 1939336 T ORDSET (NIL) -9 NIL 1939500) (-788 1938246 1938368 1938561 "ORDSET-" 1938566 NIL ORDSET- (NIL T) -8 NIL NIL) (-787 1936860 1937661 1937689 "ORDRING" 1937891 T ORDRING (NIL) -9 NIL 1938015) (-786 1936505 1936599 1936743 "ORDRING-" 1936748 NIL ORDRING- (NIL T) -8 NIL NIL) (-785 1935868 1936349 1936377 "ORDMON" 1936382 T ORDMON (NIL) -9 NIL 1936403) (-784 1935030 1935177 1935372 "ORDFUNS" 1935717 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-783 1934542 1934901 1934929 "ORDFIN" 1934934 T ORDFIN (NIL) -9 NIL 1934955) (-782 1931054 1933128 1933537 "ORDCOMP" 1934166 NIL ORDCOMP (NIL T) -8 NIL NIL) (-781 1930320 1930447 1930633 "ORDCOMP2" 1930914 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-780 1926827 1927710 1928547 "OPTPROB" 1929503 T OPTPROB (NIL) -8 NIL NIL) (-779 1923669 1924298 1924992 "OPTPACK" 1926153 T OPTPACK (NIL) -7 NIL NIL) (-778 1921395 1922131 1922159 "OPTCAT" 1922974 T OPTCAT (NIL) -9 NIL 1923620) (-777 1921163 1921202 1921268 "OPQUERY" 1921349 T OPQUERY (NIL) -7 NIL NIL) (-776 1918299 1919490 1919990 "OP" 1920695 NIL OP (NIL T) -8 NIL NIL) (-775 1915064 1917096 1917465 "ONECOMP" 1917963 NIL ONECOMP (NIL T) -8 NIL NIL) (-774 1914369 1914484 1914658 "ONECOMP2" 1914936 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-773 1913788 1913894 1914024 "OMSERVER" 1914259 T OMSERVER (NIL) -7 NIL NIL) (-772 1910677 1913229 1913269 "OMSAGG" 1913330 NIL OMSAGG (NIL T) -9 NIL 1913394) (-771 1909300 1909563 1909845 "OMPKG" 1910415 T OMPKG (NIL) -7 NIL NIL) (-770 1908730 1908833 1908861 "OM" 1909160 T OM (NIL) -9 NIL NIL) (-769 1907269 1908282 1908450 "OMLO" 1908611 NIL OMLO (NIL T T) -8 NIL NIL) (-768 1906199 1906346 1906572 "OMEXPR" 1907095 NIL OMEXPR (NIL T) -7 NIL NIL) (-767 1905517 1905745 1905881 "OMERR" 1906083 T OMERR (NIL) -8 NIL NIL) (-766 1904695 1904938 1905098 "OMERRK" 1905377 T OMERRK (NIL) -8 NIL NIL) (-765 1904173 1904372 1904480 "OMENC" 1904607 T OMENC (NIL) -8 NIL NIL) (-764 1898068 1899253 1900424 "OMDEV" 1903022 T OMDEV (NIL) -8 NIL NIL) (-763 1897137 1897308 1897502 "OMCONN" 1897894 T OMCONN (NIL) -8 NIL NIL) (-762 1895753 1896739 1896767 "OINTDOM" 1896772 T OINTDOM (NIL) -9 NIL 1896793) (-761 1891515 1892745 1893460 "OFMONOID" 1895070 NIL OFMONOID (NIL T) -8 NIL NIL) (-760 1890953 1891452 1891497 "ODVAR" 1891502 NIL ODVAR (NIL T) -8 NIL NIL) (-759 1888078 1890450 1890635 "ODR" 1890828 NIL ODR (NIL T T NIL) -8 NIL NIL) (-758 1880384 1887857 1887981 "ODPOL" 1887986 NIL ODPOL (NIL T) -8 NIL NIL) (-757 1874207 1880256 1880361 "ODP" 1880366 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-756 1872973 1873188 1873463 "ODETOOLS" 1873981 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-755 1869942 1870598 1871314 "ODESYS" 1872306 NIL ODESYS (NIL T T) -7 NIL NIL) (-754 1864846 1865754 1866777 "ODERTRIC" 1869017 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-753 1864272 1864354 1864548 "ODERED" 1864758 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-752 1861174 1861722 1862397 "ODERAT" 1863695 NIL ODERAT (NIL T T) -7 NIL NIL) (-751 1858142 1858606 1859202 "ODEPRRIC" 1860703 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-750 1856011 1856580 1857089 "ODEPROB" 1857653 T ODEPROB (NIL) -8 NIL NIL) (-749 1852543 1853026 1853672 "ODEPRIM" 1855490 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-748 1851796 1851898 1852156 "ODEPAL" 1852435 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-747 1847998 1848779 1849633 "ODEPACK" 1850962 T ODEPACK (NIL) -7 NIL NIL) (-746 1847035 1847142 1847370 "ODEINT" 1847887 NIL ODEINT (NIL T T) -7 NIL NIL) (-745 1841136 1842561 1844008 "ODEIFTBL" 1845608 T ODEIFTBL (NIL) -8 NIL NIL) (-744 1836480 1837266 1838224 "ODEEF" 1840295 NIL ODEEF (NIL T T) -7 NIL NIL) (-743 1835817 1835906 1836135 "ODECONST" 1836385 NIL ODECONST (NIL T T T) -7 NIL NIL) (-742 1833975 1834608 1834636 "ODECAT" 1835239 T ODECAT (NIL) -9 NIL 1835768) (-741 1830847 1833687 1833806 "OCT" 1833888 NIL OCT (NIL T) -8 NIL NIL) (-740 1830485 1830528 1830655 "OCTCT2" 1830798 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-739 1825319 1827757 1827797 "OC" 1828893 NIL OC (NIL T) -9 NIL 1829750) (-738 1822546 1823294 1824284 "OC-" 1824378 NIL OC- (NIL T T) -8 NIL NIL) (-737 1821925 1822367 1822395 "OCAMON" 1822400 T OCAMON (NIL) -9 NIL 1822421) (-736 1821483 1821798 1821826 "OASGP" 1821831 T OASGP (NIL) -9 NIL 1821851) (-735 1820771 1821234 1821262 "OAMONS" 1821302 T OAMONS (NIL) -9 NIL 1821345) (-734 1820212 1820619 1820647 "OAMON" 1820652 T OAMON (NIL) -9 NIL 1820672) (-733 1819517 1820009 1820037 "OAGROUP" 1820042 T OAGROUP (NIL) -9 NIL 1820062) (-732 1819207 1819257 1819345 "NUMTUBE" 1819461 NIL NUMTUBE (NIL T) -7 NIL NIL) (-731 1812780 1814298 1815834 "NUMQUAD" 1817691 T NUMQUAD (NIL) -7 NIL NIL) (-730 1808536 1809524 1810549 "NUMODE" 1811775 T NUMODE (NIL) -7 NIL NIL) (-729 1805940 1806786 1806814 "NUMINT" 1807731 T NUMINT (NIL) -9 NIL 1808487) (-728 1804888 1805085 1805303 "NUMFMT" 1805742 T NUMFMT (NIL) -7 NIL NIL) (-727 1791267 1794204 1796734 "NUMERIC" 1802397 NIL NUMERIC (NIL T) -7 NIL NIL) (-726 1785668 1790720 1790814 "NTSCAT" 1790819 NIL NTSCAT (NIL T T T T) -9 NIL 1790857) (-725 1784862 1785027 1785220 "NTPOLFN" 1785507 NIL NTPOLFN (NIL T) -7 NIL NIL) (-724 1772678 1781704 1782514 "NSUP" 1784084 NIL NSUP (NIL T) -8 NIL NIL) (-723 1772314 1772371 1772478 "NSUP2" 1772615 NIL NSUP2 (NIL T T) -7 NIL NIL) (-722 1762276 1772093 1772223 "NSMP" 1772228 NIL NSMP (NIL T T) -8 NIL NIL) (-721 1760708 1761009 1761366 "NREP" 1761964 NIL NREP (NIL T) -7 NIL NIL) (-720 1759299 1759551 1759909 "NPCOEF" 1760451 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-719 1758365 1758480 1758696 "NORMRETR" 1759180 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-718 1756418 1756708 1757115 "NORMPK" 1758073 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-717 1756103 1756131 1756255 "NORMMA" 1756384 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-716 1755930 1756060 1756089 "NONE" 1756094 T NONE (NIL) -8 NIL NIL) (-715 1755719 1755748 1755817 "NONE1" 1755894 NIL NONE1 (NIL T) -7 NIL NIL) (-714 1755204 1755266 1755451 "NODE1" 1755651 NIL NODE1 (NIL T T) -7 NIL NIL) (-713 1753498 1754367 1754622 "NNI" 1754969 T NNI (NIL) -8 NIL NIL) (-712 1751918 1752231 1752595 "NLINSOL" 1753166 NIL NLINSOL (NIL T) -7 NIL NIL) (-711 1748085 1749053 1749975 "NIPROB" 1751016 T NIPROB (NIL) -8 NIL NIL) (-710 1746842 1747076 1747378 "NFINTBAS" 1747847 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-709 1745550 1745781 1746062 "NCODIV" 1746610 NIL NCODIV (NIL T T) -7 NIL NIL) (-708 1745312 1745349 1745424 "NCNTFRAC" 1745507 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-707 1743492 1743856 1744276 "NCEP" 1744937 NIL NCEP (NIL T) -7 NIL NIL) (-706 1742404 1743143 1743171 "NASRING" 1743281 T NASRING (NIL) -9 NIL 1743355) (-705 1742199 1742243 1742337 "NASRING-" 1742342 NIL NASRING- (NIL T) -8 NIL NIL) (-704 1741353 1741852 1741880 "NARNG" 1741997 T NARNG (NIL) -9 NIL 1742088) (-703 1741045 1741112 1741246 "NARNG-" 1741251 NIL NARNG- (NIL T) -8 NIL NIL) (-702 1739924 1740131 1740366 "NAGSP" 1740830 T NAGSP (NIL) -7 NIL NIL) (-701 1731348 1732994 1734629 "NAGS" 1738309 T NAGS (NIL) -7 NIL NIL) (-700 1729912 1730216 1730543 "NAGF07" 1731041 T NAGF07 (NIL) -7 NIL NIL) (-699 1724494 1725774 1727070 "NAGF04" 1728636 T NAGF04 (NIL) -7 NIL NIL) (-698 1717526 1719124 1720741 "NAGF02" 1722897 T NAGF02 (NIL) -7 NIL NIL) (-697 1712790 1713880 1714987 "NAGF01" 1716439 T NAGF01 (NIL) -7 NIL NIL) (-696 1706450 1708008 1709585 "NAGE04" 1711233 T NAGE04 (NIL) -7 NIL NIL) (-695 1697691 1699794 1701906 "NAGE02" 1704358 T NAGE02 (NIL) -7 NIL NIL) (-694 1693684 1694621 1695575 "NAGE01" 1696757 T NAGE01 (NIL) -7 NIL NIL) (-693 1691491 1692022 1692577 "NAGD03" 1693149 T NAGD03 (NIL) -7 NIL NIL) (-692 1683277 1685196 1687141 "NAGD02" 1689566 T NAGD02 (NIL) -7 NIL NIL) (-691 1677136 1678549 1679977 "NAGD01" 1681869 T NAGD01 (NIL) -7 NIL NIL) (-690 1673393 1674203 1675028 "NAGC06" 1676331 T NAGC06 (NIL) -7 NIL NIL) (-689 1671870 1672199 1672552 "NAGC05" 1673060 T NAGC05 (NIL) -7 NIL NIL) (-688 1671254 1671371 1671513 "NAGC02" 1671748 T NAGC02 (NIL) -7 NIL NIL) (-687 1670316 1670873 1670913 "NAALG" 1670992 NIL NAALG (NIL T) -9 NIL 1671053) (-686 1670151 1670180 1670270 "NAALG-" 1670275 NIL NAALG- (NIL T T) -8 NIL NIL) (-685 1664101 1665209 1666396 "MULTSQFR" 1669047 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-684 1663420 1663495 1663679 "MULTFACT" 1664013 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-683 1656614 1660525 1660577 "MTSCAT" 1661637 NIL MTSCAT (NIL T T) -9 NIL 1662151) (-682 1656326 1656380 1656472 "MTHING" 1656554 NIL MTHING (NIL T) -7 NIL NIL) (-681 1656118 1656151 1656211 "MSYSCMD" 1656286 T MSYSCMD (NIL) -7 NIL NIL) (-680 1652230 1654873 1655193 "MSET" 1655831 NIL MSET (NIL T) -8 NIL NIL) (-679 1649326 1651792 1651833 "MSETAGG" 1651838 NIL MSETAGG (NIL T) -9 NIL 1651872) (-678 1645182 1646724 1647465 "MRING" 1648629 NIL MRING (NIL T T) -8 NIL NIL) (-677 1644752 1644819 1644948 "MRF2" 1645109 NIL MRF2 (NIL T T T) -7 NIL NIL) (-676 1644370 1644405 1644549 "MRATFAC" 1644711 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-675 1641982 1642277 1642708 "MPRFF" 1644075 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-674 1636002 1641837 1641933 "MPOLY" 1641938 