diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 1342 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1130 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1285 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8416 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 26270 |
5 files changed, 19219 insertions, 19224 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 61e51a5f..aa5e867a 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2243771 . 3429209006) +(2242565 . 3429259028) (-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."))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . 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}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4267 . T) (-4265 . T) (-4264 . T) ((-4272 "*") . T) (-4263 . T) (-4268 . T) (-4262 . T) (-4087 . T)) +((-4266 . T) (-4264 . T) (-4263 . T) ((-4271 "*") . T) (-4262 . T) (-4267 . T) (-4261 . T) (-4100 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -1345) +(-31 R -1334) ((|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 -975) (QUOTE (-530))))) (-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 -4270))) +((|HasAttribute| |#1| (QUOTE -4269))) (-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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-4087 . T)) +((-4100 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4270 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4270 . T) (-4100 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#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."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . 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 -1345 UP UPUP -2113) +(-39 -1334 UP UPUP -4076) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4263 |has| (-388 |#2|) (-344)) (-4268 |has| (-388 |#2|) (-344)) (-4262 |has| (-388 |#2|) (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-388 |#2|) (QUOTE (-138))) (|HasCategory| (-388 |#2|) (QUOTE (-140))) (|HasCategory| (-388 |#2|) (QUOTE (-330))) (-1476 (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-349))) (-1476 (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (-1476 (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-330))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1476 (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344))))) -(-40 R -1345) +((-4262 |has| (-388 |#2|) (-344)) (-4267 |has| (-388 |#2|) (-344)) (-4261 |has| (-388 |#2|) (-344)) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-388 |#2|) (QUOTE (-138))) (|HasCategory| (-388 |#2|) (QUOTE (-140))) (|HasCategory| (-388 |#2|) (QUOTE (-330))) (-1461 (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-349))) (-1461 (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (-1461 (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-330))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1461 (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344))))) +(-40 R -1334) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) @@ -102,23 +102,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-289)))) (-43 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4267 |has| |#1| (-522)) (-4265 . T) (-4264 . T)) +((-4266 |has| |#1| (-522)) (-4264 . T) (-4263 . T)) ((|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-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."))) -((-4270 . T) (-4271 . T)) -((-1476 (-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|))))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-1461 (-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|))))))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-795))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-344)))) (-46 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-47) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| $ (QUOTE (-984))) (|HasCategory| $ (LIST (QUOTE -975) (QUOTE (-530))))) (-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}."))) -((-4267 . T)) +((-4266 . 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 -1345) +(-53 |Base| R -1334) ((|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"))) -((-4270 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4270 . T) (-4100 . 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}"))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-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}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) -(-59 -3901) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +(-59 -3907) ((|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 -3901) +(-60 -3907) ((|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 -3901) +(-61 -3907) ((|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 -3901) +(-62 -3907) ((|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 -3901) +(-63 -3907) ((|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 -3901) +(-64 -3907) ((|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 -3901) +(-65 -3907) ((|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 -3901) +(-66 -3907) ((|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 -3901) +(-67 -3907) ((|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 -3901) +(-68 -3907) ((|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 -3901) +(-69 -3907) ((|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 -3901) +(-70 -3907) ((|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 -3901) +(-71 -3907) ((|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 -3901) +(-72 -3907) ((|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 -3901) +(-75 -3907) ((|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 -3901) +(-76 -3907) ((|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 -3901) +(-77 -3907) ((|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 -3901) +(-78 -3907) ((|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 -3901) +(-79 -3907) ((|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 -3901) +(-80 -3907) ((|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 -3901) +(-81 -3907) ((|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 -3901) +(-82 -3907) ((|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 -3901) +(-83 -3907) ((|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 -3901) +(-84 -3907) ((|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 -3901) +(-85 -3907) ((|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 -3901) +(-86 -3907) ((|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 -3901) +(-87 -3907) ((|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 (-344)))) (-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}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-90 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -306,15 +306,15 @@ NIL NIL (-94) ((|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\"."))) -((-4270 . T)) +((-4269 . T)) NIL (-95) ((|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."))) -((-4270 . T) ((-4272 "*") . T) (-4271 . T) (-4267 . T) (-4265 . T) (-4264 . T) (-4263 . T) (-4268 . T) (-4262 . T) (-4261 . T) (-4260 . T) (-4259 . T) (-4258 . T) (-4266 . T) (-4269 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4257 . T)) +((-4269 . T) ((-4271 "*") . T) (-4270 . T) (-4266 . T) (-4264 . T) (-4263 . T) (-4262 . T) (-4267 . T) (-4261 . T) (-4260 . T) (-4259 . T) (-4258 . T) (-4257 . T) (-4265 . T) (-4268 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4256 . T)) NIL (-96 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}."))) -((-4267 . T)) +((-4266 . T)) NIL (-97 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}."))) @@ -330,15 +330,15 @@ NIL NIL (-100 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}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-101 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 (-4272 "*")))) +((|HasAttribute| |#1| (QUOTE (-4271 "*")))) (-102) ((|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"))) -((-4270 . T)) +((-4269 . T)) NIL (-103 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."))) @@ -346,12 +346,12 @@ NIL NIL (-104 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."))) -((-4271 . T) (-4087 . T)) +((-4270 . T) (-4100 . T)) NIL (-105) ((|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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1476 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1461 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) (-106) ((|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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -362,11 +362,11 @@ NIL NIL (-108) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4271 . T) (-4270 . T)) +((-4270 . T) (-4269 . T)) ((-12 (|HasCategory| (-110) (QUOTE (-1027))) (|HasCategory| (-110) (LIST (QUOTE -291) (QUOTE (-110))))) (|HasCategory| (-110) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-110) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-110) (QUOTE (-1027))) (|HasCategory| (-110) (LIST (QUOTE -571) (QUOTE (-804))))) (-109 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}"))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) NIL (-110) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -380,25 +380,25 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-113 -1345 UP) +(-113 -1334 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 (-114 |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}."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-115 |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}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-114 |#1|) (QUOTE (-850))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-114 |#1|) (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-140))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-114 |#1|) (QUOTE (-960))) (|HasCategory| (-114 |#1|) (QUOTE (-768))) (-1476 (|HasCategory| (-114 |#1|) (QUOTE (-768))) (|HasCategory| (-114 |#1|) (QUOTE (-795)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (QUOTE (-1075))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (QUOTE (-216))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -291) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -268) (LIST (QUOTE -114) (|devaluate| |#1|)) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (QUOTE (-289))) (|HasCategory| (-114 |#1|) (QUOTE (-515))) (|HasCategory| (-114 |#1|) (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-850)))) (|HasCategory| (-114 |#1|) (QUOTE (-138))))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-114 |#1|) (QUOTE (-850))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-114 |#1|) (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-140))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-114 |#1|) (QUOTE (-960))) (|HasCategory| (-114 |#1|) (QUOTE (-768))) (-1461 (|HasCategory| (-114 |#1|) (QUOTE (-768))) (|HasCategory| (-114 |#1|) (QUOTE (-795)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (QUOTE (-1075))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-114 |#1|) (QUOTE (-216))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -291) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (LIST (QUOTE -268) (LIST (QUOTE -114) (|devaluate| |#1|)) (LIST (QUOTE -114) (|devaluate| |#1|)))) (|HasCategory| (-114 |#1|) (QUOTE (-289))) (|HasCategory| (-114 |#1|) (QUOTE (-515))) (|HasCategory| (-114 |#1|) (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-114 |#1|) (QUOTE (-850)))) (|HasCategory| (-114 |#1|) (QUOTE (-138))))) (-116 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4271))) +((|HasAttribute| |#1| (QUOTE -4270))) (-117 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-4087 . T)) +((-4100 . T)) NIL (-118 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."))) @@ -406,15 +406,15 @@ NIL NIL (-119 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"))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-120 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-121) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-122 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -422,20 +422,20 @@ NIL NIL (-123 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4270 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4270 . T) (-4100 . T)) NIL (-124 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-125 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."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-126) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127)))))) (-1476 (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (|HasCategory| (-127) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-127) (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-127) (QUOTE (-1027)))) (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-127) (QUOTE (-1027))) (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (|HasCategory| (-127) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127)))))) (-1461 (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (|HasCategory| (-127) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-127) (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-127) (QUOTE (-1027)))) (|HasCategory| (-127) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-127) (QUOTE (-1027))) (-12 (|HasCategory| (-127) (QUOTE (-1027))) (|HasCategory| (-127) (LIST (QUOTE -291) (QUOTE (-127))))) (|HasCategory| (-127) (LIST (QUOTE -571) (QUOTE (-804))))) (-127) ((|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 @@ -450,13 +450,13 @@ NIL NIL (-130) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4272 "*") . T)) +(((-4271 "*") . T)) NIL -(-131 |minix| -3024 S T$) +(-131 |minix| -3148 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-132 |minix| -3024 R) +(-132 |minix| -3148 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -466,8 +466,8 @@ NIL NIL (-134) ((|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}."))) -((-4270 . T) (-4260 . T) (-4271 . T)) -((-1476 (-12 (|HasCategory| (-137) (QUOTE (-349))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-137) (QUOTE (-349))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4259 . T) (-4270 . T)) +((-1461 (-12 (|HasCategory| (-137) (QUOTE (-349))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-137) (QUOTE (-349))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) (-135 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 @@ -482,7 +482,7 @@ NIL NIL (-138) ((|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."))) -((-4267 . T)) +((-4266 . T)) NIL (-139 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}."))) @@ -490,9 +490,9 @@ NIL NIL (-140) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4267 . T)) +((-4266 . T)) NIL -(-141 -1345 UP UPUP) +(-141 -1334 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 @@ -503,14 +503,14 @@ NIL (-143 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 -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasAttribute| |#1| (QUOTE -4270))) +((|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasAttribute| |#1| (QUOTE -4269))) (-144 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."))) -((-4087 . T)) +((-4100 . T)) NIL (-145 |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."))) -((-4265 . T) (-4264 . T) (-4267 . T)) +((-4264 . T) (-4263 . T) (-4266 . T)) NIL (-146) ((|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."))) @@ -524,7 +524,7 @@ 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 -(-149 R -1345) +(-149 R -1334) ((|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 @@ -551,10 +551,10 @@ NIL (-155 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 (-850))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-941))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-993))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-344))) (|HasAttribute| |#2| (QUOTE -4266)) (|HasAttribute| |#2| (QUOTE -4269)) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-795)))) +((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-941))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-993))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-344))) (|HasAttribute| |#2| (QUOTE -4265)) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-795)))) (-156 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})"))) -((-4263 -1476 (|has| |#1| (-522)) (-12 (|has| |#1| (-289)) (|has| |#1| (-850)))) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4266 |has| |#1| (-6 -4266)) (-4269 |has| |#1| (-6 -4269)) (-4136 . T) (-4087 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 -1461 (|has| |#1| (-522)) (-12 (|has| |#1| (-289)) (|has| |#1| (-850)))) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) (-4265 |has| |#1| (-6 -4265)) (-4268 |has| |#1| (-6 -4268)) (-4146 . T) (-4100 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-157 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."))) @@ -566,8 +566,8 @@ NIL NIL (-159 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}."))) -((-4263 -1476 (|has| |#1| (-522)) (-12 (|has| |#1| (-289)) (|has| |#1| (-850)))) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4266 |has| |#1| (-6 -4266)) (-4269 |has| |#1| (-6 -4269)) (-4136 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-216))) (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-776)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-795)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-960)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-1121)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-850))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-850)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-850))))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| |#1| (QUOTE (-993))) (-12 (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-515))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-216))) (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasAttribute| |#1| (QUOTE -4266)) (|HasAttribute| |#1| (QUOTE -4269)) (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-330))))) +((-4262 -1461 (|has| |#1| (-522)) (-12 (|has| |#1| (-289)) (|has| |#1| (-850)))) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) (-4265 |has| |#1| (-6 -4265)) (-4268 |has| |#1| (-6 -4268)) (-4146 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1461 (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-216))) (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-776)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-795)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-960)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-1121)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-850))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-850)))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-850))))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (QUOTE (-522)))) (-1461 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| |#1| (QUOTE (-993))) (-12 (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-515))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-216))) (-12 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasAttribute| |#1| (QUOTE -4265)) (|HasAttribute| |#1| (QUOTE -4268)) (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-330))))) (-160 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 @@ -578,11 +578,11 @@ NIL NIL (-162) ((|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."))) -(((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-163 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}."))) -(((-4272 "*") . T) (-4263 . T) (-4268 . T) (-4262 . T) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") . T) (-4262 . T) (-4267 . T) (-4261 . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-164) ((|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}."))) @@ -616,7 +616,7 @@ 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|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-172 R -1345) +(-172 R -1334) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -724,19 +724,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|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 -(-199 -1345 UP UPUP R) +(-199 -1334 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 -(-200 -1345 FP) +(-200 -1334 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 (-201) ((|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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1476 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) -(-202 R -1345) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1461 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) +(-202 R -1334) ((|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 @@ -750,19 +750,19 @@ NIL NIL (-205 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}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-206 |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}."))) -((-4267 . T)) +((-4266 . T)) NIL -(-207 R -1345) +(-207 R -1334) ((|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 (-208) ((|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}."))) -((-4125 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4136 . T) (-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-209) ((|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)}.}"))) @@ -770,15 +770,15 @@ NIL NIL (-210 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}"))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4271 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-211 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 (-212 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."))) -((-4271 . T) (-4087 . T)) +((-4270 . T) (-4100 . T)) NIL (-213 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}."))) @@ -786,7 +786,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-214 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}."))) -((-4267 . T)) +((-4266 . T)) NIL (-215 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -794,87 +794,87 @@ NIL NIL (-216) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4267 . T)) +((-4266 . T)) NIL (-217 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4270))) +((|HasAttribute| |#1| (QUOTE -4269))) (-218 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}."))) -((-4271 . T) (-4087 . T)) +((-4270 . T) (-4100 . T)) NIL (-219) ((|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 -(-220 S -3024 R) +(-220 S -3148 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 (-344))) (|HasCategory| |#3| (QUOTE (-741))) (|HasCategory| |#3| (QUOTE (-793))) (|HasAttribute| |#3| (QUOTE -4267)) (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#3| (QUOTE (-675))) (|HasCategory| |#3| (QUOTE (-128))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (QUOTE (-1027)))) -(-221 -3024 R) +((|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (QUOTE (-741))) (|HasCategory| |#3| (QUOTE (-793))) (|HasAttribute| |#3| (QUOTE -4266)) (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#3| (QUOTE (-675))) (|HasCategory| |#3| (QUOTE (-128))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (QUOTE (-1027)))) +(-221 -3148 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"))) -((-4264 |has| |#2| (-984)) (-4265 |has| |#2| (-984)) (-4267 |has| |#2| (-6 -4267)) ((-4272 "*") |has| |#2| (-162)) (-4270 . T) (-4087 . T)) +((-4263 |has| |#2| (-984)) (-4264 |has| |#2| (-984)) (-4266 |has| |#2| (-6 -4266)) ((-4271 "*") |has| |#2| (-162)) (-4269 . T) (-4100 . T)) NIL -(-222 -3024 A B) +(-222 -3148 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 -(-223 -3024 R) +(-223 -3148 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."))) -((-4264 |has| |#2| (-984)) (-4265 |has| |#2| (-984)) (-4267 |has| |#2| (-6 -4267)) ((-4272 "*") |has| |#2| (-162)) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-128))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-675))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (|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}.") 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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 (-216)))) (-235 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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) NIL (-236 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}."))) -((-4270 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4270 . T) (-4100 . T)) NIL (-237) ((|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."))) @@ -914,8 +914,8 @@ NIL NIL (-246 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"))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#3| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#3| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#3| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#3| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-850))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#3| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#3| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#3| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#3| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4267)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-247 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 @@ -960,11 +960,11 @@ 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 -(-258 R -1345) +(-258 R -1334) ((|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 -(-259 R -1345) +(-259 R -1334) ((|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 @@ -986,7 +986,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027)))) (-264 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}."))) -((-4271 . T) (-4087 . T)) +((-4270 . T) (-4100 . T)) NIL (-265 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}."))) @@ -1007,18 +1007,18 @@ NIL (-269 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 -4271))) +((|HasAttribute| |#1| (QUOTE -4270))) (-270 |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 -(-271 S R |Mod| -4004 -3842 |exactQuo|) +(-271 S R |Mod| -1920 -3683 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-272) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4263 . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-273) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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"))) @@ -1034,21 +1034,21 @@ NIL NIL (-276 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."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|)))))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-278) ((|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 -(-279 -1345 S) +(-279 -1334 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 -(-280 E -1345) +(-280 E -1334) ((|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 @@ -1086,7 +1086,7 @@ NIL NIL (-289) ((|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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-290 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1096,7 +1096,7 @@ 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 -(-292 -1345) +(-292 -1334) ((|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 @@ -1106,8 +1106,8 @@ NIL NIL (-294 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))}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-140))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-960))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-768))) (-1476 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-768))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-795)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1075))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-216))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -291) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -268) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-289))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-515))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-795))) (-12 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| $ (QUOTE (-138)))) (-1476 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (-12 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| $ (QUOTE (-138)))))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-140))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-960))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-768))) (-1461 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-768))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-795)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1075))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-216))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -291) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (LIST (QUOTE -268) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-289))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-515))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-795))) (-12 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| $ (QUOTE (-138)))) (-1461 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (-12 (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (|HasCategory| $ (QUOTE (-138)))))) (-295 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 @@ -1118,9 +1118,9 @@ NIL NIL (-297 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."))) -((-4267 -1476 (-3340 (|has| |#1| (-984)) (|has| |#1| (-593 (-530)))) (-12 (|has| |#1| (-522)) (-1476 (-3340 (|has| |#1| (-984)) (|has| |#1| (-593 (-530)))) (|has| |#1| (-984)) (|has| |#1| (-453)))) (|has| |#1| (-984)) (|has| |#1| (-453))) (-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) ((-4272 "*") |has| |#1| (-522)) (-4263 |has| |#1| (-522)) (-4268 |has| 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(QUOTE (-984))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))))) (-1461 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-984)))) (-1461 (-12 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| $ (QUOTE (-984))) (|HasCategory| $ (LIST (QUOTE -975) (QUOTE (-530))))) +(-298 R -1334) ((|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 @@ -1130,8 +1130,8 @@ NIL NIL (-300 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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2366) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1461 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1545) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2746) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-301 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 @@ -1142,7 +1142,7 @@ NIL NIL (-303 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."))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) ((|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-740)))) (-304 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1158,19 +1158,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162)))) (-307 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-308 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."))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) -(-309 S -1345) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +(-309 S -1334) ((|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 (-349)))) -(-310 -1345) +(-310 -1334) ((|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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-311) ((|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."))) @@ -1188,15 +1188,15 @@ 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 -(-315 S -1345 UP UPUP R) +(-315 S -1334 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 -(-316 -1345 UP UPUP R) +(-316 -1334 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 -(-317 -1345 UP UPUP R) +(-317 -1334 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 @@ -1210,32 +1210,32 @@ NIL NIL (-320 |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.}"))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#3| (LIST (QUOTE -975) (QUOTE (-360)))) (|HasCategory| $ (QUOTE (-984))) (|HasCategory| $ (LIST (QUOTE -975) (QUOTE (-530))))) (-321 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 -(-322 S -1345 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."))) +(-322 S -1334 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}.")) (|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 (-349))) (|HasCategory| |#2| (QUOTE (-344)))) -(-323 -1345 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."))) -((-4263 |has| (-388 |#2|) (-344)) (-4268 |has| (-388 |#2|) (-344)) (-4262 |has| (-388 |#2|) (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +(-323 -1334 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}.")) (|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."))) +((-4262 |has| (-388 |#2|) (-344)) (-4267 |has| (-388 |#2|) (-344)) (-4261 |has| (-388 |#2|) (-344)) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-324 |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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) (-325 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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-326 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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-327 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 @@ -1250,33 +1250,33 @@ NIL NIL (-330) ((|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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL -(-331 R UP -1345) +(-331 R UP -1334) ((|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 (-332 |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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) (-333 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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-334 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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-335 |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}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| (-851 |#1|) (QUOTE (-138))) (|HasCategory| (-851 |#1|) (QUOTE (-349)))) (|HasCategory| (-851 |#1|) (QUOTE (-140))) (|HasCategory| (-851 |#1|) (QUOTE (-349))) (|HasCategory| (-851 |#1|) (QUOTE (-138)))) (-336 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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) -(-337 -1345 GF) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +(-337 -1334 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 @@ -1284,21 +1284,21 @@ 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 -(-339 -1345 FP FPP) +(-339 -1334 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 (-340 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}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-138)))) (-341 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 (-342 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4267 . T)) +((-4266 . T)) NIL (-343 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1306,7 +1306,7 @@ NIL NIL (-344) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-345 |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."))) @@ -1322,7 +1322,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-522)))) (-348 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4267 |has| |#1| (-522)) (-4265 . T) (-4264 . T)) +((-4266 |has| |#1| (-522)) (-4264 . T) (-4263 . T)) NIL (-349) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1334,7 +1334,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-344)))) (-351 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) NIL (-352 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1343,14 +1343,14 @@ NIL (-353 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4271)) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027)))) +((|HasAttribute| |#1| (QUOTE -4270)) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027)))) (-354 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4270 . T) (-4087 . T)) +((-4269 . T) (-4100 . T)) NIL (-355 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4265 . T) (-4264 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4264 . T) (-4263 . T)) NIL (-356 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."))) @@ -1362,7 +1362,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-358 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}"))) -((-4267 . T)) +((-4266 . T)) NIL (-359 |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}."))) @@ -1370,7 +1370,7 @@ NIL NIL (-360) ((|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}."))) -((-4253 . T) (-4261 . T) (-4125 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4252 . T) (-4260 . T) (-4136 . T) (-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-361 |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}."))) @@ -1378,23 +1378,23 @@ NIL NIL (-362 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}"))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) ((|HasCategory| |#1| (QUOTE (-162)))) (-363 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}."))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) NIL (-364) ((|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}."))) -((-4087 . T)) +((-4100 . T)) NIL (-365) ((|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.}"))) -((-4087 . T)) +((-4100 . T)) NIL (-366 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."))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) ((|HasCategory| |#1| (QUOTE (-162)))) (-367 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1402,7 +1402,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-795)))) (-368) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-369) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1414,13 +1414,13 @@ NIL NIL (-371 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) NIL (-372) ((|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 -(-373 -1345 UP UPUP R) +(-373 -1334 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 @@ -1434,27 +1434,27 @@ NIL NIL (-376) ((|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."))) -((-4087 . T)) +((-4100 . T)) NIL (-377) ((|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.}"))) -((-4087 . T)) +((-4100 . T)) NIL (-378) ((|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 -(-379 -3901 |returnType| -2582 |symbols|) +(-379 -3907 |returnType| -2739 |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 -(-380 -1345 UP) +(-380 -1334 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-381 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-4087 . T)) +((-4100 . T)) NIL (-382 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1462,15 +1462,15 @@ NIL NIL (-383) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-384 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4253)) (|HasAttribute| |#1| (QUOTE -4261))) +((|HasAttribute| |#1| (QUOTE -4252)) (|HasAttribute| |#1| (QUOTE -4260))) (-385) ((|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\"."))) -((-4125 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4136 . T) (-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-386 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."))) @@ -1482,15 +1482,15 @@ NIL NIL (-388 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."))) -((-4257 -12 (|has| |#1| (-6 -4268)) (|has| |#1| (-432)) (|has| |#1| (-6 -4257))) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-768))) (-1476 (|HasCategory| |#1| (QUOTE (-768))) (|HasCategory| |#1| (QUOTE (-795)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-1075))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776))))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-515))) (-12 (|HasAttribute| |#1| (QUOTE -4268)) (|HasAttribute| |#1| (QUOTE -4257)) (|HasCategory| |#1| (QUOTE (-432)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +((-4256 -12 (|has| |#1| (-6 -4267)) (|has| |#1| (-432)) (|has| |#1| (-6 -4256))) (-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-768))) (-1461 (|HasCategory| |#1| (QUOTE (-768))) (|HasCategory| |#1| (QUOTE (-795)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-1075))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776))))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-776)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-515))) (-12 (|HasAttribute| |#1| (QUOTE -4267)) (|HasAttribute| |#1| (QUOTE -4256)) (|HasCategory| |#1| (QUOTE (-432)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-389 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 (-390 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) NIL (-391 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1504,11 +1504,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-394 R -1345 UP A) +(-394 R -1334 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4267 . T)) +((-4266 . T)) NIL -(-395 R -1345 UP A |ibasis|) +(-395 R -1334 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -975) (|devaluate| |#2|)))) @@ -1522,12 +1522,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-344)))) (-398 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) -((-4267 |has| |#1| (-522)) (-4265 . T) (-4264 . T)) +((-4266 |has| |#1| (-522)) (-4264 . T) (-4263 . T)) NIL (-399 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."