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-673 1635492 1635527 1635735 "MPCPF" 1635961 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-672 1635008 1635051 1635234 "MPC3" 1635443 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-671 1634209 1634290 1634509 "MPC2" 1634923 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-670 1632510 1632847 1633237 "MONOTOOL" 1633869 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-669 1631635 1631970 1631998 "MONOID" 1632275 T MONOID (NIL) -9 NIL 1632447) (-668 1631013 1631176 1631419 "MONOID-" 1631424 NIL MONOID- (NIL T) -8 NIL NIL) (-667 1621994 1627980 1628039 "MONOGEN" 1628713 NIL MONOGEN (NIL T T) -9 NIL 1629169) (-666 1619212 1619947 1620947 "MONOGEN-" 1621066 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-665 1618072 1618492 1618520 "MONADWU" 1618912 T MONADWU (NIL) -9 NIL 1619150) (-664 1617444 1617603 1617851 "MONADWU-" 1617856 NIL MONADWU- (NIL T) -8 NIL NIL) (-663 1616830 1617048 1617076 "MONAD" 1617283 T MONAD (NIL) -9 NIL 1617395) (-662 1616515 1616593 1616725 "MONAD-" 1616730 NIL MONAD- (NIL T) -8 NIL NIL) (-661 1614766 1615428 1615707 "MOEBIUS" 1616268 NIL MOEBIUS (NIL T) -8 NIL NIL) (-660 1614160 1614538 1614578 "MODULE" 1614583 NIL MODULE (NIL T) -9 NIL 1614609) (-659 1613728 1613824 1614014 "MODULE-" 1614019 NIL MODULE- (NIL T T) -8 NIL NIL) (-658 1611399 1612094 1612420 "MODRING" 1613553 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-657 1608355 1609520 1610037 "MODOP" 1610931 NIL MODOP (NIL T T) -8 NIL NIL) (-656 1606542 1606994 1607335 "MODMONOM" 1608154 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-655 1596221 1604746 1605168 "MODMON" 1606170 NIL MODMON (NIL T T) -8 NIL NIL) (-654 1593347 1595065 1595341 "MODFIELD" 1596096 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-653 1592351 1592628 1592818 "MMLFORM" 1593177 T MMLFORM (NIL) -8 NIL NIL) (-652 1591877 1591920 1592099 "MMAP" 1592302 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-651 1590114 1590891 1590931 "MLO" 1591348 NIL MLO (NIL T) -9 NIL 1591589) (-650 1587481 1587996 1588598 "MLIFT" 1589595 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-649 1586872 1586956 1587110 "MKUCFUNC" 1587392 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-648 1586471 1586541 1586664 "MKRECORD" 1586795 NIL MKRECORD (NIL T T) -7 NIL NIL) (-647 1585519 1585680 1585908 "MKFUNC" 1586282 NIL MKFUNC (NIL T) -7 NIL NIL) (-646 1584907 1585011 1585167 "MKFLCFN" 1585402 NIL MKFLCFN (NIL T) -7 NIL NIL) (-645 1584333 1584700 1584789 "MKCHSET" 1584851 NIL MKCHSET (NIL T) -8 NIL NIL) (-644 1583610 1583712 1583897 "MKBCFUNC" 1584226 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-643 1580294 1583164 1583300 "MINT" 1583494 T MINT (NIL) -8 NIL NIL) (-642 1579106 1579349 1579626 "MHROWRED" 1580049 NIL MHROWRED (NIL T) -7 NIL NIL) (-641 1574377 1577551 1577975 "MFLOAT" 1578702 T MFLOAT (NIL) -8 NIL NIL) (-640 1573734 1573810 1573981 "MFINFACT" 1574289 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-639 1570049 1570897 1571781 "MESH" 1572870 T MESH (NIL) -7 NIL NIL) (-638 1568439 1568751 1569104 "MDDFACT" 1569736 NIL MDDFACT (NIL T) -7 NIL NIL) (-637 1565282 1567599 1567640 "MDAGG" 1567895 NIL MDAGG (NIL T) -9 NIL 1568038) (-636 1554980 1564575 1564782 "MCMPLX" 1565095 T MCMPLX (NIL) -8 NIL NIL) (-635 1554121 1554267 1554467 "MCDEN" 1554829 NIL MCDEN (NIL T T) -7 NIL NIL) (-634 1552011 1552281 1552661 "MCALCFN" 1553851 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-633 1549633 1550156 1550717 "MATSTOR" 1551482 NIL MATSTOR (NIL T) -7 NIL NIL) (-632 1545642 1549008 1549255 "MATRIX" 1549418 NIL MATRIX (NIL T) -8 NIL NIL) (-631 1541411 1542115 1542851 "MATLIN" 1544999 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-630 1531609 1534747 1534823 "MATCAT" 1539661 NIL MATCAT (NIL T T T) -9 NIL 1541078) (-629 1527974 1528987 1530342 "MATCAT-" 1530347 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-628 1526576 1526729 1527060 "MATCAT2" 1527809 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-627 1524688 1525012 1525396 "MAPPKG3" 1526251 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-626 1523669 1523842 1524064 "MAPPKG2" 1524512 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-625 1522168 1522452 1522779 "MAPPKG1" 1523375 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-624 1521779 1521837 1521960 "MAPHACK3" 1522104 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-623 1521371 1521432 1521546 "MAPHACK2" 1521711 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-622 1520809 1520912 1521054 "MAPHACK1" 1521262 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-621 1518917 1519511 1519814 "MAGMA" 1520538 NIL MAGMA (NIL T) -8 NIL NIL) (-620 1515391 1517161 1517621 "M3D" 1518490 NIL M3D (NIL T) -8 NIL NIL) (-619 1509547 1513762 1513803 "LZSTAGG" 1514585 NIL LZSTAGG (NIL T) -9 NIL 1514880) (-618 1505520 1506678 1508135 "LZSTAGG-" 1508140 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-617 1502636 1503413 1503899 "LWORD" 1505066 NIL LWORD (NIL T) -8 NIL NIL) (-616 1495796 1502407 1502541 "LSQM" 1502546 NIL LSQM (NIL NIL T) -8 NIL NIL) (-615 1495020 1495159 1495387 "LSPP" 1495651 NIL LSPP (NIL T T T T) -7 NIL NIL) (-614 1492832 1493133 1493589 "LSMP" 1494709 NIL LSMP (NIL T T T T) -7 NIL NIL) (-613 1489611 1490285 1491015 "LSMP1" 1492134 NIL LSMP1 (NIL T) -7 NIL NIL) (-612 1483538 1488780 1488821 "LSAGG" 1488883 NIL LSAGG (NIL T) -9 NIL 1488961) (-611 1480233 1481157 1482370 "LSAGG-" 1482375 NIL LSAGG- (NIL T T) -8 NIL NIL) (-610 1477859 1479377 1479626 "LPOLY" 1480028 NIL LPOLY (NIL T T) -8 NIL NIL) (-609 1477441 1477526 1477649 "LPEFRAC" 1477768 NIL LPEFRAC (NIL T) -7 NIL NIL) (-608 1475788 1476535 1476788 "LO" 1477273 NIL LO (NIL T T T) -8 NIL NIL) (-607 1475442 1475554 1475582 "LOGIC" 1475693 T LOGIC (NIL) -9 NIL 1475773) (-606 1475304 1475327 1475398 "LOGIC-" 1475403 NIL LOGIC- (NIL T) -8 NIL NIL) (-605 1474497 1474637 1474830 "LODOOPS" 1475160 NIL LODOOPS (NIL T T) -7 NIL NIL) (-604 1471915 1474414 1474479 "LODO" 1474484 NIL LODO (NIL T NIL) -8 NIL NIL) (-603 1470461 1470696 1471047 "LODOF" 1471662 NIL LODOF (NIL T T) -7 NIL NIL) (-602 1466881 1469317 1469357 "LODOCAT" 1469789 NIL LODOCAT (NIL T) -9 NIL 1470000) (-601 1466615 1466673 1466799 "LODOCAT-" 1466804 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-600 1463929 1466456 1466574 "LODO2" 1466579 NIL LODO2 (NIL T T) -8 NIL NIL) (-599 1461358 1463866 1463911 "LODO1" 1463916 NIL LODO1 (NIL T) -8 NIL NIL) (-598 1460221 1460386 1460697 "LODEEF" 1461181 NIL LODEEF (NIL T T T) -7 NIL NIL) (-597 1455508 1458352 1458393 "LNAGG" 1459340 NIL LNAGG (NIL T) -9 NIL 1459784) (-596 1454655 1454869 1455211 "LNAGG-" 1455216 NIL LNAGG- (NIL T T) -8 NIL NIL) (-595 1450820 1451582 1452220 "LMOPS" 1454071 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-594 1450218 1450580 1450620 "LMODULE" 1450680 NIL LMODULE (NIL T) -9 NIL 1450722) (-593 1447464 1449863 1449986 "LMDICT" 1450128 NIL LMDICT (NIL T) -8 NIL NIL) (-592 1440691 1446410 1446708 "LIST" 1447199 NIL LIST (NIL T) -8 NIL NIL) (-591 1440216 1440290 1440429 "LIST3" 1440611 NIL LIST3 (NIL T T T) -7 NIL NIL) (-590 1439223 1439401 1439629 "LIST2" 1440034 NIL LIST2 (NIL T T) -7 NIL NIL) (-589 1437357 1437669 1438068 "LIST2MAP" 1438870 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-588 1436070 1436750 1436790 "LINEXP" 1437043 NIL LINEXP (NIL T) -9 NIL 1437191) (-587 1434717 1434977 1435274 "LINDEP" 1435822 NIL LINDEP (NIL T T) -7 NIL NIL) (-586 1431484 1432203 1432980 "LIMITRF" 1433972 NIL LIMITRF (NIL T) -7 NIL NIL) (-585 1429764 1430059 1430474 "LIMITPS" 1431179 NIL LIMITPS (NIL T T) -7 NIL NIL) (-584 1424219 1429275 1429503 "LIE" 1429585 NIL LIE (NIL T T) -8 NIL NIL) (-583 1423270 1423713 1423753 "LIECAT" 1423893 NIL LIECAT (NIL T) -9 NIL 1424044) (-582 1423111 1423138 1423226 "LIECAT-" 1423231 NIL LIECAT- (NIL T T) -8 NIL NIL) (-581 1415723 1422560 1422725 "LIB" 1422966 T LIB (NIL) -8 NIL NIL) (-580 1411360 1412241 1413176 "LGROBP" 1414840 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-579 1409226 1409500 1409862 "LF" 1411081 NIL LF (NIL T T) -7 NIL NIL) (-578 1408066 1408758 1408786 "LFCAT" 1408993 T LFCAT (NIL) -9 NIL 1409132) (-577 1404978 1405604 1406290 "LEXTRIPK" 1407432 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-576 1401684 1402548 1403051 "LEXP" 1404558 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-575 1400082 1400395 1400796 "LEADCDET" 1401366 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-574 1399278 1399352 1399579 "LAZM3PK" 1400003 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-573 1394195 1397357 1397894 "LAUPOL" 1398791 NIL LAUPOL (NIL T T) -8 NIL NIL) (-572 1393762 1393806 1393973 "LAPLACE" 1394145 NIL LAPLACE (NIL T T) -7 NIL NIL) (-571 1391690 1392863 1393114 "LA" 1393595 NIL LA (NIL T T T) -8 NIL NIL) (-570 1390753 1391347 1391387 "LALG" 1391448 NIL LALG (NIL T) -9 NIL 1391506) (-569 1390468 1390527 1390662 "LALG-" 1390667 NIL LALG- (NIL T T) -8 NIL NIL) (-568 1389378 1389565 1389862 "KOVACIC" 1390268 NIL KOVACIC (NIL T T) -7 NIL NIL) (-567 1389213 1389237 1389278 "KONVERT" 1389340 NIL KONVERT (NIL T) -9 NIL NIL) (-566 1389048 1389072 1389113 "KOERCE" 1389175 NIL KOERCE (NIL T) -9 NIL NIL) (-565 1386782 1387542 1387935 "KERNEL" 1388687 NIL KERNEL (NIL T) -8 NIL NIL) (-564 1386284 1386365 1386495 "KERNEL2" 1386696 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-563 1380136 1384824 1384878 "KDAGG" 1385255 NIL KDAGG (NIL T T) -9 NIL 1385461) (-562 1379665 1379789 1379994 "KDAGG-" 1379999 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-561 1372840 1379326 1379481 "KAFILE" 1379543 NIL KAFILE (NIL T) -8 NIL NIL) (-560 1367295 1372351 1372579 "JORDAN" 1372661 NIL JORDAN (NIL T T) -8 NIL NIL) (-559 1367024 1367083 1367170 "JAVACODE" 1367228 T JAVACODE (NIL) -8 NIL NIL) (-558 1363324 1365230 1365284 "IXAGG" 1366213 NIL IXAGG (NIL T T) -9 NIL 1366672) (-557 1362243 1362549 1362968 "IXAGG-" 1362973 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-556 1357828 1362165 1362224 "IVECTOR" 1362229 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-555 1356594 1356831 1357097 "ITUPLE" 1357595 NIL ITUPLE (NIL T) -8 NIL NIL) (-554 1355030 1355207 1355513 "ITRIGMNP" 1356416 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-553 1353775 1353979 1354262 "ITFUN3" 1354806 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-552 1353407 1353464 1353573 "ITFUN2" 1353712 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-551 1351209 1352280 1352577 "ITAYLOR" 1353142 NIL ITAYLOR (NIL T) -8 NIL NIL) (-550 1340197 1345395 1346554 "ISUPS" 1350082 NIL ISUPS (NIL T) -8 NIL NIL) (-549 1339301 1339441 1339677 "ISUMP" 1340044 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-548 1334565 1339102 1339181 "ISTRING" 1339254 NIL ISTRING (NIL NIL) -8 NIL NIL) (-547 1333778 1333859 1334074 "IRURPK" 1334479 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-546 1332714 1332915 1333155 "IRSN" 1333558 T IRSN (NIL) -7 NIL NIL) (-545 1330749 1331104 1331539 "IRRF2F" 1332352 NIL IRRF2F (NIL T) -7 NIL NIL) (-544 1330496 1330534 1330610 "IRREDFFX" 1330705 NIL IRREDFFX (NIL T) -7 NIL NIL) (-543 1329111 1329370 1329669 "IROOT" 1330229 NIL IROOT (NIL T) -7 NIL NIL) (-542 1325749 1326800 1327490 "IR" 1328453 NIL IR (NIL T) -8 NIL NIL) (-541 1323362 1323857 1324423 "IR2" 1325227 NIL IR2 (NIL T T) -7 NIL NIL) (-540 1322438 1322551 1322771 "IR2F" 1323245 NIL IR2F (NIL T T) -7 NIL NIL) (-539 1322229 1322263 1322323 "IPRNTPK" 1322398 T IPRNTPK (NIL) -7 NIL NIL) (-538 1318783 1322118 1322187 "IPF" 1322192 NIL IPF (NIL NIL) -8 NIL NIL) (-537 1317100 1318708 1318765 "IPADIC" 1318770 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-536 1316599 1316657 1316846 "INVLAPLA" 1317036 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-535 1306248 1308601 1310987 "INTTR" 1314263 NIL INTTR (NIL T T) -7 NIL NIL) (-534 1302596 1303337 1304200 "INTTOOLS" 1305434 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-533 1302182 1302273 1302390 "INTSLPE" 1302499 T INTSLPE (NIL) -7 NIL NIL) (-532 1300132 1302105 1302164 "INTRVL" 1302169 NIL INTRVL (NIL T) -8 NIL NIL) (-531 1297739 1298251 1298825 "INTRF" 1299617 NIL INTRF (NIL T) -7 NIL NIL) (-530 1297154 1297251 1297392 "INTRET" 1297637 NIL INTRET (NIL T) -7 NIL NIL) (-529 1295156 1295545 1296014 "INTRAT" 1296762 NIL INTRAT (NIL T T) -7 NIL NIL) (-528 1292389 1292972 1293597 "INTPM" 1294641 NIL INTPM (NIL T T) -7 NIL NIL) (-527 1289098 1289697 1290441 "INTPAF" 1291775 NIL INTPAF (NIL T T T) -7 NIL NIL) (-526 1284341 1285287 1286322 "INTPACK" 1288083 T INTPACK (NIL) -7 NIL NIL) (-525 1281195 1284070 1284197 "INT" 1284234 T INT (NIL) -8 NIL NIL) (-524 1280447 1280599 1280807 "INTHERTR" 1281037 NIL INTHERTR (NIL T T) -7 NIL NIL) (-523 1279886 1279966 1280154 "INTHERAL" 1280361 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-522 1277732 1278175 1278632 "INTHEORY" 1279449 T INTHEORY (NIL) -7 NIL NIL) (-521 1269054 1270675 1272453 "INTG0" 1276084 NIL INTG0 (NIL T T T) -7 NIL NIL) (-520 1249627 1254417 1259227 "INTFTBL" 1264264 T INTFTBL (NIL) -8 NIL NIL) (-519 1248876 1249014 1249187 "INTFACT" 1249486 NIL INTFACT (NIL T) -7 NIL NIL) (-518 1246267 1246713 1247276 "INTEF" 1248430 NIL INTEF (NIL T T) -7 NIL NIL) (-517 1244729 1245478 1245506 "INTDOM" 1245807 T INTDOM (NIL) -9 NIL 1246014) (-516 1244098 1244272 1244514 "INTDOM-" 1244519 NIL INTDOM- (NIL T) -8 NIL NIL) (-515 1240591 1242523 1242577 "INTCAT" 1243376 NIL INTCAT (NIL T) -9 NIL 1243695) (-514 1240064 1240166 1240294 "INTBIT" 1240483 T INTBIT (NIL) -7 NIL NIL) (-513 1238739 1238893 1239206 "INTALG" 1239909 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-512 1238196 1238286 1238456 "INTAF" 1238643 NIL INTAF (NIL T T) -7 NIL NIL) (-511 1231650 1238006 1238146 "INTABL" 1238151 NIL INTABL (NIL T T T) -8 NIL NIL) (-510 1226601 1229330 1229358 "INS" 1230326 T INS (NIL) -9 NIL 1231007) (-509 1223841 1224612 1225586 "INS-" 1225659 NIL INS- (NIL T) -8 NIL NIL) (-508 1222620 1222847 1223144 "INPSIGN" 1223594 NIL INPSIGN (NIL T T) -7 NIL NIL) (-507 1221738 1221855 1222052 "INPRODPF" 1222500 NIL INPRODPF (NIL T T) -7 NIL NIL) (-506 1220632 1220749 1220986 "INPRODFF" 1221618 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-505 1219632 1219784 1220044 "INNMFACT" 1220468 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-504 1218829 1218926 1219114 "INMODGCD" 1219531 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-503 1217338 1217582 1217906 "INFSP" 1218574 NIL INFSP (NIL T T T) -7 NIL NIL) (-502 1216522 1216639 1216822 "INFPROD0" 1217218 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-501 1213533 1214691 1215182 "INFORM" 1216039 T INFORM (NIL) -8 NIL NIL) (-500 1213143 1213203 1213301 "INFORM1" 1213468 NIL INFORM1 (NIL T) -7 NIL NIL) (-499 1212666 1212755 1212869 "INFINITY" 1213049 T INFINITY (NIL) -7 NIL NIL) (-498 1211283 1211532 1211853 "INEP" 1212414 NIL INEP (NIL T T T) -7 NIL NIL) (-497 1210559 1211180 1211245 "INDE" 1211250 NIL INDE (NIL T) -8 NIL NIL) (-496 1210123 1210191 1210308 "INCRMAPS" 1210486 NIL INCRMAPS (NIL T) -7 NIL NIL) (-495 1205434 1206359 1207303 "INBFF" 1209211 NIL INBFF (NIL T) -7 NIL NIL) (-494 1201929 1205279 1205382 "IMATRIX" 1205387 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-493 1200641 1200764 1201079 "IMATQF" 1201785 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-492 1198861 1199088 1199425 "IMATLIN" 1200397 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-491 1193487 1198785 1198843 "ILIST" 1198848 NIL ILIST (NIL T NIL) -8 NIL NIL) (-490 1191440 1193347 1193460 "IIARRAY2" 1193465 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-489 1186808 1191351 1191415 "IFF" 1191420 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-488 1181851 1186100 1186288 "IFARRAY" 1186665 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-487 1181058 1181755 1181828 "IFAMON" 1181833 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-486 1180642 1180707 1180761 "IEVALAB" 1180968 NIL IEVALAB (NIL T T) -9 NIL NIL) (-485 1180317 1180385 1180545 "IEVALAB-" 1180550 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-484 1179975 1180231 1180294 "IDPO" 1180299 NIL IDPO (NIL T T) -8 NIL NIL) (-483 1179252 1179864 1179939 "IDPOAMS" 1179944 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-482 1178586 1179141 1179216 "IDPOAM" 1179221 NIL IDPOAM (NIL T T) -8 NIL NIL) (-481 1177672 1177922 1177975 "IDPC" 1178388 NIL IDPC (NIL T T) -9 NIL 1178537) (-480 1177168 1177564 1177637 "IDPAM" 1177642 NIL IDPAM (NIL T T) -8 NIL NIL) (-479 1176571 1177060 1177133 "IDPAG" 1177138 NIL IDPAG (NIL T T) -8 NIL NIL) (-478 1172826 1173674 1174569 "IDECOMP" 1175728 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-477 1165699 1166749 1167796 "IDEAL" 1171862 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-476 1164863 1164975 1165174 "ICDEN" 1165583 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-475 1163962 1164343 1164490 "ICARD" 1164736 T ICARD (NIL) -8 NIL NIL) (-474 1162034 1162347 1162750 "IBPTOOLS" 1163639 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-473 1157648 1161654 1161767 "IBITS" 1161953 NIL IBITS (NIL NIL) -8 NIL NIL) (-472 1154371 1154947 1155642 "IBATOOL" 1157065 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-471 1152151 1152612 1153145 "IBACHIN" 1153906 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-470 1150028 1151997 1152100 "IARRAY2" 1152105 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-469 1146181 1149954 1150011 "IARRAY1" 1150016 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-468 1140119 1144599 1145077 "IAN" 1145723 T IAN (NIL) -8 NIL NIL) (-467 1139630 1139687 1139860 "IALGFACT" 1140056 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-466 1139158 1139271 1139299 "HYPCAT" 1139506 T HYPCAT (NIL) -9 NIL NIL) (-465 1138696 1138813 1138999 "HYPCAT-" 1139004 NIL HYPCAT- (NIL T) -8 NIL NIL) (-464 1135376 1136707 1136748 "HOAGG" 1137729 NIL HOAGG (NIL T) -9 NIL 1138408) (-463 1133970 1134369 1134895 "HOAGG-" 1134900 NIL HOAGG- (NIL T T) -8 NIL NIL) (-462 1127800 1133411 1133577 "HEXADEC" 1133824 T HEXADEC (NIL) -8 NIL NIL) (-461 1126548 1126770 1127033 "HEUGCD" 1127577 NIL HEUGCD (NIL T) -7 NIL NIL) (-460 1125651 1126385 1126515 "HELLFDIV" 1126520 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-459 1123879 1125428 1125516 "HEAP" 1125595 NIL HEAP (NIL T) -8 NIL NIL) (-458 1117746 1123794 1123856 "HDP" 1123861 NIL HDP (NIL NIL T) -8 NIL NIL) (-457 1111458 1117383 1117534 "HDMP" 1117647 NIL HDMP (NIL NIL T) -8 NIL NIL) (-456 1110783 1110922 1111086 "HB" 1111314 T HB (NIL) -7 NIL NIL) (-455 1104280 1110629 1110733 "HASHTBL" 1110738 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-454 