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -291) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -268) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-1139))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-1139)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-432)))) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -291) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -268) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-1139))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-1139)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-432)))) (-400 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 @@ -1554,17 +1554,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-349)))) (-406 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4270 . T) (-4260 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4259 . T) (-4270 . T) (-4100 . T)) NIL -(-407 R -1345) +(-407 R -1334) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-408 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4257 -12 (|has| |#1| (-6 -4257)) (|has| |#2| (-6 -4257))) (-4264 . T) (-4265 . T) (-4267 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4257)) (|HasAttribute| |#2| (QUOTE -4257)))) -(-409 R -1345) +((-4256 -12 (|has| |#1| (-6 -4256)) (|has| |#2| (-6 -4256))) (-4263 . T) (-4264 . T) (-4266 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4256)) (|HasAttribute| |#2| (QUOTE -4256)))) +(-409 R -1334) ((|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 @@ -1574,17 +1574,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (-411 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}."))) -((-4267 -1476 (|has| |#1| (-984)) (|has| |#1| (-453))) (-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) ((-4272 "*") |has| |#1| (-522)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-522)) (-4262 |has| |#1| (-522)) (-4087 . T)) +((-4266 -1461 (|has| |#1| (-984)) (|has| |#1| (-453))) (-4264 |has| |#1| (-162)) (-4263 |has| |#1| (-162)) ((-4271 "*") |has| |#1| (-522)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-522)) (-4261 |has| |#1| (-522)) (-4100 . T)) NIL -(-412 R -1345) +(-412 R -1334) ((|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 -(-413 R -1345) +(-413 R -1334) ((|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)))) -(-414 R -1345) +(-414 R -1334) ((|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 @@ -1592,7 +1592,7 @@ 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 -(-416 R -1345 UP) +(-416 R -1334 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 -975) (QUOTE (-47))))) @@ -1610,17 +1610,17 @@ NIL NIL (-420) ((|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}."))) -((-4087 . T)) +((-4100 . T)) NIL (-421) ((|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.}"))) -((-4087 . T)) +((-4100 . T)) NIL (-422 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 -(-423 R UP -1345) +(-423 R UP -1334) ((|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 @@ -1658,16 +1658,16 @@ NIL NIL (-432) ((|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}."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-433 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"))) -((-4267 |has| (-388 (-893 |#1|)) (-522)) (-4265 . T) (-4264 . T)) +((-4266 |has| (-388 (-893 |#1|)) (-522)) (-4264 . T) (-4263 . T)) ((|HasCategory| (-388 (-893 |#1|)) (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| (-388 (-893 |#1|)) (QUOTE (-522)))) (-434 |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"))) -(((-4272 "*") |has| |#2| (-162)) (-4263 |has| |#2| (-522)) (-4268 |has| |#2| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-850))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (-1476 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) +(((-4271 "*") |has| |#2| (-162)) (-4262 |has| |#2| (-522)) (-4267 |has| |#2| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#2| (QUOTE (-850))) (-1461 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1461 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (-1461 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#2| (QUOTE -4267)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) (-435 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 @@ -1694,7 +1694,7 @@ NIL NIL (-441 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) NIL (-442 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1702,7 +1702,7 @@ NIL NIL (-443 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4271 . T) (-4270 . T)) +((-4270 . T) (-4269 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#4| (LIST (QUOTE -291) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#4| (LIST (QUOTE -571) (QUOTE (-804))))) (-444 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}."))) @@ -1732,59 +1732,59 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-451 |lv| -1345 R) +(-451 |lv| -1334 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL (-452 S) -((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) +((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) NIL NIL (-453) -((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|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}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4267 . T)) +((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) +((-4266 . T)) NIL (-454 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. 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T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2366) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1461 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1545) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2746) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-455 |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."))) -((-4271 . 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T)) +((-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|)))))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-795))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-456 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)}"))) -((-4271 . T) (-4270 . T)) +((-4270 . T) (-4269 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#4| (LIST (QUOTE -291) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#4| (LIST (QUOTE -571) (QUOTE (-804))))) (-457) ((|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}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-458 |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."))) -((-4270 . T) (-4271 . 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T)) +((-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|)))))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-459) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-460 |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 (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))))) (|HasCategory| (-530) (QUOTE (-795))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (QUOTE (-984)))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530))))) (-1461 (|HasCategory| |#2| (QUOTE (-984))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-1027)))) (|HasAttribute| |#2| (QUOTE -4266)) (|HasCategory| |#2| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (-462) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Symbol|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|List| (|Symbol|))) "\\spad{headAst [f,{}x1,{}..,{}xn]} constructs a function definition header."))) NIL NIL (-463 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}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) -(-464 -1345 UP UPUP R) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +(-464 -1334 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 @@ -1794,15 +1794,15 @@ NIL NIL (-466) ((|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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1476 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1461 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) (-467 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 -4270)) (|HasAttribute| |#1| (QUOTE -4271)) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) +((|HasAttribute| |#1| (QUOTE -4269)) (|HasAttribute| |#1| (QUOTE -4270)) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (-468 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-4087 . T)) +((-4100 . T)) NIL (-469) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) @@ -1816,33 +1816,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-472 -1345 UP |AlExt| |AlPol|) +(-472 -1334 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-473) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| $ (QUOTE (-984))) (|HasCategory| $ (LIST (QUOTE -975) (QUOTE (-530))))) (-474 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-475 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."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-476 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 -(-477 R UP -1345) +(-477 R UP -1334) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-478 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4271 . T) (-4270 . T)) +((-4270 . T) (-4269 . T)) ((-12 (|HasCategory| (-110) (QUOTE (-1027))) (|HasCategory| (-110) (LIST (QUOTE -291) (QUOTE (-110))))) (|HasCategory| (-110) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-110) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-110) (QUOTE (-1027))) (|HasCategory| (-110) (LIST (QUOTE -571) (QUOTE (-804))))) (-479 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)}."))) @@ -1856,7 +1856,7 @@ 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 -(-482 -1345 |Expon| |VarSet| |DPoly|) +(-482 -1334 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-1099))))) @@ -1902,32 +1902,32 @@ NIL ((|HasCategory| |#2| (QUOTE (-740)))) (-493 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-494 |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}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((-1476 (|HasCategory| (-543 |#1|) (QUOTE (-138))) (|HasCategory| (-543 |#1|) (QUOTE (-349)))) (|HasCategory| (-543 |#1|) (QUOTE (-140))) (|HasCategory| (-543 |#1|) (QUOTE (-349))) (|HasCategory| (-543 |#1|) (QUOTE (-138)))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((-1461 (|HasCategory| (-543 |#1|) (QUOTE (-138))) (|HasCategory| (-543 |#1|) (QUOTE (-349)))) (|HasCategory| (-543 |#1|) (QUOTE (-140))) (|HasCategory| (-543 |#1|) (QUOTE (-349))) (|HasCategory| (-543 |#1|) (QUOTE (-138)))) (-495 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}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-496 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."))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-497 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 -4271))) +((|HasAttribute| |#3| (QUOTE -4270))) (-498 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 -4271))) +((|HasAttribute| |#7| (QUOTE -4270))) (-499 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."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4271 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-500 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 @@ -1940,7 +1940,7 @@ 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 -(-503 K -1345 |Par|) +(-503 K -1334 |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 @@ -1960,7 +1960,7 @@ 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 -(-508 K -1345 |Par|) +(-508 K -1334 |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 @@ -1990,17 +1990,17 @@ NIL NIL (-515) ((|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."))) -((-4268 . T) (-4269 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4267 . T) (-4268 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-516 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) -(-517 R -1345) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|)))))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +(-517 R -1334) ((|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 -(-518 R0 -1345 UP UPUP R) +(-518 R0 -1334 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 @@ -2010,7 +2010,7 @@ NIL NIL (-520 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."))) -((-4125 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4136 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-521 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."))) @@ -2018,9 +2018,9 @@ NIL NIL (-522) ((|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."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL -(-523 R -1345) +(-523 R -1334) ((|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 @@ -2032,7 +2032,7 @@ 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 -(-526 R -1345 L) +(-526 R -1334 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 -607) (|devaluate| |#2|)))) @@ -2040,31 +2040,31 @@ 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 -(-528 -1345 UP UPUP R) +(-528 -1334 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 -(-529 -1345 UP) +(-529 -1334 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 (-530) ((|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}."))) -((-4252 . T) (-4258 . T) (-4262 . T) (-4257 . T) (-4268 . T) (-4269 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4251 . T) (-4257 . T) (-4261 . T) (-4256 . T) (-4267 . T) (-4268 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-531) ((|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 -(-532 R -1345 L) +(-532 R -1334 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 -607) (|devaluate| |#2|)))) -(-533 R -1345) +(-533 R -1334) ((|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 -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-1063)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-583))))) -(-534 -1345 UP) +(-534 -1334 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 @@ -2072,53 +2072,53 @@ 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 -(-536 -1345) +(-536 -1334) ((|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 (-537 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."))) -((-4125 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4136 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-538) ((|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 -(-539 R -1345) +(-539 R -1334) ((|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 -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-266))) (|HasCategory| |#2| (QUOTE (-583))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-266)))) (|HasCategory| |#1| (QUOTE (-522)))) -(-540 -1345 UP) +(-540 -1334 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 -(-541 R -1345) +(-541 R -1334) ((|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 (-542 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-543 |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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| $ (QUOTE (-140))) (|HasCategory| $ (QUOTE (-138))) (|HasCategory| $ (QUOTE (-349)))) (-544) ((|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 -(-545 R -1345) +(-545 R -1334) ((|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 -(-546 E -1345) +(-546 E -1334) ((|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 -(-547 -1345) +(-547 -1334) ((|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}."))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) ((|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-1099))))) (-548 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"))) @@ -2142,19 +2142,19 @@ NIL NIL (-553 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (-1476 (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027)))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (-1461 (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027)))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) (-554 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 (-555 |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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-530)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-530)) (|devaluate| |#1|)))) (|HasCategory| (-530) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-530)))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-530)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-530)) (|devaluate| |#1|)))) (|HasCategory| (-530) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -2366) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-530)))))) (-556 |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.}"))) -((-4265 |has| |#1| (-522)) (-4264 |has| |#1| (-522)) ((-4272 "*") |has| |#1| (-522)) (-4263 |has| |#1| (-522)) (-4267 . T)) +((-4264 |has| |#1| (-522)) (-4263 |has| |#1| (-522)) ((-4271 "*") |has| |#1| (-522)) (-4262 |has| |#1| (-522)) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-522)))) (-557 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),{}..]}."))) @@ -2164,7 +2164,7 @@ 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 -(-559 R -1345 FG) +(-559 R -1334 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 @@ -2174,15 +2174,15 @@ NIL NIL (-561 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-562 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 -4271)) (|HasCategory| |#2| (QUOTE (-795))) (|HasAttribute| |#1| (QUOTE -4270)) (|HasCategory| |#3| (QUOTE (-1027)))) +((|HasAttribute| |#1| (QUOTE -4270)) (|HasCategory| |#2| (QUOTE (-795))) (|HasAttribute| |#1| (QUOTE -4269)) (|HasCategory| |#3| (QUOTE (-1027)))) (-563 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-4087 . T)) +((-4100 . T)) NIL (-564) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2190,19 +2190,19 @@ NIL NIL (-565 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)."))) -((-4267 -1476 (-3340 (|has| |#2| (-348 |#1|)) (|has| |#1| (-522))) (-12 (|has| |#2| (-398 |#1|)) (|has| |#1| (-522)))) (-4265 . T) (-4264 . T)) -((-1476 (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) +((-4266 -1461 (-3380 (|has| |#2| (-348 |#1|)) (|has| |#1| (-522))) (-12 (|has| |#2| (-398 |#1|)) (|has| |#1| (-522)))) (-4264 . T) (-4263 . T)) +((-1461 (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-566 |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."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| (-1082) (QUOTE (-795))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| (-1082) (QUOTE (-795))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-567 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 (-568 |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}."))) -((-4271 . T) (-4087 . T)) +((-4270 . T) (-4100 . T)) NIL (-569 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"))) @@ -2220,7 +2220,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-573 -1345 UP) +(-573 -1334 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2230,19 +2230,19 @@ NIL NIL (-575 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."))) -((-4267 . T)) +((-4266 . T)) NIL (-576 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}."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-793)))) -(-577 R -1345) +(-577 R -1334) ((|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 (-578 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"))) -((-4265 . T) (-4264 . T) ((-4272 "*") . T) (-4263 . T) (-4267 . T)) +((-4264 . T) (-4263 . T) ((-4271 "*") . T) (-4262 . T) (-4266 . T)) ((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (-579 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."))) @@ -2254,7 +2254,7 @@ NIL NIL (-581 |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}}."))) -((-4267 . T)) +((-4266 . T)) NIL (-582 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}}."))) @@ -2264,30 +2264,30 @@ 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 -(-584 R -1345) +(-584 R -1334) ((|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 -(-585 |lv| -1345) +(-585 |lv| -1334) ((|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 (-586) ((|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."))) -((-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1806) (QUOTE (-51))))))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-1082) (QUOTE (-795))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1874) (QUOTE (-51))))))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-1082) (QUOTE (-795))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) (-587 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-344)))) (-588 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4265 . T) (-4264 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4264 . T) (-4263 . T)) NIL (-589 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4267 -1476 (-3340 (|has| |#2| (-348 |#1|)) (|has| |#1| (-522))) (-12 (|has| |#2| (-398 |#1|)) (|has| |#1| (-522)))) (-4265 . T) (-4264 . T)) -((-1476 (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) +((-4266 -1461 (-3380 (|has| |#2| (-348 |#1|)) (|has| |#1| (-522))) (-12 (|has| |#2| (-398 |#1|)) (|has| |#1| (-522)))) (-4264 . T) (-4263 . T)) +((-1461 (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -398) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -348) (|devaluate| |#1|)))) (-590 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 @@ -2299,10 +2299,10 @@ NIL (-592 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 -((-3694 (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-344)))) +((-3676 (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-344)))) (-593 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}."))) -((-4267 . T)) +((-4266 . T)) NIL (-594 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}."))) @@ -2318,12 +2318,12 @@ NIL NIL (-597 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."))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-598 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-599 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2335,22 +2335,22 @@ NIL (-601 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 -4271))) +((|HasAttribute| |#1| (QUOTE -4270))) (-602 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})}."))) -((-4087 . T)) +((-4100 . T)) NIL -(-603 R -1345 L) +(-603 R -1334 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 (-604 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}}"))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-344)))) (-605 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-344)))) (-606 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2358,15 +2358,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-344)))) (-607 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}."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) NIL -(-608 -1345 UP) +(-608 -1334 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)))) -(-609 A -3955) +(-609 A -2235) ((|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}}"))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-344)))) (-610 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."))) @@ -2382,7 +2382,7 @@ NIL NIL (-613 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}."))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) ((|HasCategory| |#1| (QUOTE (-739)))) (-614 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."))) @@ -2390,7 +2390,7 @@ NIL NIL (-615 |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) (-4265 . T) (-4264 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4264 . T) (-4263 . T)) ((|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-162)))) (-616 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}."))) @@ -2398,13 +2398,13 @@ NIL NIL (-617 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}."))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL -(-618 -1345) +(-618 -1334) ((|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 -(-619 -1345 |Row| |Col| M) +(-619 -1334 |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 @@ -2414,8 +2414,8 @@ NIL NIL (-621 |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."))) -((-4267 . T) (-4270 . T) (-4264 . T) (-4265 . T)) -((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (-1476 (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-522))) (-1476 (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-162)))) +((-4266 . T) (-4269 . T) (-4263 . T) (-4264 . T)) +((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE (-4271 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (-1461 (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-522))) (-1461 (|HasAttribute| |#2| (QUOTE (-4271 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-162)))) (-622 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2426,12 +2426,12 @@ NIL NIL (-624 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-4087 . T)) +((-4100 . T)) NIL (-625 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 -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-626 |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 @@ -2467,10 +2467,10 @@ NIL (-634 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 (-4272 "*"))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-522)))) +((|HasAttribute| |#2| (QUOTE (-4271 "*"))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-522)))) (-635 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"))) -((-4270 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4270 . T) (-4100 . T)) NIL (-636 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."))) @@ -2478,8 +2478,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522)))) (-637 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."))) -((-4270 . T) (-4271 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4272 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-522))) (|HasAttribute| |#1| (QUOTE (-4271 "*"))) (|HasCategory| |#1| (QUOTE (-344))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-638 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 @@ -2488,7 +2488,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}."))) NIL NIL -(-640 S -1345 FLAF FLAS) +(-640 S -1334 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 @@ -2498,11 +2498,11 @@ NIL NIL (-642) ((|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"))) -((-4263 . T) (-4268 |has| (-647) (-344)) (-4262 |has| (-647) (-344)) (-4136 . T) (-4269 |has| (-647) (-6 -4269)) (-4266 |has| (-647) (-6 -4266)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-647) (QUOTE (-140))) (|HasCategory| (-647) (QUOTE (-138))) (|HasCategory| (-647) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-647) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-647) (QUOTE (-349))) (|HasCategory| (-647) (QUOTE (-344))) (|HasCategory| (-647) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-647) (QUOTE (-216))) (-1476 (|HasCategory| (-647) (QUOTE (-344))) (|HasCategory| (-647) (QUOTE (-330)))) (|HasCategory| (-647) (QUOTE (-330))) (|HasCategory| (-647) (LIST (QUOTE -268) (QUOTE (-647)) (QUOTE (-647)))) (|HasCategory| (-647) (LIST (QUOTE -291) (QUOTE (-647)))) (|HasCategory| (-647) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-647)))) (|HasCategory| (-647) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-647) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-647) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-647) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (-1476 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-344))) (|HasCategory| (-647) (QUOTE (-330)))) (|HasCategory| (-647) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-647) (QUOTE (-960))) (|HasCategory| (-647) (QUOTE (-1121))) (-12 (|HasCategory| (-647) (QUOTE (-941))) (|HasCategory| (-647) (QUOTE (-1121)))) (-1476 (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-344))) (-12 (|HasCategory| (-647) (QUOTE (-330))) (|HasCategory| (-647) (QUOTE (-850))))) (-1476 (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (-12 (|HasCategory| (-647) (QUOTE (-344))) (|HasCategory| (-647) (QUOTE (-850)))) (-12 (|HasCategory| (-647) (QUOTE (-330))) (|HasCategory| (-647) (QUOTE (-850))))) (|HasCategory| (-647) (QUOTE (-515))) (-12 (|HasCategory| (-647) (QUOTE (-993))) (|HasCategory| (-647) (QUOTE (-1121)))) (|HasCategory| (-647) (QUOTE (-993))) (-1476 (|HasCategory| (-647) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-647) (QUOTE (-344)))) (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850))) (-1476 (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-344)))) (-1476 (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-522)))) (-12 (|HasCategory| (-647) (QUOTE (-216))) (|HasCategory| (-647) (QUOTE (-344)))) (-12 (|HasCategory| (-647) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-647) (QUOTE (-344)))) (|HasCategory| (-647) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-647) (QUOTE (-795))) (|HasCategory| (-647) (QUOTE (-522))) (|HasAttribute| (-647) (QUOTE -4269)) (|HasAttribute| (-647) (QUOTE -4266)) (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-138)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-330))))) +((-4262 . T) (-4267 |has| (-647) (-344)) (-4261 |has| (-647) (-344)) (-4146 . T) (-4268 |has| (-647) (-6 -4268)) (-4265 |has| (-647) (-6 -4265)) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-647) (QUOTE (-140))) (|HasCategory| (-647) (QUOTE (-138))) (|HasCategory| (-647) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-647) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-647) (QUOTE (-349))) (|HasCategory| (-647) (QUOTE (-344))) (|HasCategory| (-647) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-647) (QUOTE (-216))) (-1461 (|HasCategory| (-647) (QUOTE (-344))) (|HasCategory| (-647) (QUOTE (-330)))) (|HasCategory| (-647) (QUOTE (-330))) (|HasCategory| (-647) (LIST (QUOTE -268) (QUOTE (-647)) (QUOTE (-647)))) (|HasCategory| (-647) (LIST (QUOTE -291) (QUOTE (-647)))) (|HasCategory| (-647) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-647)))) (|HasCategory| (-647) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-647) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-647) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-647) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (-1461 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-344))) (|HasCategory| (-647) (QUOTE (-330)))) (|HasCategory| (-647) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-647) (QUOTE (-960))) (|HasCategory| (-647) (QUOTE (-1121))) (-12 (|HasCategory| (-647) (QUOTE (-941))) (|HasCategory| (-647) (QUOTE (-1121)))) (-1461 (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-344))) (-12 (|HasCategory| (-647) (QUOTE (-330))) (|HasCategory| (-647) (QUOTE (-850))))) (-1461 (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (-12 (|HasCategory| (-647) (QUOTE (-344))) (|HasCategory| (-647) (QUOTE (-850)))) (-12 (|HasCategory| (-647) (QUOTE (-330))) (|HasCategory| (-647) (QUOTE (-850))))) (|HasCategory| (-647) (QUOTE (-515))) (-12 (|HasCategory| (-647) (QUOTE (-993))) (|HasCategory| (-647) (QUOTE (-1121)))) (|HasCategory| (-647) (QUOTE (-993))) (-1461 (|HasCategory| (-647) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-647) (QUOTE (-344)))) (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850))) (-1461 (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-344)))) (-1461 (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-522)))) (-12 (|HasCategory| (-647) (QUOTE (-216))) (|HasCategory| (-647) (QUOTE (-344)))) (-12 (|HasCategory| (-647) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-647) (QUOTE (-344)))) (|HasCategory| (-647) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-647) (QUOTE (-795))) (|HasCategory| (-647) (QUOTE (-522))) (|HasAttribute| (-647) (QUOTE -4268)) (|HasAttribute| (-647) (QUOTE -4265)) (-12 (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-138)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-647) (QUOTE (-289))) (|HasCategory| (-647) (QUOTE (-850)))) (|HasCategory| (-647) (QUOTE (-330))))) (-643 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}."))) -((-4271 . T) (-4087 . T)) +((-4270 . T) (-4100 . T)) NIL (-644 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}."))) @@ -2512,13 +2512,13 @@ 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 -(-646 OV E -1345 PG) +(-646 OV E -1334 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 (-647) ((|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}"))) -((-4125 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4136 . T) (-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-648 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."))) @@ -2526,7 +2526,7 @@ NIL NIL (-649) ((|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}"))) -((-4269 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4268 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-650 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"))) @@ -2548,7 +2548,7 @@ 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 -(-655 S -3286 I) +(-655 S -3340 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 @@ -2558,7 +2558,7 @@ NIL NIL (-657 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)}.}"))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) NIL (-658 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}."))) @@ -2568,25 +2568,25 @@ 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 -(-660 R |Mod| -4004 -3842 |exactQuo|) +(-660 R |Mod| -1920 -3683 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-661 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4266 |has| |#1| (-344)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-330))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4265 |has| |#1| (-344)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-330))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasAttribute| |#1| (QUOTE -4267)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-662 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-663 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) (-4267 . T)) +((-4264 |has| |#1| (-162)) (-4263 |has| |#1| (-162)) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140)))) -(-664 R |Mod| -4004 -3842 |exactQuo|) +(-664 R |Mod| -1920 -3683 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4267 . T)) +((-4266 . T)) NIL (-665 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2594,11 +2594,11 @@ NIL NIL (-666 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) NIL -(-667 -1345) +(-667 -1334) ((|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]]}."))) -((-4267 . T)) +((-4266 . T)) NIL (-668 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."))) @@ -2622,17 +2622,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-330))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-349)))) (-673 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."))) -((-4263 |has| |#1| (-344)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 |has| |#1| (-344)) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-674 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."))) +((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL (-675) -((|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."))) +((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-676 -1345 UP) +(-676 -1334 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 @@ -2650,8 +2650,8 @@ NIL NIL (-680 |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."))) -(((-4272 "*") |has| |#2| (-162)) (-4263 |has| |#2| (-522)) (-4268 |has| |#2| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-850))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (-1476 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) +(((-4271 "*") |has| |#2| (-162)) (-4262 |has| |#2| (-522)) (-4267 |has| |#2| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#2| (QUOTE (-850))) (-1461 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1461 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-806 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (-1461 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#2| (QUOTE -4267)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) (-681 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2666,15 +2666,15 @@ NIL NIL (-684 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) (-4267 . T)) +((-4264 |has| |#1| (-162)) (-4263 |has| |#1| (-162)) (-4266 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-795)))) (-685 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4260 . T) (-4271 . T) (-4087 . T)) +((-4259 . T) (-4270 . T) (-4100 . T)) NIL (-686 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}."))) -((-4270 . T) (-4260 . T) (-4271 . T)) +((-4269 . T) (-4259 . T) (-4270 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-687) ((|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."))) @@ -2686,7 +2686,7 @@ NIL NIL (-689 |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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4265 . T) (-4264 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4264 . T) (-4263 . T) (-4266 . T)) NIL (-690 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"))) @@ -2702,7 +2702,7 @@ NIL NIL (-693 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}."))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) NIL (-694) ((|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}."))) @@ -2784,15 +2784,15 @@ 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 -(-714 -1345) +(-714 -1334) ((|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 -(-715 P -1345) +(-715 P -1334) ((|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 -(-716 UP -1345) +(-716 UP -1334) ((|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 @@ -2806,9 +2806,9 @@ NIL NIL (-719) ((|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."))) -(((-4272 "*") . T)) +(((-4271 "*") . T)) NIL -(-720 R -1345) +(-720 R -1334) ((|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 @@ -2828,7 +2828,7 @@ 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 -(-725 -1345 |ExtF| |SUEx| |ExtP| |n|) +(-725 -1334 |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 @@ -2842,23 +2842,23 @@ NIL NIL (-728 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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . 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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 (-730 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)}"))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4266 |has| |#1| (-344)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4265 |has| |#1| (-344)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasAttribute| |#1| (QUOTE -4267)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-731 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 -388) (QUOTE (-530)))))) (-732 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.}"))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-733 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}."))) @@ -2910,25 +2910,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-993))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-349)))) (-745 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) NIL -(-746 -1476 R OS S) +(-746 -1461 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-747 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (-1476 (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) +((-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (-1461 (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1461 (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-938 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (-748) ((|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 -(-749 R -1345 L) +(-749 R -1334 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 -(-750 R -1345) +(-750 R -1334) ((|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 @@ -2936,7 +2936,7 @@ 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 -(-752 R -1345) +(-752 R -1334) ((|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 @@ -2944,11 +2944,11 @@ 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 -(-754 -1345 UP UPUP R) +(-754 -1334 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 -(-755 -1345 UP L LQ) +(-755 -1334 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 @@ -2956,41 +2956,41 @@ 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 -(-757 -1345 UP L LQ) +(-757 -1334 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 -(-758 -1345 UP) +(-758 -1334 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 -(-759 -1345 L UP A LO) +(-759 -1334 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 -(-760 -1345 UP) +(-760 -1334 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)))) -(-761 -1345 LO) +(-761 -1334 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}.") 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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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(|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."))) -(((-4272 "*") |has| |#2| (-344)) (-4263 |has| |#2| (-344)) (-4268 |has| |#2| (-344)) (-4262 |has| |#2| (-344)) (-4267 . T) (-4265 . T) (-4264 . T)) +(((-4271 "*") |has| |#2| (-344)) (-4262 |has| |#2| (-344)) (-4267 |has| |#2| (-344)) (-4261 |has| |#2| (-344)) (-4266 . T) (-4264 . T) (-4263 . T)) ((|HasCategory| |#2| (QUOTE (-344)))) (-766 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}))."))) @@ -3002,7 +3002,7 @@ NIL NIL (-768) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-769) ((|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}"))) @@ -3030,7 +3030,7 @@ NIL NIL (-775 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}."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-216)))) (-776) ((|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."))) @@ -3042,7 +3042,7 @@ NIL NIL (-778 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4270 . T) (-4260 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4259 . T) (-4270 . T) (-4100 . T)) NIL (-779) ((|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."))) @@ -3054,11 +3054,11 @@ NIL NIL (-781 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."))) -((-4267 |has| |#1| (-793))) -((|HasCategory| |#1| (QUOTE (-793))) (-1476 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-793)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-515))) (-1476 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4266 |has| |#1| (-793))) +((|HasCategory| |#1| (QUOTE (-793))) (-1461 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-793)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-515))) (-1461 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-21)))) (-782 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) (-4267 . T)) +((-4264 |has| |#1| (-162)) (-4263 |has| |#1| (-162)) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140)))) (-783) ((|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)."))) @@ -3082,13 +3082,13 @@ NIL NIL (-788 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."))) -((-4267 |has| |#1| (-793))) -((|HasCategory| |#1| (QUOTE (-793))) (-1476 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-793)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-515))) (-1476 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4266 |has| |#1| (-793))) +((|HasCategory| |#1| (QUOTE (-793))) (-1461 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-793)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-515))) (-1461 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-21)))) (-789) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-790 -3024 S) +(-790 -3148 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 @@ -3102,7 +3102,7 @@ NIL NIL (-793) ((|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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4267 . T)) +((-4266 . T)) NIL (-794 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3118,19 +3118,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162)))) (-797 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) NIL (-798 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 (-344))) (|HasCategory| |#1| (QUOTE (-522)))) -(-799 R |sigma| -1535) +(-799 R |sigma| -2903) ((|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."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-344)))) -(-800 |x| R |sigma| -1535) +(-800 |x| R |sigma| -2903) ((|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."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-344)))) (-801 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..)}."))) @@ -3158,7 +3158,7 @@ NIL NIL (-807 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|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) -((-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) (-4267 . T)) +((-4264 |has| |#1| (-162)) (-4263 |has| |#1| (-162)) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344)))) (-808 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3170,24 +3170,24 @@ NIL NIL (-810 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-811 |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)."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-812 |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)."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-811 |#1|) (QUOTE (-850))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-811 |#1|) (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-140))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-811 |#1|) (QUOTE (-960))) (|HasCategory| (-811 |#1|) (QUOTE (-768))) (-1476 (|HasCategory| (-811 |#1|) (QUOTE (-768))) (|HasCategory| (-811 |#1|) (QUOTE (-795)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (QUOTE (-1075))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (QUOTE (-216))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -291) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -268) (LIST (QUOTE -811) (|devaluate| |#1|)) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (QUOTE (-289))) (|HasCategory| (-811 |#1|) (QUOTE (-515))) (|HasCategory| (-811 |#1|) (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-850)))) (|HasCategory| (-811 |#1|) (QUOTE (-138))))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-811 |#1|) (QUOTE (-850))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-811 |#1|) (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-140))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-811 |#1|) (QUOTE (-960))) (|HasCategory| (-811 |#1|) (QUOTE (-768))) (-1461 (|HasCategory| (-811 |#1|) (QUOTE (-768))) (|HasCategory| (-811 |#1|) (QUOTE (-795)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (QUOTE (-1075))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-811 |#1|) (QUOTE (-216))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -491) (QUOTE (-1099)) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -291) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (LIST (QUOTE -268) (LIST (QUOTE -811) (|devaluate| |#1|)) (LIST (QUOTE -811) (|devaluate| |#1|)))) (|HasCategory| (-811 |#1|) (QUOTE (-289))) (|HasCategory| (-811 |#1|) (QUOTE (-515))) (|HasCategory| (-811 |#1|) (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-811 |#1|) (QUOTE (-850)))) (|HasCategory| (-811 |#1|) (QUOTE (-138))))) (-813 |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)}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-768))) (-1476 (|HasCategory| |#2| (QUOTE (-768))) (|HasCategory| |#2| (QUOTE (-795)))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -268) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-768))) (-1461 (|HasCategory| |#2| (QUOTE (-768))) (|HasCategory| |#2| (QUOTE (-795)))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -268) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-795))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) (-814 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 (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))))) (-815) ((|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 @@ -3243,7 +3243,7 @@ NIL (-828 |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 (-3694 (|HasCategory| |#2| (QUOTE (-984)))) (-3694 (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (-3694 (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099))))) +((-12 (-3676 (|HasCategory| |#2| (QUOTE (-984)))) (-3676 (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))))) (-12 (|HasCategory| |#2| (QUOTE (-984))) (-3676 (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099))))) (-829 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 @@ -3252,7 +3252,7 @@ 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 -(-831 R -3286) +(-831 R -3340) ((|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 @@ -3276,7 +3276,7 @@ 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 -(-837 UP -1345) +(-837 UP -1334) ((|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 @@ -3294,19 +3294,19 @@ NIL NIL (-841 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}."))) -((-4267 . T)) +((-4266 . T)) NIL (-842 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 (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-843 |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 (-844 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."))) -((-4267 . T)) +((-4266 . T)) NIL (-845 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3314,8 +3314,8 @@ NIL NIL (-846 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4267 . T)) -((-1476 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-795)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-795)))) +((-4266 . T)) +((-1461 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-795)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-795)))) (-847 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 @@ -3330,13 +3330,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-138)))) (-850) ((|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}."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-851 |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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) ((|HasCategory| $ (QUOTE (-140))) (|HasCategory| $ (QUOTE (-138))) (|HasCategory| $ (QUOTE (-349)))) -(-852 R0 -1345 UP UPUP R) +(-852 R0 -1334 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 @@ -3350,7 +3350,7 @@ NIL NIL (-855 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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-856 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."))) @@ -3364,7 +3364,7 @@ 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 -(-859 -1345) +(-859 -1334) ((|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 @@ -3374,17 +3374,17 @@ NIL NIL (-861) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-862) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4272 "*") . T)) +(((-4271 "*") . T)) NIL -(-863 -1345 P) +(-863 -1334 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-864 |xx| -1345) +(-864 |xx| -1334) ((|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 @@ -3408,7 +3408,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-870 R -1345) +(-870 R -1334) ((|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 @@ -3420,7 +3420,7 @@ 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 -(-873 S R -1345) +(-873 S R -1334) ((|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 @@ -3440,11 +3440,11 @@ 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 -827) (|devaluate| |#1|)))) -(-878 R -1345 -3286) +(-878 R -1334 -3340) ((|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 -(-879 -3286) +(-879 -3340) ((|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 @@ -3466,8 +3466,8 @@ NIL NIL (-884 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-885 |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 @@ -3487,12 +3487,12 @@ NIL (-889 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 (-850))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#4| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#4| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#4| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#4| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#4| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-795)))) +((|HasCategory| |#2| (QUOTE (-850))) (|HasAttribute| |#2| (QUOTE -4267)) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#4| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#4| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#4| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#4| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#4| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-795)))) (-890 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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) NIL -(-891 E V R P -1345) +(-891 E V R P -1334) ((|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 @@ -3502,9 +3502,9 @@ NIL NIL (-893 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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) -(-894 E V R P -1345) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-850))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4267)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +(-894 E V R P -1334) ((|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 (-432)))) @@ -3526,13 +3526,13 @@ NIL NIL (-899 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"))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-900) ((|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 -(-901 -1345) +(-901 -1334) ((|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 @@ -3546,12 +3546,12 @@ NIL NIL (-904 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}"))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-128)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-128)))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4267))) (-905 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"))) -((-4267 -12 (|has| |#2| (-453)) (|has| |#1| (-453)))) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-795))))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE 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(-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-349)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-453)))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675)))) (-12 (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-741))))) (-12 (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-675)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-128))) (|HasCategory| |#2| (QUOTE (-128)))) (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-795))))) (-906) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3566,7 +3566,7 @@ NIL NIL (-909 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4270 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4270 . T) (-4100 . T)) NIL (-910 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}}"))) @@ -3582,7 +3582,7 @@ NIL NIL (-913 |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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-914) ((|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}."))) @@ -3594,7 +3594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-522)))) (-916 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."))) -((-4270 . T) (-4087 . T)) +((-4269 . T) (-4100 . T)) NIL (-917 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."))) @@ -3610,7 +3610,7 @@ NIL NIL (-920 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}."))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-921 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3628,7 +3628,7 @@ 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 -(-925 K R UP -1345) +(-925 K R UP -1334) ((|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 @@ -3658,7 +3658,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-768))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-1075)))) (-932 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}."))) -((-4087 . T) (-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4100 . T) (-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-933 |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}."))) @@ -3666,7 +3666,7 @@ NIL NIL (-934 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."))) -((-4270 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4270 . T) (-4100 . T)) NIL (-935 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}."))) @@ -3674,7 +3674,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-993))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-272)))) (-936 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}."))) -((-4263 |has| |#1| (-272)) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 |has| |#1| (-272)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-937 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}."))) @@ -3682,12 +3682,12 @@ NIL NIL (-938 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.}"))) -((-4263 |has| |#1| (-272)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-272))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-272))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-515))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))))) +((-4262 |has| |#1| (-272)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (QUOTE (-272))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-272))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -491) (QUOTE (-1099)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -268) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-515))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))))) (-939 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}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-940 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3696,14 +3696,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-942 -1345 UP UPUP |radicnd| |n|) +(-942 -1334 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4263 |has| (-388 |#2|) (-344)) (-4268 |has| (-388 |#2|) (-344)) (-4262 |has| (-388 |#2|) (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-388 |#2|) (QUOTE (-138))) (|HasCategory| (-388 |#2|) (QUOTE (-140))) (|HasCategory| (-388 |#2|) (QUOTE (-330))) (-1476 (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-349))) (-1476 (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (-1476 (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-330))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1476 (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344))))) +((-4262 |has| (-388 |#2|) (-344)) (-4267 |has| (-388 |#2|) (-344)) (-4261 |has| (-388 |#2|) (-344)) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-388 |#2|) (QUOTE (-138))) (|HasCategory| (-388 |#2|) (QUOTE (-140))) (|HasCategory| (-388 |#2|) (QUOTE (-330))) (-1461 (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (|HasCategory| (-388 |#2|) (QUOTE (-344))) (|HasCategory| (-388 |#2|) (QUOTE (-349))) (-1461 (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (|HasCategory| (-388 |#2|) (QUOTE (-330)))) (-1461 (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-330))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1461 (|HasCategory| (-388 |#2|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-388 |#2|) (QUOTE (-344)))) (-12 (|HasCategory| (-388 |#2|) (QUOTE (-216))) (|HasCategory| (-388 |#2|) (QUOTE (-344))))) (-943 |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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1476 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-530) (QUOTE (-850))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-1099)))) (|HasCategory| (-530) (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-140))) (|HasCategory| (-530) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-960))) (|HasCategory| (-530) (QUOTE (-768))) (-1461 (|HasCategory| (-530) (QUOTE (-768))) (|HasCategory| (-530) (QUOTE (-795)))) (|HasCategory| (-530) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-1075))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| (-530) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| (-530) (QUOTE (-216))) (|HasCategory| (-530) (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| (-530) (LIST (QUOTE -491) (QUOTE (-1099)) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -291) (QUOTE (-530)))) (|HasCategory| (-530) (LIST (QUOTE -268) (QUOTE (-530)) (QUOTE (-530)))) (|HasCategory| (-530) (QUOTE (-289))) (|HasCategory| (-530) (QUOTE (-515))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-530) (LIST (QUOTE -593) (QUOTE (-530)))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| (-530) (QUOTE (-850)))) (|HasCategory| (-530) (QUOTE (-138))))) (-944) ((|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 @@ -3723,10 +3723,10 @@ NIL (-948 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 -4271)) (|HasCategory| |#2| (QUOTE (-1027)))) +((|HasAttribute| |#1| (QUOTE -4270)) (|HasCategory| |#2| (QUOTE (-1027)))) (-949 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}."))) -((-4087 . T)) +((-4100 . T)) NIL (-950 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}}"))) @@ -3734,21 +3734,21 @@ NIL NIL (-951) ((|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}}"))) -((-4263 . T) (-4268 . T) (-4262 . T) (-4265 . T) (-4264 . T) ((-4272 "*") . T) (-4267 . T)) +((-4262 . T) (-4267 . T) (-4261 . T) (-4264 . T) (-4263 . T) ((-4271 "*") . T) (-4266 . T)) NIL -(-952 R -1345) +(-952 R -1334) ((|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 -(-953 R -1345) +(-953 R -1334) ((|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 -(-954 -1345 UP) +(-954 -1334 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 -(-955 -1345 UP) +(-955 -1334 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 @@ -3778,9 +3778,9 @@ NIL NIL (-962 |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"))) -((-4263 . T) (-4268 . T) (-4262 . T) (-4265 . T) (-4264 . T) ((-4272 "*") . T) (-4267 . T)) -((-1476 (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (QUOTE (-530))))) -(-963 -1345 L) +((-4262 . T) (-4267 . T) (-4261 . T) (-4264 . T) (-4263 . T) ((-4271 "*") . T) (-4266 . T)) +((-1461 (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-388 (-530)) (LIST (QUOTE -975) (QUOTE (-530))))) +(-963 -1334 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 @@ -3790,12 +3790,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1027)))) (-965 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."))) -((-4271 . T) (-4270 . T)) +((-4270 . T) (-4269 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#4| (LIST (QUOTE -291) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#4| (LIST (QUOTE -571) (QUOTE (-804))))) (-966 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 (-4272 "*")))) +((|HasAttribute| |#1| (QUOTE (-4271 "*")))) (-967 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 @@ -3816,14 +3816,14 @@ 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 -(-972 -1345 |Expon| |VarSet| |FPol| |LFPol|) +(-972 -1334 |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"))) -(((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-973) ((|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.}"))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1099))) (LIST (QUOTE |:|) (QUOTE -1806) (QUOTE (-51))))))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-1099) (QUOTE (-795))) (|HasCategory| (-51) (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (QUOTE (-1099))) (LIST (QUOTE |:|) (QUOTE -1874) (QUOTE (-51))))))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-1099) (QUOTE (-795))) (|HasCategory| (-51) (QUOTE (-1027))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) (-974 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 @@ -3854,7 +3854,7 @@ NIL NIL (-981 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}."))) -((-4271 . T) (-4270 . T)) +((-4270 . T) (-4269 . T)) ((-12 (|HasCategory| (-728 |#1| (-806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-728 |#1| (-806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -728) (|devaluate| |#1|) (LIST (QUOTE -806) (|devaluate| |#2|)))))) (|HasCategory| (-728 |#1| (-806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-728 |#1| (-806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| (-806 |#2|) (QUOTE (-349))) (|HasCategory| (-728 |#1| (-806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-982) ((|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"))) @@ -3866,9 +3866,9 @@ NIL NIL (-984) ((|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."))) -((-4267 . T)) +((-4266 . T)) NIL -(-985 |xx| -1345) +(-985 |xx| -1334) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3878,12 +3878,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-289))) (|HasCategory| |#4| (QUOTE (-344))) (|HasCategory| |#4| (QUOTE (-522))) (|HasCategory| |#4| (QUOTE (-162)))) (-987 |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"))) -((-4270 . T) (-4087 . T) (-4265 . T) (-4264 . T)) +((-4269 . T) (-4100 . T) (-4264 . T) (-4263 . T)) NIL (-988 |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}."))) -((-4270 . T) (-4265 . T) (-4264 . T)) -((-1476 (-12 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (QUOTE (-344)))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (QUOTE (-289))) (|HasCategory| |#3| (QUOTE (-522))) (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))))) +((-4269 . T) (-4264 . T) (-4263 . T)) +((-1461 (-12 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (QUOTE (-344)))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (QUOTE (-289))) (|HasCategory| |#3| (QUOTE (-522))) (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| |#3| (QUOTE (-1027))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|))))) (-989 |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 @@ -3902,7 +3902,7 @@ NIL NIL (-993) ((|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."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-994 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -3910,19 +3910,19 @@ NIL NIL (-995) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4258 . T) (-4262 . T) (-4257 . T) (-4268 . T) (-4269 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4257 . T) (-4261 . T) (-4256 . T) (-4267 . T) (-4268 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-996) ((|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}"))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1099))) (LIST (QUOTE |:|) (QUOTE -1806) (QUOTE (-51))))))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (QUOTE (-1027))) (|HasCategory| (-1099) (QUOTE (-795))) (|HasCategory| (-51) (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (QUOTE (-1099))) (LIST (QUOTE |:|) (QUOTE -1874) (QUOTE (-51))))))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-51) (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| (-51) (QUOTE (-1027))) (|HasCategory| (-51) (LIST (QUOTE -291) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (QUOTE (-1027))) (|HasCategory| (-1099) (QUOTE (-795))) (|HasCategory| (-51) (QUOTE (-1027))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-51) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (LIST (QUOTE -571) (QUOTE (-804))))) (-997 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -932) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#4| (LIST (QUOTE -572) (QUOTE (-1099))))) (-998 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) NIL (-999 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}"))) @@ -3942,7 +3942,7 @@ NIL NIL (-1003 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}."))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-1004 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."))) @@ -3952,11 +3952,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1006 |Base| R -1345) +(-1006 |Base| R -1334) ((|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 -(-1007 |Base| R -1345) +(-1007 |Base| R -1334) ((|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 @@ -3970,8 +3970,8 @@ NIL NIL (-1010 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."))) -((-4263 |has| |#1| (-344)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-330)))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344))))) +((-4262 |has| |#1| (-344)) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-330))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-330)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-349))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-330)))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-12 (|HasCategory| |#1| (QUOTE (-330))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099))))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344)))) (-12 (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (QUOTE (-344))))) (-1011 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 @@ -3994,8 +3994,8 @@ NIL NIL (-1016 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"))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-850))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1017 (-1099)) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-216))) (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4267)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-1017 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 @@ -4014,7 +4014,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1027)))) (-1021 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."))) -((-4087 . T)) +((-4100 . T)) NIL (-1022 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -4022,7 +4022,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#1| (QUOTE (-1027)))) (-1023 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-4087 . T)) +((-4100 . T)) NIL (-1024 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -4030,7 +4030,7 @@ NIL NIL (-1025 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4260 . T) (-4087 . T)) +((-4259 . T) (-4100 . T)) NIL (-1026 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}."))) @@ -4046,8 +4046,8 @@ NIL NIL (-1029 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)}}"))) -((-4270 . T) (-4260 . T) (-4271 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4259 . T) (-4270 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1030 |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 @@ -4074,29 +4074,29 @@ NIL NIL (-1036 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.}"))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-1037) ((|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."))) NIL NIL (-1038 S) -((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) +((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL (-1039) -((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) +((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL (-1040 |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}."))) -((-4264 |has| |#3| (-984)) (-4265 |has| |#3| (-984)) (-4267 |has| |#3| (-6 -4267)) ((-4272 "*") |has| |#3| (-162)) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-128))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-162))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-216))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-675))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-741))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (LIST (QUOTE -291) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-984))) (|HasCategory| |#3| (LIST 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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 (-432)))) -(-1042 R -1345) +(-1042 R -1334) ((|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 @@ -4114,19 +4114,19 @@ NIL NIL (-1046) ((|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."))) -((-4258 . T) (-4262 . T) (-4257 . T) (-4268 . T) (-4269 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4257 . T) (-4261 . T) (-4256 . T) (-4267 . T) (-4268 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1047 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4270 . T) (-4271 . T) (-4087 . T)) +((-4269 . T) (-4270 . T) (-4100 . T)) NIL (-1048 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-344))) (|HasAttribute| |#3| (QUOTE (-4272 "*"))) (|HasCategory| |#3| (QUOTE (-162)))) +((|HasCategory| |#3| (QUOTE (-344))) (|HasAttribute| |#3| (QUOTE (-4271 "*"))) (|HasCategory| |#3| (QUOTE (-162)))) (-1049 |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."))) -((-4087 . T) (-4270 . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4100 . T) (-4269 . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1050 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}."))) @@ -4134,17 +4134,17 @@ NIL NIL (-1051 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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-850))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-850))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (|HasCategory| |#1| (QUOTE (-432))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4267)) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-138))))) (-1052 |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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344)))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344)))) (-1053 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}"))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL -(-1054 UP -1345) +(-1054 UP -1334) ((|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 @@ -4190,19 +4190,19 @@ NIL NIL (-1065 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."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -291) (LIST (QUOTE -1064) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027))) (-1476 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -291) (LIST (QUOTE -1064) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027))))) (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -291) (LIST (QUOTE -1064) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027))) (-1461 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -571) (QUOTE (-804)))) (-12 (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -291) (LIST (QUOTE -1064) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1064 |#1| |#2|) (QUOTE (-1027))))) (|HasCategory| (-1064 |#1| |#2|) (LIST (QUOTE -571) (QUOTE (-804))))) (-1066 |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}."))) -((-4267 . T) (-4259 |has| |#2| (-6 (-4272 "*"))) (-4270 . T) (-4264 . T) (-4265 . T)) -((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (-1476 (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-344))) (-1476 (|HasAttribute| |#2| (QUOTE (-4272 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-162)))) +((-4266 . T) (-4258 |has| |#2| (-6 (-4271 "*"))) (-4269 . T) (-4263 . T) (-4264 . T)) +((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE (-4271 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (-1461 (-12 (|HasCategory| |#2| (QUOTE (-216))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (QUOTE (-289))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-344))) (-1461 (|HasAttribute| |#2| (QUOTE (-4271 "*"))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasCategory| |#2| (QUOTE (-216)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-162)))) (-1067 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1068) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-1069 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.}"))) @@ -4210,24 +4210,24 @@ NIL NIL (-1070 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."))) -((-4271 . T) (-4270 . T)) +((-4270 . T) (-4269 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#4| (LIST (QUOTE -291) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#4| (LIST (QUOTE -571) (QUOTE (-804))))) (-1071 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}."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1072 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 (-1073 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})}."))) -((-4087 . T)) +((-4100 . T)) NIL (-1074 |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."))) -((-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-795))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|)))))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-795))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-1075) ((|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 @@ -4250,20 +4250,20 @@ NIL NIL (-1080 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."))) -((-4271 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1081) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-1082) NIL -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137)))))) (|HasCategory| (-137) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| (-137) (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| (-137) (QUOTE (-1027))) (-12 (|HasCategory| (-137) (QUOTE (-1027))) (|HasCategory| (-137) (LIST (QUOTE -291) (QUOTE (-137))))) (|HasCategory| (-137) (LIST (QUOTE -571) (QUOTE (-804))))) (-1083 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#1|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (QUOTE (-1027))) (|HasCategory| (-1082) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (QUOTE (-1082))) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#1|)))))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (QUOTE (-1027))) (|HasCategory| (-1082) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-1084 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 @@ -4290,9 +4290,9 @@ NIL NIL (-1090 |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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|)))) (|HasCategory| (-719) (QUOTE (-1039))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|)))) (|HasCategory| (-719) (QUOTE (-1039))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasSignature| |#1| (LIST (QUOTE -2366) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1545) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2746) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-1098) ((|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 @@ -4334,8 +4334,8 @@ NIL NIL (-1101 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-6 -4268)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| (-911) (QUOTE (-128))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4268))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-6 -4267)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-432))) (-12 (|HasCategory| (-911) (QUOTE (-128))) (|HasCategory| |#1| (QUOTE (-522)))) (-1461 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasAttribute| |#1| (QUOTE -4267))) (-1102) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4366,8 +4366,8 @@ NIL NIL (-1109 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4270 . T) (-4271 . T)) -((-12 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2940) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1806) (|devaluate| |#2|)))))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1476 (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) +((-4269 . T) (-4270 . T)) +((-12 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -291) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3078) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1874) (|devaluate| |#2|)))))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1027)))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -572) (QUOTE (-506)))) (-12 (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (LIST (QUOTE -291) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#2| (QUOTE (-1027))) (-1461 (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#2| (LIST (QUOTE -571) (QUOTE (-804)))) (|HasCategory| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (LIST (QUOTE -571) (QUOTE (-804))))) (-1110 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 @@ -4378,7 +4378,7 @@ NIL NIL (-1112 |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})}."))) -((-4271 . T) (-4087 . T)) +((-4270 . T) (-4100 . T)) NIL (-1113 |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."))) @@ -4418,8 +4418,8 @@ NIL NIL (-1122 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4271 . T) (-4270 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1027))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1123 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4428,7 +4428,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1125 R -1345) +(-1125 R -1334) ((|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 @@ -4436,7 +4436,7 @@ 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 -(-1127 R -1345) +(-1127 R -1334) ((|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 -572) (LIST (QUOTE -833) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -827) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -827) (|devaluate| |#1|))))) @@ -4446,12 +4446,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-349)))) (-1129 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-1130 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344)))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-140))) (|HasCategory| |#1| (QUOTE (-138))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-344)))) (-1131 |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 @@ -4464,13 +4464,13 @@ 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 (-1027))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) -(-1134 -1345) +(-1134 -1334) ((|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 (-1135) ((|constructor| (NIL "The fundamental Type."))) -((-4087 . T)) +((-4100 . T)) NIL (-1136 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}.}"))) @@ -4486,7 +4486,7 @@ NIL NIL (-1139) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1140 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) @@ -4494,7 +4494,7 @@ NIL NIL (-1141 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1142 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)}."))) @@ -4502,16 +4502,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-344)))) (-1143 |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. 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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 @@ -4546,8 +4546,8 @@ NIL NIL (-1154 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. 