1102033 1103908 1104087 "HACKPI" 1104121 T HACKPI (NIL) -8 NIL NIL) (-453 1097729 1101887 1101999 "GTSET" 1102004 NIL GTSET (NIL T T T T) -8 NIL NIL) (-452 1091255 1097607 1097705 "GSTBL" 1097710 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-451 1083488 1090291 1090555 "GSERIES" 1091046 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-450 1082511 1082964 1082992 "GROUP" 1083253 T GROUP (NIL) -9 NIL 1083412) (-449 1081627 1081850 1082194 "GROUP-" 1082199 NIL GROUP- (NIL T) -8 NIL NIL) (-448 1079996 1080315 1080702 "GROEBSOL" 1081304 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-447 1078937 1079199 1079250 "GRMOD" 1079779 NIL GRMOD (NIL T T) -9 NIL 1079947) (-446 1078705 1078741 1078869 "GRMOD-" 1078874 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-445 1074031 1075059 1076059 "GRIMAGE" 1077725 T GRIMAGE (NIL) -8 NIL NIL) (-444 1072498 1072758 1073082 "GRDEF" 1073727 T GRDEF (NIL) -7 NIL NIL) (-443 1071942 1072058 1072199 "GRAY" 1072377 T GRAY (NIL) -7 NIL NIL) (-442 1071176 1071556 1071607 "GRALG" 1071760 NIL GRALG (NIL T T) -9 NIL 1071852) (-441 1070837 1070910 1071073 "GRALG-" 1071078 NIL GRALG- (NIL T T T) -8 NIL NIL) (-440 1067645 1070426 1070602 "GPOLSET" 1070744 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-439 1067001 1067058 1067315 "GOSPER" 1067582 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-438 1062760 1063439 1063965 "GMODPOL" 1066700 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-437 1061765 1061949 1062187 "GHENSEL" 1062572 NIL GHENSEL (NIL T T) -7 NIL NIL) (-436 1055831 1056674 1057700 "GENUPS" 1060849 NIL GENUPS (NIL T T) -7 NIL NIL) (-435 1055528 1055579 1055668 "GENUFACT" 1055774 NIL GENUFACT (NIL T) -7 NIL NIL) (-434 1054940 1055017 1055182 "GENPGCD" 1055446 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-433 1054414 1054449 1054662 "GENMFACT" 1054899 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-432 1052982 1053237 1053544 "GENEEZ" 1054157 NIL GENEEZ (NIL T T) -7 NIL NIL) (-431 1046856 1052595 1052756 "GDMP" 1052905 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-430 1036233 1040627 1041733 "GCNAALG" 1045839 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-429 1034655 1035527 1035555 "GCDDOM" 1035810 T GCDDOM (NIL) -9 NIL 1035967) (-428 1034125 1034252 1034467 "GCDDOM-" 1034472 NIL GCDDOM- (NIL T) -8 NIL NIL) (-427 1032797 1032982 1033286 "GB" 1033904 NIL GB (NIL T T T T) -7 NIL NIL) (-426 1021417 1023743 1026135 "GBINTERN" 1030488 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-425 1019254 1019546 1019967 "GBF" 1021092 NIL GBF (NIL T T T T) -7 NIL NIL) (-424 1018035 1018200 1018467 "GBEUCLID" 1019070 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-423 1017384 1017509 1017658 "GAUSSFAC" 1017906 T GAUSSFAC (NIL) -7 NIL NIL) (-422 1015761 1016063 1016376 "GALUTIL" 1017103 NIL GALUTIL (NIL T) -7 NIL NIL) (-421 1014078 1014352 1014675 "GALPOLYU" 1015488 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-420 1011467 1011757 1012162 "GALFACTU" 1013775 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-419 1003273 1004772 1006380 "GALFACT" 1009899 NIL GALFACT (NIL T) -7 NIL NIL) (-418 1000661 1001319 1001347 "FVFUN" 1002503 T FVFUN (NIL) -9 NIL 1003223) (-417 999927 1000109 1000137 "FVC" 1000428 T FVC (NIL) -9 NIL 1000611) (-416 999569 999724 999805 "FUNCTION" 999879 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-415 997239 997790 998279 "FT" 999100 T FT (NIL) -8 NIL NIL) (-414 996057 996540 996743 "FTEM" 997056 T FTEM (NIL) -8 NIL NIL) (-413 994322 994610 995012 "FSUPFACT" 995749 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-412 992719 993008 993340 "FST" 994010 T FST (NIL) -8 NIL NIL) (-411 991894 992000 992194 "FSRED" 992601 NIL FSRED (NIL T T) -7 NIL NIL) (-410 990573 990828 991182 "FSPRMELT" 991609 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-409 987658 988096 988595 "FSPECF" 990136 NIL FSPECF (NIL T T) -7 NIL NIL) (-408 970032 978589 978629 "FS" 982467 NIL FS (NIL T) -9 NIL 984749) (-407 958682 961672 965728 "FS-" 966025 NIL FS- (NIL T T) -8 NIL NIL) (-406 958198 958252 958428 "FSINT" 958623 NIL FSINT (NIL T T) -7 NIL NIL) (-405 956479 957191 957494 "FSERIES" 957977 NIL FSERIES (NIL T T) -8 NIL NIL) (-404 955497 955613 955843 "FSCINT" 956359 NIL FSCINT (NIL T T) -7 NIL NIL) (-403 951732 954442 954483 "FSAGG" 954853 NIL FSAGG (NIL T) -9 NIL 955112) (-402 949494 950095 950891 "FSAGG-" 950986 NIL FSAGG- (NIL T T) -8 NIL NIL) (-401 948536 948679 948906 "FSAGG2" 949347 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-400 946195 946474 947027 "FS2UPS" 948254 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-399 945781 945824 945977 "FS2" 946146 NIL FS2 (NIL T T T T) -7 NIL NIL) (-398 944641 944812 945120 "FS2EXPXP" 945606 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-397 944067 944182 944334 "FRUTIL" 944521 NIL FRUTIL (NIL T) -7 NIL NIL) (-396 935487 939566 940922 "FR" 942743 NIL FR (NIL T) -8 NIL NIL) (-395 930564 933207 933247 "FRNAALG" 934643 NIL FRNAALG (NIL T) -9 NIL 935250) (-394 926242 927313 928588 "FRNAALG-" 929338 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-393 925880 925923 926050 "FRNAAF2" 926193 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-392 924245 924737 925031 "FRMOD" 925693 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-391 921967 922636 922952 "FRIDEAL" 924036 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-390 921166 921253 921540 "FRIDEAL2" 921874 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-389 920424 920832 920873 "FRETRCT" 920878 NIL FRETRCT (NIL T) -9 NIL 921049) (-388 919536 919767 920118 "FRETRCT-" 920123 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-387 916746 917966 918025 "FRAMALG" 918907 NIL FRAMALG (NIL T T) -9 NIL 919199) (-386 914879 915335 915965 "FRAMALG-" 916188 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-385 908781 914354 914630 "FRAC" 914635 NIL FRAC (NIL T) -8 NIL NIL) (-384 908417 908474 908581 "FRAC2" 908718 NIL FRAC2 (NIL T T) -7 NIL NIL) (-383 908053 908110 908217 "FR2" 908354 NIL FR2 (NIL T T) -7 NIL NIL) (-382 902727 905640 905668 "FPS" 906787 T FPS (NIL) -9 NIL 907343) (-381 902176 902285 902449 "FPS-" 902595 NIL FPS- (NIL T) -8 NIL NIL) (-380 899625 901322 901350 "FPC" 901575 T FPC (NIL) -9 NIL 901717) (-379 899418 899458 899555 "FPC-" 899560 NIL FPC- (NIL T) -8 NIL NIL) (-378 898297 898907 898948 "FPATMAB" 898953 NIL FPATMAB (NIL T) -9 NIL 899105) (-377 895997 896473 896899 "FPARFRAC" 897934 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-376 891390 891889 892571 "FORTRAN" 895429 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-375 889106 889606 890145 "FORT" 890871 T FORT (NIL) -7 NIL NIL) (-374 886782 887344 887372 "FORTFN" 888432 T FORTFN (NIL) -9 NIL 889056) (-373 886546 886596 886624 "FORTCAT" 886683 T FORTCAT (NIL) -9 NIL 886745) (-372 884606 885089 885488 "FORMULA" 886167 T FORMULA (NIL) -8 NIL NIL) (-371 884394 884424 884493 "FORMULA1" 884570 NIL FORMULA1 (NIL T) -7 NIL NIL) (-370 883917 883969 884142 "FORDER" 884336 NIL FORDER (NIL T T T T) -7 NIL NIL) (-369 883013 883177 883370 "FOP" 883744 T FOP (NIL) -7 NIL NIL) (-368 881621 882293 882467 "FNLA" 882895 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-367 880290 880679 880707 "FNCAT" 881279 T FNCAT (NIL) -9 NIL 881572) (-366 879856 880249 880277 "FNAME" 880282 T FNAME (NIL) -8 NIL NIL) (-365 878516 879489 879517 "FMTC" 879522 T FMTC (NIL) -9 NIL 879557) (-364 874834 876041 876669 "FMONOID" 877921 NIL FMONOID (NIL T) -8 NIL NIL) (-363 874054 874577 874725 "FM" 874730 NIL FM (NIL T T) -8 NIL NIL) (-362 871478 872124 872152 "FMFUN" 873296 T FMFUN (NIL) -9 NIL 874004) (-361 870747 870928 870956 "FMC" 871246 T FMC (NIL) -9 NIL 871428) (-360 867977 868811 868864 "FMCAT" 870046 NIL FMCAT (NIL T T) -9 NIL 870540) (-359 866872 867745 867844 "FM1" 867922 NIL FM1 (NIL T T) -8 NIL NIL) (-358 864646 865062 865556 "FLOATRP" 866423 NIL FLOATRP (NIL T) -7 NIL NIL) (-357 858132 862302 862932 "FLOAT" 864036 T FLOAT (NIL) -8 NIL NIL) (-356 855570 856070 856648 "FLOATCP" 857599 NIL FLOATCP (NIL T) -7 NIL NIL) (-355 854359 855207 855247 "FLINEXP" 855252 NIL FLINEXP (NIL T) -9 NIL 855345) (-354 853514 853749 854076 "FLINEXP-" 854081 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-353 852590 852734 852958 "FLASORT" 853366 NIL FLASORT (NIL T T) -7 NIL NIL) (-352 849809 850651 850703 "FLALG" 851930 NIL FLALG (NIL T T) -9 NIL 852397) (-351 843594 847296 847337 "FLAGG" 848599 NIL FLAGG (NIL T) -9 NIL 849251) (-350 842320 842659 843149 "FLAGG-" 843154 NIL FLAGG- (NIL T T) -8 NIL NIL) (-349 841362 841505 841732 "FLAGG2" 842173 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-348 838335 839353 839412 "FINRALG" 840540 NIL FINRALG (NIL T T) -9 NIL 841048) (-347 837495 837724 838063 "FINRALG-" 838068 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-346 836902 837115 837143 "FINITE" 837339 T FINITE (NIL) -9 NIL 837446) (-345 829362 831523 831563 "FINAALG" 835230 NIL FINAALG (NIL T) -9 NIL 836683) (-344 824703 825744 826888 "FINAALG-" 828267 NIL FINAALG- (NIL T T) -8 NIL NIL) (-343 824098 824458 824561 "FILE" 824633 NIL FILE (NIL T) -8 NIL NIL) (-342 822783 823095 823149 "FILECAT" 823833 NIL FILECAT (NIL T T) -9 NIL 824049) (-341 820646 822202 822230 "FIELD" 822270 T FIELD (NIL) -9 NIL 822350) (-340 819266 819651 820162 "FIELD-" 820167 NIL FIELD- (NIL T) -8 NIL NIL) (-339 817081 817903 818249 "FGROUP" 818953 NIL FGROUP (NIL T) -8 NIL NIL) (-338 816171 816335 816555 "FGLMICPK" 816913 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-337 811973 816096 816153 "FFX" 816158 NIL FFX (NIL T NIL) -8 NIL NIL) (-336 811574 811635 811770 "FFSLPE" 811906 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-335 807567 808346 809142 "FFPOLY" 810810 NIL FFPOLY (NIL T) -7 NIL NIL) (-334 807071 807107 807316 "FFPOLY2" 807525 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-333 802892 806990 807053 "FFP" 807058 NIL FFP (NIL T NIL) -8 NIL NIL) (-332 798260 802803 802867 "FF" 802872 NIL FF (NIL NIL NIL) -8 NIL NIL) (-331 793356 797603 797793 "FFNBX" 798114 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-330 788265 792491 792749 "FFNBP" 793210 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-329 782868 787549 787760 "FFNB" 788098 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-328 781700 781898 782213 "FFINTBAS" 782665 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-327 777924 780164 780192 "FFIELDC" 780812 T FFIELDC (NIL) -9 NIL 781188) (-326 776587 776957 777454 "FFIELDC-" 777459 NIL FFIELDC- (NIL T) -8 NIL NIL) (-325 776157 776202 776326 "FFHOM" 776529 NIL FFHOM (NIL T T T) -7 NIL NIL) (-324 773855 774339 774856 "FFF" 775672 NIL FFF (NIL T) -7 NIL NIL) (-323 769443 773597 773698 "FFCGX" 773798 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-322 765045 769175 769282 "FFCGP" 769386 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-321 760198 764772 764880 "FFCG" 764981 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-320 742144 751267 751353 "FFCAT" 756518 NIL FFCAT (NIL T T T) -9 NIL 758005) (-319 737342 738389 739703 "FFCAT-" 740933 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-318 736753 736796 737031 "FFCAT2" 737293 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-317 725953 729743 730960 "FEXPR" 735608 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-316 724953 725388 725429 "FEVALAB" 725513 NIL FEVALAB (NIL T) -9 NIL 725774) (-315 724112 724322 724660 "FEVALAB-" 724665 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-314 722705 723495 723698 "FDIV" 724011 NIL FDIV (NIL T T T T) -8 NIL NIL) (-313 719772 720487 720602 "FDIVCAT" 722170 NIL FDIVCAT (NIL T T T T) -9 NIL 722607) (-312 719534 719561 719731 "FDIVCAT-" 719736 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-311 718754 718841 719118 "FDIV2" 719441 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-310 717440 717699 717988 "FCPAK1" 718485 T FCPAK1 (NIL) -7 NIL NIL) (-309 716568 716940 717081 "FCOMP" 717331 NIL FCOMP (NIL T) -8 NIL NIL) (-308 700203 703617 707178 "FC" 713027 T FC (NIL) -8 NIL NIL) (-307 692799 696845 696885 "FAXF" 698687 NIL FAXF (NIL T) -9 NIL 699378) (-306 690078 690733 691558 "FAXF-" 692023 NIL FAXF- (NIL T T) -8 NIL NIL) (-305 685178 689454 689630 "FARRAY" 689935 NIL FARRAY (NIL T) -8 NIL NIL) (-304 680569 682640 682692 "FAMR" 683704 NIL FAMR (NIL T T) -9 NIL 684164) (-303 679460 679762 680196 "FAMR-" 680201 NIL FAMR- (NIL T T T) -8 NIL NIL) (-302 678656 679382 679435 "FAMONOID" 679440 NIL FAMONOID (NIL T) -8 NIL NIL) (-301 676489 677173 677226 "FAMONC" 678167 NIL FAMONC (NIL T T) -9 NIL 678552) (-300 675181 676243 676380 "FAGROUP" 676385 NIL FAGROUP (NIL T) -8 NIL NIL) (-299 672984 673303 673705 "FACUTIL" 674862 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-298 672083 672268 672490 "FACTFUNC" 672794 NIL FACTFUNC (NIL T) -7 NIL NIL) (-297 664403 671334 671546 "EXPUPXS" 671939 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-296 661886 662426 663012 "EXPRTUBE" 663837 T EXPRTUBE (NIL) -7 NIL NIL) (-295 658080 658672 659409 "EXPRODE" 661225 NIL EXPRODE (NIL T T) -7 NIL NIL) (-294 643239 656739 657165 "EXPR" 657686 NIL EXPR (NIL T) -8 NIL NIL) (-293 637667 638254 639066 "EXPR2UPS" 642537 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-292 637303 637360 637467 "EXPR2" 637604 NIL EXPR2 (NIL T T) -7 NIL NIL) (-291 628657 636440 636735 "EXPEXPAN" 637141 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-290 628484 628614 628643 "EXIT" 628648 T EXIT (NIL) -8 NIL NIL) (-289 628111 628173 628286 "EVALCYC" 628416 NIL EVALCYC (NIL T) -7 NIL NIL) (-288 627652 627770 627811 "EVALAB" 627981 NIL EVALAB (NIL T) -9 NIL 628085) (-287 627133 627255 627476 "EVALAB-" 627481 NIL EVALAB- (NIL T T) -8 NIL NIL) (-286 624596 625908 625936 "EUCDOM" 626491 T EUCDOM (NIL) -9 NIL 626841) (-285 623001 623443 624033 "EUCDOM-" 624038 NIL EUCDOM- (NIL T) -8 NIL NIL) (-284 610579 613327 616067 "ESTOOLS" 620281 T ESTOOLS (NIL) -7 NIL NIL) (-283 610215 610272 610379 "ESTOOLS2" 610516 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-282 609966 610008 610088 "ESTOOLS1" 610167 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-281 603904 605628 605656 "ES" 608420 T ES (NIL) -9 NIL 609826) (-280 598851 600138 601955 "ES-" 602119 NIL ES- (NIL T) -8 NIL NIL) (-279 595226 595986 596766 "ESCONT" 598091 T ESCONT (NIL) -7 NIL NIL) (-278 594971 595003 595085 "ESCONT1" 595188 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-277 594646 594696 594796 "ES2" 594915 NIL ES2 (NIL T T) -7 NIL NIL) (-276 594276 594334 594443 "ES1" 594582 NIL ES1 (NIL T T) -7 NIL NIL) (-275 593492 593621 593797 "ERROR" 594120 T ERROR (NIL) -7 NIL NIL) (-274 586995 593351 593442 "EQTBL" 593447 NIL EQTBL (NIL T T) -8 NIL NIL) (-273 579432 582313 583760 "EQ" 585581 NIL -1369 (NIL T) -8 NIL NIL) (-272 579064 579121 579230 "EQ2" 579369 NIL EQ2 (NIL T T) -7 NIL NIL) (-271 574356 575402 576495 "EP" 578003 NIL EP (NIL T) -7 NIL NIL) (-270 572938 573239 573556 "ENV" 574059 T ENV (NIL) -8 NIL NIL) (-269 572098 572662 572690 "ENTIRER" 572695 T ENTIRER (NIL) -9 NIL 572740) (-268 568554 570053 570423 "EMR" 571897 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-267 567698 567883 567937 "ELTAGG" 568317 NIL ELTAGG (NIL T T) -9 NIL 568528) (-266 567417 567479 567620 "ELTAGG-" 567625 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-265 567206 567235 567289 "ELTAB" 567373 NIL ELTAB (NIL T T) -9 NIL NIL) (-264 566332 566478 566677 "ELFUTS" 567057 NIL ELFUTS (NIL T T) -7 NIL NIL) (-263 566074 566130 566158 "ELEMFUN" 566263 T ELEMFUN (NIL) -9 NIL NIL) (-262 565944 565965 566033 "ELEMFUN-" 566038 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-261 560836 564045 564086 "ELAGG" 565026 NIL ELAGG (NIL T) -9 NIL 565489) (-260 559121 559555 560218 "ELAGG-" 560223 NIL ELAGG- (NIL T T) -8 NIL NIL) (-259 557778 558058 558353 "ELABEXPR" 558846 T ELABEXPR (NIL) -8 NIL NIL) (-258 550646 552445 553272 "EFUPXS" 557054 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-257 544096 545897 546707 "EFULS" 549922 NIL EFULS (NIL T T T) -8 NIL NIL) (-256 541527 541885 542363 "EFSTRUC" 543728 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-255 530599 532164 533724 "EF" 540042 NIL EF (NIL T T) -7 NIL NIL) (-254 529700 530084 530233 "EAB" 530470 T EAB (NIL) -8 NIL NIL) (-253 528913 529659 529687 "E04UCFA" 529692 T E04UCFA (NIL) -8 NIL NIL) (-252 528126 528872 528900 "E04NAFA" 528905 T E04NAFA (NIL) -8 NIL NIL) (-251 527339 528085 528113 "E04MBFA" 528118 T E04MBFA (NIL) -8 NIL NIL) (-250 526552 527298 527326 "E04JAFA" 527331 T E04JAFA (NIL) -8 NIL NIL) (-249 525767 526511 526539 "E04GCFA" 526544 T E04GCFA (NIL) -8 NIL NIL) (-248 524982 525726 525754 "E04FDFA" 525759 T E04FDFA (NIL) -8 NIL NIL) (-247 524195 524941 524969 "E04DGFA" 524974 T E04DGFA (NIL) -8 NIL NIL) (-246 518380 519725 521087 "E04AGNT" 522853 T E04AGNT (NIL) -7 NIL NIL) (-245 517107 517587 517627 "DVARCAT" 518102 NIL DVARCAT (NIL T) -9 NIL 518300) (-244 516311 516523 516837 "DVARCAT-" 516842 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-243 509173 516113 516240 "DSMP" 516245 NIL DSMP (NIL T T T) -8 NIL NIL) (-242 503983 505118 506186 "DROPT" 508125 T DROPT (NIL) -8 NIL NIL) (-241 503648 503707 503805 "DROPT1" 503918 NIL DROPT1 (NIL T) -7 NIL NIL) (-240 498763 499889 501026 "DROPT0" 502531 T DROPT0 (NIL) -7 NIL NIL) (-239 497108 497433 497819 "DRAWPT" 498397 T DRAWPT (NIL) -7 NIL NIL) (-238 491695 492618 493697 "DRAW" 496082 NIL DRAW (NIL T) -7 NIL NIL) (-237 491328 491381 491499 "DRAWHACK" 491636 NIL DRAWHACK (NIL T) -7 NIL NIL) (-236 490059 490328 490619 "DRAWCX" 491057 T DRAWCX (NIL) -7 NIL NIL) (-235 489577 489645 489795 "DRAWCURV" 489985 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-234 480048 482007 484122 "DRAWCFUN" 487482 T DRAWCFUN (NIL) -7 NIL NIL) (-233 476862 478744 478785 "DQAGG" 479414 NIL DQAGG (NIL T) -9 NIL 479687) (-232 465369 472107 472189 "DPOLCAT" 474027 NIL DPOLCAT (NIL T T T T) -9 NIL 474571) (-231 460209 461555 463512 "DPOLCAT-" 463517 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-230 453005 460071 460168 "DPMO" 460173 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-229 445704 452786 452952 "DPMM" 452957 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-228 445124 445327 445441 "DOMAIN" 445610 T DOMAIN (NIL) -8 NIL NIL) (-227 438836 444761 444912 "DMP" 445025 NIL DMP (NIL NIL T) -8 NIL NIL) (-226 438436 438492 438636 "DLP" 438774 NIL DLP (NIL T) -7 NIL NIL) (-225 432080 437537 437764 "DLIST" 438241 NIL DLIST (NIL T) -8 NIL NIL) (-224 428927 430936 430977 "DLAGG" 431527 NIL DLAGG (NIL T) -9 NIL 431756) (-223 427637 428329 428357 "DIVRING" 428507 T DIVRING (NIL) -9 