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T)) -((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1476 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1476 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE -4268)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1476 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) +(((-4271 "*") |has| |#2| (-162)) (-4262 |has| |#2| (-522)) (-4265 |has| |#2| (-344)) (-4267 |has| |#2| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (-1461 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-522)))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-360)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-360))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -827) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -827) (QUOTE (-530))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-360)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -572) (LIST (QUOTE -833) (QUOTE (-530)))))) (-12 (|HasCategory| (-1012) (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#2| (LIST (QUOTE -572) (QUOTE (-506))))) (|HasCategory| |#2| (QUOTE (-795))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-140))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (-1461 (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (-1461 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| |#2| (QUOTE (-216))) (|HasAttribute| |#2| (QUOTE -4267)) (|HasCategory| |#2| (QUOTE (-432))) (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (-1461 (-12 (|HasCategory| $ (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (QUOTE (-138))))) (-1155 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 @@ -4558,15 +4558,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-432))) (|HasCategory| |#2| (QUOTE (-522))) (|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (QUOTE (-1075)))) (-1157 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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4266 |has| |#1| (-344)) (-4268 |has| |#1| (-6 -4268)) (-4265 . T) (-4264 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4265 |has| |#1| (-344)) (-4267 |has| |#1| (-6 -4267)) (-4264 . T) (-4263 . T) (-4266 . T)) NIL (-1158 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 -841) (QUOTE (-1099)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2258) (LIST (|devaluate| |#2|) (QUOTE (-1099)))))) +((|HasCategory| |#2| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2366) (LIST (|devaluate| |#2|) (QUOTE (-1099)))))) (-1159 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1160 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4578,7 +4578,7 @@ NIL NIL (-1162 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1163 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)}."))) @@ -4586,27 +4586,27 @@ NIL NIL (-1164 |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)}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1165 |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)}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2366) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1461 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1545) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2746) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1166 |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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4268 |has| |#1| (-344)) (-4262 |has| |#1| (-344)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1476 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4267 |has| |#1| (-344)) (-4261 |has| |#1| (-344)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#1| (QUOTE (-162))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530))) (|devaluate| |#1|)))) (|HasCategory| (-388 (-530)) (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-1461 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-522)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasSignature| |#1| (LIST (QUOTE -2366) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -388) (QUOTE (-530)))))) (-1461 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1545) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2746) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-1167 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))}."))) -(((-4272 "*") |has| (-1166 |#2| |#3| |#4|) (-162)) (-4263 |has| (-1166 |#2| |#3| |#4|) (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-140))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-162))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-344))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-432))) (-1476 (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-522)))) +(((-4271 "*") |has| (-1166 |#2| |#3| |#4|) (-162)) (-4262 |has| (-1166 |#2| |#3| |#4|) (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-140))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-162))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (QUOTE (-530)))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-344))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-432))) (-1461 (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (LIST (QUOTE -975) (LIST (QUOTE -388) (QUOTE (-530)))))) (|HasCategory| (-1166 |#2| |#3| |#4|) (QUOTE (-522)))) (-1168 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4271))) +((|HasAttribute| |#1| (QUOTE -4270))) (-1169 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-4087 . T)) +((-4100 . T)) NIL (-1170 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4615,26 +4615,26 @@ NIL (-1171 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-530)))) (|HasCategory| |#2| (QUOTE (-900))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1637) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1099))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#2| (QUOTE (-900))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE -2746) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1545) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1099))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#2| (QUOTE (-344)))) (-1172 |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."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1173 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|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}."))) -(((-4272 "*") |has| |#1| (-162)) (-4263 |has| |#1| (-522)) (-4264 . T) (-4265 . T) (-4267 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1476 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|)))) (|HasCategory| (-719) (QUOTE (-1039))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasSignature| |#1| (LIST (QUOTE -2258) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasCategory| |#1| (QUOTE (-344))) (-1476 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1637) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2596) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) +(((-4271 "*") |has| |#1| (-162)) (-4262 |has| |#1| (-522)) (-4263 . T) (-4264 . T) (-4266 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasCategory| |#1| (QUOTE (-522))) (-1461 (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-140))) (-12 (|HasCategory| |#1| (LIST (QUOTE -841) (QUOTE (-1099)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-719)) (|devaluate| |#1|)))) (|HasCategory| (-719) (QUOTE (-1039))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasSignature| |#1| (LIST (QUOTE -2366) (LIST (|devaluate| |#1|) (QUOTE (-1099)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-719))))) (|HasCategory| |#1| (QUOTE (-344))) (-1461 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-530)))) (|HasCategory| |#1| (QUOTE (-900))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasSignature| |#1| (LIST (QUOTE -1545) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1099))))) (|HasSignature| |#1| (LIST (QUOTE -2746) (LIST (LIST (QUOTE -597) (QUOTE (-1099))) (|devaluate| |#1|))))))) (-1174 |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 -(-1175 -1345 UP L UTS) +(-1175 -1334 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 (-522)))) (-1176) ((|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."))) -((-4087 . T)) +((-4100 . T)) NIL (-1177 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4646,7 +4646,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-941))) (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (QUOTE (-675))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1179 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4271 . T) (-4270 . T) (-4087 . T)) +((-4270 . T) (-4269 . T) (-4100 . T)) NIL (-1180 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4654,8 +4654,8 @@ NIL NIL (-1181 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4271 . T) (-4270 . T)) -((-1476 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1476 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1476 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) +((-4270 . T) (-4269 . T)) +((-1461 (-12 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|))))) (-1461 (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (|HasCategory| |#1| (LIST (QUOTE -572) (QUOTE (-506)))) (-1461 (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-795))) (|HasCategory| (-530) (QUOTE (-795))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-675))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-984)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -291) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -571) (QUOTE (-804))))) (-1182) ((|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|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4682,68 +4682,68 @@ NIL NIL (-1188 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4265 . T) (-4264 . T)) +((-4264 . T) (-4263 . T)) NIL (-1189 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 -(-1190 K R UP -1345) +(-1190 K R UP -1334) ((|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 (-1191 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"))) -((-4265 |has| |#1| (-162)) (-4264 |has| |#1| (-162)) (-4267 . T)) +((-4264 |has| |#1| (-162)) (-4263 |has| |#1| (-162)) (-4266 . T)) ((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344)))) (-1192 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}}."))) -((-4271 . T) (-4270 . T)) +((-4270 . T) (-4269 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#4| (LIST (QUOTE -291) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -572) (QUOTE (-506)))) (|HasCategory| |#4| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-522))) (|HasCategory| |#3| (QUOTE (-349))) (|HasCategory| |#4| (LIST (QUOTE -571) (QUOTE (-804))))) (-1193 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}."))) -((-4264 . T) (-4265 . T) (-4267 . T)) +((-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1194 |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."))) -((-4267 . T) (-4263 |has| |#2| (-6 -4263)) (-4265 . T) (-4264 . T)) -((|HasCategory| |#2| (QUOTE (-162))) (|HasAttribute| |#2| (QUOTE -4263))) +((-4266 . T) (-4262 |has| |#2| (-6 -4262)) (-4264 . T) (-4263 . T)) +((|HasCategory| |#2| (QUOTE (-162))) (|HasAttribute| |#2| (QUOTE -4262))) (-1195 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 (-1196 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4263 |has| |#2| (-6 -4263)) (-4265 . T) (-4264 . T) (-4267 . T)) +((-4262 |has| |#2| (-6 -4262)) (-4264 . T) (-4263 . T) (-4266 . T)) NIL -(-1197 S -1345) +(-1197 S -1334) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-140)))) -(-1198 -1345) +(-1198 -1334) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4262 . T) (-4268 . T) (-4263 . T) ((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +((-4261 . T) (-4267 . T) (-4262 . T) ((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL (-1199 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4263 |has| |#2| (-6 -4263)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (LIST (QUOTE -666) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasAttribute| |#2| (QUOTE -4263))) +((-4262 |has| |#2| (-6 -4262)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#2| (QUOTE (-162))) (|HasCategory| |#2| (LIST (QUOTE -666) (LIST (QUOTE -388) (QUOTE (-530))))) (|HasAttribute| |#2| (QUOTE -4262))) (-1200 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4263 |has| |#2| (-6 -4263)) (-4265 . T) (-4264 . T) (-4267 . T)) +((-4262 |has| |#2| (-6 -4262)) (-4264 . T) (-4263 . T) (-4266 . T)) NIL (-1201 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4263 |has| |#1| (-6 -4263)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#1| (QUOTE (-162))) (|HasAttribute| |#1| (QUOTE -4263))) +((-4262 |has| |#1| (-6 -4262)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#1| (QUOTE (-162))) (|HasAttribute| |#1| (QUOTE -4262))) (-1202 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4267 . T) (-4268 |has| |#1| (-6 -4268)) (-4263 |has| |#1| (-6 -4263)) (-4265 . T) (-4264 . T)) -((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasAttribute| |#1| (QUOTE -4267)) (|HasAttribute| |#1| (QUOTE -4268)) (|HasAttribute| |#1| (QUOTE -4263))) +((-4266 . T) (-4267 |has| |#1| (-6 -4267)) (-4262 |has| |#1| (-6 -4262)) (-4264 . T) (-4263 . T)) +((|HasCategory| |#1| (QUOTE (-162))) (|HasCategory| |#1| (QUOTE (-344))) (|HasAttribute| |#1| (QUOTE -4266)) (|HasAttribute| |#1| (QUOTE -4267)) (|HasAttribute| |#1| (QUOTE -4262))) (-1203 |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."))) -((-4263 |has| |#2| (-6 -4263)) (-4265 . T) (-4264 . T) (-4267 . T)) -((|HasCategory| |#2| (QUOTE (-162))) (|HasAttribute| |#2| (QUOTE -4263))) +((-4262 |has| |#2| (-6 -4262)) (-4264 . T) (-4263 . T) (-4266 . T)) +((|HasCategory| |#2| (QUOTE (-162))) (|HasAttribute| |#2| (QUOTE -4262))) (-1204 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 @@ -4758,7 +4758,7 @@ NIL NIL (-1207 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4272 "*") . T) (-4264 . T) (-4265 . T) (-4267 . T)) +(((-4271 "*") . T) (-4263 . T) (-4264 . T) (-4266 . T)) NIL NIL NIL @@ -4776,4 +4776,4 @@ NIL NIL NIL NIL -((-3 NIL 2243751 2243756 2243761 2243766) (-2 NIL 2243731 2243736 2243741 2243746) (-1 NIL 2243711 2243716 2243721 2243726) (0 NIL 2243691 2243696 2243701 2243706) (-1207 "ZMOD.spad" 2243500 2243513 2243629 2243686) (-1206 "ZLINDEP.spad" 2242544 2242555 2243490 2243495) (-1205 "ZDSOLVE.spad" 2232393 2232415 2242534 2242539) (-1204 "YSTREAM.spad" 2231886 2231897 2232383 2232388) (-1203 "XRPOLY.spad" 2231106 2231126 2231742 2231811) (-1202 "XPR.spad" 2228835 2228848 2230824 2230923) (-1201 "XPOLY.spad" 2228390 2228401 2228691 2228760) (-1200 "XPOLYC.spad" 2227707 2227723 2228316 2228385) (-1199 "XPBWPOLY.spad" 2226144 2226164 2227487 2227556) (-1198 "XF.spad" 2224605 2224620 2226046 2226139) (-1197 "XF.spad" 2223046 2223063 2224489 2224494) (-1196 "XFALG.spad" 2220070 2220086 2222972 2223041) (-1195 "XEXPPKG.spad" 2219321 2219347 2220060 2220065) (-1194 "XDPOLY.spad" 2218935 2218951 2219177 2219246) (-1193 "XALG.spad" 2218533 2218544 2218891 2218930) (-1192 "WUTSET.spad" 2214372 2214389 2218179 2218206) (-1191 "WP.spad" 2213386 2213430 2214230 2214297) (-1190 "WFFINTBS.spad" 2210949 2210971 2213376 2213381) (-1189 "WEIER.spad" 2209163 2209174 2210939 2210944) (-1188 "VSPACE.spad" 2208836 2208847 2209131 2209158) (-1187 "VSPACE.spad" 2208529 2208542 2208826 2208831) (-1186 "VOID.spad" 2208119 2208128 2208519 2208524) (-1185 "VIEW.spad" 2205741 2205750 2208109 2208114) (-1184 "VIEWDEF.spad" 2200938 2200947 2205731 2205736) (-1183 "VIEW3D.spad" 2184773 2184782 2200928 2200933) (-1182 "VIEW2D.spad" 2172510 2172519 2184763 2184768) (-1181 "VECTOR.spad" 2171187 2171198 2171438 2171465) (-1180 "VECTOR2.spad" 2169814 2169827 2171177 2171182) (-1179 "VECTCAT.spad" 2167702 2167713 2169770 2169809) (-1178 "VECTCAT.spad" 2165411 2165424 2167481 2167486) (-1177 "VARIABLE.spad" 2165191 2165206 2165401 2165406) (-1176 "UTYPE.spad" 2164825 2164834 2165171 2165186) (-1175 "UTSODETL.spad" 2164118 2164142 2164781 2164786) (-1174 "UTSODE.spad" 2162306 2162326 2164108 2164113) (-1173 "UTS.spad" 2157095 2157123 2160773 2160870) (-1172 "UTSCAT.spad" 2154546 2154562 2156993 2157090) (-1171 "UTSCAT.spad" 2151641 2151659 2154090 2154095) (-1170 "UTS2.spad" 2151234 2151269 2151631 2151636) (-1169 "URAGG.spad" 2145856 2145867 2151214 2151229) (-1168 "URAGG.spad" 2140452 2140465 2145812 2145817) (-1167 "UPXSSING.spad" 2138098 2138124 2139536 2139669) (-1166 "UPXS.spad" 2135125 2135153 2136230 2136379) (-1165 "UPXSCONS.spad" 2132882 2132902 2133257 2133406) (-1164 "UPXSCCA.spad" 2131340 2131360 2132728 2132877) (-1163 "UPXSCCA.spad" 2129940 2129962 2131330 2131335) (-1162 "UPXSCAT.spad" 2128521 2128537 2129786 2129935) (-1161 "UPXS2.spad" 2128062 2128115 2128511 2128516) (-1160 "UPSQFREE.spad" 2126474 2126488 2128052 2128057) (-1159 "UPSCAT.spad" 2124067 2124091 2126372 2126469) (-1158 "UPSCAT.spad" 2121366 2121392 2123673 2123678) (-1157 "UPOLYC.spad" 2116344 2116355 2121208 2121361) (-1156 "UPOLYC.spad" 2111214 2111227 2116080 2116085) (-1155 "UPOLYC2.spad" 2110683 2110702 2111204 2111209) (-1154 "UP.spad" 2107728 2107743 2108236 2108389) (-1153 "UPMP.spad" 2106618 2106631 2107718 2107723) (-1152 "UPDIVP.spad" 2106181 2106195 2106608 2106613) (-1151 "UPDECOMP.spad" 2104418 2104432 2106171 2106176) (-1150 "UPCDEN.spad" 2103625 2103641 2104408 2104413) (-1149 "UP2.spad" 2102987 2103008 2103615 2103620) (-1148 "UNISEG.spad" 2102340 2102351 2102906 2102911) (-1147 "UNISEG2.spad" 2101833 2101846 2102296 2102301) (-1146 "UNIFACT.spad" 2100934 2100946 2101823 2101828) (-1145 "ULS.spad" 2091493 2091521 2092586 2093015) (-1144 "ULSCONS.spad" 2085536 2085556 2085908 2086057) (-1143 "ULSCCAT.spad" 2083133 2083153 2085356 2085531) (-1142 "ULSCCAT.spad" 2080864 2080886 2083089 2083094) (-1141 "ULSCAT.spad" 2079080 2079096 2080710 2080859) (-1140 "ULS2.spad" 2078592 2078645 2079070 2079075) (-1139 "UFD.spad" 2077657 2077666 2078518 2078587) (-1138 "UFD.spad" 2076784 2076795 2077647 2077652) (-1137 "UDVO.spad" 2075631 2075640 2076774 2076779) (-1136 "UDPO.spad" 2073058 2073069 2075587 2075592) (-1135 "TYPE.spad" 2072980 2072989 2073038 2073053) (-1134 "TWOFACT.spad" 2071630 2071645 2072970 2072975) (-1133 "TUPLE.spad" 2071016 2071027 2071529 2071534) (-1132 "TUBETOOL.spad" 2067853 2067862 2071006 2071011) (-1131 "TUBE.spad" 2066494 2066511 2067843 2067848) (-1130 "TS.spad" 2065083 2065099 2066059 2066156) (-1129 "TSETCAT.spad" 2052198 2052215 2065039 2065078) (-1128 "TSETCAT.spad" 2039311 2039330 2052154 2052159) (-1127 "TRMANIP.spad" 2033677 2033694 2039017 2039022) (-1126 "TRIMAT.spad" 2032636 2032661 2033667 2033672) (-1125 "TRIGMNIP.spad" 2031153 2031170 2032626 2032631) (-1124 "TRIGCAT.spad" 2030665 2030674 2031143 2031148) (-1123 "TRIGCAT.spad" 2030175 2030186 2030655 2030660) (-1122 "TREE.spad" 2028746 2028757 2029782 2029809) (-1121 "TRANFUN.spad" 2028577 2028586 2028736 2028741) (-1120 "TRANFUN.spad" 2028406 2028417 2028567 2028572) (-1119 "TOPSP.spad" 2028080 2028089 2028396 2028401) (-1118 "TOOLSIGN.spad" 2027743 2027754 2028070 2028075) (-1117 "TEXTFILE.spad" 2026300 2026309 2027733 2027738) (-1116 "TEX.spad" 2023317 2023326 2026290 2026295) (-1115 "TEX1.spad" 2022873 2022884 2023307 2023312) (-1114 "TEMUTL.spad" 2022428 2022437 2022863 2022868) (-1113 "TBCMPPK.spad" 2020521 2020544 2022418 2022423) (-1112 "TBAGG.spad" 2019545 2019568 2020489 2020516) (-1111 "TBAGG.spad" 2018589 2018614 2019535 2019540) (-1110 "TANEXP.spad" 2017965 2017976 2018579 2018584) (-1109 "TABLE.spad" 2016376 2016399 2016646 2016673) (-1108 "TABLEAU.spad" 2015857 2015868 2016366 2016371) (-1107 "TABLBUMP.spad" 2012640 2012651 2015847 2015852) (-1106 "SYSTEM.spad" 2011914 2011923 2012630 2012635) (-1105 "SYSSOLP.spad" 2009387 2009398 2011904 2011909) (-1104 "SYNTAX.spad" 2005579 2005588 2009377 2009382) (-1103 "SYMTAB.spad" 2003635 2003644 2005569 2005574) (-1102 "SYMS.spad" 1999620 1999629 2003625 2003630) (-1101 "SYMPOLY.spad" 1998630 1998641 1998712 1998839) (-1100 "SYMFUNC.spad" 1998105 1998116 1998620 1998625) (-1099 "SYMBOL.spad" 1995441 1995450 1998095 1998100) (-1098 "SWITCH.spad" 1992198 1992207 1995431 1995436) (-1097 "SUTS.spad" 1989097 1989125 1990665 1990762) (-1096 "SUPXS.spad" 1986111 1986139 1987229 1987378) (-1095 "SUP.spad" 1982883 1982894 1983664 1983817) (-1094 "SUPFRACF.spad" 1981988 1982006 1982873 1982878) (-1093 "SUP2.spad" 1981378 1981391 1981978 1981983) (-1092 "SUMRF.spad" 1980344 1980355 1981368 1981373) (-1091 "SUMFS.spad" 1979977 1979994 1980334 1980339) (-1090 "SULS.spad" 1970523 1970551 1971629 1972058) (-1089 "SUCH.spad" 1970203 1970218 1970513 1970518) (-1088 "SUBSPACE.spad" 1962210 1962225 1970193 1970198) (-1087 "SUBRESP.spad" 1961370 1961384 1962166 1962171) (-1086 "STTF.spad" 1957469 1957485 1961360 1961365) (-1085 "STTFNC.spad" 1953937 1953953 1957459 1957464) (-1084 "STTAYLOR.spad" 1946335 1946346 1953818 1953823) (-1083 "STRTBL.spad" 1944840 1944857 1944989 1945016) (-1082 "STRING.spad" 1944249 1944258 1944263 1944290) (-1081 "STRICAT.spad" 1944025 1944034 1944205 1944244) (-1080 "STREAM.spad" 1940793 1940804 1943550 1943565) (-1079 "STREAM3.spad" 1940338 1940353 1940783 1940788) (-1078 "STREAM2.spad" 1939406 1939419 1940328 1940333) (-1077 "STREAM1.spad" 1939110 1939121 1939396 1939401) (-1076 "STINPROD.spad" 1938016 1938032 1939100 1939105) (-1075 "STEP.spad" 1937217 1937226 1938006 1938011) (-1074 "STBL.spad" 1935743 1935771 1935910 1935925) (-1073 "STAGG.spad" 1934808 1934819 1935723 1935738) (-1072 "STAGG.spad" 1933881 1933894 1934798 1934803) (-1071 "STACK.spad" 1933232 1933243 1933488 1933515) (-1070 "SREGSET.spad" 1930936 1930953 1932878 1932905) (-1069 "SRDCMPK.spad" 1929481 1929501 1930926 1930931) (-1068 "SRAGG.spad" 1924566 1924575 1929437 1929476) (-1067 "SRAGG.spad" 1919683 1919694 1924556 1924561) (-1066 "SQMATRIX.spad" 1917309 1917327 1918217 1918304) (-1065 "SPLTREE.spad" 1911861 1911874 1916745 1916772) (-1064 "SPLNODE.spad" 1908449 1908462 1911851 1911856) (-1063 "SPFCAT.spad" 1907226 1907235 1908439 1908444) (-1062 "SPECOUT.spad" 1905776 1905785 1907216 1907221) (-1061 "spad-parser.spad" 1905241 1905250 1905766 1905771) (-1060 "SPACEC.spad" 1889254 1889265 1905231 1905236) (-1059 "SPACE3.spad" 1889030 1889041 1889244 1889249) (-1058 "SORTPAK.spad" 1888575 1888588 1888986 1888991) (-1057 "SOLVETRA.spad" 1886332 1886343 1888565 1888570) (-1056 "SOLVESER.spad" 1884852 1884863 1886322 1886327) (-1055 "SOLVERAD.spad" 1880862 1880873 1884842 1884847) (-1054 "SOLVEFOR.spad" 1879282 1879300 1880852 1880857) (-1053 "SNTSCAT.spad" 1878870 1878887 1879238 1879277) (-1052 "SMTS.spad" 1877130 1877156 1878435 1878532) (-1051 "SMP.spad" 1874572 1874592 1874962 1875089) (-1050 "SMITH.spad" 1873415 1873440 1874562 1874567) (-1049 "SMATCAT.spad" 1871513 1871543 1873347 1873410) (-1048 "SMATCAT.spad" 1869555 1869587 1871391 1871396) (-1047 "SKAGG.spad" 1868504 1868515 1869511 1869550) (-1046 "SINT.spad" 1866812 1866821 1868370 1868499) (-1045 "SIMPAN.spad" 1866540 1866549 1866802 1866807) (-1044 "SIG.spad" 1866137 1866146 1866530 1866535) (-1043 "SIGNRF.spad" 1865245 1865256 1866127 1866132) (-1042 "SIGNEF.spad" 1864514 1864531 1865235 1865240) (-1041 "SHP.spad" 1862432 1862447 1864470 1864475) (-1040 "SHDP.spad" 1853468 1853495 1853977 1854106) (-1039 "SGROUP.spad" 1852934 1852943 1853458 1853463) (-1038 "SGROUP.spad" 1852398 1852409 1852924 1852929) (-1037 "SGCF.spad" 1845279 1845288 1852388 1852393) (-1036 "SFRTCAT.spad" 1844195 1844212 1845235 1845274) (-1035 "SFRGCD.spad" 1843258 1843278 1844185 1844190) (-1034 "SFQCMPK.spad" 1837895 1837915 1843248 1843253) (-1033 "SFORT.spad" 1837330 1837344 1837885 1837890) (-1032 "SEXOF.spad" 1837173 1837213 1837320 1837325) (-1031 "SEX.spad" 1837065 1837074 1837163 1837168) (-1030 "SEXCAT.spad" 1834169 1834209 1837055 1837060) (-1029 "SET.spad" 1832469 1832480 1833590 1833629) (-1028 "SETMN.spad" 1830903 1830920 1832459 1832464) (-1027 "SETCAT.spad" 1830388 1830397 1830893 1830898) (-1026 "SETCAT.spad" 1829871 1829882 1830378 1830383) (-1025 "SETAGG.spad" 1826380 1826391 1829839 1829866) (-1024 "SETAGG.spad" 1822909 1822922 1826370 1826375) (-1023 "SEGXCAT.spad" 1822021 1822034 1822889 1822904) (-1022 "SEG.spad" 1821834 1821845 1821940 1821945) (-1021 "SEGCAT.spad" 1820653 1820664 1821814 1821829) (-1020 "SEGBIND.spad" 1819725 1819736 1820608 1820613) (-1019 "SEGBIND2.spad" 1819421 1819434 1819715 1819720) (-1018 "SEG2.spad" 1818846 1818859 1819377 1819382) (-1017 "SDVAR.spad" 1818122 1818133 1818836 1818841) (-1016 "SDPOL.spad" 1815515 1815526 1815806 1815933) (-1015 "SCPKG.spad" 1813594 1813605 1815505 1815510) (-1014 "SCOPE.spad" 1812739 1812748 1813584 1813589) (-1013 "SCACHE.spad" 1811421 1811432 1812729 1812734) (-1012 "SAOS.spad" 1811293 1811302 1811411 1811416) (-1011 "SAERFFC.spad" 1811006 1811026 1811283 1811288) (-1010 "SAE.spad" 1809184 1809200 1809795 1809930) (-1009 "SAEFACT.spad" 1808885 1808905 1809174 1809179) (-1008 "RURPK.spad" 1806526 1806542 1808875 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(-706 "NAGF07.spad" 1198541 1198549 1200138 1200143) (-705 "NAGF04.spad" 1192773 1192781 1198531 1198536) (-704 "NAGF02.spad" 1186582 1186590 1192763 1192768) (-703 "NAGF01.spad" 1182185 1182193 1186572 1186577) (-702 "NAGE04.spad" 1175645 1175653 1182175 1182180) (-701 "NAGE02.spad" 1165987 1165995 1175635 1175640) (-700 "NAGE01.spad" 1161871 1161879 1165977 1165982) (-699 "NAGD03.spad" 1159791 1159799 1161861 1161866) (-698 "NAGD02.spad" 1152322 1152330 1159781 1159786) (-697 "NAGD01.spad" 1146435 1146443 1152312 1152317) (-696 "NAGC06.spad" 1142222 1142230 1146425 1146430) (-695 "NAGC05.spad" 1140691 1140699 1142212 1142217) (-694 "NAGC02.spad" 1139946 1139954 1140681 1140686) (-693 "NAALG.spad" 1139481 1139491 1139914 1139941) (-692 "NAALG.spad" 1139036 1139048 1139471 1139476) (-691 "MULTSQFR.spad" 1135994 1136011 1139026 1139031) (-690 "MULTFACT.spad" 1135377 1135394 1135984 1135989) (-689 "MTSCAT.spad" 1133411 1133432 1135275 1135372) (-688 "MTHING.spad" 1133068 1133078 1133401 1133406) (-687 "MSYSCMD.spad" 1132502 1132510 1133058 1133063) (-686 "MSET.spad" 1130444 1130454 1132208 1132247) (-685 "MSETAGG.spad" 1130277 1130287 1130400 1130439) (-684 "MRING.spad" 1127248 1127260 1129985 1130052) (-683 "MRF2.spad" 1126816 1126830 1127238 1127243) (-682 "MRATFAC.spad" 1126362 1126379 1126806 1126811) (-681 "MPRFF.spad" 1124392 1124411 1126352 1126357) (-680 "MPOLY.spad" 1121830 1121845 1122189 1122316) (-679 "MPCPF.spad" 1121094 1121113 1121820 1121825) (-678 "MPC3.spad" 1120909 1120949 1121084 1121089) (-677 "MPC2.spad" 1120551 1120584 1120899 1120904) (-676 "MONOTOOL.spad" 1118886 1118903 1120541 1120546) (-675 "MONOID.spad" 1118060 1118068 1118876 1118881) (-674 "MONOID.spad" 1117232 1117242 1118050 1118055) (-673 "MONOGEN.spad" 1115978 1115991 1117092 1117227) (-672 "MONOGEN.spad" 1114746 1114761 1115862 1115867) (-671 "MONADWU.spad" 1112760 1112768 1114736 1114741) (-670 "MONADWU.spad" 1110772 1110782 1112750 1112755) (-669 "MONAD.spad" 1109916 1109924 1110762 1110767) (-668 "MONAD.spad" 1109058 1109068 1109906 1109911) (-667 "MOEBIUS.spad" 1107744 1107758 1109038 1109053) (-666 "MODULE.spad" 1107614 1107624 1107712 1107739) (-665 "MODULE.spad" 1107504 1107516 1107604 1107609) (-664 "MODRING.spad" 1106835 1106874 1107484 1107499) (-663 "MODOP.spad" 1105494 1105506 1106657 1106724) (-662 "MODMONOM.spad" 1105026 1105044 1105484 1105489) (-661 "MODMON.spad" 1101731 1101747 1102507 1102660) (-660 "MODFIELD.spad" 1101089 1101128 1101633 1101726) (-659 "MMLFORM.spad" 1099949 1099957 1101079 1101084) (-658 "MMAP.spad" 1099689 1099723 1099939 1099944) (-657 "MLO.spad" 1098116 1098126 1099645 1099684) (-656 "MLIFT.spad" 1096688 1096705 1098106 1098111) (-655 "MKUCFUNC.spad" 1096221 1096239 1096678 1096683) (-654 "MKRECORD.spad" 1095823 1095836 1096211 1096216) (-653 "MKFUNC.spad" 1095204 1095214 1095813 1095818) (-652 "MKFLCFN.spad" 1094160 1094170 1095194 1095199) (-651 "MKCHSET.spad" 1093936 1093946 1094150 1094155) (-650 "MKBCFUNC.spad" 1093421 1093439 1093926 1093931) (-649 "MINT.spad" 1092860 1092868 1093323 1093416) (-648 "MHROWRED.spad" 1091361 1091371 1092850 1092855) (-647 "MFLOAT.spad" 1089806 1089814 1091251 1091356) (-646 "MFINFACT.spad" 1089206 1089228 1089796 1089801) (-645 "MESH.spad" 1086938 1086946 1089196 1089201) (-644 "MDDFACT.spad" 1085131 1085141 1086928 1086933) (-643 "MDAGG.spad" 1084406 1084416 1085099 1085126) (-642 "MCMPLX.spad" 1080386 1080394 1081000 1081201) (-641 "MCDEN.spad" 1079594 1079606 1080376 1080381) (-640 "MCALCFN.spad" 1076696 1076722 1079584 1079589) (-639 "MAYBE.spad" 1075945 1075956 1076686 1076691) (-638 "MATSTOR.spad" 1073221 1073231 1075935 1075940) (-637 "MATRIX.spad" 1071925 1071935 1072409 1072436) (-636 "MATLIN.spad" 1069251 1069275 1071809 1071814) (-635 "MATCAT.spad" 1060824 1060846 1069207 1069246) (-634 "MATCAT.spad" 1052281 1052305 1060666 1060671) (-633 "MATCAT2.spad" 1051549 1051597 1052271 1052276) (-632 "MAPPKG3.spad" 1050448 1050462 1051539 1051544) (-631 "MAPPKG2.spad" 1049782 1049794 1050438 1050443) (-630 "MAPPKG1.spad" 1048600 1048610 1049772 1049777) (-629 "MAPHACK3.spad" 1048408 1048422 1048590 1048595) (-628 "MAPHACK2.spad" 1048173 1048185 1048398 1048403) (-627 "MAPHACK1.spad" 1047803 1047813 1048163 1048168) (-626 "MAGMA.spad" 1045593 1045610 1047793 1047798) (-625 "M3D.spad" 1043291 1043301 1044973 1044978) (-624 "LZSTAGG.spad" 1040509 1040519 1043271 1043286) (-623 "LZSTAGG.spad" 1037735 1037747 1040499 1040504) (-622 "LWORD.spad" 1034440 1034457 1037725 1037730) (-621 "LSQM.spad" 1032668 1032682 1033066 1033117) (-620 "LSPP.spad" 1032201 1032218 1032658 1032663) (-619 "LSMP.spad" 1031041 1031069 1032191 1032196) (-618 "LSMP1.spad" 1028845 1028859 1031031 1031036) (-617 "LSAGG.spad" 1028502 1028512 1028801 1028840) (-616 "LSAGG.spad" 1028191 1028203 1028492 1028497) (-615 "LPOLY.spad" 1027145 1027164 1028047 1028116) (-614 "LPEFRAC.spad" 1026402 1026412 1027135 1027140) (-613 "LO.spad" 1025803 1025817 1026336 1026363) (-612 "LOGIC.spad" 1025405 1025413 1025793 1025798) (-611 "LOGIC.spad" 1025005 1025015 1025395 1025400) (-610 "LODOOPS.spad" 1023923 1023935 1024995 1025000) (-609 "LODO.spad" 1023309 1023325 1023605 1023644) (-608 "LODOF.spad" 1022353 1022370 1023266 1023271) (-607 "LODOCAT.spad" 1021011 1021021 1022309 1022348) (-606 "LODOCAT.spad" 1019667 1019679 1020967 1020972) (-605 "LODO2.spad" 1018942 1018954 1019349 1019388) (-604 "LODO1.spad" 1018344 1018354 1018624 1018663) (-603 "LODEEF.spad" 1017116 1017134 1018334 1018339) (-602 "LNAGG.spad" 1012908 1012918 1017096 1017111) (-601 "LNAGG.spad" 1008674 1008686 1012864 1012869) (-600 "LMOPS.spad" 1005410 1005427 1008664 1008669) (-599 "LMODULE.spad" 1005052 1005062 1005400 1005405) (-598 "LMDICT.spad" 1004335 1004345 1004603 1004630) (-597 "LIST.spad" 1002053 1002063 1003482 1003509) (-596 "LIST3.spad" 1001344 1001358 1002043 1002048) (-595 "LIST2.spad" 999984 999996 1001334 1001339) (-594 "LIST2MAP.spad" 996861 996873 999974 999979) (-593 "LINEXP.spad" 996293 996303 996841 996856) (-592 "LINDEP.spad" 995070 995082 996205 996210) (-591 "LIMITRF.spad" 992984 992994 995060 995065) (-590 "LIMITPS.spad" 991867 991880 992974 992979) (-589 "LIE.spad" 989881 989893 991157 991302) (-588 "LIECAT.spad" 989357 989367 989807 989876) (-587 "LIECAT.spad" 988861 988873 989313 989318) (-586 "LIB.spad" 986909 986917 987520 987535) (-585 "LGROBP.spad" 984262 984281 986899 986904) (-584 "LF.spad" 983181 983197 984252 984257) (-583 "LFCAT.spad" 982200 982208 983171 983176) (-582 "LEXTRIPK.spad" 977703 977718 982190 982195) (-581 "LEXP.spad" 975706 975733 977683 977698) (-580 "LEADCDET.spad" 974090 974107 975696 975701) (-579 "LAZM3PK.spad" 972794 972816 974080 974085) (-578 "LAUPOL.spad" 971485 971498 972389 972458) (-577 "LAPLACE.spad" 971058 971074 971475 971480) (-576 "LA.spad" 970498 970512 970980 971019) (-575 "LALG.spad" 970274 970284 970478 970493) (-574 "LALG.spad" 970058 970070 970264 970269) (-573 "KOVACIC.spad" 968771 968788 970048 970053) (-572 "KONVERT.spad" 968493 968503 968761 968766) (-571 "KOERCE.spad" 968230 968240 968483 968488) (-570 "KERNEL.spad" 966765 966775 968014 968019) (-569 "KERNEL2.spad" 966468 966480 966755 966760) (-568 "KDAGG.spad" 965559 965581 966436 966463) (-567 "KDAGG.spad" 964670 964694 965549 965554) (-566 "KAFILE.spad" 963633 963649 963868 963895) (-565 "JORDAN.spad" 961460 961472 962923 963068) (-564 "JAVACODE.spad" 961226 961234 961450 961455) (-563 "IXAGG.spad" 959339 959363 961206 961221) (-562 "IXAGG.spad" 957317 957343 959186 959191) (-561 "IVECTOR.spad" 956090 956105 956245 956272) (-560 "ITUPLE.spad" 955235 955245 956080 956085) (-559 "ITRIGMNP.spad" 954046 954065 955225 955230) (-558 "ITFUN3.spad" 953540 953554 954036 954041) (-557 "ITFUN2.spad" 953270 953282 953530 953535) (-556 "ITAYLOR.spad" 951062 951077 953106 953231) (-555 "ISUPS.spad" 943473 943488 950036 950133) (-554 "ISUMP.spad" 942970 942986 943463 943468) (-553 "ISTRING.spad" 941973 941986 942139 942166) (-552 "IRURPK.spad" 940686 940705 941963 941968) (-551 "IRSN.spad" 938646 938654 940676 940681) (-550 "IRRF2F.spad" 937121 937131 938602 938607) (-549 "IRREDFFX.spad" 936722 936733 937111 937116) (-548 "IROOT.spad" 935053 935063 936712 936717) (-547 "IR.spad" 932843 932857 934909 934936) (-546 "IR2.spad" 931863 931879 932833 932838) (-545 "IR2F.spad" 931063 931079 931853 931858) (-544 "IPRNTPK.spad" 930823 930831 931053 931058) (-543 "IPF.spad" 930388 930400 930628 930721) (-542 "IPADIC.spad" 930149 930175 930314 930383) (-541 "INVLAPLA.spad" 929794 929810 930139 930144) (-540 "INTTR.spad" 923040 923057 929784 929789) (-539 "INTTOOLS.spad" 920752 920768 922615 922620) (-538 "INTSLPE.spad" 920058 920066 920742 920747) (-537 "INTRVL.spad" 919624 919634 919972 920053) (-536 "INTRF.spad" 917988 918002 919614 919619) (-535 "INTRET.spad" 917420 917430 917978 917983) (-534 "INTRAT.spad" 916095 916112 917410 917415) (-533 "INTPM.spad" 914458 914474 915738 915743) (-532 "INTPAF.spad" 912226 912244 914390 914395) (-531 "INTPACK.spad" 902536 902544 912216 912221) (-530 "INT.spad" 901897 901905 902390 902531) (-529 "INTHERTR.spad" 901163 901180 901887 901892) (-528 "INTHERAL.spad" 900829 900853 901153 901158) (-527 "INTHEORY.spad" 897242 897250 900819 900824) (-526 "INTG0.spad" 890705 890723 897174 897179) (-525 "INTFTBL.spad" 884734 884742 890695 890700) (-524 "INTFACT.spad" 883793 883803 884724 884729) (-523 "INTEF.spad" 882108 882124 883783 883788) (-522 "INTDOM.spad" 880723 880731 882034 882103) (-521 "INTDOM.spad" 879400 879410 880713 880718) (-520 "INTCAT.spad" 877653 877663 879314 879395) (-519 "INTBIT.spad" 877156 877164 877643 877648) (-518 "INTALG.spad" 876338 876365 877146 877151) (-517 "INTAF.spad" 875830 875846 876328 876333) (-516 "INTABL.spad" 874348 874379 874511 874538) (-515 "INS.spad" 871744 871752 874250 874343) (-514 "INS.spad" 869226 869236 871734 871739) (-513 "INPSIGN.spad" 868660 868673 869216 869221) (-512 "INPRODPF.spad" 867726 867745 868650 868655) (-511 "INPRODFF.spad" 866784 866808 867716 867721) (-510 "INNMFACT.spad" 865755 865772 866774 866779) (-509 "INMODGCD.spad" 865239 865269 865745 865750) (-508 "INFSP.spad" 863524 863546 865229 865234) (-507 "INFPROD0.spad" 862574 862593 863514 863519) (-506 "INFORM.spad" 859842 859850 862564 862569) (-505 "INFORM1.spad" 859467 859477 859832 859837) (-504 "INFINITY.spad" 859019 859027 859457 859462) (-503 "INEP.spad" 857551 857573 859009 859014) (-502 "INDE.spad" 857280 857297 857541 857546) (-501 "INCRMAPS.spad" 856701 856711 857270 857275) (-500 "INBFF.spad" 852471 852482 856691 856696) (-499 "IMATRIX.spad" 851416 851442 851928 851955) (-498 "IMATQF.spad" 850510 850554 851372 851377) (-497 "IMATLIN.spad" 849115 849139 850466 850471) (-496 "ILIST.spad" 847771 847786 848298 848325) (-495 "IIARRAY2.spad" 847159 847197 847378 847405) (-494 "IFF.spad" 846569 846585 846840 846933) (-493 "IFARRAY.spad" 844056 844071 845752 845779) (-492 "IFAMON.spad" 843918 843935 844012 844017) (-491 "IEVALAB.spad" 843307 843319 843908 843913) (-490 "IEVALAB.spad" 842694 842708 843297 843302) (-489 "IDPO.spad" 842492 842504 842684 842689) (-488 "IDPOAMS.spad" 842248 842260 842482 842487) (-487 "IDPOAM.spad" 841968 841980 842238 842243) (-486 "IDPC.spad" 840902 840914 841958 841963) (-485 "IDPAM.spad" 840647 840659 840892 840897) (-484 "IDPAG.spad" 840394 840406 840637 840642) (-483 "IDECOMP.spad" 837631 837649 840384 840389) (-482 "IDEAL.spad" 832554 832593 837566 837571) (-481 "ICDEN.spad" 831705 831721 832544 832549) (-480 "ICARD.spad" 830894 830902 831695 831700) (-479 "IBPTOOLS.spad" 829487 829504 830884 830889) (-478 "IBITS.spad" 828686 828699 829123 829150) (-477 "IBATOOL.spad" 825561 825580 828676 828681) (-476 "IBACHIN.spad" 824048 824063 825551 825556) (-475 "IARRAY2.spad" 823036 823062 823655 823682) (-474 "IARRAY1.spad" 822081 822096 822219 822246) (-473 "IAN.spad" 820296 820304 821899 821992) (-472 "IALGFACT.spad" 819897 819930 820286 820291) (-471 "HYPCAT.spad" 819321 819329 819887 819892) (-470 "HYPCAT.spad" 818743 818753 819311 819316) (-469 "HOSTNAME.spad" 818551 818559 818733 818738) (-468 "HOAGG.spad" 815809 815819 818531 818546) (-467 "HOAGG.spad" 812852 812864 815576 815581) (-466 "HEXADEC.spad" 810724 810732 811322 811415) (-465 "HEUGCD.spad" 809739 809750 810714 810719) (-464 "HELLFDIV.spad" 809329 809353 809729 809734) (-463 "HEAP.spad" 808721 808731 808936 808963) (-462 "HEADAST.spad" 808280 808288 808711 808716) (-461 "HDP.spad" 799448 799464 799825 799954) (-460 "HDMP.spad" 796627 796642 797245 797372) (-459 "HB.spad" 794864 794872 796617 796622) (-458 "HASHTBL.spad" 793334 793365 793545 793572) (-457 "HACKPI.spad" 792817 792825 793236 793329) (-456 "GTSET.spad" 791756 791772 792463 792490) (-455 "GSTBL.spad" 790275 790310 790449 790464) (-454 "GSERIES.spad" 787442 787469 788407 788556) (-453 "GROUP.spad" 786616 786624 787422 787437) (-452 "GROUP.spad" 785798 785808 786606 786611) (-451 "GROEBSOL.spad" 784286 784307 785788 785793) (-450 "GRMOD.spad" 782857 782869 784276 784281) (-449 "GRMOD.spad" 781426 781440 782847 782852) (-448 "GRIMAGE.spad" 774031 774039 781416 781421) (-447 "GRDEF.spad" 772410 772418 774021 774026) (-446 "GRAY.spad" 770869 770877 772400 772405) (-445 "GRALG.spad" 769916 769928 770859 770864) (-444 "GRALG.spad" 768961 768975 769906 769911) (-443 "GPOLSET.spad" 768415 768438 768643 768670) (-442 "GOSPER.spad" 767680 767698 768405 768410) (-441 "GMODPOL.spad" 766818 766845 767648 767675) (-440 "GHENSEL.spad" 765887 765901 766808 766813) (-439 "GENUPS.spad" 761988 762001 765877 765882) (-438 "GENUFACT.spad" 761565 761575 761978 761983) (-437 "GENPGCD.spad" 761149 761166 761555 761560) (-436 "GENMFACT.spad" 760601 760620 761139 761144) (-435 "GENEEZ.spad" 758540 758553 760591 760596) (-434 "GDMP.spad" 755561 755578 756337 756464) (-433 "GCNAALG.spad" 749456 749483 755355 755422) (-432 "GCDDOM.spad" 748628 748636 749382 749451) (-431 "GCDDOM.spad" 747862 747872 748618 748623) (-430 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"BGAGG.spad" 117062 117072 117845 117872) (-103 "BGAGG.spad" 116267 116279 117052 117057) (-102 "BFUNCT.spad" 115831 115839 116247 116262) (-101 "BEZOUT.spad" 114965 114992 115781 115786) (-100 "BBTREE.spad" 111784 111794 114572 114599) (-99 "BASTYPE.spad" 111457 111464 111774 111779) (-98 "BASTYPE.spad" 111128 111137 111447 111452) (-97 "BALFACT.spad" 110568 110580 111118 111123) (-96 "AUTOMOR.spad" 110015 110024 110548 110563) (-95 "ATTREG.spad" 106734 106741 109767 110010) (-94 "ATTRBUT.spad" 102757 102764 106714 106729) (-93 "ATRIG.spad" 102227 102234 102747 102752) (-92 "ATRIG.spad" 101695 101704 102217 102222) (-91 "ASTCAT.spad" 101599 101606 101685 101690) (-90 "ASTCAT.spad" 101501 101510 101589 101594) (-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 2242545 2242550 2242555 2242560) (-2 NIL 2242525 2242530 2242535 2242540) (-1 NIL 2242505 2242510 2242515 2242520) (0 NIL 2242485 2242490 2242495 2242500) (-1207 "ZMOD.spad" 2242294 2242307 2242423 2242480) (-1206 "ZLINDEP.spad" 2241338 2241349 2242284 2242289) (-1205 "ZDSOLVE.spad" 2231187 2231209 2241328 2241333) (-1204 "YSTREAM.spad" 2230680 2230691 2231177 2231182) (-1203 "XRPOLY.spad" 2229900 2229920 2230536 2230605) (-1202 "XPR.spad" 2227629 2227642 2229618 2229717) (-1201 "XPOLY.spad" 2227184 2227195 2227485 2227554) (-1200 "XPOLYC.spad" 2226501 2226517 2227110 2227179) (-1199 "XPBWPOLY.spad" 2224938 2224958 2226281 2226350) (-1198 "XF.spad" 2223399 2223414 2224840 2224933) (-1197 "XF.spad" 2221840 2221857 2223283 2223288) (-1196 "XFALG.spad" 2218864 2218880 2221766 2221835) (-1195 "XEXPPKG.spad" 2218115 2218141 2218854 2218859) (-1194 "XDPOLY.spad" 2217729 2217745 2217971 2218040) (-1193 "XALG.spad" 2217327 2217338 2217685 2217724) (-1192 "WUTSET.spad" 2213166 2213183 2216973 2217000) (-1191 "WP.spad" 2212180 2212224 2213024 2213091) (-1190 "WFFINTBS.spad" 2209743 2209765 2212170 2212175) (-1189 "WEIER.spad" 2207957 2207968 2209733 2209738) (-1188 "VSPACE.spad" 2207630 2207641 2207925 2207952) (-1187 "VSPACE.spad" 2207323 2207336 2207620 2207625) (-1186 "VOID.spad" 2206913 2206922 2207313 2207318) (-1185 "VIEW.spad" 2204535 2204544 2206903 2206908) (-1184 "VIEWDEF.spad" 2199732 2199741 2204525 2204530) (-1183 "VIEW3D.spad" 2183567 2183576 2199722 2199727) (-1182 "VIEW2D.spad" 2171304 2171313 2183557 2183562) (-1181 "VECTOR.spad" 2169981 2169992 2170232 2170259) (-1180 "VECTOR2.spad" 2168608 2168621 2169971 2169976) (-1179 "VECTCAT.spad" 2166496 2166507 2168564 2168603) (-1178 "VECTCAT.spad" 2164205 2164218 2166275 2166280) (-1177 "VARIABLE.spad" 2163985 2164000 2164195 2164200) (-1176 "UTYPE.spad" 2163619 2163628 2163965 2163980) (-1175 "UTSODETL.spad" 2162912 2162936 2163575 2163580) (-1174 "UTSODE.spad" 2161100 2161120 2162902 2162907) (-1173 "UTS.spad" 2155889 2155917 2159567 2159664) (-1172 "UTSCAT.spad" 2153340 2153356 2155787 2155884) (-1171 "UTSCAT.spad" 2150435 2150453 2152884 2152889) (-1170 "UTS2.spad" 2150028 2150063 2150425 2150430) (-1169 "URAGG.spad" 2144650 2144661 2150008 2150023) (-1168 "URAGG.spad" 2139246 2139259 2144606 2144611) (-1167 "UPXSSING.spad" 2136892 2136918 2138330 2138463) (-1166 "UPXS.spad" 2133919 2133947 2135024 2135173) (-1165 "UPXSCONS.spad" 2131676 2131696 2132051 2132200) (-1164 "UPXSCCA.spad" 2130134 2130154 2131522 2131671) (-1163 "UPXSCCA.spad" 2128734 2128756 2130124 2130129) (-1162 "UPXSCAT.spad" 2127315 2127331 2128580 2128729) (-1161 "UPXS2.spad" 2126856 2126909 2127305 2127310) (-1160 "UPSQFREE.spad" 2125268 2125282 2126846 2126851) (-1159 "UPSCAT.spad" 2122861 2122885 2125166 2125263) (-1158 "UPSCAT.spad" 2120160 2120186 2122467 2122472) (-1157 "UPOLYC.spad" 2115138 2115149 2120002 2120155) (-1156 "UPOLYC.spad" 2110008 2110021 2114874 2114879) (-1155 "UPOLYC2.spad" 2109477 2109496 2109998 2110003) (-1154 "UP.spad" 2106522 2106537 2107030 2107183) (-1153 "UPMP.spad" 2105412 2105425 2106512 2106517) (-1152 "UPDIVP.spad" 2104975 2104989 2105402 2105407) (-1151 "UPDECOMP.spad" 2103212 2103226 2104965 2104970) (-1150 "UPCDEN.spad" 2102419 2102435 2103202 2103207) (-1149 "UP2.spad" 2101781 2101802 2102409 2102414) (-1148 "UNISEG.spad" 2101134 2101145 2101700 2101705) (-1147 "UNISEG2.spad" 2100627 2100640 2101090 2101095) (-1146 "UNIFACT.spad" 2099728 2099740 2100617 2100622) (-1145 "ULS.spad" 2090287 2090315 2091380 2091809) (-1144 "ULSCONS.spad" 2084330 2084350 2084702 2084851) (-1143 "ULSCCAT.spad" 2081927 2081947 2084150 2084325) (-1142 "ULSCCAT.spad" 2079658 2079680 2081883 2081888) (-1141 "ULSCAT.spad" 2077874 2077890 2079504 2079653) (-1140 "ULS2.spad" 2077386 2077439 2077864 2077869) (-1139 "UFD.spad" 2076451 2076460 2077312 2077381) (-1138 "UFD.spad" 2075578 2075589 2076441 2076446) (-1137 "UDVO.spad" 2074425 2074434 2075568 2075573) (-1136 "UDPO.spad" 2071852 2071863 2074381 2074386) (-1135 "TYPE.spad" 2071774 2071783 2071832 2071847) (-1134 "TWOFACT.spad" 2070424 2070439 2071764 2071769) (-1133 "TUPLE.spad" 2069810 2069821 2070323 2070328) (-1132 "TUBETOOL.spad" 2066647 2066656 2069800 2069805) (-1131 "TUBE.spad" 2065288 2065305 2066637 2066642) (-1130 "TS.spad" 2063877 2063893 2064853 2064950) (-1129 "TSETCAT.spad" 2050992 2051009 2063833 2063872) (-1128 "TSETCAT.spad" 2038105 2038124 2050948 2050953) (-1127 "TRMANIP.spad" 2032471 2032488 2037811 2037816) (-1126 "TRIMAT.spad" 2031430 2031455 2032461 2032466) (-1125 "TRIGMNIP.spad" 2029947 2029964 2031420 2031425) (-1124 "TRIGCAT.spad" 2029459 2029468 2029937 2029942) (-1123 "TRIGCAT.spad" 2028969 2028980 2029449 2029454) (-1122 "TREE.spad" 2027540 2027551 2028576 2028603) (-1121 "TRANFUN.spad" 2027371 2027380 2027530 2027535) (-1120 "TRANFUN.spad" 2027200 2027211 2027361 2027366) (-1119 "TOPSP.spad" 2026874 2026883 2027190 2027195) (-1118 "TOOLSIGN.spad" 2026537 2026548 2026864 2026869) (-1117 "TEXTFILE.spad" 2025094 2025103 2026527 2026532) (-1116 "TEX.spad" 2022111 2022120 2025084 2025089) (-1115 "TEX1.spad" 2021667 2021678 2022101 2022106) (-1114 "TEMUTL.spad" 2021222 2021231 2021657 2021662) (-1113 "TBCMPPK.spad" 2019315 2019338 2021212 2021217) (-1112 "TBAGG.spad" 2018339 2018362 2019283 2019310) (-1111 "TBAGG.spad" 2017383 2017408 2018329 2018334) (-1110 "TANEXP.spad" 2016759 2016770 2017373 2017378) (-1109 "TABLE.spad" 2015170 2015193 2015440 2015467) (-1108 "TABLEAU.spad" 2014651 2014662 2015160 2015165) (-1107 "TABLBUMP.spad" 2011434 2011445 2014641 2014646) (-1106 "SYSTEM.spad" 2010708 2010717 2011424 2011429) (-1105 "SYSSOLP.spad" 2008181 2008192 2010698 2010703) (-1104 "SYNTAX.spad" 2004373 2004382 2008171 2008176) (-1103 "SYMTAB.spad" 2002429 2002438 2004363 2004368) (-1102 "SYMS.spad" 1998414 1998423 2002419 2002424) (-1101 "SYMPOLY.spad" 1997424 1997435 1997506 1997633) (-1100 "SYMFUNC.spad" 1996899 1996910 1997414 1997419) (-1099 "SYMBOL.spad" 1994235 1994244 1996889 1996894) (-1098 "SWITCH.spad" 1990992 1991001 1994225 1994230) (-1097 "SUTS.spad" 1987891 1987919 1989459 1989556) (-1096 "SUPXS.spad" 1984905 1984933 1986023 1986172) (-1095 "SUP.spad" 1981677 1981688 1982458 1982611) (-1094 "SUPFRACF.spad" 1980782 1980800 1981667 1981672) (-1093 "SUP2.spad" 1980172 1980185 1980772 1980777) (-1092 "SUMRF.spad" 1979138 1979149 1980162 1980167) (-1091 "SUMFS.spad" 1978771 1978788 1979128 1979133) (-1090 "SULS.spad" 1969317 1969345 1970423 1970852) (-1089 "SUCH.spad" 1968997 1969012 1969307 1969312) (-1088 "SUBSPACE.spad" 1961004 1961019 1968987 1968992) (-1087 "SUBRESP.spad" 1960164 1960178 1960960 1960965) (-1086 "STTF.spad" 1956263 1956279 1960154 1960159) (-1085 "STTFNC.spad" 1952731 1952747 1956253 1956258) (-1084 "STTAYLOR.spad" 1945129 1945140 1952612 1952617) (-1083 "STRTBL.spad" 1943634 1943651 1943783 1943810) (-1082 "STRING.spad" 1943043 1943052 1943057 1943084) (-1081 "STRICAT.spad" 1942819 1942828 1942999 1943038) (-1080 "STREAM.spad" 1939587 1939598 1942344 1942359) (-1079 "STREAM3.spad" 1939132 1939147 1939577 1939582) (-1078 "STREAM2.spad" 1938200 1938213 1939122 1939127) (-1077 "STREAM1.spad" 1937904 1937915 1938190 1938195) (-1076 "STINPROD.spad" 1936810 1936826 1937894 1937899) (-1075 "STEP.spad" 1936011 1936020 1936800 1936805) (-1074 "STBL.spad" 1934537 1934565 1934704 1934719) (-1073 "STAGG.spad" 1933602 1933613 1934517 1934532) (-1072 "STAGG.spad" 1932675 1932688 1933592 1933597) (-1071 "STACK.spad" 1932026 1932037 1932282 1932309) (-1070 "SREGSET.spad" 1929730 1929747 1931672 1931699) (-1069 "SRDCMPK.spad" 1928275 1928295 1929720 1929725) (-1068 "SRAGG.spad" 1923360 1923369 1928231 1928270) (-1067 "SRAGG.spad" 1918477 1918488 1923350 1923355) (-1066 "SQMATRIX.spad" 1916103 1916121 1917011 1917098) (-1065 "SPLTREE.spad" 1910655 1910668 1915539 1915566) (-1064 "SPLNODE.spad" 1907243 1907256 1910645 1910650) (-1063 "SPFCAT.spad" 1906020 1906029 1907233 1907238) (-1062 "SPECOUT.spad" 1904570 1904579 1906010 1906015) (-1061 "spad-parser.spad" 1904035 1904044 1904560 1904565) (-1060 "SPACEC.spad" 1888048 1888059 1904025 1904030) (-1059 "SPACE3.spad" 1887824 1887835 1888038 1888043) (-1058 "SORTPAK.spad" 1887369 1887382 1887780 1887785) (-1057 "SOLVETRA.spad" 1885126 1885137 1887359 1887364) (-1056 "SOLVESER.spad" 1883646 1883657 1885116 1885121) (-1055 "SOLVERAD.spad" 1879656 1879667 1883636 1883641) (-1054 "SOLVEFOR.spad" 1878076 1878094 1879646 1879651) (-1053 "SNTSCAT.spad" 1877664 1877681 1878032 1878071) (-1052 "SMTS.spad" 1875924 1875950 1877229 1877326) (-1051 "SMP.spad" 1873366 1873386 1873756 1873883) (-1050 "SMITH.spad" 1872209 1872234 1873356 1873361) (-1049 "SMATCAT.spad" 1870307 1870337 1872141 1872204) (-1048 "SMATCAT.spad" 1868349 1868381 1870185 1870190) (-1047 "SKAGG.spad" 1867298 1867309 1868305 1868344) (-1046 "SINT.spad" 1865606 1865615 1867164 1867293) (-1045 "SIMPAN.spad" 1865334 1865343 1865596 1865601) (-1044 "SIG.spad" 1864931 1864940 1865324 1865329) (-1043 "SIGNRF.spad" 1864039 1864050 1864921 1864926) (-1042 "SIGNEF.spad" 1863308 1863325 1864029 1864034) (-1041 "SHP.spad" 1861226 1861241 1863264 1863269) (-1040 "SHDP.spad" 1852262 1852289 1852771 1852900) (-1039 "SGROUP.spad" 1851870 1851879 1852252 1852257) (-1038 "SGROUP.spad" 1851476 1851487 1851860 1851865) (-1037 "SGCF.spad" 1844357 1844366 1851466 1851471) (-1036 "SFRTCAT.spad" 1843273 1843290 1844313 1844352) (-1035 "SFRGCD.spad" 1842336 1842356 1843263 1843268) (-1034 "SFQCMPK.spad" 1836973 1836993 1842326 1842331) (-1033 "SFORT.spad" 1836408 1836422 1836963 1836968) (-1032 "SEXOF.spad" 1836251 1836291 1836398 1836403) (-1031 "SEX.spad" 1836143 1836152 1836241 1836246) (-1030 "SEXCAT.spad" 1833247 1833287 1836133 1836138) (-1029 "SET.spad" 1831547 1831558 1832668 1832707) (-1028 "SETMN.spad" 1829981 1829998 1831537 1831542) (-1027 "SETCAT.spad" 1829466 1829475 1829971 1829976) (-1026 "SETCAT.spad" 1828949 1828960 1829456 1829461) (-1025 "SETAGG.spad" 1825458 1825469 1828917 1828944) (-1024 "SETAGG.spad" 1821987 1822000 1825448 1825453) (-1023 "SEGXCAT.spad" 1821099 1821112 1821967 1821982) (-1022 "SEG.spad" 1820912 1820923 1821018 1821023) (-1021 "SEGCAT.spad" 1819731 1819742 1820892 1820907) (-1020 "SEGBIND.spad" 1818803 1818814 1819686 1819691) (-1019 "SEGBIND2.spad" 1818499 1818512 1818793 1818798) (-1018 "SEG2.spad" 1817924 1817937 1818455 1818460) (-1017 "SDVAR.spad" 1817200 1817211 1817914 1817919) (-1016 "SDPOL.spad" 1814593 1814604 1814884 1815011) (-1015 "SCPKG.spad" 1812672 1812683 1814583 1814588) (-1014 "SCOPE.spad" 1811817 1811826 1812662 1812667) (-1013 "SCACHE.spad" 1810499 1810510 1811807 1811812) (-1012 "SAOS.spad" 1810371 1810380 1810489 1810494) (-1011 "SAERFFC.spad" 1810084 1810104 1810361 1810366) (-1010 "SAE.spad" 1808262 1808278 1808873 1809008) (-1009 "SAEFACT.spad" 1807963 1807983 1808252 1808257) (-1008 "RURPK.spad" 1805604 1805620 1807953 1807958) (-1007 "RULESET.spad" 1805045 1805069 1805594 1805599) (-1006 "RULE.spad" 1803249 1803273 1805035 1805040) (-1005 "RULECOLD.spad" 1803101 1803114 1803239 1803244) (-1004 "RSETGCD.spad" 1799479 1799499 1803091 1803096) (-1003 "RSETCAT.spad" 1789251 1789268 1799435 1799474) (-1002 "RSETCAT.spad" 1779055 1779074 1789241 1789246) (-1001 "RSDCMPK.spad" 1777507 1777527 1779045 1779050) (-1000 "RRCC.spad" 1775891 1775921 1777497 1777502) (-999 "RRCC.spad" 1774274 1774305 1775881 1775886) (-998 "RPOLCAT.spad" 1753635 1753649 1774142 1774269) (-997 "RPOLCAT.spad" 1732711 1732727 1753220 1753225) (-996 "ROUTINE.spad" 1728575 1728583 1731358 1731385) (-995 "ROMAN.spad" 1727808 1727816 1728441 1728570) (-994 "ROIRC.spad" 1726889 1726920 1727798 1727803) (-993 "RNS.spad" 1725793 1725801 1726791 1726884) (-992 "RNS.spad" 1724783 1724793 1725783 1725788) (-991 "RNG.spad" 1724519 1724527 1724773 1724778) (-990 "RMODULE.spad" 1724158 1724168 1724509 1724514) (-989 "RMCAT2.spad" 1723567 1723623 1724148 1724153) (-988 "RMATRIX.spad" 1722247 1722265 1722734 1722773) (-987 "RMATCAT.spad" 1717769 1717799 1722191 1722242) (-986 "RMATCAT.spad" 1713193 1713225 1717617 1717622) (-985 "RINTERP.spad" 1713082 1713101 1713183 1713188) (-984 "RING.spad" 1712440 1712448 1713062 1713077) (-983 "RING.spad" 1711806 1711816 1712430 1712435) (-982 "RIDIST.spad" 1711191 1711199 1711796 1711801) (-981 "RGCHAIN.spad" 1709771 1709786 1710676 1710703) (-980 "RF.spad" 1707386 1707396 1709761 1709766) (-979 "RFFACTOR.spad" 1706849 1706859 1707376 1707381) (-978 "RFFACT.spad" 1706585 1706596 1706839 1706844) (-977 "RFDIST.spad" 1705574 1705582 1706575 1706580) (-976 "RETSOL.spad" 1704992 1705004 1705564 1705569) (-975 "RETRACT.spad" 1704342 1704352 1704982 1704987) (-974 "RETRACT.spad" 1703690 1703702 1704332 1704337) (-973 "RESULT.spad" 1701751 1701759 1702337 1702364) (-972 "RESRING.spad" 1701099 1701145 1701689 1701746) (-971 "RESLATC.spad" 1700424 1700434 1701089 1701094) (-970 "REPSQ.spad" 1700154 1700164 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249761 249788) (-204 "DEGRED.spad" 249087 249101 249462 249467) (-203 "DEFINTRF.spad" 246612 246622 249077 249082) (-202 "DEFINTEF.spad" 245108 245124 246602 246607) (-201 "DECIMAL.spad" 242992 243000 243578 243671) (-200 "DDFACT.spad" 240791 240808 242982 242987) (-199 "DBLRESP.spad" 240389 240413 240781 240786) (-198 "DBASE.spad" 238961 238971 240379 240384) (-197 "DATABUF.spad" 238449 238462 238951 238956) (-196 "D03FAFA.spad" 238277 238285 238439 238444) (-195 "D03EEFA.spad" 238097 238105 238267 238272) (-194 "D03AGNT.spad" 237177 237185 238087 238092) (-193 "D02EJFA.spad" 236639 236647 237167 237172) (-192 "D02CJFA.spad" 236117 236125 236629 236634) (-191 "D02BHFA.spad" 235607 235615 236107 236112) (-190 "D02BBFA.spad" 235097 235105 235597 235602) (-189 "D02AGNT.spad" 229901 229909 235087 235092) (-188 "D01WGTS.spad" 228220 228228 229891 229896) (-187 "D01TRNS.spad" 228197 228205 228210 228215) (-186 "D01GBFA.spad" 227719 227727 228187 228192) (-185 "D01FCFA.spad" 227241 227249 227709 227714) (-184 "D01ASFA.spad" 226709 226717 227231 227236) (-183 "D01AQFA.spad" 226155 226163 226699 226704) (-182 "D01APFA.spad" 225579 225587 226145 226150) (-181 "D01ANFA.spad" 225073 225081 225569 225574) (-180 "D01AMFA.spad" 224583 224591 225063 225068) (-179 "D01ALFA.spad" 224123 224131 224573 224578) (-178 "D01AKFA.spad" 223649 223657 224113 224118) (-177 "D01AJFA.spad" 223172 223180 223639 223644) (-176 "D01AGNT.spad" 219231 219239 223162 223167) (-175 "CYCLOTOM.spad" 218737 218745 219221 219226) (-174 "CYCLES.spad" 215569 215577 218727 218732) (-173 "CVMP.spad" 214986 214996 215559 215564) (-172 "CTRIGMNP.spad" 213476 213492 214976 214981) (-171 "CTORCALL.spad" 213064 213072 213466 213471) (-170 "CSTTOOLS.spad" 212307 212320 213054 213059) (-169 "CRFP.spad" 206011 206024 212297 212302) (-168 "CRAPACK.spad" 205054 205064 206001 206006) (-167 "CPMATCH.spad" 204554 204569 204979 204984) (-166 "CPIMA.spad" 204259 204278 204544 204549) (-165 "COORDSYS.spad" 199152 199162 204249 204254) (-164 "CONTOUR.spad" 198554 198562 199142 199147) (-163 "CONTFRAC.spad" 194166 194176 198456 198549) (-162 "COMRING.spad" 193840 193848 194104 194161) (-161 "COMPPROP.spad" 193354 193362 193830 193835) (-160 "COMPLPAT.spad" 193121 193136 193344 193349) (-159 "COMPLEX.spad" 187154 187164 187398 187659) (-158 "COMPLEX2.spad" 186867 186879 187144 187149) (-157 "COMPFACT.spad" 186469 186483 186857 186862) (-156 "COMPCAT.spad" 184525 184535 186191 186464) (-155 "COMPCAT.spad" 182288 182300 183956 183961) (-154 "COMMUPC.spad" 182034 182052 182278 182283) (-153 "COMMONOP.spad" 181567 181575 182024 182029) (-152 "COMM.spad" 181376 181384 181557 181562) (-151 "COMBOPC.spad" 180281 180289 181366 181371) (-150 "COMBINAT.spad" 179026 179036 180271 180276) (-149 "COMBF.spad" 176394 176410 179016 179021) (-148 "COLOR.spad" 175231 175239 176384 176389) (-147 "CMPLXRT.spad" 174940 174957 175221 175226) (-146 "CLIP.spad" 171032 171040 174930 174935) (-145 "CLIF.spad" 169671 169687 170988 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117845 117872) (-103 "BGAGG.spad" 116267 116279 117052 117057) (-102 "BFUNCT.spad" 115831 115839 116247 116262) (-101 "BEZOUT.spad" 114965 114992 115781 115786) (-100 "BBTREE.spad" 111784 111794 114572 114599) (-99 "BASTYPE.spad" 111457 111464 111774 111779) (-98 "BASTYPE.spad" 111128 111137 111447 111452) (-97 "BALFACT.spad" 110568 110580 111118 111123) (-96 "AUTOMOR.spad" 110015 110024 110548 110563) (-95 "ATTREG.spad" 106734 106741 109767 110010) (-94 "ATTRBUT.spad" 102757 102764 106714 106729) (-93 "ATRIG.spad" 102227 102234 102747 102752) (-92 "ATRIG.spad" 101695 101704 102217 102222) (-91 "ASTCAT.spad" 101599 101606 101685 101690) (-90 "ASTCAT.spad" 101501 101510 101589 101594) (-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 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 3afc9f26..b731f09c 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(143433 . 3429209011) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(143433 . 3429259033) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) #0#) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) (((|#2| |#2|) . T)) ((((-530)) . T)) -((($ $) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((|#2| |#2|) . T) ((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530))))) +((($ $) -1461 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((|#2| |#2|) . T) ((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#2|) . T)) -((($) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((|#2|) . T) (((-388 (-530))) |has| |#2| (-37 (-388 (-530))))) +((($) -1461 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((|#2|) . T) (((-388 (-530))) |has| |#2| (-37 (-388 (-530))))) (|has| |#1| (-850)) ((((-804)) . T)) ((((-804)) . T)) @@ -23,28 +23,28 @@ ((((-208)) . T) (((-804)) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1|) . T)) -(-1476 (|has| |#1| (-21)) (|has| |#1| (-793))) -((($ $) . 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T) (((-208)) . T) (((-360)) . T) (((-833 (-360))) . T)) ((((-804)) . T)) -(-1476 (|has| |#1| (-21)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +(-1461 (|has| |#1| (-21)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) (((|#1|) |has| |#1| (-162))) (((|#1| $) |has| |#1| (-268 |#1| |#1|))) ((((-804)) . T)) @@ -256,15 +256,15 @@ (|has| |#1| (-795)) (|has| |#1| (-1027)) (((|#1|) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) ((((-127)) . 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T)) (((|#1| (-911)) . T)) (((#0=(-811 |#1|) $) |has| #0# (-268 #0# #0#))) @@ -273,7 +273,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1075)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) (|has| (-1167 |#1| |#2| |#3| |#4|) (-138)) (|has| (-1167 |#1| |#2| |#3| |#4|) (-140)) (|has| |#1| (-138)) @@ -290,20 +290,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-984))) ((((-804)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) #0#) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) (((|#1|) . 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T)) ((((-530) (-127)) . T)) ((((-804)) . T)) @@ -660,22 +660,22 @@ (|has| |#1| (-1027)) (((|#2|) . T)) ((((-506)) |has| |#2| (-572 (-506))) (((-833 (-360))) |has| |#2| (-572 (-833 (-360)))) (((-833 (-530))) |has| |#2| (-572 (-833 (-530))))) -(((|#4|) -1476 (|has| |#4| (-162)) (|has| |#4| (-344)))) -(((|#3|) -1476 (|has| |#3| (-162)) (|has| |#3| (-344)))) +(((|#4|) -1461 (|has| |#4| (-162)) (|has| |#4| (-344)))) +(((|#3|) -1461 (|has| |#3| (-162)) (|has| |#3| (-344)))) ((((-804)) . T)) (((|#1|) . T)) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-850))) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-850))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-850))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-850))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-850))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-850))) ((($ $) . T) ((#0=(-1099) $) |has| |#1| (-216)) ((#0# |#1|) |has| |#1| (-216)) ((#1=(-766 (-1099)) |#1|) . T) ((#1# $) . 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T)) (|has| (-388 |#2|) (-140)) (|has| (-388 |#2|) (-138)) @@ -688,22 +688,22 @@ (|has| |#1| (-522)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-804)) . T)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) (|has| |#1| (-37 (-388 (-530)))) -((((-369) (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-369) (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#2| (-1075)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (((|#1|) . T)) ((((-369) (-1082)) . T)) (|has| |#1| (-522)) ((((-114 |#1|)) . T)) ((((-127)) . T)) ((((-530) |#1|) . T)) -(-1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1461 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#2|) . T)) ((((-804)) . T)) ((((-767 |#1|)) . T)) @@ -716,7 +716,7 @@ (((|#1|) |has| |#1| (-162))) ((((-804)) . T)) ((((-506)) |has| |#1| (-572 (-506)))) -(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1461 (|has| |#1| (-795)) (|has| |#1| (-1027))) (((|#2|) |has| |#2| (-291 |#2|))) (((#0=(-530) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -726,7 +726,7 @@ (((#0=(-530) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) ((($) . T) (((-530)) . T) (((-388 (-530))) . T)) (|has| |#2| (-349)) -(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1461 (|has| |#1| (-795)) (|has| |#1| (-1027))) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) @@ -737,9 +737,9 @@ ((((-1097 |#1| |#2| |#3|) $) -12 (|has| (-1097 |#1| |#2| |#3|) (-268 (-1097 |#1| |#2| |#3|) (-1097 |#1| |#2| |#3|))) (|has| |#1| (-344))) (($ $) . T)) ((((-804)) . T)) ((((-804)) . T)) -((($) . T) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +((($) . T) (((-388 (-530))) -1461 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((($ $) . T)) ((($ $) . T)) ((((-804)) . T)) @@ -749,12 +749,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((((-388 (-530))) . 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T) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) . T)) +((($) . T) (((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) . T)) (|has| |#1| (-776)) ((((-388 (-530))) |has| |#1| (-975 (-388 (-530)))) (((-530)) |has| |#1| (-975 (-530))) ((|#1|) . T)) (|has| |#1| (-1027)) @@ -819,8 +819,8 @@ (((|#3|) |has| |#3| (-1027))) (|has| |#3| (-349)) (((|#1|) . T) (((-804)) . T)) -((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) ((|#1|) |has| |#1| (-162))) -(((|#1|) |has| |#1| (-162)) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522)))) +((((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) ((|#1|) |has| |#1| (-162))) +(((|#1|) |has| |#1| (-162)) (((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1461 (|has| |#1| (-344)) (|has| |#1| (-522)))) ((((-804)) . T)) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#2|) . T)) @@ -830,30 +830,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-162))) ((((-388 (-530))) . T) (((-530)) . T)) -((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-522))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) -((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-522))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($ $) -1461 (|has| |#1| (-162)) (|has| |#1| (-522))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +((($) -1461 (|has| |#1| (-162)) (|has| |#1| (-522))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) ((((-137)) . T)) (((|#1|) . T)) ((((-137)) . T)) -((($) -1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984)))) +((($) -1461 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((|#2|) -1461 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984)))) ((((-137)) . T)) (((|#1| |#2| |#3|) . T)) -(-1476 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) +(-1461 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) (|has| $ (-140)) (|has| $ (-140)) (|has| |#1| (-1027)) ((((-804)) . T)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-453)) (|has| |#1| (-522)) (|has| |#1| (-984)) (|has| |#1| (-1039))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-453)) (|has| |#1| (-522)) (|has| |#1| (-984)) (|has| |#1| (-1039))) ((($ $) |has| |#1| (-268 $ $)) ((|#1| $) |has| |#1| (-268 |#1| |#1|))) (((|#1| (-388 (-530))) . T)) (((|#1|) . T)) ((((-1099)) . T)) (|has| |#1| (-522)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-522)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) @@ -864,7 +864,7 @@ (|has| |#1| (-140)) (|has| |#1| (-138)) (|has| |#4| (-793)) -(((|#2| (-223 (-2167 |#1|) (-719)) (-806 |#1|)) . T)) +(((|#2| (-223 (-2267 |#1|) (-719)) (-806 |#1|)) . T)) (|has| |#3| (-793)) (((|#1| (-502 |#3|) |#3|) . T)) (|has| |#1| (-140)) @@ -878,21 +878,21 @@ (|has| |#1| (-138)) ((((-388 (-530))) |has| |#2| (-344)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1476 (|has| |#1| (-330)) (|has| |#1| (-349))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1461 (|has| |#1| (-330)) (|has| |#1| (-349))) ((((-1066 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-162)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-216)) (|has| |#2| (-984))) -(((|#2|) . T) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) -(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) -(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) +(((|#2|) . T) (((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) +(-1461 (|has| |#3| (-741)) (|has| |#3| (-793))) +(-1461 (|has| |#3| (-741)) (|has| |#3| (-793))) ((((-804)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-647)) . T)) -(-1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) (|has| |#1| (-522)) (((|#1|) . T)) (((|#1|) . T)) @@ -914,10 +914,10 @@ (((|#1| (-388 (-530))) . T)) (((|#3|) . T) (((-570 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((#0=(-1097 |#1| |#2| |#3|) #0#) -12 (|has| (-1097 |#1| |#2| |#3|) (-291 (-1097 |#1| |#2| |#3|))) (|has| |#1| (-344))) (((-1099) #0#) -12 (|has| (-1097 |#1| |#2| |#3|) (-491 (-1099) (-1097 |#1| |#2| |#3|))) (|has| |#1| (-344)))) @@ -925,8 +925,8 @@ ((((-804)) . T)) ((((-804)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) -(((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) (((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))))) +(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) +(((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) (((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) |has| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (-291 (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))))) ((((-804)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -937,10 +937,10 @@ ((($ $) . T) ((#0=(-806 |#1|) $) . T) ((#0# |#2|) . 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T)) -((($) -1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330)) (|has| |#1| (-522))) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +((($) -1461 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330)) (|has| |#1| (-522))) (((-388 (-530))) -1461 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) ((((-530) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -983,37 +983,37 @@ (-12 (|has| |#1| (-349)) (|has| |#2| (-349))) ((((-804)) . T)) ((((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|)) ((|#1| |#1|) |has| |#1| (-291 |#1|))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-291 |#1|))) (|has| |#1| (-349)) @@ -1021,31 +1021,31 @@ (|has| |#1| (-349)) ((((-1099) $) |has| |#1| (-491 (-1099) $)) (($ $) |has| |#1| (-291 $)) ((|#1| |#1|) |has| |#1| (-291 |#1|)) (((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|))) ((((-1099)) |has| |#1| (-841 (-1099)))) -(-1476 (-12 (|has| |#1| (-216)) (|has| |#1| (-344))) (|has| |#1| (-330))) +(-1461 (-12 (|has| |#1| (-216)) (|has| |#1| (-344))) (|has| |#1| (-330))) ((((-369) (-1046)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-369) |#1|) . T)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-1027)) ((((-804)) . T)) ((((-804)) . T)) ((((-851 |#1|)) . T)) -((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) -((((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) |has| |#1| (-162)) (($) -1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850)))) +((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +((((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) |has| |#1| (-162)) (($) -1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-811 |#1|)) |has| #0# (-291 #0#))) (((|#1| |#2|) . T)) -(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) -(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1461 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1461 (|has| |#2| (-741)) (|has| |#2| (-793))) (-12 (|has| |#1| (-741)) (|has| |#2| (-741))) (((|#1|) . T)) (-12 (|has| |#1| (-741)) (|has| |#2| (-741))) -(-1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (|has| |#1| (-1121)) (((#0=(-530) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) ((((-388 (-530))) . T) (($) . T)) @@ -1056,8 +1056,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-388 (-530)) #0#) . T)) (|has| |#1| (-344)) ((((-530)) . T) (((-388 (-530))) . T) (($) . T)) -((($ $) . T) ((#0=(-388 (-530)) #0#) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1| |#1|) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((($ $) . T) ((#0=(-388 (-530)) #0#) -1461 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1| |#1|) . T)) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1|) . T) (($) . T) (((-388 (-530))) . T)) ((((-804)) . T)) ((((-804)) . T)) @@ -1072,14 +1072,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-793)) (|has| |#1| (-793)) -((($) . T) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) -(-1476 (|has| |#1| (-162)) (|has| |#1| (-522))) -(((#0=(-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) #0#) |has| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))))) +((($) . T) (((-388 (-530))) -1461 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +(-1461 (|has| |#1| (-162)) (|has| |#1| (-522))) +(((#0=(-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) #0#) |has| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (-291 (-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))))) ((($) . T)) (|has| |#2| (-795)) ((($) . T)) (((|#2|) |has| |#2| (-1027))) -((((-804)) -1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-571 (-804))) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((-1181 |#2|)) . T)) +((((-804)) -1461 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-571 (-804))) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((-1181 |#2|)) . T)) (|has| |#1| (-795)) (|has| |#1| (-795)) ((((-1082) (-51)) . T)) @@ -1087,10 +1087,10 @@ ((((-804)) . T)) ((((-530)) |has| #0=(-388 |#2|) (-593 (-530))) ((#0#) . T)) ((((-530) (-137)) . T)) -((((-530) (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T) ((|#1| |#2|) . T)) +((((-530) (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T) ((|#1| |#2|) . T)) ((((-388 (-530))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-804)) . T)) ((((-851 |#1|)) . T)) (|has| |#1| (-344)) @@ -1115,31 +1115,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-162))) -((((-530) (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T) ((|#1| |#2|) . T)) +((((-530) (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#3|) . 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T)) (|has| |#2| (-793)) (-12 (|has| |#2| (-216)) (|has| |#2| (-984))) (|has| |#1| (-522)) (|has| |#1| (-1075)) ((((-1082) |#1|) . T)) -(-1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) -(((#0=(-388 (-530)) #0#) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1| |#1|) . T)) +(-1461 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(((#0=(-388 (-530)) #0#) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($ $) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1| |#1|) . T)) ((((-388 (-530))) |has| |#1| (-975 (-530))) (((-530)) |has| |#1| (-975 (-530))) (((-1099)) |has| |#1| (-975 (-1099))) ((|#1|) . T)) ((((-530) |#2|) . T)) ((((-388 (-530))) |has| |#1| (-975 (-388 (-530)))) (((-530)) |has| |#1| (-975 (-530))) ((|#1|) . T)) ((((-530)) |has| |#1| (-827 (-530))) (((-360)) |has| |#1| (-827 (-360)))) -((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1|) . T)) +((((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1|) . T)) (((|#1|) . T)) ((((-597 |#4|)) . T) (((-804)) . T)) ((((-506)) |has| |#4| (-572 (-506)))) @@ -1152,17 +1152,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1099)) |has| (-388 |#2|) (-841 (-1099)))) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) #0#) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-804)) -1476 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-571 (-804))) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) (((-1181 |#3|)) . T)) +((((-804)) -1461 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-571 (-804))) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) (((-1181 |#3|)) . T)) ((((-530) |#2|) . T)) -(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) -(((|#2| |#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($ $) |has| |#2| (-162))) +(-1461 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(((|#2| |#2|) -1461 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($ $) |has| |#2| (-162))) ((((-804)) . T)) ((((-804)) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T) ((|#2|) . T)) ((((-804)) . T)) ((((-804)) . T)) ((((-1082) (-1099) (-530) (-208) (-804)) . T)) @@ -1197,8 +1197,8 @@ (|has| |#1| (-37 (-388 (-530)))) ((((-804)) . T)) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -(((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($) |has| |#2| (-162))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +(((|#2|) -1461 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-984))) (($) |has| |#2| (-162))) (|has| $ (-140)) ((((-388 |#2|)) . T)) ((((-388 (-530))) |has| #0=(-388 |#2|) (-975 (-388 (-530)))) (((-530)) |has| #0# (-975 (-530))) ((#0#) . T)) @@ -1209,11 +1209,11 @@ (((|#3|) |has| |#3| (-162))) (|has| |#1| (-140)) (|has| |#1| (-138)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) (((|#1|) . T)) (((|#2|) . T)) @@ -1244,7 +1244,7 @@ ((((-938 |#1|)) . T) ((|#1|) . T)) ((((-804)) . T)) ((((-804)) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-388 (-530))) . T) (((-388 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1095 |#1|)) . T)) ((((-530)) . T) (($) . T) (((-388 (-530))) . T)) @@ -1252,9 +1252,9 @@ (|has| |#1| (-795)) (((|#2|) . T)) ((((-530)) . T) (($) . T) (((-388 (-530))) . T)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) ((((-530) |#2|) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#2|) . T)) ((((-530) |#3|) . T)) (((|#2|) . T)) @@ -1269,7 +1269,7 @@ (((|#3|) -12 (|has| |#3| (-291 |#3|)) (|has| |#3| (-1027)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) #0#) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-344)) (((|#2|) . T) (((-530)) |has| |#2| (-975 (-530))) (((-388 (-530))) |has| |#2| (-975 (-388 (-530))))) @@ -1299,19 +1299,19 @@ (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1| |#2|) . T)) ((((-530) (-137)) . T)) -(((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) -((($) -1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +(((#0=(-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) #0#) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) +((($) -1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (|has| |#1| (-795)) (((|#2| (-719) (-1012)) . T)) (((|#1| |#2|) . T)) -(-1476 (|has| |#1| (-162)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-162)) (|has| |#1| (-522))) (|has| |#1| (-739)) (((|#1|) |has| |#1| (-162))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-1476 (|has| |#1| (-140)) (-12 (|has| |#1| (-344)) (|has| |#2| (-140)))) -(-1476 (|has| |#1| (-138)) (-12 (|has| |#1| (-344)) (|has| |#2| (-138)))) +(-1461 (|has| |#1| (-140)) (-12 (|has| |#1| (-344)) (|has| |#2| (-140)))) +(-1461 (|has| |#1| (-138)) (-12 (|has| |#1| (-344)) (|has| |#2| (-138)))) (((|#4|) . T)) (|has| |#1| (-138)) ((((-1082) |#1|) . T)) @@ -1324,10 +1324,10 @@ (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#3|) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) -(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1461 (|has| |#1| (-795)) (|has| |#1| (-1027))) (((|#1|) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027))) (((-899 |#1|)) . T)) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027))) (((-899 |#1|)) . T)) (|has| |#1| (-793)) (|has| |#1| (-793)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) @@ -1340,8 +1340,8 @@ ((($) . T)) ((((-369) (-1082)) . T)) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) -((((-804)) -1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-571 (-804))) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((-1181 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2940 (-1082)) (|:| -1806 #0#))) . T)) +((((-804)) -1461 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-571 (-804))) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((-1181 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3078 (-1082)) (|:| -1874 #0#))) . T)) (((|#1|) . T)) ((((-804)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) @@ -1349,7 +1349,7 @@ (|has| |#2| (-138)) (|has| |#2| (-140)) (|has| |#1| (-453)) -(-1476 (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +(-1461 (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) (|has| |#1| (-344)) ((((-804)) . T)) (|has| |#1| (-37 (-388 (-530)))) @@ -1358,8 +1358,8 @@ (|has| |#1| (-793)) (|has| |#1| (-793)) ((((-804)) . T)) -((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) ((|#1|) |has| |#1| (-162))) -(((|#1|) |has| |#1| (-162)) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522)))) +((((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-344)) ((|#1|) |has| |#1| (-162))) +(((|#1|) |has| |#1| (-162)) (((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1461 (|has| |#1| (-344)) (|has| |#1| (-522)))) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#1| |#2|) . T)) ((((-1099)) |has| |#1| (-841 (-1099)))) @@ -1367,7 +1367,7 @@ ((((-804)) . T)) ((((-804)) . T)) (|has| |#1| (-1027)) -(((|#2| (-461 (-2167 |#1|) (-719)) (-806 |#1|)) . T)) +(((|#2| (-461 (-2267 |#1|) (-719)) (-806 |#1|)) . T)) ((((-388 (-530))) . #0=(|has| |#2| (-344))) (($) . #0#)) (((|#1| (-502 (-1099)) (-1099)) . T)) (((|#1|) . T)) @@ -1387,16 +1387,16 @@ (|has| |#1| (-140)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) -((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) . T)) ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-1099) (-51)) . T)) ((($ $) . T)) (((|#1| (-530)) . T)) ((((-851 |#1|)) . T)) -(((|#1|) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984))) (($) -1476 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)))) +(((|#1|) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984))) (($) -1461 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)))) (((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) |has| |#1| (-975 (-388 (-530))))) (|has| |#1| (-795)) (|has| |#1| (-795)) @@ -1411,13 +1411,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) (((|#1|) |has| |#1| (-162))) (((|#4| |#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) -(((|#3|) -1476 (|has| |#3| (-162)) (|has| |#3| (-344)))) +(((|#3|) -1461 (|has| |#3| (-162)) (|has| |#3| (-344)))) (|has| |#2| (-795)) (|has| |#1| (-795)) -(-1476 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-850))) +(-1461 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-850))) ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) ((((-530) |#2|) . T)) -(((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)))) +(((|#2|) -1461 (|has| |#2| (-162)) (|has| |#2| (-344)))) (|has| |#1| (-330)) (((|#3| |#3|) -12 (|has| |#3| (-291 |#3|)) (|has| |#3| (-1027)))) ((($) . T) (((-388 (-530))) . T)) @@ -1425,7 +1425,7 @@ (|has| |#1| (-768)) (|has| |#1| (-768)) (((|#1|) . T)) -(-1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-793)) (|has| |#1| (-793)) (|has| |#1| (-793)) @@ -1434,13 +1434,13 @@ ((((-530)) . T) (($) . T) (((-388 (-530))) . T)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-37 (-388 (-530)))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-1099)) |has| |#1| (-841 (-1099))) (((-1012)) . T)) (((|#1|) . T)) (|has| |#1| (-793)) -(((#0=(-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) #0#) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))))) +(((#0=(-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) #0#) |has| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (-291 (-2 (|:| -3078 (-1082)) (|:| -1874 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (|has| |#1| (-1027)) (((|#1|) . T)) @@ -1459,7 +1459,7 @@ (((|#1|) . T)) ((((-137)) . T)) (((|#2|) |has| |#2| (-162))) -(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1461 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((|#1|) . T)) (|has| |#1| (-138)) (|has| |#1| (-140)) @@ -1481,32 +1481,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) ((#0=(-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) #0#) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))))) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-850))) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-850))) +(((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) ((#0=(-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) #0#) |has| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (-291 (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-850))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-850))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -1476 (|has| |#3| (-162)) (|has| |#3| (-344)))) +(((|#3|) -1461 (|has| |#3| (-162)) (|has| |#3| (-344)))) (|has| |#1| (-795)) (|has| |#1| (-522)) ((((-543 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-1476 (-12 (|has| |#1| (-344)) (|has| |#2| (-768))) (-12 (|has| |#1| (-344)) (|has| |#2| (-795)))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (-12 (|has| |#1| (-344)) (|has| |#2| (-768))) (-12 (|has| |#1| (-344)) (|has| |#2| (-795)))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) ((((-851 |#1|)) . T)) (((|#1| (-474 |#1| |#3|) (-474 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-719)) . 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T)) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) . T)) ((((-388 |#2|)) . T) (((-388 (-530))) . T) (($) . T)) ((((-622 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1514,17 +1514,17 @@ ((((-804)) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) ((((-804)) . T)) -((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) ((((-804)) . T)) ((((-804)) . T)) ((((-804)) . T)) (((|#2|) . 