NIL 428615) (-222 426625 426878 427271 "DIVRING-" 427276 NIL DIVRING- (NIL T) -8 NIL NIL) (-221 424727 425084 425490 "DISPLAY" 426239 T DISPLAY (NIL) -7 NIL NIL) (-220 418616 424641 424704 "DIRPROD" 424709 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-219 417464 417667 417932 "DIRPROD2" 418409 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-218 406983 412988 413041 "DIRPCAT" 413449 NIL DIRPCAT (NIL NIL T) -9 NIL 414288) (-217 404309 404951 405832 "DIRPCAT-" 406169 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-216 403596 403756 403942 "DIOSP" 404143 T DIOSP (NIL) -7 NIL NIL) (-215 400299 402509 402550 "DIOPS" 402984 NIL DIOPS (NIL T) -9 NIL 403213) (-214 399848 399962 400153 "DIOPS-" 400158 NIL DIOPS- (NIL T T) -8 NIL NIL) (-213 398720 399358 399386 "DIFRING" 399573 T DIFRING (NIL) -9 NIL 399682) (-212 398366 398443 398595 "DIFRING-" 398600 NIL DIFRING- (NIL T) -8 NIL NIL) (-211 396156 397438 397478 "DIFEXT" 397837 NIL DIFEXT (NIL T) -9 NIL 398130) (-210 394442 394870 395535 "DIFEXT-" 395540 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-209 391765 393975 394016 "DIAGG" 394021 NIL DIAGG (NIL T) -9 NIL 394041) (-208 391149 391306 391558 "DIAGG-" 391563 NIL DIAGG- (NIL T T) -8 NIL NIL) (-207 386614 390108 390385 "DHMATRIX" 390918 NIL DHMATRIX (NIL T) -8 NIL NIL) (-206 382226 383135 384145 "DFSFUN" 385624 T DFSFUN (NIL) -7 NIL NIL) (-205 377012 380940 381305 "DFLOAT" 381881 T DFLOAT (NIL) -8 NIL NIL) (-204 375245 375526 375921 "DFINTTLS" 376720 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-203 372278 373280 373678 "DERHAM" 374912 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-202 370127 372053 372142 "DEQUEUE" 372222 NIL DEQUEUE (NIL T) -8 NIL NIL) (-201 369345 369478 369673 "DEGRED" 369989 NIL DEGRED (NIL T T) -7 NIL NIL) (-200 365745 366490 367342 "DEFINTRF" 368573 NIL DEFINTRF (NIL T) -7 NIL NIL) (-199 363276 363745 364343 "DEFINTEF" 365264 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-198 357106 362717 362883 "DECIMAL" 363130 T DECIMAL (NIL) -8 NIL NIL) (-197 354618 355076 355582 "DDFACT" 356650 NIL DDFACT (NIL T T) -7 NIL NIL) (-196 354214 354257 354408 "DBLRESP" 354569 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-195 351924 352258 352627 "DBASE" 353972 NIL DBASE (NIL T) -8 NIL NIL) (-194 351059 351883 351911 "D03FAFA" 351916 T D03FAFA (NIL) -8 NIL NIL) (-193 350195 351018 351046 "D03EEFA" 351051 T D03EEFA (NIL) -8 NIL NIL) (-192 348145 348611 349100 "D03AGNT" 349726 T D03AGNT (NIL) -7 NIL NIL) (-191 347463 348104 348132 "D02EJFA" 348137 T D02EJFA (NIL) -8 NIL NIL) (-190 346781 347422 347450 "D02CJFA" 347455 T D02CJFA (NIL) -8 NIL NIL) (-189 346099 346740 346768 "D02BHFA" 346773 T D02BHFA (NIL) -8 NIL NIL) (-188 345417 346058 346086 "D02BBFA" 346091 T D02BBFA (NIL) -8 NIL NIL) (-187 338615 340203 341809 "D02AGNT" 343831 T D02AGNT (NIL) -7 NIL NIL) (-186 336384 336906 337452 "D01WGTS" 338089 T D01WGTS (NIL) -7 NIL NIL) (-185 335487 336343 336371 "D01TRNS" 336376 T D01TRNS (NIL) -8 NIL NIL) (-184 334590 335446 335474 "D01GBFA" 335479 T D01GBFA (NIL) -8 NIL NIL) (-183 333693 334549 334577 "D01FCFA" 334582 T D01FCFA (NIL) -8 NIL NIL) (-182 332796 333652 333680 "D01ASFA" 333685 T D01ASFA (NIL) -8 NIL NIL) (-181 331899 332755 332783 "D01AQFA" 332788 T D01AQFA (NIL) -8 NIL NIL) (-180 331002 331858 331886 "D01APFA" 331891 T D01APFA (NIL) -8 NIL NIL) (-179 330105 330961 330989 "D01ANFA" 330994 T D01ANFA (NIL) -8 NIL NIL) (-178 329208 330064 330092 "D01AMFA" 330097 T D01AMFA (NIL) -8 NIL NIL) (-177 328311 329167 329195 "D01ALFA" 329200 T D01ALFA (NIL) -8 NIL NIL) (-176 327414 328270 328298 "D01AKFA" 328303 T D01AKFA (NIL) -8 NIL NIL) (-175 326517 327373 327401 "D01AJFA" 327406 T D01AJFA (NIL) -8 NIL NIL) (-174 319821 321370 322929 "D01AGNT" 324978 T D01AGNT (NIL) -7 NIL NIL) (-173 319158 319286 319438 "CYCLOTOM" 319689 T CYCLOTOM (NIL) -7 NIL NIL) (-172 315893 316606 317333 "CYCLES" 318451 T CYCLES (NIL) -7 NIL NIL) (-171 315205 315339 315510 "CVMP" 315754 NIL CVMP (NIL T) -7 NIL NIL) (-170 312986 313244 313619 "CTRIGMNP" 314933 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-169 312497 312686 312785 "CTORCALL" 312907 T CTORCALL (NIL) -8 NIL NIL) (-168 311871 311970 312123 "CSTTOOLS" 312394 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-167 307670 308327 309085 "CRFP" 311183 NIL CRFP (NIL T T) -7 NIL NIL) (-166 306717 306902 307130 "CRAPACK" 307474 NIL CRAPACK (NIL T) -7 NIL NIL) (-165 306101 306202 306406 "CPMATCH" 306593 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-164 305826 305854 305960 "CPIMA" 306067 NIL CPIMA (NIL T T T) -7 NIL NIL) (-163 302190 302862 303580 "COORDSYS" 305161 NIL COORDSYS (NIL T) -7 NIL NIL) (-162 301574 301703 301853 "CONTOUR" 302060 T CONTOUR (NIL) -8 NIL NIL) (-161 297435 299577 300069 "CONTFRAC" 301114 NIL CONTFRAC (NIL T) -8 NIL NIL) (-160 296589 297153 297181 "COMRING" 297186 T COMRING (NIL) -9 NIL 297237) (-159 295670 295947 296131 "COMPPROP" 296425 T COMPPROP (NIL) -8 NIL NIL) (-158 295331 295366 295494 "COMPLPAT" 295629 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-157 285312 295140 295249 "COMPLEX" 295254 NIL COMPLEX (NIL T) -8 NIL NIL) (-156 284948 285005 285112 "COMPLEX2" 285249 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-155 284666 284701 284799 "COMPFACT" 284907 NIL COMPFACT (NIL T T) -7 NIL NIL) (-154 269001 279295 279335 "COMPCAT" 280337 NIL COMPCAT (NIL T) -9 NIL 281730) (-153 258516 261440 265067 "COMPCAT-" 265423 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-152 258247 258275 258377 "COMMUPC" 258482 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-151 258042 258075 258134 "COMMONOP" 258208 T COMMONOP (NIL) -7 NIL NIL) (-150 257625 257793 257880 "COMM" 257975 T COMM (NIL) -8 NIL NIL) (-149 256874 257068 257096 "COMBOPC" 257434 T COMBOPC (NIL) -9 NIL 257609) (-148 255770 255980 256222 "COMBINAT" 256664 NIL COMBINAT (NIL T) -7 NIL NIL) (-147 251968 252541 253181 "COMBF" 255192 NIL COMBF (NIL T T) -7 NIL NIL) (-146 250754 251084 251319 "COLOR" 251753 T COLOR (NIL) -8 NIL NIL) (-145 250394 250441 250566 "CMPLXRT" 250701 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-144 245896 246924 248004 "CLIP" 249334 T CLIP (NIL) -7 NIL NIL) (-143 244234 245004 245242 "CLIF" 245724 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-142 240457 242381 242422 "CLAGG" 243351 NIL CLAGG (NIL T) -9 NIL 243887) (-141 238879 239336 239919 "CLAGG-" 239924 NIL CLAGG- (NIL T T) -8 NIL NIL) (-140 238423 238508 238648 "CINTSLPE" 238788 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-139 235924 236395 236943 "CHVAR" 237951 NIL CHVAR (NIL T T T) -7 NIL NIL) (-138 235147 235711 235739 "CHARZ" 235744 T CHARZ (NIL) -9 NIL 235758) (-137 234901 234941 235019 "CHARPOL" 235101 NIL CHARPOL (NIL T) -7 NIL NIL) (-136 234008 234605 234633 "CHARNZ" 234680 T CHARNZ (NIL) -9 NIL 234735) (-135 232033 232698 233033 "CHAR" 233693 T CHAR (NIL) -8 NIL NIL) (-134 231759 231820 231848 "CFCAT" 231959 T CFCAT (NIL) -9 NIL NIL) (-133 231004 231115 231297 "CDEN" 231643 NIL CDEN (NIL T T T) -7 NIL NIL) (-132 226996 230157 230437 "CCLASS" 230744 T CCLASS (NIL) -8 NIL NIL) (-131 226915 226941 226976 "CATEGORY" 226981 T -10 (NIL) -8 NIL NIL) (-130 221967 222944 223697 "CARTEN" 226218 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-129 221075 221223 221444 "CARTEN2" 221814 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-128 219373 220227 220483 "CARD" 220839 T CARD (NIL) -8 NIL NIL) (-127 218746 219074 219102 "CACHSET" 219234 T CACHSET (NIL) -9 NIL 219311) (-126 218243 218539 218567 "CABMON" 218617 T CABMON (NIL) -9 NIL 218673) (-125 217411 217790 217933 "BYTE" 218120 T BYTE (NIL) -8 NIL NIL) (-124 213359 217358 217392 "BYTEARY" 217397 T BYTEARY (NIL) -8 NIL NIL) (-123 210916 213051 213158 "BTREE" 213285 NIL BTREE (NIL T) -8 NIL NIL) (-122 208414 210564 210686 "BTOURN" 210826 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205833 207886 207927 "BTCAT" 207995 NIL BTCAT (NIL T) -9 NIL 208072) (-120 205500 205580 205729 "BTCAT-" 205734 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200721 204592 204620 "BTAGG" 204876 T BTAGG (NIL) -9 NIL 205055) (-118 200144 200288 200518 "BTAGG-" 200523 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197188 199422 199637 "BSTREE" 199961 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196326 196452 196636 "BRILL" 197044 NIL BRILL (NIL T) -7 NIL NIL) (-115 193028 195055 195096 "BRAGG" 195745 NIL BRAGG (NIL T) -9 NIL 196002) (-114 191557 191963 192518 "BRAGG-" 192523 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184765 190903 191087 "BPADICRT" 191405 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183069 184702 184747 "BPADIC" 184752 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182769 182799 182912 "BOUNDZRO" 183033 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178284 179375 180242 "BOP" 181922 T BOP (NIL) -8 NIL NIL) (-109 175905 176349 176869 "BOP1" 177797 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174540 175245 175463 "BOOLEAN" 175707 T BOOLEAN (NIL) -8 NIL NIL) (-107 173907 174285 174337 "BMODULE" 174342 NIL BMODULE (NIL T T) -9 NIL 174406) (-106 169717 173705 173778 "BITS" 173854 T BITS (NIL) -8 NIL NIL) (-105 168814 169249 169401 "BINFILE" 169585 T BINFILE (NIL) -8 NIL NIL) (-104 168226 168348 168490 "BINDING" 168692 T BINDING (NIL) -8 NIL