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T)) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) ((($ $) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((($ $) . T)) ((((-530) (-110)) . T)) ((($) . T)) (((|#1|) . T)) ((((-530)) . T)) ((((-110)) . T)) -(-1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-37 (-388 (-530)))) (((|#1| (-530)) . T)) ((($) . T)) @@ -1595,7 +1595,7 @@ (((|#1| (-1145 |#1| |#2| |#3|)) . T)) (((|#1| (-719)) . T)) (((|#1|) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-804)) . T)) (|has| |#1| (-1027)) ((((-1082) |#1|) . T)) @@ -1615,18 +1615,18 @@ (((|#1|) . T)) ((((-530)) . T)) ((((-804)) . T)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-330))) (|has| |#1| (-140)) ((((-804)) . T)) (((|#3|) . T)) -(-1476 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1461 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((((-804)) . T)) ((((-1166 |#2| |#3| |#4|)) . T) (((-1167 |#1| |#2| |#3| |#4|)) . T)) ((((-804)) . T)) -((((-47)) -12 (|has| |#1| (-522)) (|has| |#1| (-975 (-530)))) (((-570 $)) . T) ((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) -1476 (-12 (|has| |#1| (-522)) (|has| |#1| (-975 (-530)))) (|has| |#1| (-975 (-388 (-530))))) (((-388 (-893 |#1|))) |has| |#1| (-522)) (((-893 |#1|)) |has| |#1| (-984)) (((-1099)) . T)) +((((-47)) -12 (|has| |#1| (-522)) (|has| |#1| (-975 (-530)))) (((-570 $)) . T) ((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) -1461 (-12 (|has| |#1| (-522)) (|has| |#1| (-975 (-530)))) (|has| |#1| (-975 (-388 (-530))))) (((-388 (-893 |#1|))) |has| |#1| (-522)) (((-893 |#1|)) |has| |#1| (-984)) (((-1099)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-719)) . T)) -((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) |has| |#1| (-162))) +((($) -1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) |has| |#1| (-162))) (((|#1|) |has| |#1| (-291 |#1|))) ((((-1167 |#1| |#2| |#3| |#4|)) . T)) ((((-530)) |has| |#1| (-827 (-530))) (((-360)) |has| |#1| (-827 (-360)))) @@ -1634,14 +1634,14 @@ (|has| |#1| (-522)) (((|#1|) . T)) ((((-804)) . T)) -(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) (((|#1|) |has| |#1| (-162))) ((($) |has| |#1| (-522)) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1027))) -(((|#2|) -1476 (|has| |#2| (-162)) (|has| |#2| (-344)))) +(((|#2|) -1461 (|has| |#2| (-162)) (|has| |#2| (-344)))) ((((-1166 |#2| |#3| |#4|)) . T)) ((((-110)) . T)) (|has| |#1| (-768)) @@ -1651,8 +1651,8 @@ (|has| |#1| (-793)) (|has| |#1| (-793)) (((|#1| (-530) (-1012)) . T)) -(-1476 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +(-1461 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (((|#1| (-388 (-530)) (-1012)) . T)) (((|#1| (-719) (-1012)) . T)) (|has| |#1| (-795)) @@ -1668,28 +1668,28 @@ (((|#1|) . T)) (|has| |#1| (-1027)) ((((-530)) -12 (|has| |#1| (-344)) (|has| |#2| (-593 (-530)))) ((|#2|) |has| |#1| (-344))) -(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1461 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((|#2|) |has| |#2| (-162))) (((|#1|) |has| |#1| (-162))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) ((((-804)) . T)) (|has| |#3| (-793)) ((((-804)) . T)) ((((-1166 |#2| |#3| |#4|) (-300 |#2| |#3| |#4|)) . T)) ((((-804)) . T)) -(((|#1| |#1|) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984)))) +(((|#1| |#1|) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984)))) (((|#1|) . T)) ((((-530)) . T)) ((((-530)) . T)) -(((|#1|) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984)))) +(((|#1|) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-984)))) (((|#2|) |has| |#2| (-344))) ((($) . T) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-344))) (|has| |#1| (-795)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) |has| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))))) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-850))) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) |has| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (-291 (-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-850))) (((|#2|) . T) (((-530)) |has| |#2| (-593 (-530)))) ((((-804)) . T)) ((((-804)) . T)) @@ -1725,18 +1725,18 @@ (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) (((|#1|) . T)) -(-1476 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-162)) (|has| |#2| (-793)) (|has| |#2| (-984))) (((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) . T) (($ $) . T)) ((((-804)) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (|has| |#1| (-344)) (|has| |#1| (-344)) (|has| (-388 |#2|) (-216)) (|has| |#1| (-850)) (((|#2|) |has| |#2| (-984))) -(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) (|has| |#1| (-344)) (((|#1|) |has| |#1| (-162))) (((|#1| |#1|) . T)) @@ -1761,7 +1761,7 @@ (((|#1| (-388 (-530)) (-1012)) . T)) (((|#1| (-719) (-1012)) . T)) (((#0=(-388 |#2|) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-530)) -1476 (|has| (-388 (-530)) (-975 (-530))) (|has| |#1| (-975 (-530)))) (((-388 (-530))) . T)) +(((|#1|) . T) (((-530)) -1461 (|has| (-388 (-530)) (-975 (-530))) (|has| |#1| (-975 (-530)))) (((-388 (-530))) . T)) (((|#1| (-561 |#1| |#3|) (-561 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-162))) (((|#1|) . T)) @@ -1780,24 +1780,24 @@ ((((-647)) . T)) (((|#2|) |has| |#2| (-162))) (|has| |#2| (-793)) -((((-110)) |has| |#1| (-1027)) (((-804)) -1476 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027)))) +((((-110)) |has| |#1| (-1027)) (((-804)) -1461 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 (-51)))) . T)) ((((-804)) . T)) ((((-530) |#1|) . T)) ((((-647)) . T) (((-388 (-530))) . T) (((-530)) . T)) (((|#1| |#1|) |has| |#1| (-162))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) (((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) ((((-360)) . T)) ((((-647)) . T)) ((((-388 (-530))) . #0=(|has| |#2| (-344))) (($) . #0#)) (((|#1|) |has| |#1| (-162))) ((((-388 (-893 |#1|))) . T)) (((|#2| |#2|) . T)) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#2|) . T)) (|has| |#2| (-795)) (((|#3|) |has| |#3| (-984))) @@ -1807,14 +1807,14 @@ (|has| |#1| (-795)) ((((-1099)) |has| |#2| (-841 (-1099)))) ((((-804)) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-388 (-530))) . T) (($) . T)) (|has| |#1| (-453)) (|has| |#1| (-349)) (|has| |#1| (-349)) (|has| |#1| (-349)) (|has| |#1| (-344)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-453)) (|has| |#1| (-522)) (|has| |#1| (-984)) (|has| |#1| (-1039))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-453)) (|has| |#1| (-522)) (|has| |#1| (-984)) (|has| |#1| (-1039))) (|has| |#1| (-37 (-388 (-530)))) ((((-114 |#1|)) . T)) ((((-114 |#1|)) . T)) @@ -1835,11 +1835,11 @@ (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-795)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-140)) (|has| |#1| (-138)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)))) ((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)))) ((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((|#2|) . T)) (((|#3|) . T)) ((((-114 |#1|)) . T)) @@ -1857,11 +1857,11 @@ ((((-506)) |has| |#1| (-572 (-506))) (((-833 (-530))) |has| |#1| (-572 (-833 (-530)))) (((-833 (-360))) |has| |#1| (-572 (-833 (-360)))) (((-360)) . #0=(|has| |#1| (-960))) (((-208)) . #0#)) (((|#1|) |has| |#1| (-344))) ((((-804)) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((($ $) . T) (((-570 $) $) . T)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) ((($) . T) (((-1167 |#1| |#2| |#3| |#4|)) . T) (((-388 (-530))) . T)) -((($) -1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-522))) +((($) -1461 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-522))) (|has| |#1| (-344)) (|has| |#1| (-344)) (|has| |#1| (-344)) @@ -1872,11 +1872,11 @@ ((((-360)) . T)) (((|#3|) -12 (|has| |#3| (-291 |#3|)) (|has| |#3| (-1027)))) ((((-804)) . T)) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-850))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-850))) (((|#1|) . T)) (|has| |#1| (-795)) (|has| |#1| (-795)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) (((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (|has| |#1| (-1027)) @@ -1885,13 +1885,13 @@ (|has| |#1| (-138)) (|has| |#1| (-140)) ((((-530)) . T)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (((#0=(-1166 |#2| |#3| |#4|)) . T) (((-388 (-530))) |has| #0# (-37 (-388 (-530)))) (($) . T)) ((((-530)) . T)) (|has| |#1| (-344)) -(-1476 (-12 (|has| (-1173 |#1| |#2| |#3|) (-140)) (|has| |#1| (-344))) (|has| |#1| (-140))) -(-1476 (-12 (|has| (-1173 |#1| |#2| |#3|) (-138)) (|has| |#1| (-344))) (|has| |#1| (-138))) +(-1461 (-12 (|has| (-1173 |#1| |#2| |#3|) (-140)) (|has| |#1| (-344))) (|has| |#1| (-140))) +(-1461 (-12 (|has| (-1173 |#1| |#2| |#3|) (-138)) (|has| |#1| (-344))) (|has| |#1| (-138))) (|has| |#1| (-344)) (|has| |#1| (-138)) (|has| |#1| (-140)) @@ -1908,18 +1908,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-530)) |has| |#1| (-593 (-530)))) (((|#3|) |has| |#3| (-162))) -(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1461 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) ((((-530)) . T)) (((|#1| $) |has| |#1| (-268 |#1| |#1|))) ((((-388 (-530))) . T) (($) . T) (((-388 |#1|)) . T) ((|#1|) . T)) ((((-804)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -1476 (|has| |#1| (-272)) (|has| |#1| (-344))) ((#0=(-388 (-530)) #0#) |has| |#1| (-344))) -((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -1461 (|has| |#1| (-272)) (|has| |#1| (-344))) ((#0=(-388 (-530)) #0#) |has| |#1| (-344))) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) . T)) ((($) . T)) ((((-530) |#1|) . T)) ((((-1099)) |has| (-388 |#2|) (-841 (-1099)))) -(((|#1|) . T) (($) -1476 (|has| |#1| (-272)) (|has| |#1| (-344))) (((-388 (-530))) |has| |#1| (-344))) +(((|#1|) . T) (($) -1461 (|has| |#1| (-272)) (|has| |#1| (-344))) (((-388 (-530))) |has| |#1| (-344))) ((((-506)) |has| |#2| (-572 (-506)))) ((((-637 |#2|)) . T) (((-804)) . T)) (((|#1|) . T)) @@ -1927,8 +1927,8 @@ (((|#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) ((((-811 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -(-1476 (|has| |#4| (-741)) (|has| |#4| (-793))) -(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) +(-1461 (|has| |#4| (-741)) (|has| |#4| (-793))) +(-1461 (|has| |#3| (-741)) (|has| |#3| (-793))) ((((-804)) . T)) ((((-804)) . T)) (((|#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) @@ -1944,17 +1944,17 @@ ((((-388 (-530))) . T) (($) . T)) ((((-388 (-530))) . T) (($) . T)) ((((-388 (-530))) . T) (($) . T)) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-1139))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-1139))) ((($) . T)) ((((-388 (-530))) |has| #0=(-388 |#2|) (-975 (-388 (-530)))) (((-530)) |has| #0# (-975 (-530))) ((#0#) . T)) (((|#2|) . T) (((-530)) |has| |#2| (-593 (-530)))) (((|#1| (-719)) . T)) (|has| |#1| (-795)) (((|#1|) . T) (((-530)) |has| |#1| (-593 (-530)))) -((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) (((-388 (-530))) -1476 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) +((($) -1461 (|has| |#1| (-344)) (|has| |#1| (-330))) (((-388 (-530))) -1461 (|has| |#1| (-344)) (|has| |#1| (-330))) ((|#1|) . T)) ((((-530)) . T)) (|has| |#1| (-37 (-388 (-530)))) -((((-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))))) +((((-2 (|:| -3078 (-1082)) (|:| -1874 (-51)))) |has| (-2 (|:| -3078 (-1082)) (|:| -1874 (-51))) (-291 (-2 (|:| -3078 (-1082)) (|:| -1874 (-51)))))) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (|has| |#1| (-793)) (|has| |#1| (-37 (-388 (-530)))) @@ -1979,24 +1979,24 @@ (((|#1| |#2|) . T)) ((((-137)) . T)) ((((-728 |#1| (-806 |#2|))) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (|has| |#1| (-1121)) (((|#1|) . T)) -(-1476 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) +(-1461 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-349)) (|has| |#3| (-675)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984)) (|has| |#3| (-1027))) ((((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|))) (((|#2|) . T)) -((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) -((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($ $) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) +((($) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((((-851 |#1|)) . T)) ((($) . T)) ((((-388 (-893 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) ((((-506)) |has| |#4| (-572 (-506)))) ((((-804)) . T) (((-597 |#4|)) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-793)) -(((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) (((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) |has| (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|)) (-291 (-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))))) +(((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))) (((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) |has| (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|)) (-291 (-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))))) (|has| |#1| (-1027)) (|has| |#1| (-344)) (|has| |#1| (-795)) @@ -2004,16 +2004,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-388 (-530))) . T)) -((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) |has| |#1| (-162))) +((($) -1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) |has| |#1| (-162))) (|has| |#1| (-138)) (|has| |#1| (-140)) -(-1476 (-12 (|has| (-1097 |#1| |#2| |#3|) (-140)) (|has| |#1| (-344))) (|has| |#1| (-140))) -(-1476 (-12 (|has| (-1097 |#1| |#2| |#3|) (-138)) (|has| |#1| (-344))) (|has| |#1| (-138))) +(-1461 (-12 (|has| (-1097 |#1| |#2| |#3|) (-140)) (|has| |#1| (-344))) (|has| |#1| (-140))) +(-1461 (-12 (|has| (-1097 |#1| |#2| |#3|) (-138)) (|has| |#1| (-344))) (|has| |#1| (-138))) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-140)) (|has| |#1| (-138)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) (|has| |#1| (-793)) (((|#1| |#2|) . T)) @@ -2036,9 +2036,9 @@ ((((-804)) . T)) ((((-804)) . T)) ((((-506)) |has| |#1| (-572 (-506)))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|)) ((|#1| |#1|) |has| |#1| (-291 |#1|))) -(((|#1|) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)))) +(((|#1|) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)))) ((((-297 |#1|)) . T)) (((|#2|) |has| |#2| (-344))) (((|#2|) . T)) @@ -2059,13 +2059,13 @@ (|has| |#1| (-138)) (|has| |#1| (-140)) ((($ $) . T)) -(-1476 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027))) +(-1461 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027))) (|has| |#1| (-522)) (((|#2|) . T)) ((((-530)) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (((|#1|) . T)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) ((((-543 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2074,7 +2074,7 @@ ((($) . T)) (((|#1|) . T)) ((((-804)) . T)) -(((|#2|) |has| |#2| (-6 (-4272 "*")))) +(((|#2|) |has| |#2| (-6 (-4271 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2091,12 +2091,12 @@ (((|#1| |#2|) . T)) ((((-1099) |#1|) . T)) (((|#4|) . T)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-330))) ((((-1099) (-51)) . T)) ((((-1166 |#2| |#3| |#4|) (-300 |#2| |#3| |#4|)) . T)) ((((-388 (-530))) |has| |#1| (-975 (-388 (-530)))) (((-530)) |has| |#1| (-975 (-530))) ((|#1|) . T)) ((((-804)) . T)) -(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) +(-1461 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-349)) (|has| |#2| (-675)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984)) (|has| |#2| (-1027))) (((#0=(-1167 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-388 (-530)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-162)) ((#0=(-388 (-530)) #0#) |has| |#1| (-522)) (($ $) |has| |#1| (-522))) (((|#1|) . T) (($) . T) (((-388 (-530))) . T)) @@ -2115,14 +2115,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((|#2| |#3|) . T)) -(-1476 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1461 (|has| |#2| (-344)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) (((|#1| (-502 |#2|)) . T)) (((|#1| (-719)) . T)) (((|#1| (-502 (-1017 (-1099)))) . T)) (((|#1|) |has| |#1| (-162))) (((|#1|) . T)) (|has| |#2| (-850)) -(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1461 (|has| |#2| (-741)) (|has| |#2| (-793))) ((((-804)) . T)) ((($ $) . T) ((#0=(-1166 |#2| |#3| |#4|) #0#) . T) ((#1=(-388 (-530)) #1#) |has| #0# (-37 (-388 (-530))))) ((((-851 |#1|)) . T)) @@ -2131,13 +2131,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-344)) -(-1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330)) (|has| |#1| (-522))) (|has| |#1| (-344)) ((($) . T) ((#0=(-1166 |#2| |#3| |#4|)) . T) (((-388 (-530))) |has| #0# (-37 (-388 (-530))))) (((|#1| |#2|) . T)) ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) -(-1476 (-12 (|has| |#1| (-289)) (|has| |#1| (-850))) (|has| |#1| (-344)) (|has| |#1| (-330))) -(-1476 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) +(-1461 (-12 (|has| |#1| (-289)) (|has| |#1| (-850))) (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-841 (-1099))) (|has| |#1| (-984))) ((((-530)) |has| |#1| (-593 (-530))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-804)) . T)) @@ -2169,27 +2169,27 @@ (((|#1|) |has| |#1| (-162))) ((((-804)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) -(((|#2|) -1476 (|has| |#2| (-6 (-4272 "*"))) (|has| |#2| (-162)))) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(((|#2|) -1461 (|has| |#2| (-6 (-4271 "*"))) (|has| |#2| (-162)))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (|has| |#2| (-795)) (|has| |#2| (-850)) (|has| |#1| (-850)) (((|#2|) |has| |#2| (-162))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) ((((-804)) . T)) ((((-804)) . T)) ((((-506)) . T) (((-530)) . T) (((-833 (-530))) . T) (((-360)) . T) (((-208)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 (-51)))) . T)) (((|#1|) . T)) ((((-804)) . T)) (((|#1| |#2|) . T)) (((|#1| (-388 (-530))) . T)) (((|#1|) . T)) -(-1476 (|has| |#1| (-272)) (|has| |#1| (-344))) +(-1461 (|has| |#1| (-272)) (|has| |#1| (-344))) ((((-137)) . T)) ((((-388 |#2|)) . T) (((-388 (-530))) . T) (($) . T)) (|has| |#1| (-793)) @@ -2204,7 +2204,7 @@ ((((-388 (-530))) . T) (($) . T)) ((((-804)) . T)) ((((-804)) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-804)) . T)) ((((-804)) . T)) @@ -2215,7 +2215,7 @@ (((|#1|) . T)) ((((-597 (-137))) . T) (((-1082)) . T)) ((((-804)) . T)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) ((((-1099) |#1|) |has| |#1| (-491 (-1099) |#1|)) ((|#1| |#1|) |has| |#1| (-291 |#1|))) (|has| |#1| (-795)) ((((-804)) . T)) @@ -2227,16 +2227,16 @@ ((((-804)) . T) (((-597 |#4|)) . T)) (((|#2|) . T)) ((((-851 |#1|)) . T) (((-388 (-530))) . T) (($) . T)) -(-1476 (|has| |#4| (-162)) (|has| |#4| (-675)) (|has| |#4| (-793)) (|has| |#4| (-984))) -(-1476 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1461 (|has| |#4| (-162)) (|has| |#4| (-675)) (|has| |#4| (-793)) (|has| |#4| (-984))) +(-1461 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((((-1099) (-51)) . T)) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) -(-1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-793)) (|has| |#2| (-984))) (|has| |#1| (-850)) (|has| |#1| (-850)) (((|#2|) . T)) @@ -2251,12 +2251,12 @@ (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (|has| |#1| (-768)) (((#0=(-851 |#1|) #0#) . T) (($ $) . T) ((#1=(-388 (-530)) #1#) . T)) ((((-388 |#2|)) . T)) (|has| |#1| (-793)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) . T) ((#1=(-530) #1#) . T) (($ $) . T)) ((((-851 |#1|)) . T) (($) . T) (((-388 (-530))) . T)) (((|#2|) |has| |#2| (-984)) (((-530)) -12 (|has| |#2| (-593 (-530))) (|has| |#2| (-984)))) @@ -2266,25 +2266,25 @@ (|has| |#1| (-138)) (((|#2|) . T)) ((((-804)) . T)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) -((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2940 (-1099)) (|:| -1806 #0#))) . T)) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3078 (-1099)) (|:| -1874 #0#))) . T)) (|has| |#1| (-330)) ((((-530)) . T)) ((((-804)) . T)) (((#0=(-1167 |#1| |#2| |#3| |#4|) $) |has| #0# (-268 #0# #0#))) (|has| |#1| (-344)) (((#0=(-1012) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-330))) (((#0=(-388 (-530)) #0#) . T) ((#1=(-647) #1#) . T) (($ $) . T)) ((((-297 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) |has| |#1| (-344))) (|has| |#1| (-1027)) (((|#1|) . T)) -(((|#1|) -1476 (|has| |#2| (-348 |#1|)) (|has| |#2| (-398 |#1|)))) -(((|#1|) -1476 (|has| |#2| (-348 |#1|)) (|has| |#2| (-398 |#1|)))) +(((|#1|) -1461 (|has| |#2| (-348 |#1|)) (|has| |#2| (-398 |#1|)))) +(((|#1|) -1461 (|has| |#2| (-348 |#1|)) (|has| |#2| (-398 |#1|)))) (((|#2|) . T)) ((((-388 (-530))) . T) (((-647)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2303,7 +2303,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-530)) . T)) -(-1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) (((|#2|) . T) (((-530)) |has| |#2| (-593 (-530)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2340,7 +2340,7 @@ (|has| |#2| (-960)) ((($) . T)) (|has| |#1| (-850)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2348,24 +2348,24 @@ ((($) . T)) (|has| |#1| (-344)) ((((-851 |#1|)) . T)) -((($) -1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1461 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) -(-1476 (|has| |#1| (-349)) (|has| |#1| (-795))) +(-1461 (|has| |#1| (-349)) (|has| |#1| (-795))) (((|#1|) . T)) ((((-804)) . T)) ((((-1099)) -12 (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-841 (-1099))))) ((((-388 |#2|) |#3|) . T)) ((($) . T) (((-388 (-530))) . T)) ((((-719) |#1|) . T)) -(((|#2| (-223 (-2167 |#1|) (-719))) . T)) +(((|#2| (-223 (-2267 |#1|) (-719))) . T)) (((|#1| (-502 |#3|)) . T)) ((((-388 (-530))) . T)) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((((-804)) . T)) -(((#0=(-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) #0#) |has| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))))) +(((#0=(-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) #0#) |has| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (-291 (-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))))) (|has| |#1| (-850)) (|has| |#2| (-344)) -(-1476 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-159 (-360))) . T) (((-208)) . T) (((-360)) . T)) ((((-804)) . T)) (((|#1|) . T)) @@ -2382,11 +2382,11 @@ (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-37 (-388 (-530)))) (-12 (|has| |#1| (-515)) (|has| |#1| (-776))) ((((-804)) . T)) -((((-1099)) -1476 (-12 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (|has| |#1| (-841 (-1099)))) (-12 (|has| |#1| (-344)) (|has| |#2| (-841 (-1099)))))) +((((-1099)) -1461 (-12 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (|has| |#1| (-841 (-1099)))) (-12 (|has| |#1| (-344)) (|has| |#2| (-841 (-1099)))))) (|has| |#1| (-344)) ((((-1099)) -12 (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-841 (-1099))))) (|has| |#1| (-344)) @@ -2396,7 +2396,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-344))) (((|#2|) |has| |#1| (-344))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-162))) (((|#1|) . T)) @@ -2421,30 +2421,30 @@ ((((-360)) -12 (|has| |#1| (-344)) (|has| |#2| (-827 (-360)))) (((-530)) -12 (|has| |#1| (-344)) (|has| |#2| (-827 (-530))))) (|has| |#1| (-344)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-344)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) (|has| |#1| (-344)) (|has| |#1| (-522)) (((|#4| |#4|) -12 (|has| |#4| (-291 |#4|)) (|has| |#4| (-1027)))) (((|#3|) . T)) (((|#1|) . T)) -(-1476 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) (((|#2|) . T)) (((|#2|) . T)) -(-1476 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +(-1461 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (|has| |#1| (-37 (-388 (-530)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-388 (-530)))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) ((((-1082) |#1|) . T)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-349))) (|has| |#1| (-140)) ((((-543 |#1|)) . T)) ((($) . T)) @@ -2452,7 +2452,7 @@ (|has| |#1| (-522)) (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-37 (-388 (-530)))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-330))) (|has| |#1| (-140)) ((((-804)) . T)) ((($) . T)) @@ -2477,7 +2477,7 @@ (|has| |#1| (-739)) (|has| |#1| (-739)) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-112)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2498,7 +2498,7 @@ ((((-530)) . T)) ((((-804)) . T)) ((((-530)) . T)) -(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1461 (|has| |#2| (-741)) (|has| |#2| (-793))) ((((-159 (-360))) . T) (((-208)) . T) (((-360)) . T)) ((((-804)) . T)) ((((-804)) . T)) @@ -2510,9 +2510,9 @@ (((|#1|) . T) (($) . T) (((-388 (-530))) . T)) (|has| |#1| (-344)) (|has| |#1| (-344)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) -(-1476 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +(-1461 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-453)) (|has| |#1| (-675)) (|has| |#1| (-841 (-1099))) (|has| |#1| (-984)) (|has| |#1| (-1039)) (|has| |#1| (-1027))) (|has| |#1| (-1075)) ((((-530) |#1|) . T)) (((|#1|) . T)) @@ -2530,8 +2530,8 @@ (((|#1|) . T)) (|has| |#1| (-522)) ((((-388 |#2|)) . T) (((-388 (-530))) . T) (($) . T)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) ((((-360)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2540,7 +2540,7 @@ (|has| |#1| (-522)) (|has| |#1| (-1027)) ((((-728 |#1| (-806 |#2|))) |has| (-728 |#1| (-806 |#2|)) (-291 (-728 |#1| (-806 |#2|))))) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-850)) @@ -2550,12 +2550,12 @@ (|has| |#1| (-216)) (((|#1| (-502 (-1017 (-1099)))) . T)) (|has| |#2| (-344)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 (-51)))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) ((((-804)) . T)) ((((-804)) . T)) -(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) +(-1461 (|has| |#3| (-741)) (|has| |#3| (-793))) ((((-804)) . T)) ((((-1046)) . T) (((-804)) . T)) ((((-804)) . T)) @@ -2565,8 +2565,8 @@ ((((-530)) . T)) (((|#3|) . T)) ((((-804)) . T)) -(-1476 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) -(-1476 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) +(-1461 (|has| |#1| (-289)) (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-162)) (|has| |#1| (-522)) (|has| |#1| (-984))) (((#0=(-543 |#1|) #0#) . T) (($ $) . T) ((#1=(-388 (-530)) #1#) . T)) ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) (((|#1|) |has| |#1| (-162))) @@ -2574,12 +2574,12 @@ ((((-543 |#1|)) . T) (($) . T) (((-388 (-530))) . T)) ((($) . T) (((-388 (-530))) . T)) ((($) . T) (((-388 (-530))) . T)) -(((|#2|) |has| |#2| (-6 (-4272 "*")))) +(((|#2|) |has| |#2| (-6 (-4271 "*")))) (((|#1|) . T)) (((|#1|) . T)) ((((-804)) |has| |#1| (-571 (-804)))) ((((-276 |#3|)) . T)) -(((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530)))) ((|#2| |#2|) . T) (($ $) -1476 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +(((#0=(-388 (-530)) #0#) |has| |#2| (-37 (-388 (-530)))) ((|#2| |#2|) . T) (($ $) -1461 (|has| |#2| (-162)) (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) . T)) @@ -2587,20 +2587,20 @@ (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) (((|#1|) . T) (((-388 (-530))) . T) (($) . T)) -((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . T) ((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530))))) -((($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1| |#1|) . 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T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (|has| |#2| (-850)) (|has| |#1| (-850)) -((($) -1476 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1461 (|has| |#1| (-162)) (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#1|) . T)) -((((-2 (|:| -2940 (-1082)) (|:| -1806 |#1|))) . T)) +((((-2 (|:| -3078 (-1082)) (|:| -1874 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2614,10 +2614,10 @@ (((|#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027)))) (((#0=(-388 (-530)) #0#) . T)) ((((-388 (-530))) . T)) -(-1476 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-25)) (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) (((|#1|) . T)) (((|#1|) . T)) -(-1476 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-506)) . T)) ((((-804)) . T)) ((((-1099)) |has| |#2| (-841 (-1099))) (((-1012)) . T)) @@ -2632,12 +2632,12 @@ ((($ $) . T) ((#0=(-388 (-530)) #0#) . T)) ((((-1099)) |has| |#1| (-841 (-1099)))) ((((-851 |#1|)) . T) (((-388 (-530))) . T) (($) . T)) -((($) . T) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) . T)) -(((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530)))) ((|#1| |#1|) . T) (($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-522)))) +((($) . T) (((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#1|) . T)) +(((#0=(-388 (-530)) #0#) |has| |#1| (-37 (-388 (-530)))) ((|#1| |#1|) . T) (($ $) -1461 (|has| |#1| (-162)) (|has| |#1| (-522)))) ((($) . T) (((-388 (-530))) . T)) (((|#1|) . T) (((-388 (-530))) . T) (((-530)) . T) (($) . T)) (((|#2|) |has| |#2| (-984)) (((-530)) -12 (|has| |#2| (-593 (-530))) (|has| |#2| (-984)))) -((((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) . T) (($) -1476 (|has| |#1| (-162)) (|has| |#1| (-522)))) +((((-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((|#1|) . T) (($) -1461 (|has| |#1| (-162)) (|has| |#1| (-522)))) (|has| |#1| (-522)) (((|#1|) |has| |#1| (-344))) ((((-530)) . T)) @@ -2656,8 +2656,8 @@ ((((-804)) . T)) (|has| |#2| (-768)) (|has| |#2| (-768)) -((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#2|) |has| |#1| (-344)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) . T)) +((((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) ((|#2|) |has| |#1| (-344)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1|) . T) (((-530)) |has| |#1| (-975 (-530))) (((-388 (-530))) |has| |#1| (-975 (-388 (-530))))) ((((-530)) |has| |#1| (-827 (-530))) (((-360)) |has| |#1| (-827 (-360)))) @@ -2683,12 +2683,12 @@ (((|#2| (-719)) . T)) ((((-1099)) . T)) ((((-811 |#1|)) . T)) -(-1476 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984))) -(-1476 (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1461 (|has| |#3| (-25)) (|has| |#3| (-128)) (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-741)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1461 (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((((-804)) . T)) (((|#1|) . T)) -(-1476 (|has| |#2| (-741)) (|has| |#2| (-793))) -(-1476 (-12 (|has| |#1| (-741)) (|has| |#2| (-741))) (-12 (|has| |#1| (-795)) (|has| |#2| (-795)))) +(-1461 (|has| |#2| (-741)) (|has| |#2| (-793))) +(-1461 (-12 (|has| |#1| (-741)) (|has| |#2| (-741))) (-12 (|has| |#1| (-795)) (|has| |#2| (-795)))) ((((-811 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-349)) @@ -2714,7 +2714,7 @@ (((|#1|) . T)) ((((-804)) . T)) (|has| |#2| (-850)) -((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) . T)) ((((-506)) |has| |#2| (-572 (-506))) (((-833 (-360))) |has| |#2| (-572 (-833 (-360)))) (((-833 (-530))) |has| |#2| (-572 (-833 (-530))))) ((((-804)) . T)) ((((-804)) . T)) @@ -2747,12 +2747,12 @@ ((((-388 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1027)) -(((|#2| (-461 (-2167 |#1|) (-719))) . T)) +(((|#2| (-461 (-2267 |#1|) (-719))) . T)) ((((-530) |#1|) . T)) ((((-1082)) . T) (((-804)) . T)) (((|#2| |#2|) . T)) (((|#1| (-502 (-1099))) . T)) -(-1476 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-530)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2762,9 +2762,9 @@ ((($) . T) (((-388 (-530))) . T)) ((($) . T)) ((($) . 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T)) @@ -2863,25 +2863,25 @@ (((|#1|) |has| |#2| (-398 |#1|))) (((|#1|) |has| |#2| (-398 |#1|))) ((((-851 |#1|)) . T) (((-388 (-530))) . T) (($) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) ((((-804)) . T)) -((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) |has| (-2 (|:| -2940 (-1099)) (|:| -1806 (-51))) (-291 (-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))))) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) |has| (-2 (|:| -3078 (-1099)) (|:| -1874 (-51))) (-291 (-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) ((((-530) |#1|) . T)) ((((-530) |#1|) . T)) ((((-530) |#1|) . 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T)) -(-1476 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1461 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-388 (-530)))) ((((-804)) . T)) @@ -2889,15 +2889,15 @@ (((|#1|) |has| |#1| (-162)) (($) |has| |#1| (-522)) (((-388 (-530))) |has| |#1| (-522))) (((|#2|) . T) (((-530)) |has| |#2| (-593 (-530)))) (|has| |#1| (-344)) -(-1476 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (-12 (|has| |#1| (-344)) (|has| |#2| (-216)))) +(-1461 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (-12 (|has| |#1| (-344)) (|has| |#2| (-216)))) (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-344)) (((|#1|) . T)) -(((#0=(-388 (-530)) #0#) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($ $) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1| |#1|) . T)) +(((#0=(-388 (-530)) #0#) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($ $) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1| |#1|) . T)) ((((-530) |#1|) . T)) ((((-297 |#1|)) . T)) (((#0=(-647) (-1095 #0#)) . T)) -((((-388 (-530))) -1476 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1476 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1|) . T)) +((((-388 (-530))) -1461 (|has| |#1| (-37 (-388 (-530)))) (|has| |#1| (-344))) (($) -1461 (|has| |#1| (-162)) (|has| |#1| (-344)) (|has| |#1| (-522))) ((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (|has| |#1| (-793)) ((($ $) . T) ((#0=(-806 |#1|) $) . T) ((#0# |#2|) . T)) @@ -2914,12 +2914,12 @@ (((#0=(-1167 |#1| |#2| |#3| |#4|)) |has| #0# (-291 #0#))) ((($) . T)) (((|#1|) . 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T)) -(-1476 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) -(-1476 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-128)) (|has| |#2| (-128))) (-12 (|has| |#1| (-741)) (|has| |#2| (-741)))) +(-1461 (|has| |#2| (-128)) (|has| |#2| (-162)) (|has| |#2| (-344)) (|has| |#2| (-741)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-128)) (|has| |#2| (-128))) (-12 (|has| |#1| (-741)) (|has| |#2| (-741)))) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) ((($) . T) (((-811 |#1|)) . T) (((-388 (-530))) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) @@ -2956,15 +2956,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-388 |#2|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-388 (-530)) #0#) . T) (($ $) . T)) ((((-530)) . T)) @@ -2993,32 +2993,32 @@ ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-344))) ((((-1099)) . T) (((-804)) . T)) (|has| |#1| (-344)) -((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) +((((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) |has| |#2| (-162)) (($) -1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-388 (-530))) |has| |#2| (-37 (-388 (-530)))) ((|#2|) . T)) -((($) -1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) +((($) -1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((|#1|) |has| |#1| (-162)) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) ((((-1031)) . T)) ((((-804)) . 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T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1|) |has| |#1| (-162))) (((|#1|) |has| |#1| (-162))) ((((-388 (-530))) . T) (($) . T)) (((|#1| (-530)) . T)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-344)) (|has| |#1| (-344)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) -(-1476 (|has| |#1| (-162)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-162)) (|has| |#1| (-522))) (((|#1| (-530)) . T)) (((|#1| (-388 (-530))) . T)) (((|#1| (-719)) . T)) @@ -3033,16 +3033,16 @@ ((((-833 (-360))) . T) (((-833 (-530))) . T) (((-1099)) . T) (((-506)) . T)) (((|#1|) . T)) ((((-804)) . 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T)) -(-1476 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) +(-1461 (|has| |#2| (-162)) (|has| |#2| (-675)) (|has| |#2| (-793)) (|has| |#2| (-984))) ((((-1099)) -12 (|has| |#2| (-841 (-1099))) (|has| |#2| (-984)))) -(-1476 (-12 (|has| |#1| (-453)) (|has| |#2| (-453))) (-12 (|has| |#1| (-675)) (|has| |#2| (-675)))) +(-1461 (-12 (|has| |#1| (-453)) (|has| |#2| (-453))) (-12 (|has| |#1| (-675)) (|has| |#2| (-675)))) (|has| |#1| (-138)) (|has| |#1| (-140)) (|has| |#1| (-344)) @@ -3066,7 +3066,7 @@ ((((-1082) (-1099) (-530) (-208) (-804)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-1476 (|has| |#1| (-330)) (|has| |#1| (-349))) +(-1461 (|has| |#1| (-330)) (|has| |#1| (-349))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-804)) . T)) @@ -3074,7 +3074,7 @@ ((($) . T) ((|#1|) . T) (((-388 (-530))) |has| |#1| (-37 (-388 (-530))))) (((|#2|) |has| |#2| (-1027)) (((-530)) -12 (|has| |#2| (-975 (-530))) (|has| |#2| (-1027))) (((-388 (-530))) -12 (|has| |#2| (-975 (-388 (-530)))) (|has| |#2| (-1027)))) ((((-506)) |has| |#1| (-572 (-506)))) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-795)) (|has| |#1| (-1027)))) ((($) . T) (((-388 (-530))) . T)) (|has| |#1| (-850)) (|has| |#1| (-850)) @@ -3083,14 +3083,14 @@ ((((-804)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-162))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-522))) -(-1476 (|has| |#1| (-21)) (|has| |#1| (-793))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-522))) +(-1461 (|has| |#1| (-21)) (|has| |#1| (-793))) (((|#2|) . T)) -(-1476 (|has| |#1| (-21)) (|has| |#1| (-793))) +(-1461 (|has| |#1| (-21)) (|has| |#1| (-793))) (((|#1|) |has| |#1| (-162))) (((|#1|) . T)) (((|#1|) . T)) -((((-804)) -1476 (-12 (|has| |#1| (-571 (-804))) (|has| |#2| (-571 (-804)))) (-12 (|has| |#1| (-1027)) (|has| |#2| (-1027))))) +((((-804)) -1461 (-12 (|has| |#1| (-571 (-804))) (|has| |#2| (-571 (-804)))) (-12 (|has| |#1| (-1027)) (|has| |#2| (-1027))))) ((((-388 |#2|) |#3|) . T)) ((((-388 (-530))) . T) (($) . T)) (|has| |#1| (-37 (-388 (-530)))) @@ -3102,17 +3102,17 @@ (((|#1|) . T) (((-388 (-530))) . T) (((-530)) . T) (($) . T)) (((#0=(-530) #0#) . T)) ((($) . T) (((-388 (-530))) . T)) -(-1476 (|has| |#4| (-162)) (|has| |#4| (-675)) (|has| |#4| (-793)) (|has| |#4| (-984))) -(-1476 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) +(-1461 (|has| |#4| (-162)) (|has| |#4| (-675)) (|has| |#4| (-793)) (|has| |#4| (-984))) +(-1461 (|has| |#3| (-162)) (|has| |#3| (-675)) (|has| |#3| (-793)) (|has| |#3| (-984))) (|has| |#4| (-741)) -(-1476 (|has| |#4| (-741)) (|has| |#4| (-793))) +(-1461 (|has| |#4| (-741)) (|has| |#4| (-793))) (|has| |#4| (-793)) (|has| |#3| (-741)) -(-1476 (|has| |#3| (-741)) (|has| |#3| (-793))) +(-1461 (|has| |#3| (-741)) (|has| |#3| (-793))) (|has| |#3| (-793)) ((((-530)) . T)) (((|#2|) . T)) -((((-1099)) -1476 (-12 (|has| (-1097 |#1| |#2| |#3|) (-841 (-1099))) (|has| |#1| (-344))) (-12 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (|has| |#1| (-841 (-1099)))))) +((((-1099)) -1461 (-12 (|has| (-1097 |#1| |#2| |#3|) (-841 (-1099))) (|has| |#1| (-344))) (-12 (|has| |#1| (-15 * (|#1| (-530) |#1|))) (|has| |#1| (-841 (-1099)))))) ((((-1099)) -12 (|has| |#1| (-15 * (|#1| (-388 (-530)) |#1|))) (|has| |#1| (-841 (-1099))))) ((((-1099)) -12 (|has| |#1| (-15 * (|#1| (-719) |#1|))) (|has| |#1| (-841 (-1099))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3127,11 +3127,11 @@ ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) ((((-1064 |#1| |#2|)) . T)) ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) -(((|#2|) . T) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) -((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) . T)) ((($) . T)) (|has| |#1| (-960)) -(((|#2|) . T) (((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) ((((-804)) . T)) ((((-506)) |has| |#2| (-572 (-506))) (((-833 (-530))) |has| |#2| (-572 (-833 (-530)))) (((-833 (-360))) |has| |#2| (-572 (-833 (-360)))) (((-360)) . #0=(|has| |#2| (-960))) (((-208)) . #0#)) ((((-1099) (-51)) . T)) @@ -3143,15 +3143,15 @@ ((((-1097 |#1| |#2| |#3|)) . T)) ((((-1097 |#1| |#2| |#3|)) . T) (((-1090 |#1| |#2| |#3|)) . T)) ((((-804)) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((((-530) |#1|) . T)) ((((-1097 |#1| |#2| |#3|)) |has| |#1| (-344))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-344)) -(((|#3|) . T) ((|#2|) . T) (($) -1476 (|has| |#4| (-162)) (|has| |#4| (-793)) (|has| |#4| (-984))) ((|#4|) -1476 (|has| |#4| (-162)) (|has| |#4| (-344)) (|has| |#4| (-984)))) -(((|#2|) . T) (($) -1476 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((|#3|) -1476 (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-984)))) +(((|#3|) . T) ((|#2|) . T) (($) -1461 (|has| |#4| (-162)) (|has| |#4| (-793)) (|has| |#4| (-984))) ((|#4|) -1461 (|has| |#4| (-162)) (|has| |#4| (-344)) (|has| |#4| (-984)))) +(((|#2|) . T) (($) -1461 (|has| |#3| (-162)) (|has| |#3| (-793)) (|has| |#3| (-984))) ((|#3|) -1461 (|has| |#3| (-162)) (|has| |#3| (-344)) (|has| |#3| (-984)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-344)) @@ -3163,7 +3163,7 @@ ((((-804)) . T)) ((((-804)) . T)) (((|#1|) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) ((((-127)) . T) (((-804)) . T)) ((((-530) |#1|) . T)) (((|#1|) . T)) @@ -3171,31 +3171,31 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-344)) (|has| |#2| (-268 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-850))) -(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-432)) (|has| |#1| (-850))) +(-1461 (|has| |#1| (-795)) (|has| |#1| (-1027))) ((((-804)) . T)) ((((-804)) . T)) ((((-804)) . T)) (((|#1| (-502 |#2|)) . T)) -((((-2 (|:| -2940 (-1099)) (|:| -1806 (-51)))) . T)) +((((-2 (|:| -3078 (-1099)) (|:| -1874 (-51)))) . T)) (((|#1| (-530)) . T)) (((|#1| (-388 (-530))) . T)) (((|#1| (-719)) . T)) ((((-1104)) . T) (((-804)) . T)) ((((-114 |#1|)) . T) (($) . T) (((-388 (-530))) . T)) -(-1476 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) -(-1476 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) +(-1461 (|has| |#2| (-432)) (|has| |#2| (-522)) (|has| |#2| (-850))) +(-1461 (|has| |#1| (-432)) (|has| |#1| (-522)) (|has| |#1| (-850))) ((($) . T)) (((|#2| (-502 (-806 |#1|))) . T)) ((((-530) |#1|) . T)) (((|#2|) . T)) (((|#2| (-719)) . T)) -((((-804)) -1476 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) +((((-804)) -1461 (|has| |#1| (-571 (-804))) (|has| |#1| (-1027)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1082) |#1|) . T)) ((((-388 |#2|)) . T)) -((((-2 (|:| -2940 |#1|) (|:| -1806 |#2|))) . T)) +((((-2 (|:| -3078 |#1|) (|:| -1874 |#2|))) . T)) (|has| |#1| (-522)) (|has| |#1| (-522)) ((($) . T) ((|#2|) . T)) @@ -3203,12 +3203,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-268 |#2| |#2|))) (((|#1| (-597 |#1|)) |has| |#1| (-793))) -(-1476 (|has| |#1| (-216)) (|has| |#1| (-330))) -(-1476 (|has| |#1| (-344)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-216)) (|has| |#1| (-330))) +(-1461 (|has| |#1| (-344)) (|has| |#1| (-330))) (|has| |#1| (-1027)) (((|#1|) . T)) ((((-388 (-530))) . T) (($) . T)) -((((-938 |#1|)) . T) ((|#1|) . T) (((-530)) -1476 (|has| (-938 |#1|) (-975 (-530))) (|has| |#1| (-975 (-530)))) (((-388 (-530))) -1476 (|has| (-938 |#1|) (-975 (-388 (-530)))) (|has| |#1| (-975 (-388 (-530)))))) +((((-938 |#1|)) . T) ((|#1|) . T) (((-530)) -1461 (|has| (-938 |#1|) (-975 (-530))) (|has| |#1| (-975 (-530)))) (((-388 (-530))) -1461 (|has| (-938 |#1|) (-975 (-388 (-530)))) (|has| |#1| (-975 (-388 (-530)))))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (((|#1| |#1|) -12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) @@ -3219,9 +3219,9 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1064 |#1| |#2|) #0#) |has| (-1064 |#1| |#2|) (-291 (-1064 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) #0#) |has| (-2 (|:| -2940 |#1|) (|:| -1806 |#2|)) (-291 (-2 (|:| -2940 |#1|) (|:| -1806 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((#0=(-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) #0#) |has| (-2 (|:| -3078 |#1|) (|:| -1874 |#2|)) (-291 (-2 (|:| -3078 |#1|) (|:| -1874 |#2|))))) (((#0=(-114 |#1|)) |has| #0# (-291 #0#))) -(-1476 (|has| |#1| (-795)) (|has| |#1| (-1027))) +(-1461 (|has| |#1| (-795)) (|has| |#1| (-1027))) ((($ $) . T)) ((($ $) . T) ((#0=(-806 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-216)) ((|#2| |#1|) |has| |#1| (-216)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 59326d3b..05135bb3 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3429209004) -(4273 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3429259026) +(4272 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -461,647 +461,646 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |divisor| |choosemon| |precision| |tensorProduct| - |numberOfHues| |nextSublist| |var2StepsDefault| |ellipticCylindrical| - |nextSubsetGray| |useNagFunctions| |transform| - |permutationRepresentation| |blue| |overset?| |tubePointsDefault| - |prolateSpheroidal| |firstSubsetGray| |s17dcf| |setStatus!| - |rationalPoints| |pack!| |completeEchelonBasis| |green| |ParCond| - |tubeRadiusDefault| |dom| |oblateSpheroidal| |clipPointsDefault| - |s17def| |setCondition!| |nonSingularModel| |complexLimit| - |createRandomElement| |set| |yellow| |redmat| |dimension| |bipolar| - |drawToScale| |s17dgf| |setValue!| |algSplitSimple| |limit| - |cyclicSubmodule| |/\\| |red| |bipolarCylindrical| |stop| |adaptive| - |s17dhf| |empty?| |iifact| |hyperelliptic| |linearlyDependent?| - |standardBasisOfCyclicSubmodule| |\\/| |hasTopPredicate?| - |divideExponents| |toroidal| |figureUnits| |s17dlf| |splitNodeOf!| - |iibinom| |elliptic| |linearDependence| |areEquivalent?| - |topPredicate| |unmakeSUP| |conical| |putColorInfo| |s18acf| |remove!| - |iiperm| |integralDerivationMatrix| |solveLinear| - |isAbsolutelyIrreducible?| |setTopPredicate| |makeSUP| |modTree| - |title| |appendPoint| |s18adf| |subNodeOf?| |deleteProperty!| |iipow| - |integralRepresents| |reducedSystem| |meatAxe| |patternVariable| - |vectorise| |multiEuclideanTree| |component| |s18aef| |nodeOf?| |has?| - |iidsum| |integralCoordinates| |duplicates?| |scanOneDimSubspaces| - |withPredicates| |extend| |complexZeros| |ranges| |s18aff| - |updateStatus!| |sort| |iidprod| |yCoordinates| |mapGen| |expt| - |setPredicates| |truncate| |e| |divisorCascade| |pointLists| |s18dcf| - |extractSplittingLeaf| |ipow| |inverseIntegralMatrixAtInfinity| - |mapExpon| |showArrayValues| |predicates| |order| |graeffe| - |makeGraphImage| |s18def| |squareMatrix| |factorial| - |integralMatrixAtInfinity| |commutativeEquality| |showScalarValues| - |hasPredicate?| |terms| F |pleskenSplit| |graphImage| |mr| |s19aaf| - |transpose| |any| |multinomial| |showSummary| |inverseIntegralMatrix| - |leftMult| |solveRetract| |show| |optional?| |squareFreePart| - |reciprocalPolynomial| |groebSolve| |s19abf| |trim| |permutation| - |integralMatrix| |rightMult| |mainVariable| |multiple?| |BumInSepFFE| - |rootRadius| |testDim| |s19acf| |split| |stirling1| - |reduceBasisAtInfinity| |random| |showAttributes| |makeUnit| - |uniform01| |trace| |generic?| |multiplyExponents| |schwerpunkt| - |genericPosition| |s19adf| |upperCase!| |stirling2| - |normalizeAtInfinity| |reverse!| |normal01| |quoted?| |laurentIfCan| - |setErrorBound| |lfunc| |s20acf| |upperCase| |summation| - |complementaryBasis| |makeMulti| |exponential1| |inR?| |laurentRep| - |brillhartIrreducible?| |startPolynomial| |inHallBasis?| |s20adf| - |lowerCase!| |factorials| |integral?| |makeTerm| |chiSquare1| |isList| - |rationalPower| |brillhartTrials| |cycleElt| |reorder| |s21baf| - |lowerCase| |mkcomm| |integralAtInfinity?| |listOfMonoms| - |exponential| |isOp| |dominantTerm| |computeCycleLength| |headAst| - |s21bbf| |KrullNumber| |polarCoordinates| |integralBasisAtInfinity| - |symmetricSquare| |chiSquare| |satisfy?| |limitPlus| - |computeCycleEntry| |heap| |s21bcf| |numberOfVariables| |eq?| - |imaginary| |ramified?| |factor1| |factorFraction| |addBadValue| - |split!| |coerceP| |gcdprim| |s21bdf| |algebraicDecompose| |solid| - |ramifiedAtInfinity?| |symmetricProduct| |uniform| |badValues| - |setlast!| |powerSum| |gcdcofact| |fortranCompilerName| - |transcendentalDecompose| |solid?| |width| |singular?| - |symmetricPower| |binomial| NOT |retractable?| |setrest!| |elementary| - |gcdcofactprim| |fortranLinkerArgs| |internalDecompose| |denominators| - |singularAtInfinity?| |directSum| |poisson| OR |ListOfTerms| - |setfirst!| |alternating| |lintgcd| |aspFilename| |decompose| - |numerators| |branchPoint?| |solveLinearPolynomialEquationByFractions| - |geometric| AND |PDESolve| |cycleSplit!| |plusInfinity| |lhs| |cyclic| - |hex| |dimensionsOf| |upDateBranches| |convergents| - |branchPointAtInfinity?| |hasSolution?| |ridHack1| |leftFactor| - |concat!| |minusInfinity| |rhs| |dihedral| |every?| |restorePrecision| - |preprocess| |approximants| |rationalPoint?| |linSolve| |interpolate| - |rightFactorCandidate| |cycleTail| |cap| |any?| |antiCommutator| - |internalZeroSetSplit| |reducedForm| |absolutelyIrreducible?| |zero| - |LyndonWordsList| |nullSpace| |measure| |cycleLength| |cup| |host| - |commutator| |internalAugment| |optional| |genus| |LyndonWordsList1| - |nullity| |coerceImages| |cycleEntry| |delta| |wreath| |trueEqual| - |associator| |possiblyInfinite?| |getZechTable| |And| |lyndonIfCan| - |rowEchelon| |fixedPoints| |invmultisect| |SFunction| |factorList| - |complexEigenvalues| |explicitlyFinite?| |node| |createZechTable| |Or| - |lyndon| |column| |odd?| |multisect| |skewSFunction| - |listConjugateBases| |complexEigenvectors| |nextItem| - |createMultiplicationTable| |Not| |lyndon?| |row| |even?| |revert| - |type| |cyclotomicDecomposition| |matrixGcd| |normalizedAssociate| - |infiniteProduct| |createMultiplicationMatrix| - |numberOfComputedEntries| |maxColIndex| |numberOfCycles| - |generalLambert| |cyclotomicFactorization| |divideIfCan!| |normalize| - |evenInfiniteProduct| |createLowComplexityTable| |rst| |minColIndex| * - |cyclePartition| |evenlambert| |rangeIsFinite| |leastPower| - |outputArgs| |oddInfiniteProduct| |createLowComplexityNormalBasis| - |frst| |maxRowIndex| |coerceListOfPairs| |oddlambert| |top| - |functionIsContinuousAtEndPoints| |idealiser| |normInvertible?| - |generalInfiniteProduct| |representationType| |lazyEvaluate| |print| - |minRowIndex| |coercePreimagesImages| |lambert| |continue| - |functionIsOscillatory| |idealiserMatrix| |normFactors| |showAll?| - |createPrimitiveElement| |lazy?| |antisymmetric?| |listRepresentation| - |lagrange| |changeName| |moduleSum| |npcoef| |showAllElements| - |tableForDiscreteLogarithm| |explicitlyEmpty?| |symmetric?| - |permanent| |univariatePolynomial| |exprHasWeightCosWXorSinWX| - |mapUnivariate| |listexp| |tree| |delay| |cons| |hexDigit?| - |factorsOfCyclicGroupSize| |explicitEntries?| |diagonal?| |cycles| - |integrate| |exprHasAlgebraicWeight| |mapUnivariateIfCan| - |characteristicPolynomial| |findCycle| |escape| |sizeMultiplication| - |matrixDimensions| |square?| |cycle| |multiplyCoefficients| - |exprHasLogarithmicWeights| |mapMatrixIfCan| |realEigenvalues| - |repeating?| |ord| |getMultiplicationMatrix| |matrixConcat3D| - |rectangularMatrix| |initializeGroupForWordProblem| |quoByVar| - |combineFeatureCompatibility| |mapBivariate| |level| - |realEigenvectors| |repeating| |equation| |mkIntegral| - |getMultiplicationTable| |setelt!| |characteristic| |movedPoints| - |coefficients| |sparsityIF| |fullDisplay| |halfExtendedResultant2| - |recip| |primitive?| |identityMatrix| |round| |wordInGenerators| - |stFunc1| |relationsIdeal| |halfExtendedResultant1| |integers| - |numberOfIrreduciblePoly| |zeroMatrix| |fractionPart| - |wordInStrongGenerators| |stFunc2| |saturate| |extendedResultant| - |oddintegers| |source| |numberOfPrimitivePoly| |dec| |nullary| - |wholePart| |orbits| |stFuncN| |groebner?| |subResultantsChain| |int| - |numberOfNormalPoly| |fixedPoint| |floor| |orbit| |fixedPointExquo| - |groebnerIdeal| |lazyPseudoQuotient| |mapmult| |recur| |ceiling| - |permutationGroup| |ode1| |ideal| |lazyPseudoRemainder| |deriv| - |edf2efi| |const| |norm| |wordsForStrongGenerators| |ode2| - |leadingIdeal| |bernoulliB| |gderiv| |dfRange| |curry| - |mightHaveRoots| |strongGenerators| |ode| |bright| |backOldPos| - |eulerE| |compose| |target| |dflist| |diag| |refine| |generators| - |mpsode| |numericIfCan| |addiag| |df2mf| |curryRight| |middle| - |bivariateSLPEBR| UP2UTS |rangePascalTriangle| |complexNumericIfCan| - |lazyIntegrate| |ldf2vmf| |curryLeft| |roman| - |solveLinearPolynomialEquationByRecursion| UTS2UP |sizePascalTriangle| - |FormatArabic| |nlde| |edf2ef| |max| |constantRight| |property| - |recoverAfterFail| |factorByRecursion| LODO2FUN |fillPascalTriangle| - |ScanArabic| |powern| |vedf2vef| |factorSquareFreeByRecursion| RF2UTS - |safeCeiling| |FormatRoman| |mapdiv| |df2st| |comp| |cCos| |imagK| - |randomR| |magnitude| |delete| |safeFloor| |ScanRoman| - |lazyGintegrate| |f2st| |cSin| |imagJ| |result| |units| - |factorSFBRlcUnit| |cross| |safetyMargin| |ScanFloatIgnoreSpaces| - |power| |ldf2lst| |cLog| |imagI| |charthRoot| |dot| |sumSquares| - |sdf2lst| |cExp| |conjugate| |conditionP| |scan| |euclideanNormalForm| - |f01bsf| |smith| |entry| |getlo| |cRationalPower| |queue| - |solveLinearPolynomialEquation| |graphCurves| |euclideanGroebner| - |f01maf| |completeSmith| |gethi| |cPower| |nthRoot| - |factorSquareFreePolynomial| |drawCurves| |factorGroebnerBasis| |li| - |f01mcf| |diophantineSystem| |outputMeasure| |seriesToOutputForm| - |fractRadix| |code| |clearCache| |groebnerFactorize| |f01qcf| |csubst| - |elt| |measure2Result| |iCompose| |wholeRadix| |overlabel| |basicSet| - |credPol| |f01qdf| |particularSolution| |att2Result| |taylorQuoByVar| - |cycleRagits| |overbar| |infRittWu?| |redPol| |f01qef| |numer| - |mapSolve| |iflist2Result| |iExquo| |prefixRagits| |prime| |getCurve| - |gbasis| |f01rcf| |denom| |quadratic| |pdf2ef| |getStream| - |fractRagits| |quote| |listLoops| |critT| |f01rdf| |rule| |cubic| - |pdf2df| |getRef| |wholeRagits| |supersub| |closed?| |log10| |critM| - |f01ref| |quartic| |pi| |df2ef| |makeSeries| |radix| |presuper| - |open?| |bitand| |critB| |f02aaf| |infinity| |aLinear| |fi2df| GF2FG - |randnum| |presub| |setClosed| |critBonD| |f02abf| |aQuadratic| |mat| - FG2F |generator| |reseed| |super| |tube| |critMTonD1| |f02adf| - |aCubic| |neglist| F2FG |seed| |sub| |unitVector| |index| |critMonD1| - |kernel| |f02aef| |aQuartic| |multiEuclidean| |explogs2trigs| - |rational| |rarrow| |cosSinInfo| |draw| |redPo| |f02aff| - |radicalSolve| |option| |extendedEuclidean| |comment| |trigs2explogs| - |rational?| |assign| |loopPoints| |hMonic| |f02agf| |radicalRoots| - |euclideanSize| |swap!| |rationalIfCan| |slash| |generalTwoFactor| - |pair| |updatF| BY |f02ajf| |contractSolve| |position| |sizeLess?| - |fill!| |setvalue!| |over| |generalSqFr| |sPol| |f02akf| - |decomposeFunc| |simplifyPower| |minIndex| |setchildren!| |zag| - |twoFactor| |makeObject| |updatD| |f02awf| |unvectorise| |function| - |predicate| |number?| |maxIndex| |node?| |postfix| |setOrder| - |minGbasis| |f02axf| |bubbleSort!| |seriesSolve| |entry?| |child?| - |lo| |infix| |getOrder| |lepol| |f02bbf| |insertionSort!| |coef| - |constantToUnaryFunction| |indices| |distance| |incr| |vconcat| - |less?| |prinshINFO| |f02bjf| |check| |condition| |tubePlot| |index?| - |nodes| |hi| |hconcat| |userOrdered?| |prindINFO| |f02fjf| |lprop| - |exponentialOrder| |entries| |rename| |rspace| |largest| |fprindINFO| - |f02wef| |llprop| |completeEval| |key?| |nothing| |rename!| |vspace| - |more?| |prinpolINFO| |f02xef| |lllp| |lowerPolynomial| |symbolIfCan| - |mainValue| |hspace| |setVariableOrder| |prinb| |f04adf| |lllip| - |raisePolynomial| |argument| |mainDefiningPolynomial| |superHeight| - |getVariableOrder| |critpOrder| |f04arf| |mesh?| |parameters| - |normalDeriv| |constantKernel| |mainForm| |subHeight| - |resetVariableOrder| |tail| |makeCrit| |f04asf| |mesh| |ran| - |constantIfCan| |messagePrint| |rischDE| |pattern| |prime?| - |virtualDegree| |f04atf| |polygon?| |highCommonTerms| |kovacic| - |rischDEsys| |padecf| |rationalFunction| |alphanumeric| - |conditionsForIdempotents| |f04axf| |polygon| |mapCoef| |laplace| - |monomRDE| |pade| |taylorIfCan| |genericRightDiscriminant| |f04faf| - |closedCurve?| |log| |cond| |lcm| |nthCoef| |erf| - |trailingCoefficient| |baseRDE| |root| |removeZeroes| |alphabetic| - |genericRightTraceForm| |f04jgf| |closedCurve| |digit| |binomThmExpt| - |normalizeIfCan| |message| |polyRDE| |quotientByP| |taylorRep| - |hexDigit| |genericLeftDiscriminant| |output| |f04maf| |curve?| - |charClass| |append| |pomopo!| |polCase| |monomRDEsys| |moduloP| - |factorSquareFree| |outputList| |genericLeftTraceForm| |status| - |f04mbf| |curve| |mapExponents| |gcd| |distFact| |dilog| |baseRDEsys| - |generate| |modulus| |henselFact| |properties| |genericRightNorm| - |f04mcf| |point?| |false| |linearAssociatedLog| |sin| |identification| - |weighted| |digits| |hasHi| |translate| |genericRightTrace| |f04qaf| - |enterPointData| |linearAssociatedOrder| |compile| |incrementBy| |cos| - |LyndonCoordinates| |rdHack1| |continuedFraction| |fmecg| |upperCase?| - |genericRightMinimalPolynomial| |f07adf| |composites| - |linearAssociatedExp| |LyndonBasis| |tan| |light| |midpoint| |expand| - = |commonDenominator| |rightRankPolynomial| |f07aef| |components| - |createNormalElement| |zeroDimensional?| |cot| |midpoints| - |filterWhile| |pastel| |clearDenominator| |genericLeftNorm| |f07fdf| - |matrix| |numberOfComposites| |setLabelValue| |fglmIfCan| |realZeros| - |#| |filterUntil| |sec| |dark| |length| < |splitDenominator| - |genericLeftTrace| |f07fef| |numberOfComponents| |getCode| |groebner| - |mainCharacterization| |select| |csc| > |getSyntaxFormsFromFile| - |scripts| |double| |monicRightFactorIfCan| - |genericLeftMinimalPolynomial| |s01eaf| |create3Space| |printCode| - |lexTriangular| |asin| |algebraicOf| |surface| <= |rightFactorIfCan| - |leftRankPolynomial| |s13aaf| |outputAsScript| |printStatement| - |squareFreeLexTriangular| |acos| |ReduceOrder| >= |coordinate| - |leftFactorIfCan| |generic| |s13acf| |outputAsTex| |block| |atan| - |belong?| |setref| |partitions| |monicDecomposeIfCan| |rightUnits| - |s13adf| |abs| |returns| |acot| |operator| |deref| |conjugates| - |monicCompleteDecompose| |leftUnits| |s14aaf| |Beta| |goto| |Ci| - |asec| |ref| |shuffle| |divideIfCan| + |compBound| |s14abf| |digamma| - |repeatUntilLoop| |Si| |makeRecord| |acsc| |radicalEigenvectors| - |shufflein| |noKaratsuba| - ~= |tablePow| |s14baf| |polygamma| |Ei| - |radicalEigenvector| |close| |sinh| |sequences| |declare!| - |karatsubaOnce| / |coerce| |solveid| |s15adf| |Gamma| |iiacosh| |cosh| - |linGenPos| |radicalEigenvalues| |permutations| |karatsuba| - |construct| |testModulus| |s15aef| |besselJ| |remove| |initial| - |iiatanh| |groebgen| |tanh| |eigenMatrix| |display| |atoms| |separate| - |HenselLift| |s17acf| |besselY| |checkPrecision| |iiacoth| - |rootKerSimp| |coth| |totolex| |normalise| |makeResult| |pseudoDivide| - |s17adf| |besselI| |last| |iiasech| |leftRank| |sech| |minPol| - |gramschmidt| |is?| |pseudoQuotient| |complement| |s17aef| |besselK| - |assoc| |iiacsch| |rightRank| |csch| |computeBasis| |orthonormalBasis| - |Is| |composite| |cardinality| |s17aff| |airyAi| |specialTrigs| - |doubleRank| |asinh| |coord| |antisymmetricTensors| - |addMatchRestricted| |subResultantGcd| |internalIntegrate0| - |noLinearFactor?| |s17agf| |airyBi| |localReal?| |acosh| |insertMatch| - |resultant| |makeCos| |insertRoot!| |s17ahf| |subNode?| - |rischNormalize| |mkPrim| |changeBase| |puiseux| |atanh| |addMatch| - |discriminant| |makeSin| |s17ajf| |infLex?| |alphanumeric?| - |realElementary| |intPatternMatch| |companionBlocks| |acoth| |tower| - |getMatch| |pseudoRemainder| |iiGamma| |s17akf| |setEmpty!| - |lowerCase?| |validExponential| |primintegrate| |inv| |xCoord| |asech| - |failed?| |shiftLeft| |iiabs| |rootNormalize| |ground?| |expintegrate| - |yCoord| |optpair| |shiftRight| |bringDown| |d01anf| |algebraicSort| - |tanQ| |ground| |tanintegrate| |zCoord| |multiple| |getBadValues| - |karatsubaDivide| |newReduc| |declare| |d01apf| |moreAlgebraic?| - |callForm?| |applyQuote| |primextendedint| |leadingMonomial| |rCoord| - ~ |resetBadValues| |segment| |monicDivide| |doublyTransitive?| - |logical?| |d01aqf| |subTriSet?| |constructorName| |getIdentifier| - |expextendedint| |thetaCoord| |leadingCoefficient| |complexNumeric| - |knownInfBasis| |character?| |d01asf| |subPolSet?| |say| |getConstant| - |primlimitedint| |primitiveMonomials| |phiCoord| |OMUnknownCD?| - |complexNormalize| |open| |setelt| |rootSplit| |doubleComplex?| - |d01bbf| |internalSubPolSet?| |select!| |kernels| |explimitedint| - |color| |reductum| |ruleset| |OMParseError?| |complexElementary| - |ratDenom| |obj| |complex?| |d01fcf| |internalInfRittWu?| |delete!| - |primextintfrac| |hue| |OMwrite| |trigs| |univariate| |ratPoly| |copy| - |double?| |cache| |d01gaf| |internalSubQuasiComponent?| |retract| |sn| - |primlimintfrac| |shade| |po| |real?| |rootPower| |ffactor| |d01gbf| - |subQuasiComponent?| |parts| |isTimes| |dn| |primintfldpoly| - |nthRootIfCan| |suchThat| |OMread| |complexForm| |qfactor| |d02bbf| - |removeSuperfluousQuasiComponents| |isExpt| |sncndn| |expintfldpoly| - |expIfCan| |OMreadFile| |UpTriBddDenomInv| |factor| |autoCoerce| - |rootProduct| |UP2ifCan| |d02bhf| |subCase?| |isPower| |categoryFrame| - |monomialIntegrate| |logIfCan| |reset| |OMreadStr| |hash| - |LowTriBddDenomInv| |sqrt| |rootSimp| |anfactor| |d02cjf| - |removeSuperfluousCases| |rroot| |setProperties!| |count| - |monomialIntPoly| |sinIfCan| |OMlistCDs| |simplify| |real| - |fortranCharacter| |d02ejf| |prepareDecompose| |qroot| |getProperties| - |inverseLaplace| |write| |cosIfCan| |OMlistSymbols| |htrigs| |imag| - |fortranDoubleComplex| |d02gaf| |branchIfCan| |froot| |directProduct| - |setProperty!| |save| |iprint| |tanIfCan| |OMsupportsCD?| - |simplifyExp| |fortranComplex| |d02gbf| |startTableGcd!| |nthr| - |getProperty| |elem?| |cotIfCan| |OMsupportsSymbol?| |simplifyLog| - |fortranLogical| |d02kef| |stopTableGcd!| |port| |scopes| |notelem| - |destruct| |secIfCan| |OMunhandledSymbol| |expandPower| - |fortranInteger| |d02raf| |startTableInvSet!| |firstUncouplingMatrix| - |eigenvalues| |logpart| |cscIfCan| |OMreceive| |expandLog| - |fortranDouble| |d03edf| |stopTableInvSet!| |integral| |eigenvector| - |ratpart| |asinIfCan| |OMsend| |cos2sec| |fortranReal| |d03eef| - |stosePrepareSubResAlgo| |constant| |primitiveElement| - |generalizedEigenvector| |mkAnswer| |acosIfCan| |OMserve| |cosh2sech| - |external?| |d03faf| |stoseInternalLastSubResultant| |nextPrime| - |generalizedEigenvectors| |perfectNthPower?| |monomial| |atanIfCan| - |makeop| |cot2trig| |scalarTypeOf| |e01baf| - |stoseIntegralLastSubResultant| |arguments| |prevPrime| |eigenvectors| - |perfectNthRoot| |multivariate| |acotIfCan| |opeval| |coth2trigh| - |fortranCarriageReturn| |e01bef| |stoseLastSubResultant| |primes| - |factorAndSplit| |approxNthRoot| |variables| |asecIfCan| - |evaluateInverse| |csc2sin| |fortranLiteral| |e01bff| - |stoseInvertible?sqfreg| |selectsecond| |rightOne| |perfectSquare?| - |acscIfCan| |evaluate| |csch2sinh| |alphabetic?| |fortranLiteralLine| - |e01bgf| |stoseInvertibleSetsqfreg| |selectfirst| |search| - |basisOfRightAnnihilator| |leftOne| |perfectSqrt| |sinhIfCan| |conjug| - |sec2cos| |processTemplate| |e01bhf| |eq| |stoseInvertible?reg| - |makeprod| |basisOfLeftNucleus| |rightZero| |approxSqrt| |coshIfCan| - |adjoint| |sech2cosh| |makeFR| |iter| |e01daf| |stoseInvertibleSetreg| - |equivOperands| |leftZero| |generateIrredPoly| |tanhIfCan| - |getDatabase| |sin2csc| |musserTrials| |e01saf| |stoseInvertible?| - |equiv?| |swap| |complexExpand| |taylor| |cothIfCan| - |numericalOptimization| |sinh2csch| |stopMusserTrials| |e01sbf| - |stoseInvertibleSet| |impliesOperands| |or| |minPoly| - |complexIntegrate| |laurent| |sechIfCan| |goodnessOfFit| |tan2trig| - |numberOfFactors| |e01sef| |stoseSquareFreePart| |implies?| |freeOf?| - |dimensionOfIrreducibleRepresentation| |cschIfCan| |whatInfinity| - |tanh2trigh| |modularFactor| |e01sff| |coleman| |orOperands| - |operators| |irreducibleRepresentation| |asinhIfCan| |infinite?| - |tan2cot| |useSingleFactorBound?| |e02adf| |inverseColeman| |or?| - |mainKernel| |checkRur| |acoshIfCan| |finite?| |tanh2coth| - |useSingleFactorBound| |e02aef| |listYoungTableaus| |exp| - |andOperands| |distribute| |cAcsch| |atanhIfCan| |pureLex| |cot2tan| - |unravel| |useEisensteinCriterion?| |e02agf| |makeYoungTableau| |and?| - |rightTrim| |functionIsFracPolynomial?| |cAsech| |acothIfCan| - |totalLex| |coth2tanh| |leviCivitaSymbol| |useEisensteinCriterion| - |e02ahf| |nextColeman| |notOperand| |leftTrim| |problemPoints| - |cAcoth| |asechIfCan| |reverseLex| |removeCosSq| - |eisensteinIrreducible?| ^ |e02ajf| |nextLatticePermutation| - |variable?| |basisOfRightNucleus| |zerosOf| |cAtanh| |acschIfCan| - |leftLcm| |removeSinSq| |tryFunctionalDecomposition?| |e02akf| - |nextPartition| |term| |basisOfMiddleNucleus| |singularitiesOf| - |cAcosh| |pushdown| |rightExtendedGcd| |removeCoshSq| - |tryFunctionalDecomposition| |e02baf| |numberOfImproperPartitions| - |term?| |polynomialZeros| |cAsinh| |pushup| |rightGcd| |removeSinhSq| - |conditions| |btwFact| |e02bbf| |subSet| |equiv| |f2df| |cCsch| - |reducedDiscriminant| |rightExactQuotient| |expandTrigProducts| - |match| |beauzamyBound| |ptree| |e02bcf| |unrankImproperPartitions0| - |merge!| |ef2edf| |cSech| |idealSimplify| |rightRemainder| - |fintegrate| |call| |bombieriNorm| |e02bdf| - |unrankImproperPartitions1| |resultantEuclidean| |ocf2ocdf| |cCoth| - |definingInequation| |rightQuotient| |coefficient| |list| |rootBound| - |e02bef| |subresultantSequence| |qelt| |semiResultantEuclidean2| - |basisOfCommutingElements| |leader| |socf2socdf| |cTanh| - |definingEquations| |rightLcm| |coHeight| |kroneckerDelta| |car| - |singleFactorBound| |e02daf| |SturmHabichtSequence| - |semiResultantEuclidean1| |basisOfLeftAnnihilator| |df2fi| |cCosh| - |setStatus| |leftExtendedGcd| |extendIfCan| |reindex| |cdr| - |quadraticNorm| |e02dcf| |SturmHabichtCoefficients| |xRange| - |indiceSubResultant| |edf2fi| |loadNativeModule| |cSinh| - |quasiAlgebraicSet| |leftGcd| |algebraicVariables| |setDifference| - |infinityNorm| |e02ddf| |SturmHabicht| |yRange| - |indiceSubResultantEuclidean| |char| |edf2df| |cAcsc| - |radicalSimplify| |leftExactQuotient| - |zeroSetSplitIntoTriangularSystems| |lambda| |setIntersection| - |scaleRoots| |e02def| |countRealRoots| |zRange| - |semiIndiceSubResultantEuclidean| |expenseOfEvaluation| |cAsec| - |denominator| |leftRemainder| |zeroSetSplit| |setUnion| |shiftRoots| - |map!| |e02dff| |SturmHabichtMultiple| |substring?| - |degreeSubResultant| |numberOfOperations| |cAcot| |numerator| - |leftQuotient| |reduceByQuasiMonic| |apply| |qsetelt!| - |degreePartition| |e02gaf| |countRealRootsMultiple| - |degreeSubResultantEuclidean| |cAtan| |quadraticForm| - |monicLeftDivide| |collectQuasiMonic| |factorOfDegree| |e02zaf| - |suffix?| |pop!| |semiDegreeSubResultantEuclidean| |setImagSteps| - |float| |cAcos| |void| |back| |monicRightDivide| |removeZero| |size| - |factorsOfDegree| |e04dgf| |push!| |lastSubResultantEuclidean| - |setClipValue| |cAsin| |front| |leftDivide| |initiallyReduce| - |pascalTriangle| |e04fdf| |prefix?| |minordet| - |semiLastSubResultantEuclidean| |option?| |cCsc| |rotate!| - |rightDivide| |headReduce| |e04gcf| |determinant| - |subResultantGcdEuclidean| |range| |cSec| |dequeue!| |hermiteH| - |stronglyReduce| |first| |exp1| |e04jaf| |acsch| |diagonalProduct| - |semiSubResultantGcdEuclidean2| |colorFunction| |cCot| |enqueue!| - |laguerreL| |rewriteSetWithReduction| |rest| |log2| |null| |e04mbf| - |diagonal| |semiSubResultantGcdEuclidean1| |curveColor| |implies| - |cTan| |quatern| |legendreP| |autoReduced?| |substitute| - |rationalApproximation| |e04naf| |diagonalMatrix| |case| - |discriminantEuclidean| |pointColor| |blankSeparate| - |initiallyReduced?| |removeDuplicates| |key| |relerror| |e04ucf| - |Zero| |scalarMatrix| |semiDiscriminantEuclidean| |clip| |xor| - |bitTruth| |resultantnaif| |semicolonSeparate| |headReduced?| - |complexSolve| |e04ycf| |infix?| |One| |hermite| |chainSubResultants| - |clipBoolean| GE |contains?| |resultantEuclideannaif| |commaSeparate| - |stronglyReduced?| |filename| |complexRoots| |mask| |f01brf| - |completeHermite| |generalizedContinuumHypothesisAssumed| |schema| - |style| GT |inf| |semiResultantEuclideannaif| |pile| |reduced?| |not?| - |realRoots| |setColumn!| |generalizedContinuumHypothesisAssumed?| - |resultantReduit| |toScale| LE |qinterval| |pdct| |paren| - |normalized?| |parse| |leadingTerm| |computePowers| |positive?| - |setRow!| |resultantReduitEuclidean| |pointColorPalette| LT |interval| - |powers| |bracket| |quasiComponent| |writable?| |pow| |negative?| - |oneDimensionalArray| |semiResultantReduitEuclidean| - |curveColorPalette| |unit?| |prod| |partition| |label| |symbolTable| - |initials| |retractIfCan| |readable?| |An| |zero?| |associatedSystem| - |divide| |ravel| |var1Steps| |associates?| |complete| |exists?| - |UnVectorise| |dim| |augment| |uncouplingMatrices| |var2Steps| - |Lazard| |pushFortranOutputStack| |reshape| |unitCanonical| |pole?| - |OMconnInDevice| |getOperator| |extension| |Vectorise| - |lastSubResultant| |associatedEquations| |space| |Lazard2| - |popFortranOutputStack| |unitNormal| |OMconnOutDevice| |listBranches| - |string| |nil?| |shallowExpand| |setPoly| |lastSubResultantElseSplit| - |arrayStack| |nextsousResultant2| |tubePoints| |lfextendedint| - |OMconnectTCP| |triangular?| |buildSyntax| |outputAsFortran| - |deepExpand| |exponent| |invertibleSet| |setButtonValue| |tubeRadius| - |lflimitedint| |rewriteIdealWithRemainder| |OMbindTCP| |solve| - |setAttributeButtonStep| |clearFortranOutputStack| |exQuo| - |invertible?| |regime| |crest| |weight| |replace| |lfinfieldint| - |rewriteIdealWithHeadRemainder| |OMopenFile| |triangularSystems| - |resetAttributeButtons| |showFortranOutputStack| |moebius| - |invertibleElseSplit?| |sqfree| |cfirst| |makeVariable| |update| - |lfintegrate| |remainder| |OMopenString| |rootDirectory| - |getButtonValue| |topFortranOutputStack| |rightRecip| - |purelyAlgebraicLeadingMonomial?| |inconsistent?| |sts2stst| - |finiteBound| |lfextlimint| |headRemainder| |OMclose| |hostPlatform| - |mantissa| |decrease| |setFormula!| |leftRecip| - |algebraicCoefficients?| |numFunEvals| |clikeUniv| |sortConstraints| - |BasicMethod| |roughUnitIdeal?| |OMsetEncoding| - |nativeModuleExtension| |map| |increase| |linkToFortran| |leftPower| - |purelyTranscendental?| |setAdaptive| |weierstrass| |sumOfSquares| - |PollardSmallFactor| |roughEqualIdeals?| |OMputApp| |bumprow| - |morphism| |setLegalFortranSourceExtensions| |rightPower| - |purelyAlgebraic?| |adaptive?| |qqq| |splitLinear| |showTheFTable| - |roughSubIdeal?| |OMputAtp| |bumptab| |balancedFactorisation| - |fracPart| |derivationCoordinates| |prepareSubResAlgo| - |setScreenResolution| |integralBasis| |simpleBounds?| |clearTheFTable| - |roughBase?| |OMputAttr| |bumptab1| |mapDown!| |polyPart| |one?| - |internalLastSubResultant| |second| |screenResolution| - |localIntegralBasis| |subst| |linearMatrix| |fTable| |trivialIdeal?| - |OMputBind| |untab| |mapUp!| |fullPartialFraction| |splitSquarefree| - |integralLastSubResultant| |third| |setMaxPoints| |changeWeightLevel| - |linearPart| |palgint0| |collectUpper| |OMputBVar| |bat1| |convert| - |setleaves!| |primeFrobenius| |normalDenom| |toseLastSubResultant| - |maxPoints| |script| |characteristicSerie| |nonLinearPart| - |palgextint0| |collect| |OMputError| |bat| |balancedBinaryTree| - |discreteLog| |totalfract| |toseInvertible?| |setMinPoints| - |characteristicSet| |quadratic?| |interpret| |palglimint0| - |OMputObject| |collectUnder| |tab1| |vector| |sylvesterMatrix| - |decreasePrecision| |pushdterm| |keys| |toseInvertibleSet| |minPoints| - |medialSet| |changeNameToObjf| |palgRDE0| |OMputEndApp| - |mainVariable?| |tab| |differentiate| |bezoutMatrix| |nullary?| - |increasePrecision| |pushucoef| |toseSquareFreePart| |parametric?| - |tex| |Hausdorff| |optAttributes| |palgLODE0| |mainVariables| - |OMputEndAtp| |lex| |bezoutResultant| |arity| |bits| |pushuconst| - |quotedOperators| |plotPolar| |Frobenius| |Nul| |chineseRemainder| - |removeSquaresIfCan| |OMputEndAttr| |slex| |bezoutDiscriminant| - |unitNormalize| |numberOfMonomials| |rur| |debug3D| - |transcendenceDegree| |objects| |exponents| |divisors| - |unprotectedRemoveRedundantFactors| |OMputEndBind| |inverse| - |setright!| |bfEntry| |unit| |members| |create| |numFunEvals3D| - |extensionDegree| |base| |iisqrt2| |eulerPhi| |removeRedundantFactors| - |OMputEndBVar| |maxrow| 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|setProperties| |nilFactor| |nsqfree| - |structuralConstants| |setMinPoints3D| |rquo| |and| |brace| |iicot| - |sumOfKthPowerDivisors| |quasiMonicPolynomials| |OMputSymbol| - |printInfo!| |setProperty| |regularRepresentation| |intChoose| - |minPoints3D| |coordinates| |lquo| |leaves| |iisec| |HermiteIntegrate| - |univariate?| |OMgetApp| |startStats!| |traceMatrix| |lp| |coefChoose| - |high| |tValues| |mindegTerm| |iicsc| |palgint| - |univariatePolynomials| |OMgetAtp| |printStats!| |randomLC| |myDegree| - |low| |tRange| |product| |iiasin| |palgextint| |linear?| |OMgetAttr| - |clearTable!| |binaryTree| |minimize| |normDeriv2| |subset?| |plot| - |LiePolyIfCan| |previous| |value| |iiacos| |palglimint| - |linearPolynomials| |OMgetBind| |usingTable?| |byte| |module| - |plenaryPower| |symmetricDifference| |pointPlot| |trunc| |iiatan| - |sum| |palgRDE| |bivariate?| |OMgetBVar| |printingInfo?| - |rightRegularRepresentation| |c02aff| |difference| |calcRanges| - |degree| |basisOfNucleus| |iiacot| |palgLODE| |bivariatePolynomials| - |OMgetError| |makingStats?| |leftRegularRepresentation| |c02agf| - |intersect| |fixPredicate| |quasiRegular| |countable?| |basisOfCenter| - |iiasec| |splitConstant| |removeRoughlyRedundantFactorsInPols| - |OMgetObject| |extractIfCan| |rightTraceMatrix| |c05adf| |part?| - |patternMatch| |quasiRegular?| |basisOfLeftNucloid| |Aleph| - |binarySearchTree| |iiacsc| |pmComplexintegrate| - |removeRoughlyRedundantFactorsInPol| |OMgetEndApp| |insert!| - |leftTraceMatrix| |c05nbf| |latex| |patternMatchTimes| |constant?| - |basisOfRightNucloid| |nor| |iisinh| |pmintegrate| |interReduce| - |OMgetEndAtp| |interpretString| |rightDiscriminant| |c05pbf| |member?| - |bernoulli| |mindeg| |basisOfCentroid| |iicosh| |infieldint| - |roughBasicSet| |OMgetEndAttr| |stripCommentsAndBlanks| - |leftDiscriminant| |c06eaf| |enumerate| |chebyshevT| |maxdeg| - |radicalOfLeftTraceForm| |iitanh| |extendedint| |linear| |crushedSet| - |OMgetEndBind| |setPrologue!| |concat| 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|asimpson| |extractClosed| |rightUnit| |elColumn2!| - |selectPDERoutines| |torsionIfCan| |getGraph| |computeInt| |operation| - |generalizedInverse| |atrapezoidal| |extractIndex| |leftUnit| - |fractionFreeGauss!| |getGoodPrime| |selectOptimizationRoutines| - |putGraph| |symbol| |checkForZero| |setFieldInfo| |romberg| - |extractPoint| |match?| |rightMinimalPolynomial| |invertIfCan| - |selectIntegrationRoutines| |badNum| |graphs| |doubleFloatFormat| - |pol| |simpson| |traverse| |leftMinimalPolynomial| |copy!| |mix| - |routines| |graphStates| |integer| |bitior| |logGamma| |xn| ** - |trapezoidal| |defineProperty| |associatorDependence| |plus!| - |mainSquareFreePart| |doubleDisc| |graphState| |hypergeometric0F1| - |dAndcExp| |rombergo| |closeComponent| |lieAlgebra?| |minus!| - |mainPrimitivePart| |polyred| |makeViewport2D| |rotatez| |repSq| - |simpsono| |modifyPoint| |jordanAlgebra?| |leftScalarTimes!| - |mainContent| EQ |padicFraction| |viewport2D| |rotatey| |expPot| - |trapezoidalo| 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|stack| |ODESolve| |children| - |rightAlternative?| |bandedHessian| |times| |extendedSubResultantGcd| - |gcdPrimitive| |hitherPlane| |setnext!| |charpol| |constDsolve| - |child| |leftAlternative?| |jacobian| |exactQuotient!| - |symmetricGroup| |eyeDistance| |name| |setprevious!| |solve1| - |showTheIFTable| |birth| |error| |antiAssociative?| |bandedJacobian| - |exactQuotient| |alternatingGroup| |perspective| |body| - |shanksDiscLogAlgorithm| |innerEigenvectors| |clearTheIFTable| - |internal?| |assert| |associative?| |duplicates| - |primPartElseUnitCanonical!| |abelianGroup| |zoom| |optimize| - |reflect| |unparse| |iFTable| |root?| |antiCommutative?| - |removeDuplicates!| |primPartElseUnitCanonical| |monom| |cyclicGroup| - |rotate| |reify| |binary| |showIntensityFunctions| |leaf?| - |commutative?| |linears| |lazyResidueClass| |dihedralGroup| - |drawStyle| |separant| |packageCall| |expint| |outputForm| - |rightCharacteristicPolynomial| |ddFact| |monicModulo| |mathieu11| - |outlineRender| 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|copyInto!| |maximumExponent| |RittWuCompare| |lexGroebner| |t| - |modifyPointData| |top!| |powmod| |changeVar| |argumentListOf| |next| - |sorted?| |rowEch| |mainMonomials| |totalGroebner| |subspace| - |dequeue| |mulmod| |ratDsolve| |returnTypeOf| |digit?| |LiePoly| - |rowEchLocal| |mainCoefficients| |expressIdealMember| |makeViewport3D| - |recolor| |flatten| |submod| |indicialEquationAtInfinity| - |printHeader| |datalist| |cn| |quickSort| |rowEchelonLocal| - |leastMonomial| |principalIdeal| |viewport3D| |drawComplex| |addmod| - |reduceLODE| |returnType!| |heapSort| |normalizedDivide| - |mainMonomial| |LagrangeInterpolation| |viewDeltaYDefault| - |drawComplexVectorField| |symmetricRemainder| |singRicDE| - |argumentList!| |shellSort| |directory| |maxint| |quasiMonic?| - |psolve| |viewDeltaXDefault| |eval| |setRealSteps| |positiveRemainder| - |nil| |isQuotient| |polyRicDE| |endSubProgram| |iroot| |outputSpacing| - |reverse| |binaryFunction| |monic?| |wrregime| |viewZoomDefault| - |bit?| 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- |GospersMethod| |OMcloseConn| |getOperands| |nil| |infinite| + |Record| |Union| |stronglyReduced?| |fortranTypeOf| |read!| |c06frf| + |certainlySubVariety?| |e02ajf| |csc2sin| |meatAxe| |twoFactor| + |oblateSpheroidal| |droot| |getDatabase| |removeSquaresIfCan| + |compose| |cos2sec| |d02ejf| |lprop| |tanhIfCan| |possiblyInfinite?| + |mapMatrixIfCan| |leftRecip| |idealiserMatrix| |OMgetEndBVar| |dom| + |paraboloidal| |coerceL| |asimpson| |primitivePart| + |singularAtInfinity?| |groebner| |Is| |set| |palgint| |subPolSet?| + |palglimint0| |lyndon?| |bumptab| |exprHasLogarithmicWeights| + |polCase| |compdegd| |difference| |/\\| |imaginary| |stop| + |normalizeAtInfinity| |leftTraceMatrix| |complexRoots| |setprevious!| + |insertTop!| |rightRemainder| |\\/| |polyRicDE| |topPredicate| + |setref| |rspace| |getMatch| |c02aff| |denominator| |f01brf| + |LazardQuotient2| |nil?| |oddlambert| |contours| |copies| |unit?| + |orthonormalBasis| |component| |horizConcat| |ScanRoman| |iisec| + |reorder| |title| |cAcos| |leftExtendedGcd| |expressIdealMember| + |overbar| |d02bbf| |f02awf| |leviCivitaSymbol| |shufflein| + |cyclicGroup| |exponentialOrder| |oddintegers| |decimal| + |explicitEntries?| |removeConstantTerm| |integer?| |sin2csc| |range| + |mesh?| |rangePascalTriangle| |factorial| |asinhIfCan| |s17adf| + |conjug| |sort| |stopTableGcd!| |lifting| |realEigenvalues| + |separateFactors| |routines| |e| |fortranReal| |balancedFactorisation| + |extractClosed| |OMgetBind| |numFunEvals3D| |lSpaceBasis| |calcRanges| + |algebraicCoefficients?| |shallowExpand| |critMTonD1| |quotient| |row| + |rootOf| |weakBiRank| |concat!| |changeWeightLevel| |directSum| + |composite| |in?| |ode2| F |GospersMethod| |mr| |reverse!| |c05nbf| + |totolex| |moebius| |showSummary| |getZechTable| |signAround| + |nthFractionalTerm| |show| |OMgetEndBind| |opeval| |OMputObject| + |largest| |pseudoRemainder| |contractSolve| |LiePolyIfCan| + |clipPointsDefault| |monomRDEsys| |completeHermite| |lex| + |monicDivide| |ramified?| |minimalPolynomial| |prod| |relerror| + |diagonal?| |musserTrials| |random| |showAttributes| + |mainCharacterization| |trace| |fintegrate| |s19acf| |unmakeSUP| + |back| |extendIfCan| |makeViewport3D| |besselI| |viewpoint| + |pushNewContour| |unvectorise| |lazyGintegrate| + |functionIsContinuousAtEndPoints| |endSubProgram| |rotate| + |numberOfPrimitivePoly| |rightUnit| |getlo| |usingTable?| |solve1| + |legendre| |selectNonFiniteRoutines| |HermiteIntegrate| |s21baf| + |appendPoint| |basisOfRightNucloid| |infinite?| |outputFloating| + |primaryDecomp| |leftRemainder| + |generalizedContinuumHypothesisAssumed| + |removeSuperfluousQuasiComponents| |normalDeriv| |noKaratsuba| + |complexNumericIfCan| |lowerCase?| |even?| |invertibleElseSplit?| + |sec2cos| |infRittWu?| |numFunEvals| |repeating?| + |useEisensteinCriterion| |cSec| |d03eef| |integralMatrixAtInfinity| + |iiGamma| |basisOfLeftNucleus| |extensionDegree| |subst| |port| + |cardinality| |mdeg| |lazyPseudoDivide| |graphStates| |omError| + |fracPart| |latex| |dihedral| |sizeLess?| |normalForm| |poisson| + |degree| |iroot| |f02adf| |OMcloseConn| |recolor| |redpps| |iiacos| + |changeThreshhold| |find| |leadingCoefficientRicDE| |moduloP| + |leadingIdeal| |OMReadError?| |collectUnder| |fprindINFO| |partition| + |cycles| |normalise| |width| |linearPart| |number?| |bombieriNorm| NOT + |doublyTransitive?| |coth2trigh| |factor1| |getRef| |normal01| |byte| + |extractTop!| |lyndonIfCan| |e01saf| OR |intensity| |bezoutResultant| + |setPrologue!| |reindex| |mapCoef| |zeroSquareMatrix| |elColumn2!| + |iiasech| |e04ucf| |f2st| |getSyntaxFormsFromFile| |factorPolynomial| + AND |conical| |setPoly| |plusInfinity| |lhs| |reify| |clearTheFTable| + |octon| |tan2cot| |cRationalPower| |compiledFunction| + |screenResolution3D| |ord| |isExpt| |idealiser| |split| + |minusInfinity| |rhs| |limit| |nor| |revert| |processTemplate| + |sqfree| |objects| |showTheIFTable| |basisOfNucleus| |positiveSolve| + |tablePow| |lowerCase| |showRegion| |monicRightDivide| |nullary| + |s17akf| |rightZero| |numericalIntegration| |constantKernel| |base| + |zero| |zeroSetSplit| |s17aff| |pr2dmp| |qroot| |univariate?| |f01mcf| + |s18adf| |validExponential| |patternMatchTimes| |iisqrt2| |fill!| + |optional| |logGamma| |redPol| |schema| |clikeUniv| |mathieu12| + |list?| |lazyIntegrate| |submod| |commutativeEquality| |every?| + |isPlus| |scopes| |And| |ListOfTerms| |symFunc| |e02ahf| |dequeue!| + |stosePrepareSubResAlgo| |derivationCoordinates| |initials| |s17dcf| + |integrate| |node| |Or| |OMencodingSGML| |maxIndex| |factorSquareFree| + |stirling1| |aCubic| |cyclicParents| |wholeRagits| |viewPosDefault| + |leftRank| |modularGcd| |palgint0| |Not| |dictionary| + |stoseInvertible?| |fortranCarriageReturn| |bernoulliB| |type| + |components| |getOperands| |useSingleFactorBound?| |quoted?| |module| + |scalarMatrix| |maxrank| |e02bdf| |scale| |represents| |cyclicCopy| + |sayLength| |tab1| |f02wef| |selectPDERoutines| |queue| |deepestTail| + |stiffnessAndStabilityFactor| |rowEchelon| |getMultiplicationMatrix| * + |arity| |logical?| |factorFraction| |cyclotomicDecomposition| + |quadraticNorm| |e01bhf| |cfirst| |monicRightFactorIfCan| |iiacot| + |cSin| |outputSpacing| |putColorInfo| |top| |laplace| |setEmpty!| + |numberOfChildren| |innerint| |sinhcosh| |sortConstraints| |sh| + |print| |airyAi| |normInvertible?| |lastSubResultantElseSplit| + |continue| |binary| |wholePart| |constant?| |eulerPhi| |setvalue!| + |mkcomm| |shiftRoots| |style| |sncndn| |s14baf| |interpolate| + |removeZero| |iisinh| |readable?| |approxSqrt| |restorePrecision| + |sort!