NIL) (-103 162060 167670 167835 "BINARY" 168081 T BINARY (NIL) -8 NIL NIL) (-102 159888 161316 161357 "BGAGG" 161617 NIL BGAGG (NIL T) -9 NIL 161754) (-101 159719 159751 159842 "BGAGG-" 159847 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158817 159103 159308 "BFUNCT" 159534 T BFUNCT (NIL) -8 NIL NIL) (-99 157518 157696 157981 "BEZOUT" 158641 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154043 156378 156706 "BBTREE" 157221 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153781 153834 153860 "BASTYPE" 153977 T BASTYPE (NIL) -9 NIL NIL) (-96 153636 153665 153735 "BASTYPE-" 153740 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153074 153150 153300 "BALFACT" 153547 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151896 152493 152678 "AUTOMOR" 152919 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151622 151627 151653 "ATTREG" 151658 T ATTREG (NIL) -9 NIL NIL) (-92 149901 150319 150671 "ATTRBUT" 151288 T ATTRBUT (NIL) -8 NIL NIL) (-91 149437 149550 149576 "ATRIG" 149777 T ATRIG (NIL) -9 NIL NIL) (-90 149246 149287 149374 "ATRIG-" 149379 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147443 149022 149110 "ASTACK" 149189 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145948 146245 146610 "ASSOCEQ" 147125 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144980 145607 145731 "ASP9" 145855 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144744 144928 144967 "ASP8" 144972 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143613 144349 144491 "ASP80" 144633 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142512 143248 143380 "ASP7" 143512 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141466 142189 142307 "ASP78" 142425 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140435 141146 141263 "ASP77" 141380 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139347 140073 140204 "ASP74" 140335 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138247 138982 139114 "ASP73" 139246 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137202 137924 138042 "ASP6" 138160 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136150 136879 136997 "ASP55" 137115 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135100 135824 135943 "ASP50" 136062 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134188 134801 134911 "ASP4" 135021 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133276 133889 133999 "ASP49" 134109 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132061 132815 132983 "ASP42" 133165 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130838 131594 131764 "ASP41" 131948 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129788 130515 130633 "ASP35" 130751 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129553 129736 129775 "ASP34" 129780 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129290 129357 129433 "ASP33" 129508 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128185 128925 129057 "ASP31" 129189 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127950 128133 128172 "ASP30" 128177 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127685 127754 127830 "ASP29" 127905 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127450 127633 127672 "ASP28" 127677 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127215 127398 127437 "ASP27" 127442 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126299 126913 127024 "ASP24" 127135 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125215 125940 126070 "ASP20" 126200 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124303 124916 125026 "ASP1" 125136 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123247 123977 124096 "ASP19" 124215 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122984 123051 123127 "ASP12" 123202 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121836 122583 122727 "ASP10" 122871 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119735 121680 121771 "ARRAY2" 121776 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115551 119383 119497 "ARRAY1" 119652 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114583 114756 114977 "ARRAY12" 115374 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108943 110814 110889 "ARR2CAT" 113519 NIL ARR2CAT (NIL T T T) -9 NIL 114277) (-54 106377 107121 108075 "ARR2CAT-" 108080 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105137 105287 105590 "APPRULE" 106215 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104790 104838 104956 "APPLYORE" 105083 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103764 104055 104250 "ANY" 104613 T ANY (NIL) -8 NIL NIL) (-50 103042 103165 103322 "ANY1" 103638 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100574 101492 101817 "ANTISYM" 102767 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100089 100278 100375 "ANON" 100495 T ANON (NIL) -8 NIL NIL) (-47 94166 98634 99085 "AN" 99656 T AN (NIL) -8 NIL NIL) (-46 90520 91918 91968 "AMR" 92707 NIL AMR (NIL T T) -9 NIL 93306) (-45 89633 89854 90216 "AMR-" 90221 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74183 89550 89611 "ALIST" 89616 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71020 73777 73946 "ALGSC" 74101 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67576 68130 68737 "ALGPKG" 70460 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66853 66954 67138 "ALGMFACT" 67462 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63283 63937 "ALGMANIP" 66377 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
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((*1 *2 *2) @@ -7864,59 +13783,52 @@ ((*1 *2 *2) (-12 (-4 *3 (-37 (-385 (-525)))) (-4 *4 (-1134 *3)) (-5 *1 (-258 *3 *4 *2 *5)) (-4 *2 (-1157 *3 *4)) (-4 *5 (-916 *4)))) - ((*1 *1 *1) - (-12 (-5 *1 (-317 *2 *3 *4)) (-14 *2 (-592 (-1092))) - (-14 *3 (-592 (-1092))) (-4 *4 (-365)))) ((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1078 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-37 (-385 (-525)))) - (-5 *1 (-1079 *3)))) - ((*1 *1 *1) (-4 *1 (-1117)))) -(((*1 *2 *1) (-12 (-4 *1 (-942 *3)) (-4 *3 (-1128)) (-5 *2 (-592 *3))))) -(((*1 *1 *1) (-12 (-4 *1 (-154 *2)) (-4 *2 (-160)) (-4 *2 (-986)))) - ((*1 *1 *1) - (-12 (-5 *1 (-317 *2 *3 *4)) (-14 *2 (-592 (-1092))) - (-14 *3 (-592 (-1092))) (-4 *4 (-365)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-409 *3 *2)) - (-4 *2 (-408 *3)))) - ((*1 *2 *1) (-12 (-4 *1 (-739 *2)) (-4 *2 (-160)) (-4 *2 (-986)))) - ((*1 *1 *1) (-4 *1 (-787))) - ((*1 *2 *1) (-12 (-4 *1 (-929 *2)) (-4 *2 (-160)) (-4 *2 (-986)))) 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(|:| |under| *1) (|:| -1340 *1) (|:| |upper| *1))) + (-4 *1 (-909 *4 *5 *3 *6))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) (-4 *2 (-13 (-408 *3) (-934))))) @@ -7926,65 +13838,53 @@ ((*1 *2 *2) (-12 (-4 *3 (-37 (-385 (-525)))) (-4 *4 (-1134 *3)) (-5 *1 (-258 *3 *4 *2 *5)) (-4 *2 (-1157 *3 *4)) (-4 *5 (-916 *4)))) - ((*1 *1 *2) (-12 (-5 *1 (-309 *2)) (-4 *2 (-789)))) - ((*1 *1 *1) - (-12 (-5 *1 (-317 *2 *3 *4)) (-14 *2 (-592 (-1092))) - (-14 *3 (-592 (-1092))) (-4 *4 (-365)))) + ((*1 *1 *1) (-4 *1 (-466))) ((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1078 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-37 (-385 (-525)))) - (-5 *1 (-1079 *3)))) - ((*1 *1 *1) (-4 *1 (-1117)))) -(((*1 *2 *3) (-12 (-5 *3 (-1075)) (-5 *2 (-1179)) (-5 *1 (-799)))) - ((*1 *2 *3) (-12 (-5 *3 (-798)) (-5 *2 (-1179)) (-5 *1 (-799)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1075)) (-5 *4 (-798)) (-5 *2 (-1179)) (-5 *1 (-799)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 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(-1092))) - (-14 *3 (-592 (-1092))) (-4 *4 (-365)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-804 *3)) (-5 *2 (-525)))) - ((*1 *1 *1) (-4 *1 (-934))) - ((*1 *1 *2) (-12 (-5 *2 (-525)) (-4 *1 (-944)))) - ((*1 *1 *2) (-12 (-5 *2 (-385 (-525))) (-4 *1 (-944)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-944)) (-5 *2 (-856)))) - ((*1 *1 *1) (-4 *1 (-944)))) -(((*1 *1 *1 *1 *1) (-4 *1 (-510)))) + (-12 (-5 *2 (-1088 (-525))) (-5 *1 (-877)) (-5 *3 (-525))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-127)) (-5 *3 (-713)) (-5 *2 (-1179))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-713)) (-5 *2 (-1 (-357))) (-5 *1 (-970))))) +(((*1 *2 *3) + (-12 (-5 *3 (-525)) (|has| *1 (-6 -4250)) (-4 *1 (-382)) + (-5 *2 (-856))))) +(((*1 *2 *3 *3 *4) + (-12 (-4 *5 (-429)) (-4 *6 (-735)) (-4 *7 (-789)) + (-4 *3 (-991 *5 *6 *7)) + (-5 *2 (-592 (-2 (|:| |val| *3) (|:| -1285 *4)))) + (-5 *1 (-997 *5 *6 *7 *3 *4)) (-4 *4 (-996 *5 *6 *7 *3))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-108)) (-4 *4 (-13 (-341) (-787))) (-5 *2 (-396 *3)) + (-5 *1 (-167 *4 *3)) (-4 *3 (-1150 (-157 *4))))) + ((*1 *2 *3 *4) + (-12 (-4 *4 (-13 (-341) (-787))) (-5 *2 (-396 *3)) + (-5 *1 (-167 *4 *3)) (-4 *3 (-1150 (-157 *4)))))) +(((*1 *2 *2) + (-12 (-4 *2 (-160)) (-4 *2 (-977)) (-5 *1 (-657 *2 *3)) + (-4 *3 (-594 *2)))) + ((*1 *2 *2) (-12 (-5 *1 (-776 *2)) (-4 *2 (-160)) (-4 *2 (-977))))) +(((*1 *2 *2) (-12 (-5 *2 (-357)) (-5 *1 (-1176)))) + ((*1 *2) (-12 (-5 *2 (-357)) (-5 *1 (-1176))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-789) (-517))) (-5 *1 (-255 *3 *2)) (-4 *2 (-13 (-408 *3) (-934))))) @@ -7994,1456 +13894,336 @@ ((*1 *2 *2) (-12 (-4 *3 (-37 (-385 (-525)))) (-4 *4 (-1134 *3)) (-5 *1 (-258 *3 *4 *2 *5)) (-4 *2 (-1157 *3 *4)) (-4 *5 (-916 *4)))) - ((*1 *1 *2) (-12 (-5 *1 (-309 *2)) (-4 *2 (-789)))) - ((*1 *1 *1) - (-12 (-5 *1 (-317 *2 *3 *4)) (-14 *2 (-592 (-1092))) - (-14 *3 (-592 (-1092))) (-4 *4 (-365)))) + ((*1 *1 *1) (-4 *1 (-466))) ((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-37 (-385 (-525)))) (-5 *1 (-1078 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-37 (-385 (-525)))) - (-5 *1 (-1079 *3)))) - ((*1 *1 *1) (-4 *1 (-1117)))) + (-5 *1 (-1079 *3))))) (((*1 *2 *1) - (|partial| -12 (-5 *2 (-1 (-501) (-592 (-501)))) (-5 *1 (-110)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-501) (-592 (-501)))) (-5 *1 (-110))))) -(((*1 *1 *2 *2 *2) - (-12 (-5 *1 (-207 *2)) (-4 *2 (-13 (-341) (-1114))))) - ((*1 *1 *1 *2) (-12 (-5 *1 (-661 *2)) (-4 *2 (-341)))) - ((*1 *1 *2) (-12 (-5 *1 (-661 *2)) (-4 *2 (-341)))) - ((*1 *2 *1 *3 *4 *4) - (-12 (-5 *3 (-856)) (-5 *4 (-357)) (-5 *2 (-1179)) (-5 *1 (-1175))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-735)) (-4 *6 (-789)) (-4 *7 (-517)) - (-4 *3 (-884 *7 *5 *6)) - (-5 *2 - (-2 (|:| -4193 (-713)) (|:| -3244 *3) (|:| |radicand| (-592 *3)))) - (-5 *1 (-888 *5 *6 *7 *3 *8)) (-5 *4 (-713)) - (-4 *8 - (-13 (-341) - (-10 -8 (-15 -3114 (*3 $)) (-15 -3123 (*3 $)) (-15 -1217 ($ *3)))))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1147 *5 *4)) (-4 *4 (-429)) (-4 *4 (-762)) - (-14 *5 (-1092)) (-5 *2 (-525)) (-5 *1 (-1034 *4 *5))))) -(((*1 *1 *1 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(|:| |c1| (-385 *5)) + (|:| |c2| (-385 *5)) (|:| |deg| (-713)))) + (-5 *1 (-139 *4 *5 *3)) (-4 *3 (-1150 (-385 *5)))))) +(((*1 *2 *2) + (-12 (-5 *2 (-592 *6)) (-4 *6 (-991 *3 *4 *5)) (-4 *3 (-517)) + (-4 *4 (-735)) (-4 *5 (-789)) (-5 *1 (-910 *3 *4 *5 *6))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-632 *8)) (-4 *8 (-884 *5 *7 *6)) (-4 *5 (-13 (-286) (-138))) (-4 *6 (-13 (-789) (-567 (-1092)))) @@ -12632,7 +14653,7 @@ (|:| |wcond| (-592 (-887 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1174 (-385 (-887 *5)))) - (|:| -3094 (-592 (-1174 (-385 (-887 *5)))))))))) + (|:| -2103 (-592 (-1174 (-385 (-887 *5)))))))))) (-5 *1 (-859 *5 *6 *7 *8)) (-5 *4 (-592 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-632 *8)) (-5 *4 (-592 (-1092))) (-4 *8 (-884 *5 *7 *6)) @@ -12644,7 +14665,7 @@ (|:| |wcond| (-592 (-887 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1174 (-385 (-887 *5)))) - (|:| -3094 (-592 (-1174 (-385 (-887 *5)))))))))) + (|:| -2103 (-592 (-1174 (-385 (-887 *5)))))))))) (-5 *1 (-859 *5 *6 *7 *8)))) ((*1 *2 *3) (-12 (-5 *3 (-632 *7)) (-4 *7 (-884 *4 *6 *5)) @@ -12656,7 +14677,7 @@ (|:| |wcond| (-592 (-887 *4))) (|:| |bsoln| (-2 (|:| |partsol| (-1174 (-385 (-887 *4)))) - (|:| -3094 (-592 (-1174 (-385 (-887 *4)))))))))) + (|:| -2103 (-592 (-1174 (-385 (-887 *4)))))))))) (-5 *1 (-859 *4 *5 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-632 *9)) (-5 *5 (-856)) (-4 *9 (-884 *6 *8 *7)) @@ -12668,7 +14689,7 @@ (|:| |wcond| (-592 (-887 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1174 (-385 (-887 *6)))) - (|:| -3094 (-592 (-1174 (-385 (-887 *6)))))))))) + (|:| -2103 (-592 (-1174 (-385 (-887 *6)))))))))) (-5 *1 (-859 *6 *7 *8 *9)) (-5 *4 (-592 *9)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-632 *9)) (-5 *4 (-592 (-1092))) (-5 *5 (-856)) @@ -12680,7 +14701,7 @@ (|:| |wcond| (-592 (-887 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1174 (-385 (-887 *6)))) - (|:| -3094 (-592 (-1174 (-385 (-887 *6)))))))))) + (|:| -2103 (-592 (-1174 (-385 (-887 *6)))))))))) (-5 *1 (-859 *6 *7 *8 *9)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-632 *8)) (-5 *4 (-856)) (-4 *8 (-884 *5 *7 *6)) @@ -12692,7 +14713,7 @@ (|:| |wcond| (-592 (-887 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1174 (-385 (-887 *5)))) - (|:| -3094 (-592 (-1174 (-385 (-887 *5)))))))))) + (|:| -2103 (-592 (-1174 (-385 (-887 *5)))))))))) (-5 *1 (-859 *5 *6 *7 *8)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-632 *9)) (-5 *4 (-592 *9)) (-5 *5 (-1075)) @@ -12723,96 +14744,51 @@ (-4 *9 (-884 *6 *8 *7)) (-4 *6 (-13 (-286) (-138))) (-4 *7 (-13 (-789) (-567 (-1092)))) (-4 *8 (-735)) (-5 *2 (-525)) (-5 *1 (-859 *6 *7 *8 *9))))) -(((*1 *2 *1) (-12 (-4 *1 (-382)) (-5 *2 (-525)))) - ((*1 *2 *1) (-12 (-5 *2 (-525)) (-5 *1 (-641))))) -(((*1 *2 *2) (-12 (-5 *2 (-205)) (-5 *1 (-206)))) - ((*1 *2 *2) (-12 (-5 *2 (-157 (-205))) (-5 *1 (-206))))) -(((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1092)) (-5 *1 (-620 *3)) (-4 *3 (-1020))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-341)) (-5 *1 (-264 *3 *2)) (-4 *2 (-1165 *3))))) -(((*1 *1 *1) - (-12 (|has| *1 (-6 -4258)) (-4 *1 (-142 *2)) (-4 *2 (-1128)) - (-4 *2 (-1020))))) -(((*1 *2 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98754) (-3964 . 98338) + (-3965 . 98283) (-3966 . 98206) (-3967 . 97960) (-3968 . 97875) + (-3969 . 97820) (-3970 . 97768) (-3971 . 97483) (-3972 . 97385) + (-3973 . 97212) (-3974 . 97012) (-3975 . 96438) (-3976 . 95884) + (-3977 . 95817) (-3978 . 95714) (-3979 . 95509) (-3980 . 95341) + (-3981 . 95094) (-3982 . 94983) (-3983 . 94862) (-3984 . 94703) + (-3985 . 94601) (-3986 . 94341) (-3987 . 94205) (-3988 . 94057) + (-3989 . 93953) (-3990 . 93621) (-3991 . 93566) (-3992 . 93353) + (-3993 . 93155) (-3994 . 93081) (-3995 . 93032) (-3996 . 92977) + (-3997 . 92761) (-3998 . 92501) (-3999 . 91632) (-4000 . 89385) + (-4001 . 89121) (-4002 . 88882) (-4003 . 88609) (-4004 . 88292) + (-4005 . 88237) (-4006 . 88186) (-4007 . 87672) (-4008 . 87424) + (-4009 . 87233) (-4010 . 86824) (-4011 . 86718) (-4012 . 86529) + (-4013 . 86350) (-4014 . 86130) (-4015 . 86056) (-4016 . 85620) + (-4017 . 85567) (-4018 . 85480) (-4019 . 85400) (-4020 . 85293) + (-4021 . 85241) (-4022 . 85145) (-4023 . 85066) (-4024 . 84938) + (-4025 . 84662) (-4026 . 84585) (-4027 . 84487) (-4028 . 84226) + (-4029 . 83711) (-4030 . 83531) (-4031 . 83378) (-4032 . 83232) + (-4033 . 83164) (-4034 . 83108) (-4035 . 83021) (-4036 . 82924) + (-4037 . 82789) (-4038 . 82438) (-4039 . 81990) (-4040 . 81581) + (-4041 . 81343) (-4042 . 81229) (-4043 . 81088) (-4044 . 80912) + (-4045 . 80881) (-4046 . 80688) (-4047 . 80594) (-4048 . 80493) + (-4049 . 80392) (-4050 . 80325) (-4051 . 80209) (-4052 . 80086) + (-4053 . 80020) (-4054 . 79590) (-4055 . 79201) (-4056 . 79137) + (-4057 . 78933) (-4058 . 78849) (-4059 . 78403) (-4060 . 78078) + (-4061 . 77963) (-4062 . 77815) (-4063 . 77732) (-4064 . 77359) + (-4065 . 77044) (-4066 . 76345) (-4067 . 76292) (-4068 . 76219) + (-4069 . 76159) (-4070 . 75650) (-4071 . 75551) (-4072 . 75386) + (-4073 . 75149) (-4074 . 75062) (-4075 . 74851) (-4076 . 74251) + (-4077 . 74178) (-4078 . 74010) (-4079 . 73763) (-4080 . 73086) + (-4081 . 72745) (-4082 . 72673) (-4083 . 72566) (-4084 . 72486) + (-4085 . 72343) (-4086 . 72270) (-4087 . 72184) (-4088 . 72088) + (-4089 . 72005) (-4090 . 71912) (-4091 . 71753) (-4092 . 71643) + (-4093 . 71531) (-4094 . 71412) (-4095 . 71305) (-4096 . 70926) + (-4097 . 70819) (-4098 . 70689) (-4099 . 70606) (-4100 . 47571) + (-4101 . 47478) (-4102 . 47346) (-4103 . 47280) (-4104 . 47081) + (-4105 . 41764) (-4106 . 41499) (-4107 . 41308) (-4108 . 41204) + (-4109 . 41120) (-4110 . 40789) (-4111 . 40760) (-4112 . 40134) + (-4113 . 38979) (-4114 . 36227) (-4115 . 35526) (-4116 . 35473) + (-4117 . 35343) (-4118 . 35273) (-4119 . 35166) (-4120 . 35083) + (-4121 . 35013) (-4122 . 34915) (-4123 . 34856) (-4124 . 34747) + (-4125 . 34523) (-4126 . 34452) (-4127 . 34077) (-4128 . 33406) + (-4129 . 31837) (-4130 . 31691) (-4131 . 31604) (-4132 . 31423) + (-4133 . 31323) (-4134 . 31249) (-4135 . 31066) (-4136 . 30963) + (-4137 . 30589) (-4138 . 30492) (-4139 . 30225) (-4140 . 30072) + (-4141 . 29985) (-4142 . 29881) (-4143 . 29176) (-4144 . 29096) + (-4145 . 28719) (-4146 . 28666) (-4147 . 28523) (-4148 . 28489) + (-4149 . 28361) (-4150 . 27952) (-4151 . 27826) (-4152 . 27519) + (-4153 . 27457) (-4154 . 27356) (-4155 . 25505) (-4156 . 25434) + (-4157 . 25348) (-4158 . 25277) (-4159 . 24734) (-4160 . 24347) + (-4161 . 24252) (-4162 . 24158) (-4163 . 23809) (-4164 . 19747) + (-4165 . 19695) (-4166 . 19244) (-4167 . 19157) (-4168 . 19126) + (-4169 . 17725) (-4170 . 17547) (-4171 . 16909) (-4172 . 16537) + (-4173 . 16321) (-4174 . 16212) (-4175 . 16107) (-4176 . 15981) + (-4177 . 15684) (-4178 . 15254) (-4179 . 15202) (-4180 . 15044) + (-4181 . 14805) (-4182 . 14698) (-4183 . 14528) (-4184 . 14287) + (-4185 . 14200) (-4186 . 14082) (-4187 . 13911) (-4188 . 13746) + (-4189 . 13634) (-4190 . 13273) (-4191 . 13176) (-4192 . 13062) + (-4193 . 12978) (-4194 . 12921) (-4195 . 12477) (-4196 . 12259) + (-4197 . 12036) (-4198 . 11677) (-4199 . 11547) (-4200 . 11451) + (-4201 . 5943) (-4202 . 5843) (-4203 . 5703) (-4204 . 5578) + (-4205 . 4835) (-4206 . 4694) (-4207 . 4617) (-4208 . 4513) + (-4209 . 4217) (-4210 . 4112) (-4211 . 3724) (-4212 . 3696) + (-4213 . 3566) (-4214 . 3511) (-4215 . 3458) (-4216 . 3363) + (-4217 . 3244) (-4218 . 3082) (-4219 . 3011) (-4220 . 2558) + (-4221 . 2454) (-4222 . 2390) (-4223 . 2359) (-4224 . 2256) + (-4225 . 2161) (-4226 . 1987) (-4227 . 1785) (-4228 . 1511) + (-4229 . 1374) (-4230 . 1289) (-4231 . 1201) (-4232 . 1058) + (-4233 . 711) (-4234 . 453) (-4235 . 358) (-4236 . 274) (-4237 . 195) + (-4238 . 115) (-4239 . 30))
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