| |birth| |OMgetApp| |axesColorDefault| |mainForm| |tableau| + |bfKeys| |exprHasAlgebraicWeight| |quasiAlgebraicSet| |primintegrate| + |cyclicSubmodule| |tree| |indicialEquationAtInfinity| |cons| |fmecg| + |previous| |xn| |seriesToOutputForm| |f01qef| |node?| |setfirst!| + |hermiteH| |janko2| |diophantineSystem| |ldf2vmf| |polar| |supersub| + |minPol| |inGroundField?| |totalDifferential| |setProperty!| + |linearAssociatedExp| |notelem| |genericLeftTraceForm| |nextColeman| + |diagonals| |headReduced?| |setPosition| |e02adf| |showScalarValues| + |plenaryPower| |setStatus!| |arrayStack| |neglist| |nonQsign| + |normal?| |equiv?| |gethi| |createIrreduciblePoly| |mapDown!| + |primitiveElement| |box| |level| |torsionIfCan| |prepareSubResAlgo| + |indicialEquation| |over| |absolutelyIrreducible?| |equation| + |getProperties| |collectUpper| |matrixConcat3D| + |unrankImproperPartitions1| |nextNormalPrimitivePoly| |c06ebf| + |sylvesterMatrix| |matrixGcd| |patternVariable| |contract| + |semiDiscriminantEuclidean| |reducedForm| |createNormalElement| + |specialTrigs| |viewWriteDefault| |e01bef| |imagJ| |gderiv| |pToHdmp| + |addBadValue| |An| |laurentIfCan| |solveLinearPolynomialEquation| + |coshIfCan| |iiexp| |bits| |fixedPoints| |palgLODE| + |extendedIntegrate| |flagFactor| |d01aqf| |rootOfIrreduciblePoly| + |monomRDE| |llprop| |printHeader| |mapUnivariateIfCan| |source| + |inspect| |iisin| |dec| |inf| |expintfldpoly| |reduceBasisAtInfinity| + |s18acf| |factorsOfDegree| |orbits| |closed?| |gramschmidt| + |stoseInvertible?reg| |push| |genericLeftMinimalPolynomial| + |minimumExponent| |binaryFunction| |linear| |generalInfiniteProduct| + |rightFactorCandidate| |showIntensityFunctions| |pmintegrate| + |inverseColeman| |removeRedundantFactors| |symmetricDifference| + |integralAtInfinity?| |BasicMethod| |postfix| |LyndonBasis| + |polygamma| |formula| |curryLeft| |xCoord| |getGraph| |upperCase?| + |complexSolve| |OMencodingBinary| |alternating| |swap| |polynomial| + |subHeight| |startStats!| |decreasePrecision| |setErrorBound| + |normalizedAssociate| |preprocess| |dimensions| |OMputBind| + |shrinkable| |f04mbf| |weights| |trapezoidal| |bright| |iisqrt3| + |split!| |partitions| |hasPredicate?| |target| |generalSqFr| + |definingPolynomial| |imagk| |rectangularMatrix| |notOperand| + |stronglyReduce| |bitTruth| |completeHensel| |maxPoints3D| + |rationalPoints| |rk4| |nullity| |doubleRank| |resultantEuclidean| + |dfRange| F2FG |nrows| |createThreeSpace| |quickSort| + |euclideanGroebner| |setScreenResolution| |internalZeroSetSplit| + |clip| |adjoint| |jacobi| |factorSFBRlcUnit| |bivariatePolynomials| + |twist| |setOfMinN| |principal?| |ncols| |completeEval| |f07aef| + |zero?| |characteristicPolynomial| |scripted?| |dark| |max| |property| + |semiResultantEuclideannaif| |removeRedundantFactorsInContents| + |subTriSet?| |stoseLastSubResultant| |discreteLog| |critM| |vectorise| + |is?| |graphCurves| |scaleRoots| |pushuconst| |nextsousResultant2| + |algSplitSimple| |partialFraction| |computeInt| |checkRur| |swapRows!| + |pointPlot| |comp| |child| |limitedIntegrate| |cPower| |monic?| + |remove!| |delete| |factorGroebnerBasis| |OMputVariable| + |atrapezoidal| |or?| |insertBottom!| |makeprod| |credPol| |result| + |mapdiv| |representationType| |units| |inverseLaplace| |listOfMonoms| + |leftFactorIfCan| |infiniteProduct| |stFuncN| |e04ycf| |elem?| + |isTimes| |traceMatrix| |resetVariableOrder| |unparse| |sPol| |sign| + |reducedContinuedFraction| |problemPoints| |Ei| |collectQuasiMonic| + |whatInfinity| |shallowCopy| |entry| |subresultantVector| |factorset| + |lfextlimint| |exp1| |defineProperty| |f01rdf| |branchIfCan| |Aleph| + |zeroMatrix| |sech2cosh| |untab| |setrest!| |innerSolve| |curry| + |subtractIfCan| |li| |writeLine!| |systemSizeIF| |stFunc1| |findCycle| + |probablyZeroDim?| |hexDigit| |code| |clearCache| |makeSin| |integral| + |monomialIntPoly| |elt| |pseudoQuotient| |coerceImages| |lookup| + |lazyPseudoRemainder| |rotate!| |intcompBasis| |dequeue| |choosemon| + |trunc| |splitDenominator| |e02bcf| |d01apf| |outlineRender| + |cartesian| |totalfract| |numer| |quasiComponent| |reduction| + |leftAlternative?| |df2st| |chebyshevT| |aQuadratic| |numeric| + |computeCycleEntry| |index?| |denom| |qqq| |e02def| |dn| |radical| + |rightMult| |e01baf| |schwerpunkt| |generic| |elRow2!| |rule| + |modularGcdPrimitive| |polygon| |f01qdf| + |removeRoughlyRedundantFactorsInContents| |quasiMonic?| + |cyclicEntries| |log10| |tanNa| |rdHack1| |pi| |tanh2trigh| + |singularitiesOf| |truncate| |createPrimitivePoly| |palginfieldint| + |parametric?| |chiSquare1| |bitand| |alternative?| |factorOfDegree| + |relationsIdeal| |infinity| |leftScalarTimes!| |loopPoints| |cotIfCan| + |headRemainder| |mainDefiningPolynomial| |splitNodeOf!| |iFTable| + |binarySearchTree| |semiResultantEuclidean1| + |ScanFloatIgnoreSpacesIfCan| |univariatePolynomial| |mapUp!| + |elementary| |generator| |functionIsFracPolynomial?| + |oddInfiniteProduct| |cubic| |s17ajf| |fractionPart| + |replaceKthElement| |stoseInvertibleSetsqfreg| |viewDefaults| + |genericLeftDiscriminant| |regularRepresentation| |simpson| |index| + |eigenvector| |writable?| |kmax| |kernel| |inverse| + |complexElementary| |genericLeftTrace| |imagE| |s14abf| + |moreAlgebraic?| |draw| |createPrimitiveNormalPoly| |mulmod| + |tensorProduct| |weight| |explicitlyEmpty?| |isobaric?| |cycleEntry| + |comment| |unrankImproperPartitions0| |option| |maxdeg| + |symmetricTensors| |sinIfCan| |nodes| |adaptive3D?| |bsolve| + |clearTable!| |OMputInteger| |cCos| |rightDivide| |deriv| |pair| + |splitLinear| |toseInvertible?| BY |edf2fi| |modularFactor| |cAcosh| + |separate| |position| |jacobian| |primintfldpoly| |mat| |order| |heap| + |nthExpon| |selectODEIVPRoutines| |e04naf| |mainContent| + |countRealRoots| |OMgetFloat| |nextNormalPoly| |mainVariable| + |binaryTournament| |makeObject| |iiacsc| |genericPosition| + |exprHasWeightCosWXorSinWX| |indicialEquations| |function| |iipow| + |variationOfParameters| |psolve| |stoseIntegralLastSubResultant| + |s13acf| |halfExtendedResultant1| |continuedFraction| |ratDenom| + |divisorCascade| |particularSolution| |OMclose| |lo| |iibinom| + |Lazard2| |basisOfLeftAnnihilator| |e02zaf| |infLex?| |coef| |hMonic| + |euler| |c06gsf| |gcdcofactprim| |incr| |isList| |Hausdorff| |root?| + |laplacian| |pow| |lfinfieldint| |selectfirst| |condition| + |OMsupportsSymbol?| |f04maf| |hi| |createLowComplexityNormalBasis| + |superHeight| |clipWithRanges| |ratDsolve| |wordInStrongGenerators| + |sincos| |viewThetaDefault| |spherical| |merge!| |cAsech| |intChoose| + |pdf2df| |numberOfHues| |e01sff| |setright!| |swap!| + |fullPartialFraction| |nothing| |addPoint| |digamma| |traverse| + |linearDependenceOverZ| |ratpart| |hconcat| |completeEchelonBasis| + |binaryTree| |padicFraction| |wreath| |imagK| |radicalOfLeftTraceForm| + |innerSolve1| |multiset| |d01alf| |OMlistCDs| |torsion?| |HenselLift| + |pushdown| |f07fef| |nthRootIfCan| |callForm?| |headReduce| |lift| + |setMinPoints| |ParCond| |irreducibleFactors| |mapUnivariate| + |diagonalMatrix| |tanSum| |endOfFile?| |edf2efi| FG2F |tail| |reduce| + |s21bcf| |alphanumeric?| |showTheFTable| |complex?| |subscript| + |semiIndiceSubResultantEuclidean| |unitNormal| |printTypes| + |constantLeft| |pattern| |position!| |integers| |externalList| + |f02agf| |triangSolve| |exactQuotient!| |hostPlatform| |multiple?| + |prevPrime| |outputAsTex| |pmComplexintegrate| |s19adf| + |basisOfRightAnnihilator| |partialDenominators| |att2Result| + |fortranLinkerArgs| |optAttributes| |viewDeltaXDefault| |df2fi| + |antiCommutative?| |reducedQPowers| |negative?| + |rewriteIdealWithHeadRemainder| |log| |cond| |lcm| + |integralRepresents| |erf| |localUnquote| |elliptic| |s18aef| |pop!| + |halfExtendedSubResultantGcd2| |returnTypeOf| |bfEntry| + |rationalIfCan| |atom?| |repeatUntilLoop| |curve?| |message| + |rationalPower| |ellipticCylindrical| |output| |green| |userOrdered?| + |branchPointAtInfinity?| |rightExtendedGcd| |append| |simplifyLog| + |ef2edf| |frst| |getVariableOrder| |outputList| |asinIfCan| |status| + |coleman| |stFunc2| |minimize| |viewport2D| |gcd| |build| |dilog| + |red| |generate| |leftMinimalPolynomial| |minPoints3D| |properties| + |stopTable!| |zeroVector| |points| |s17acf| |listexp| |false| + |splitSquarefree| |sin| |randomR| |e04gcf| |acothIfCan| |translate| + |minset| |nextSublist| |tubeRadiusDefault| |iicsch| |rightTrace| + |compile| |trueEqual| |cos| |derivative| |incrementBy| |setRealSteps| + |diff| |numberOfIrreduciblePoly| |characteristicSet| |ODESolve| + |OMgetSymbol| |d01fcf| |discriminantEuclidean| |bag| |iitanh| |tan| + |OMread| |expand| |reseed| = |numberOfVariables| |realElementary| + |simplify| |algintegrate| |radicalRoots| |cot| |numberOfComponents| + |decrease| |filterWhile| |eigenvectors| |const| |block| |entries| + |removeRoughlyRedundantFactorsInPol| |matrix| |leftOne| |OMopenFile| + |nary?| |#| |expenseOfEvaluation| |sec| |primextendedint| + |filterUntil| < |showTheRoutinesTable| |irreducibleFactor| + |oneDimensionalArray| |roughSubIdeal?| |swapColumns!| |slash| + |palgLODE0| |internalDecompose| |csc| |symmetricGroup| |select| > + |double| |BumInSepFFE| |removeDuplicates!| |LiePoly| |upperCase!| + |rotatey| |unit| |taylorQuoByVar| |asin| |charClass| + |linearDependence| |OMconnOutDevice| <= + |semiDegreeSubResultantEuclidean| |ignore?| |cCosh| |hasSolution?| + |removeCoshSq| |fortranLogical| |acos| |lieAdmissible?| >= + |maxRowIndex| |nodeOf?| |bivariateSLPEBR| |prindINFO| + |compactFraction| |normDeriv2| |delay| |atan| |dmpToP| |cSech| + |brillhartTrials| |Si| |nextSubsetGray| |orOperands| |subNodeOf?| + |solveInField| |besselY| |acot| |hclf| |bipolarCylindrical| + |critpOrder| |coordinates| |reducedSystem| |saturate| + |intPatternMatch| |pointColor| |triangularSystems| |asec| + |integralLastSubResultant| |copy!| |magnitude| |determinant| + + |OMsend| |fortranCharacter| |OMgetEndApp| |meshFun2Var| + |generalTwoFactor| |exprToGenUPS| |associator| |acsc| |makeRecord| + |totalLex| |sample| - ~= |sturmSequence| |rowEchLocal| + |var2StepsDefault| |euclideanSize| |tryFunctionalDecomposition| + |rootRadius| |complexForm| |sinh| |close| |super| |declare!| / + |datalist| |coerce| |quadratic?| |semiResultantReduitEuclidean| + |readLine!| |expPot| |perfectSqrt| |primeFactor| |cosh| |whileLoop| + |perfectNthRoot| |norm| |construct| |hexDigit?| |var1StepsDefault| + |rootPoly| |operators| |changeMeasure| |remove| |initial| + |genericLeftNorm| |tanh| |setFormula!| |display| |extendedint| + |lazyVariations| |eq?| |palglimint| |f02fjf| |OMputAtp| |members| + |checkPrecision| |indiceSubResultantEuclidean| |coth| |denominators| + |mainVariables| |rCoord| |stirling2| |flexibleArray| |makeResult| + |OMputEndBVar| |ridHack1| |last| |extendedSubResultantGcd| |sech| + |pomopo!| |positiveRemainder| |areEquivalent?| |duplicates| |assoc| + |approximants| |createMultiplicationTable| |rename| + |resetAttributeButtons| |iiacoth| |csubst| |csch| |point| |power!| + |coerceListOfPairs| |listBranches| |rank| |multisect| + |genericRightMinimalPolynomial| |companionBlocks| |setStatus| + |subset?| |clearTheSymbolTable| |simplifyExp| |asinh| |idealSimplify| + |cycleElt| |radicalEigenvectors| |countRealRootsMultiple| |fibonacci| + |composites| |insert!| |showClipRegion| |updatF| |blankSeparate| + |solveLinearlyOverQ| |acosh| |f04arf| |lquo| |deleteProperty!| + |setMaxPoints3D| |curveColorPalette| |semicolonSeparate| |pack!| + |e02baf| |powern| |lazyPrem| |puiseux| |hcrf| |atanh| |series| + |leftCharacteristicPolynomial| |mix| |fortranDoubleComplex| + |outputAsScript| |leftTrace| |extendedResultant| |mainCoefficients| + |trapezoidalo| |monomials| |screenResolution| |po| |acoth| |tower| + |subResultantGcdEuclidean| |coth2tanh| |lazyIrreducibleFactors| + |squareMatrix| |comparison| |irreducibleRepresentation| + |factorsOfCyclicGroupSize| |sinhIfCan| |host| |inv| |epilogue| |asech| + |testDim| |tube| |dimension| |B1solve| |linearPolynomials| |create| + |squareFreePrim| |inrootof| |ground?| |separateDegrees| + |wordsForStrongGenerators| |lists| |getStream| |changeVar| + |upDateBranches| |topFortranOutputStack| |possiblyNewVariety?| + |leftFactor| |pseudoDivide| |ground| |f07fdf| |multiple| |min| + |resetBadValues| |acotIfCan| |declare| |OMreceive| |digits| + |positive?| |nullSpace| |makeSketch| |rootKerSimp| |digit| |edf2df| + |applyQuote| |leadingMonomial| ~ |OMputEndAtp| |crushedSet| |segment| + |sylvesterSequence| |s18dcf| |definingEquations| |constructorName| + |midpoints| |showFortranOutputStack| |plot| |leadingCoefficient| + |gcdPrimitive| |transcendentalDecompose| |transcendent?| + |complexNumeric| |parabolicCylindrical| |distance| |subResultantChain| + |say| |infinityNorm| |f02ajf| |mathieu24| |f2df| |measure2Result| + |cSinh| |primitiveMonomials| |iicot| |OMconnInDevice| |open| |setelt| + |collect| |e01sef| |conjugate| |accuracyIF| |children| + |numberOfImproperPartitions| |initiallyReduced?| |kernels| + |jordanAdmissible?| |reductum| |ruleset| |goto| |inHallBasis?| |obj| + |bipolar| |rootSimp| |gcdPolynomial| |fractRadix| |smith| + |addPointLast| |fortranComplex| |vedf2vef| |e04fdf| |setVariableOrder| + |univariate| |ipow| |copy| |mapGen| |cache| |precision| + |readLineIfCan!| |iprint| |retract| |parametersOf| |exprToUPS| + |invertIfCan| |outputForm| |skewSFunction| |sin?| |c06gqf| + |halfExtendedResultant2| |low| |limitPlus| |localIntegralBasis| + |real?| |suchThat| |randnum| |cot2tan| |printStatement| |leftNorm| + |rightTraceMatrix| |bumprow| |polyPart| |kovacic| |commutator| + |groebSolve| |makeSUP| |overset?| |factor| |autoCoerce| |convergents| + |integralCoordinates| |leftLcm| |subNode?| + |semiSubResultantGcdEuclidean1| |viewSizeDefault| |biRank| + |currentScope| |reset| |perfectNthPower?| |recur| |hash| |sqrt| + |setRow!| |mirror| |f02aff| |hasHi| |polyred| |measure| |count| + |numberOfComposites| |tanintegrate| |rightRecip| |sturmVariationsOf| + |real| |leastAffineMultiple| |degreeSubResultantEuclidean| |rightLcm| + |argumentListOf| |addiag| |pastel| |cAcsc| |write| |bezoutMatrix| + |solid?| |OMgetEndAttr| |imag| |iisech| |primPartElseUnitCanonical!| + |firstDenom| |extractSplittingLeaf| |listOfLists| |acscIfCan| |save| + |hitherPlane| |directProduct| |binomThmExpt| |symmetricRemainder| + |hasTopPredicate?| |rightAlternative?| |fractRagits| |vconcat| + |conditionP| |doubleComplex?| |debug3D| |iCompose| |cCsch| + |rightCharacteristicPolynomial| |getOperator| |central?| |universe| + |algint| |stoseSquareFreePart| |e02ddf| |lagrange| |domainOf| |times!| + |s20adf| |destruct| |cyclePartition| |anfactor| |expandLog| + |groebnerFactorize| |region| |s15aef| |solve| |d02gbf| |rootPower| + |operation| |prinb| |sumOfKthPowerDivisors| |morphism| + |leadingExponent| |inverseIntegralMatrixAtInfinity| |tanIfCan| + |tRange| |rischDEsys| |linearMatrix| |factorSquareFreeByRecursion| + |unravel| |Ci| |radPoly| |curveColor| |OMputError| |recip| |constant| + |pair?| |removeSinSq| |identitySquareMatrix| |modTree| + |selectIntegrationRoutines| |minordet| |cylindrical| |iicos| + |rischNormalize| |genericRightTrace| |meshPar2Var| |makeViewport2D| + |internalAugment| |nullary?| |c06fqf| |extension| |monomial| |any| + |df2mf| |drawToScale| |c05adf| |coHeight| |one?| |radicalSolve| + |setLabelValue| |corrPoly| |multivariate| |presub| |zCoord| |extract!| + |arguments| |listConjugateBases| |sorted?| |clipSurface| + |integerIfCan| |subMatrix| |setScreenResolution3D| |variables| + |purelyAlgebraicLeadingMonomial?| |ceiling| |tubePointsDefault| + |squareFreeLexTriangular| |d01bbf| |resultantReduitEuclidean| |scan| + |cycleLength| |evaluate| |setnext!| |singular?| |distdfact| + |stripCommentsAndBlanks| |setAttributeButtonStep| |duplicates?| + |c06gbf| |less?| |algebraicVariables| |clearDenominator| + |transcendenceDegree| |search| |radicalSimplify| |normalizeIfCan| + |s19abf| |atanIfCan| |changeName| |leadingBasisTerm| |cAtan| |d02cjf| + |eq| |bandedHessian| |triangulate| |d02gaf| |wholeRadix| + |reducedDiscriminant| |singRicDE| |divideExponents| + |setLegalFortranSourceExtensions| |iter| |abelianGroup| |implies?| + |SturmHabicht| |padecf| |besselJ| |OMgetType| |vark| + |nextsubResultant2| |lowerCase!| |evenlambert| |rotatez| + |fortranDouble| |primitive?| |exprex| |f01qcf| |product| + |startTableGcd!| |f04adf| RF2UTS |taylor| |quasiMonicPolynomials| + |tryFunctionalDecomposition?| |quote| |mkPrim| |makeUnit| |cTan| + |OMsupportsCD?| |or| |chvar| |ffactor| |useEisensteinCriterion?| + |laurent| |ref| |generalPosition| |curryRight| |f04qaf| |part?| + |hdmpToP| |lazyPquo| |fTable| |float?| |ddFact| |badNum| + |kroneckerDelta| |OMmakeConn| |pointColorPalette| |extendedEuclidean| + |multMonom| |rewriteIdealWithQuasiMonicGenerators| |genus| + |inconsistent?| |leftDiscriminant| |semiLastSubResultantEuclidean| + |newLine| |bat| |rowEch| |internalLastSubResultant| |getMeasure| + |internalSubPolSet?| |fglmIfCan| |head| |permutationGroup| |setClosed| + |cup| |euclideanNormalForm| |numberOfDivisors| |prinshINFO| |exp| + |clearFortranOutputStack| |csch2sinh| |algebraic?| |symmetricPower| + |integerBound| |Vectorise| |complexEigenvectors| |freeOf?| + |rightPower| |exponents| |newSubProgram| |rightTrim| |charpol| + |polyRDE| |makeop| |getBadValues| |s17dgf| |physicalLength| |string?| + |iiasin| |rationalFunction| |leftTrim| |leftExactQuotient| + |rightExactQuotient| |toroidal| |trim| |ReduceOrder| |identityMatrix| + |removeSuperfluousCases| |moduleSum| |repSq| |overlabel| + |numberOfFractionalTerms| |increasePrecision| |argumentList!| + |quadraticForm| |patternMatch| |relativeApprox| |iiatanh| |e02akf| + |nthr| |safeCeiling| |factorials| |rangeIsFinite| |zoom| |changeBase| + |uniform01| |select!| |mathieu23| |delta| + |removeIrreducibleRedundantFactors| |d01gbf| |e02agf| |OMputSymbol| + |conditions| |listLoops| |interval| |enterPointData| |quatern| + |middle| |frobenius| |laguerre| |shuffle| |lllip| |match| |d03edf| + |ptree| |singleFactorBound| |mainMonomials| |alphabetic?| + |OMgetEndError| |trivialIdeal?| |se2rfi| |option?| |graphs| |call| + |OMencodingUnknown| |normalElement| |f02bjf| |rootsOf| |trigs2explogs| + |LyndonWordsList1| |sts2stst| |permutation| |monicModulo| |list| + |balancedBinaryTree| |dimensionOfIrreducibleRepresentation| |f01bsf| + |exQuo| |minimumDegree| |iilog| |prolateSpheroidal| |binomial| + |leader| |ode1| |car| |compound?| |aromberg| |hdmpToDmp| + |alphanumeric| |divisors| |realZeros| |quotientByP| |critBonD| + |c06eaf| |cdr| |reflect| |rroot| |round| |palgextint| |simpsono| + |constDsolve| |loadNativeModule| |expandTrigProducts| |inRadical?| + |karatsubaDivide| |setDifference| |nextItem| |addMatch| |ParCondList| + |npcoef| |nextPartition| |char| |zeroSetSplitIntoTriangularSystems| + |colorDef| |shellSort| |cot2trig| |setIntersection| |coordinate| + |purelyAlgebraic?| |quasiRegular?| |explimitedint| |groebgen| + |basicSet| |FormatRoman| |figureUnits| |lastSubResultant| |setUnion| + |generic?| |selectOrPolynomials| |totalGroebner| |substring?| + |legendreP| |setEpilogue!| |getProperty| |subQuasiComponent?| + |integral?| |pushucoef| |apply| |monicLeftDivide| + |linearAssociatedOrder| |powers| |outputFixed| |controlPanel| + |realSolve| |doubleFloatFormat| |leastPower| |e02daf| |setValue!| + |suffix?| |check| |rational?| |invertible?| |float| |finiteBound| + |void| |raisePolynomial| |printInfo!| |size| |critT| |imagi| + |cschIfCan| |irreducible?| |conditionsForIdempotents| + |lineColorDefault| |makeYoungTableau| |divideIfCan| |setProperties!| + |stopTableInvSet!| |prefix?| |extractProperty| |fortranLiteralLine| + |term| |retractable?| |associatedEquations| |cCsc| |divisor| + |wordInGenerators| |unprotectedRemoveRedundantFactors| |modifyPoint| + |taylorRep| |ideal| |mathieu11| |first| |OMencodingXML| + |basisOfLeftNucloid| |adaptive?| |linear?| |symmetric?| |identity| + |newReduc| |firstSubsetGray| |rest| |startTableInvSet!| |null| + |discriminant| |linearlyDependentOverZ?| |isMult| |showAllElements| + |implies| |beauzamyBound| |f02abf| |enumerate| |substitute| + |anticoord| |bracket| |case| |pointSizeDefault| |color| |eigenMatrix| + |integralMatrix| |scalarTypeOf| |removeDuplicates| |key| + |toseLastSubResultant| |Zero| |multiplyExponents| |subspace| + |extractBottom!| |unaryFunction| |xor| |padicallyExpand| |maxint| + |errorKind| |binding| |tubePlot| |LyndonCoordinates| |infix?| |One| + |regime| |autoReduced?| GE |pushup| |makeTerm| |s17dlf| |filename| + |createZechTable| |reopen!| |mask| |SturmHabichtSequence| |f04axf| + |assign| GT |double?| |pol| |toseSquareFreePart| |not?| + |innerEigenvectors| |basisOfMiddleNucleus| |zeroDimPrimary?| LE + |constantRight| |argument| |outputArgs| |parse| |surface| |copyInto!| + |mvar| |jordanAlgebra?| |e01bgf| LT |fixedDivisor| |setProperty| + |and?| |complexLimit| |infix| |purelyTranscendental?| |OMputEndBind| + |permanent| |space| |makeVariable| |compBound| |symbolTable| |label| + |retractIfCan| |leftQuotient| |homogeneous?| |dioSolve| + |tableForDiscreteLogarithm| |c06ekf| |ravel| |dmp2rfi| |graeffe| |dim| + |impliesOperands| |geometric| |OMgetAttr| |OMParseError?| |reshape| + |doubleResultant| |uniform| |pushFortranOutputStack| |putGraph| + |gbasis| |getMultiplicationTable| |genericRightNorm| |atoms| + |iteratedInitials| |uncouplingMatrices| |popFortranOutputStack| |root| + |string| |cosh2sech| |extend| |countable?| |e02bef| + |rationalApproximation| |crest| |s17dhf| |rightGcd| |floor| + |outputAsFortran| |firstUncouplingMatrix| |imagI| |airyBi| + |getPickedPoints| |nilFactor| |optpair| |direction| |qinterval| + |dmpToHdmp| |size?| |Gamma| |d01gaf| |divideIfCan!| |bernoulli| + |maxPoints| |maximumExponent| |isPower| |exponent| |mathieu22| + |update| |recoverAfterFail| |inverseIntegralMatrix| |cAsin| + |createGenericMatrix| |hasoln| |getOrder| |enqueue!| |KrullNumber| + |univariateSolve| |heapSort| |conjugates| |mantissa| |nthExponent| + |minPoly| |setAdaptive| |multiEuclidean| |rischDE| |lfintegrate| + |checkForZero| |dihedralGroup| |map| |lyndon| |physicalLength!| + |basis| |nextPrimitiveNormalPoly| |dAndcExp| |pointColorDefault| + |critB| |exponential1| |s17def| |setelt!| |f04mcf| |fortranLiteral| + |nextLatticePermutation| |badValues| |constantOpIfCan| |lllp| + |clearTheIFTable| |basisOfCenter| |PDESolve| |dflist| |OMputEndAttr| + |removeZeroes| |external?| |andOperands| |localReal?| + |rightFactorIfCan| |subresultantSequence| |second| |getConstant| + |normFactors| |rotatex| |var2Steps| |empty?| |charthRoot| + |reduceByQuasiMonic| |pdct| |third| |iiacosh| |setTex!| |removeSinhSq| + |normalize| |orbit| |convert| |categoryFrame| |createRandomElement| + |outputGeneral| |RittWuCompare| |univariatePolynomials| |script| + |iiasinh| |nsqfree| |shiftRight| |complexZeros| |lepol| |squareFree| + |laguerreL| |invertibleSet| |interpret| |monicCompleteDecompose| + |factorByRecursion| |mindeg| |vector| |complexIntegrate| |f01rcf| + |keys| |unitsColorDefault| |polarCoordinates| |axes| |leftMult| + |internalSubQuasiComponent?| |front| |differentiate| |eigenvalues| + |explogs2trigs| |rk4f| |weierstrass| |tex| |prime?| + |partialNumerators| |normalizedDivide| |drawStyle| + |createNormalPrimitivePoly| |characteristic| |cycleSplit!| + |setsubMatrix!| |rombergo| |remainder| |useNagFunctions| |inR?| + |clipParametric| |iiasec| |point?| |e01bff| |variable?| |setlast!| + |distribute| |f02aaf| |characteristicSerie| |imagj| |insertMatch| + |diag| |slex| |alphabetic| |lowerPolynomial| |zeroDim?| |yellow| + |paren| |semiResultantEuclidean2| |mergeFactors| |showAll?| |btwFact| + |setFieldInfo| |d03faf| |debug| |degreePartition| |lexGroebner| |dot| + |primlimitedint| |linGenPos| |basisOfCentroid| |qPot| |iifact| D + |predicate| |leftRankPolynomial| |stiffnessAndStabilityOfODEIF| + |f02bbf| |setButtonValue| |OMgetAtp| LODO2FUN |evenInfiniteProduct| + |fixedPointExquo| |column| |monomialIntegrate| |sechIfCan| + |differentialVariables| |makeFloatFunction| |sn| |bringDown| + |leftUnits| |makeGraphImage| |bindings| |parent| + |integralBasisAtInfinity| |rewriteSetWithReduction| |infieldIntegrate| + |solveRetract| |structuralConstants| |univcase| |sumOfSquares| + |movedPoints| |virtualDegree| |rational| |true| |palgintegrate| + |separant| |Lazard| |setCondition!| |cyclic| |splitConstant| + |basisOfRightNucleus| |getExplanations| |and| |brace| |OMopenString| + |leftDivide| |mainMonomial| |basisOfCommutingElements| |internal?| + |stoseInvertible?sqfreg| |resultant| |closeComponent| |leaves| + |powerSum| |transform| |laurentRep| |quadratic| |lp| + |linearAssociatedLog| |normalized?| |bezoutDiscriminant| |refine| + |genericRightTraceForm| |symbolIfCan| |aLinear| |logpart| |deepCopy| + |modifyPointData| |createPrimitiveElement| |c06ecf| |e02bbf| |cAcsch| + |errorInfo| |parameters| |d01akf| |sumSquares| |insertionSort!| + |phiCoord| |radicalEigenvalues| |value| |sup| |romberg| + |stoseInternalLastSubResultant| |nonLinearPart| |close!| |varselect| + |tubeRadius| |printStats!| |sum| |fillPascalTriangle| |iicosh| + |hyperelliptic| |minrank| |goodnessOfFit| |logIfCan| |log2| + |deepestInitial| |equality| |primlimintfrac| |groebnerIdeal| + |OMputEndApp| |associative?| |bitCoef| |coefficients| |makeEq| + |symmetricSquare| |univariatePolynomialsGcds| + |createLowComplexityTable| |unitCanonical| |e02gaf| |makeCos| + |PollardSmallFactor| |f04atf| |expt| |froot| |wronskianMatrix| + |d01anf| |s14aaf| |bumptab1| |odd?| |hex| + |removeRoughlyRedundantFactorsInPols| |zerosOf| |rarrow| |allRootsOf| + |rootDirectory| |optional?| |setMinPoints3D| |LyndonWordsList| + |s13aaf| |top!| |identification| |lieAlgebra?| |totalDegree| + |gcdcofact| |packageCall| |LagrangeInterpolation| |findBinding| + |socf2socdf| |leadingTerm| |generators| |selectsecond| |f04jgf| + |brillhartIrreducible?| |initiallyReduce| |concat| |s18def| + |powerAssociative?| |pointLists| |unitNormalize| |OMUnknownCD?| + |subSet| |fi2df| |mainValue| |redmat| |sdf2lst| + |constantToUnaryFunction| |randomLC| |elements| |addPoint2| + |atanhIfCan| |permutationRepresentation| |pdf2ef| |elRow1!| + |OMreadStr| |lflimitedint| |lazy?| |ScanArabic| |nextPrime| + |extractPoint| |yCoordinates| |id| |removeRedundantFactorsInPols| + |tan2trig| |e04mbf| |rdregime| |OMgetInteger| |infieldint| + |cyclicEqual?| |cscIfCan| |sparsityIF| |nthFactor| |permutations| + |chiSquare| |shade| |linearlyDependent?| |lazyPseudoQuotient| + |insertRoot!| |startTable!| |table| |roughEqualIdeals?| |denomLODE| + |polygon?| |getButtonValue| |qelt| |mainVariable?| |algebraicSort| + |pquo| |palgextint0| |dimensionsOf| |new| |OMgetObject| |cAtanh| + |setPredicates| |showTheSymbolTable| |pascalTriangle| |squareFreePart| + |completeSmith| |viewWriteAvailable| |powmod| |weighted| |minus!| + |cosSinInfo| |exquo| |rst| |fortranCompilerName| |xRange| |pole?| + |currentEnv| |cTanh| |computePowers| |tracePowMod| |mpsode| |div| + |yRange| |closedCurve| |Beta| |viewDeltaYDefault| |antiAssociative?| + |indices| |divergence| |rightOne| |cyclotomic| |quo| |applyRules| + |startPolynomial| |zRange| |rquo| |e02dff| |numberOfFactors| |cExp| + |numberOfMonomials| |complexNormalize| |rightMinimalPolynomial| + |equiv| |map!| |expint| |scanOneDimSubspaces| |OMgetString| + |selectFiniteRoutines| |rewriteIdealWithRemainder| |antisymmetric?| + |rem| |blue| |qsetelt!| |hspace| |mapSolve| |fullDisplay| + |LowTriBddDenomInv| |myDegree| |viewPhiDefault| |pade| + |generalizedEigenvectors| |pureLex| |createNormalPoly| |s17ahf| + |OMputApp| |satisfy?| |karatsuba| |e04dgf| |reciprocalPolynomial| + GF2FG |secIfCan| |typeLists| |extractIfCan| |highCommonTerms| + |diagonal| |leaf?| |nextPrimitivePoly| |mapmult| |parabolic| + |acschIfCan| |superscript| |roman| |tanQ| |fortran| |tab| |OMputBVar| + |expIfCan| |supRittWu?| |left| |redPo| |mainPrimitivePart| + |internalIntegrate| |acsch| |roughBasicSet| + |standardBasisOfCyclicSubmodule| |invmultisect| |bitLength| + |complexExpand| |right| |rootSplit| |zeroDimPrime?| + |internalInfRittWu?| |drawComplexVectorField| |minColIndex| + |moebiusMu| |roughUnitIdeal?| |setOrder| |perfectSquare?| + |numericIfCan| |pushdterm| |goodPoint| |s01eaf| |lintgcd| |rk4qc| + |rur| |unexpand| |coerceP| |init| |failed?| |monicDecomposeIfCan| + |roughBase?| |bandedJacobian| |initializeGroupForWordProblem| |curve| + |partialQuotients| |listRepresentation| |taylorIfCan| |interReduce| + |monomial?| |zeroDimensional?| |SturmHabichtMultiple| |ocf2ocdf| + |coord| |testModulus| |OMbindTCP| |commutative?| |not| + |associatedSystem| |terms| |coerceS| |withPredicates| |OMputEndObject| + |OMgetError| |merge| |push!| |rowEchelonLocal| |overlap| |sqfrFactor| + |iflist2Result| |OMputAttr| |pile| |cross| |getIdentifier| |seed| + |ranges| |f01ref| |integralBasis| |cycleTail| |d01ajf| |chebyshevU| + |OMgetVariable| |youngGroup| |varList| |primes| |rules| |center| + |solveLinearPolynomialEquationByRecursion| |mainKernel| |lfunc| + |light| |OMunhandledSymbol| |minGbasis| |OMreadFile| |tubePoints| + |deleteRoutine!| |delete!| |maxrow| |generalizedInverse| |key?| + |flexible?| |leadingIndex| |factors| |cothIfCan| |iiperm| |wrregime| + |rationalPoint?| |squareFreeFactors| |createMultiplicationMatrix| + |acoshIfCan| |e02dcf| |hermite| |bat1| |OMsetEncoding| |pointData| + |exponential| |quotedOperators| |f07adf| |toseInvertibleSet| |iitan| + |extractIndex| |f02akf| |nthRoot| |SFunction| |makeCrit| |aspFilename| + |quoByVar| |lazyEvaluate| |symbol| |expenseOfEvaluationIF| |gcdprim| + |OMputEndError| |rightUnits| |groebner?| |write!| |match?| + |selectPolynomials| |mapExponents| |antisymmetricTensors| + |associatorDependence| |coefChoose| |genericRightDiscriminant| + |meshPar1Var| |OMgetEndAtp| |divide| |makeFR| |cosIfCan| + |jacobiIdentity?| |create3Space| |cAcoth| |makingStats?| + |radicalEigenvector| |integer| |bitior| |escape| |linears| + |resultantnaif| ** |leastMonomial| |shiftLeft| |parts| |enterInCache| + |degreeSubResultant| |replace| |cCoth| |reduced?| |e04jaf| + |mightHaveRoots| |lastSubResultantEuclidean| |pleskenSplit| |quartic| + |cap| |iiatan| |exactQuotient| |safetyMargin| |move| |expextendedint| + |algDsolve| |f01maf| |s18aff| |has?| |simpleBounds?| |complement| + |mergeDifference| |iExquo| |f02axf| EQ |readIfCan!| |sub| + |RemainderList| |c06gcf| UTS2UP |numberOfComputedEntries| |typeList| + |denomRicDE| |midpoint| |null?| |iomode| |UpTriBddDenomInv| + |factorAndSplit| |lfextendedint| |inc| |primextintfrac| + |sumOfDivisors| |s20acf| |hessian| |chainSubResultants| |expandPower| + |numericalOptimization| |newTypeLists| |content| |viewZoomDefault| + |OMgetEndObject| |leftUnit| |s13adf| |decomposeFunc| + |SturmHabichtCoefficients| |setleaves!| |combineFeatureCompatibility| + |nativeModuleExtension| |integralDerivationMatrix| |isOp| |minPoints| + |var1Steps| |rename!| |vertConcat| |factorSquareFreePolynomial| + |leftRegularRepresentation| |lexico| SEGMENT |plus| |decompose| + |f04asf| |plotPolar| |prefix| |s21bdf| |finite?| |principalIdeal| + |objectOf| |e01daf| |factorList| |distFact| |addMatchRestricted| + |plus!| |minRowIndex| |f04faf| |df2ef| |iiabs| |sizeMultiplication| + |OMlistSymbols| |test| |printCode| |bottom!| |gradient| |sequences| + |asechIfCan| |sizePascalTriangle| |generalizedEigenvector| + |subResultantsChain| |palgRDE| |setAdaptive3D| |OMputFloat| + |realRoots| |definingInequation| |strongGenerators| |high| + |nextIrreduciblePoly| |hue| |stack| |interpretString| |any?| |s17aef| + |numberOfOperations| |ScanFloatIgnoreSpaces| |times| |bubbleSort!| + |showTypeInOutput| |diagonalProduct| |prologue| |iidsum| |graphImage| + |clipBoolean| |currentCategoryFrame| |alternatingGroup| |rootProduct| + |squareTop| |thetaCoord| |argscript| |name| |medialSet| |maxColIndex| + |upperCase| |resetNew| |commonDenominator| |error| |prefixRagits| + |constantOperator| |sinh2csch| |trace2PowMod| |bit?| |body| + |algebraicDecompose| |vspace| |selectAndPolynomials| |simplifyPower| + |indiceSubResultant| |assert| |fortranInteger| |increase| + |mapBivariate| |OMconnectTCP| |unitVector| |optimize| |closedCurve?| + |fractionFreeGauss!| |abs| |selectMultiDimensionalRoutines| + |halfExtendedSubResultantGcd1| |unary?| |pToDmp| |c02agf| |monom| + |approxNthRoot| |dominantTerm| |noncommutativeJordanAlgebra?| + |associates?| |tanh2coth| |stoseInvertibleSetreg| |drawCurves| + |primeFrobenius| |numerators| |subResultantGcd| |solveLinear| |mesh| + |term?| |rootNormalize| |viewport3D| |ksec| |matrixDimensions| |empty| + |setColumn!| |baseRDEsys| |reverseLex| |Frobenius| |makeSeries| |expr| + |FormatArabic| |arg1| |int| |bivariate?| |htrigs| |common| + |lexTriangular| |invmod| |rightQuotient| |coercePreimagesImages| + |mainSquareFreePart| |exists?| |exprToXXP| |mkAnswer| |arg2| + |antiCommutator| |besselK| |complexEigenvalues| |seriesSolve| + |LazardQuotient| |tValues| |ode| |OMwrite| |rightDiscriminant| + |d01amf| |someBasis| |rightRankPolynomial| |tanAn| |localAbs| + |stopMusserTrials| |knownInfBasis| |karatsubaOnce| |changeNameToObjf| + |addmod| |mapExpon| |contains?| |cAcot| |squareFreePolynomial| |power| + |iicoth| |rightNorm| |solid| |variable| |s19aaf| |numberOfCycles| + |minIndex| |perspective| |UP2ifCan| |realEigenvectors| |ricDsolve| + |semiSubResultantGcdEuclidean2| |nthCoef| |summation| |returns| + |exteriorDifferential| |prime| |internalIntegrate0| |predicates| |Nul| + |triangular?| |polynomialZeros| |OMputString| |more?| |insert| + |equivOperands| |subscriptedVariables| |failed| |forLoop| |intersect| + |computeCycleLength| |critMonD1| |harmonic| |rightScalarTimes!| + |drawComplex| |useSingleFactorBound| |square?| + |generalizedContinuumHypothesisAssumed?| |d02raf| |ran| + |linkToFortran| |element?| |t| |increment| |c06fpf| |getGoodPrime| + |complete| |iiacsch| |next| |finiteBasis| |branchPoint?| + |constantCoefficientRicDE| |doubleDisc| |asecIfCan| |nlde| + |numberOfNormalPoly| |radix| |OMgetBVar| |digit?| |normalDenom| + |entry?| |firstNumer| |isAbsolutelyIrreducible?| |removeCosSq| + |flatten| |trigs| |expintegrate| |acosIfCan| |ptFunc| |nand| |cn| + |e01sbf| |modulus| |backOldPos| |lambert| |palgRDE0| |UnVectorise| + |supDimElseRittWu?| |resultantEuclideannaif| |explicitlyFinite?| + |selectSumOfSquaresRoutines| |coefficient| |character?| |solveid| + |ramifiedAtInfinity?| |c05pbf| |generalLambert| |setchildren!| + |shanksDiscLogAlgorithm| |ldf2lst| |directory| |repeating| + |limitedint| |mindegTerm| |eval| |cAsinh| |nil| |isQuotient| + |reduceLODE| |showArrayValues| |leftZero| |noLinearFactor?| |reverse| + |algebraicOf| |c06fuf| |length| |colorFunction| |currentSubProgram| + |trailingCoefficient| |updateStatus!| |transpose| |leadingSupport| + |nonSingularModel| |d02bhf| |fixPredicate| |scripts| |exptMod| + |buildSyntax| |primitivePart!| |complementaryBasis| |operator| + |rightRank| Y |numerator| |lifting1| |resultantReduit| |headAst| + |f02aef| |leftGcd| |ratPoly| |prinpolINFO| |initTable!| |approximate| + |cycle| |leftPower| |getCurve| |symbolTableOf| |printInfo| + |eisensteinIrreducible?| |OMUnknownSymbol?| |outputMeasure| |op| + |complex| |edf2ef| |e02aef| |presuper| |printingInfo?| |systemCommand| + |solveLinearPolynomialEquationByFractions| |child?| |constantIfCan| + |evaluateInverse| |height| |incrementKthElement| |OMserve| + |selectOptimizationRoutines| |commaSeparate| |getCode| + |stoseInvertibleSet| |henselFact| |chineseRemainder| |graphState| + |lambda| |symmetricProduct| |multinomial| |boundOfCauchy| |prem| + |nthFlag| |rootBound| |connect| |eulerE| |setTopPredicate| + |outerProduct| |baseRDE| |adaptive| |fixedPoint| |zag| |cAsec| + |normal| |mkIntegral| |lighting| |functionIsOscillatory| |d01asf| + |iidprod| |yCoord| |generateIrredPoly| |eyeDistance| |toScale| |cLog| + |iicsc| |rewriteSetByReducingWithParticularGenerators| |belong?| + |cyclotomicFactorization| |member?| |rk4a| |multiEuclideanTree| + |s17agf| |symbol?| |zeroOf| |s15adf| |union| |consnewpol| + |setProperties| |shift| |augment| |rightRegularRepresentation| + |cycleRagits| |subCase?| |quasiRegular| |deepExpand| |cCot| + |setImagSteps| |deref| |returnType!| |depth| |multiplyCoefficients| + |intermediateResultsIF| |prepareDecompose| |s21bbf| + |lazyPremWithDefault| |primPartElseUnitCanonical| |setClipValue| + |makeMulti| |computeBasis| |input| |d02kef| |safeFloor| |resize| + |setleft!| |messagePrint| |aQuartic| UP2UTS |f02xef| + |lazyResidueClass| |options| |rubiksGroup| |qfactor| |setMaxPoints| + |updatD| |library| |linSolve| |hypergeometric0F1| |cyclic?| + |elliptic?| |listYoungTableaus| |open?| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 2a91169d..26d296df 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4949 +1,4949 @@ -(3152502 . 3429209025) -((-4038 (((-110) (-1 (-110) |#2| |#2|) $) 63) (((-110) $) NIL)) (-4017 (($ (-1 (-110) |#2| |#2|) $) 18) (($ $) NIL)) (-2416 ((|#2| $ (-530) |#2|) NIL) ((|#2| $ (-1148 (-530)) |#2|) 34)) (-1389 (($ $) 59)) (-3856 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T) ((-850) -12 (|has| |#1| (-289)) (|has| |#1| (-850))) ((-861) -1476 (|has| |#1| (-330)) (|has| |#1| (-344)) (|has| |#1| (-289))) ((-941) -12 (|has| |#1| (-941)) (|has| |#1| (-1121))) ((-975 (-388 (-530))) |has| |#1| (-975 (-388 (-530)))) ((-975 (-530)) |has| |#1| (-975 (-530))) ((-975 |#1|) . T) ((-990 #0#) -1476 (|has| |#1| (-330)) (|has| |#1| (-344))) ((-990 |#1|) . T) ((-990 $) . T) ((-984) . T) ((-991) . T) ((-1039) . T) ((-1027) . T) ((-1075) |has| |#1| (-330)) ((-1121) |has| |#1| (-1121)) ((-1124) |has| |#1| (-1121)) ((-1135) . 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T) ((-23) . T) ((-25) . T) ((-37 #0=(-388 (-530))) -1461 (|has| |#1| (-330)) (|has| |#1| (-344))) ((-37 |#1|) . T) ((-37 $) -1461 (|has| |#1| (-522)) (|has| |#1| (-330)) (|has| |#1| (-344)) (|has| |#1| (-289))) ((-34) |has| |#1| (-1121)) ((-93) |has| |#1| (-1121)) ((-99) . T) ((-109 #0# #0#) -1461 (|has| |#1| (-330)) (|has| |#1| (-344))) ((-109 |#1| |#1|) . T) ((-109 $ $) . T) ((-128) . T) ((-138) -1461 (|has| |#1| (-330)) (|has| |#1| (-138))) ((-140) |has| |#1| (-140)) ((-571 (-804)) . T) ((-162) . T) ((-572 (-159 (-208))) |has| |#1| (-960)) ((-572 (-159 (-360))) |has| |#1| (-960)) ((-572 (-506)) |has| |#1| (-572 (-506))) ((-572 (-833 (-360))) |has| |#1| (-572 (-833 (-360)))) ((-572 (-833 (-530))) |has| |#1| (-572 (-833 (-530)))) ((-572 #1=(-1095 |#1|)) . T) ((-214 |#1|) . 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T) ((-291 |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((-349) |has| |#2| (-349)) ((-358 |#2|) |has| |#2| (-984)) ((-392 |#2|) |has| |#2| (-1027)) ((-468 |#2|) . T) ((-563 #0# |#2|) . T) ((-491 |#2| |#2|) -12 (|has| |#2| (-291 |#2|)) (|has| |#2| (-1027))) ((-599 |#2|) -1461 (|has| |#2| (-984)) (|has| |#2| (-344)) (|has| |#2| (-162))) ((-599 $) -1461 (|has| |#2| (-984)) (|has| |#2| (-793)) (|has| |#2| (-162))) ((-593 (-530)) -12 (|has| |#2| (-593 (-530))) (|has| |#2| (-984))) ((-593 |#2|) |has| |#2| (-984)) ((-666 |#2|) -1461 (|has| |#2| (-344)) (|has| |#2| (-162))) ((-675) -1461 (|has| |#2| (-984)) (|has| |#2| (-793)) (|has| |#2| (-675)) (|has| |#2| (-162))) ((-739) |has| |#2| (-793)) ((-740) -1461 (|has| |#2| (-793)) (|has| |#2| (-741))) ((-741) |has| |#2| (-741)) ((-742) -1461 (|has| |#2| (-793)) (|has| |#2| (-741))) ((-743) -1461 (|has| |#2| (-793)) (|has| |#2| (-741))) ((-793) |has| |#2| (-793)) ((-795) -1461 (|has| |#2| (-793)) (|has| |#2| (-741))) ((-841 (-1099)) -12 (|has| |#2| (-841 (-1099))) (|has| |#2| (-984))) ((-975 (-388 (-530))) -12 (|has| |#2| (-975 (-388 (-530)))) (|has| |#2| (-1027))) ((-975 (-530)) -12 (|has| |#2| (-975 (-530))) (|has| |#2| (-1027))) ((-975 |#2|) |has| |#2| (-1027)) ((-990 |#2|) -1461 (|has| |#2| (-984)) (|has| |#2| (-344)) (|has| |#2| (-162))) ((-990 $) |has| |#2| (-162)) ((-984) -1461 (|has| |#2| (-984)) (|has| |#2| (-793)) (|has| |#2| (-162))) ((-991) -1461 (|has| |#2| (-984)) (|has| |#2| (-793)) (|has| |#2| (-162))) ((-1039) -1461 (|has| |#2| (-984)) (|has| |#2| (-793)) (|has| |#2| (-675)) (|has| |#2| (-162))) ((-1027) -1461 (|has| |#2| (-1027)) (|has| |#2| (-984)) (|has| |#2| (-793)) (|has| |#2| (-741)) (|has| |#2| (-675)) (|has| |#2| (-349)) (|has| |#2| (-344)) (|has| |#2| (-162)) (|has| |#2| (-128)) (|has| |#2| (-25))) ((-1135) . 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T) ((-358 |#1|) . T) ((-392 |#1|) . T) ((-432) -1476 (|has| |#1| (-850)) (|has| |#1| (-432))) ((-491 |#2| |#1|) |has| |#1| (-216)) ((-491 |#2| $) |has| |#1| (-216)) ((-491 |#3| |#1|) . T) ((-491 |#3| $) . T) ((-491 $ $) . T) ((-522) -1476 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-599 #0#) |has| |#1| (-37 (-388 (-530)))) ((-599 |#1|) . T) ((-599 $) . T) ((-593 (-530)) |has| |#1| (-593 (-530))) ((-593 |#1|) . T) ((-666 #0#) |has| |#1| (-37 (-388 (-530)))) ((-666 |#1|) |has| |#1| (-162)) ((-666 $) -1476 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-675) . T) ((-795) |has| |#1| (-795)) ((-841 (-1099)) |has| |#1| (-841 (-1099))) ((-841 |#3|) . T) ((-827 (-360)) -12 (|has| |#1| (-827 (-360))) (|has| |#3| (-827 (-360)))) ((-827 (-530)) -12 (|has| |#1| (-827 (-530))) (|has| |#3| (-827 (-530)))) ((-890 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 #0=(-388 (-530))) |has| |#1| (-37 (-388 (-530)))) ((-37 |#1|) |has| |#1| (-162)) ((-37 $) -1461 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-99) . T) ((-109 #0# #0#) |has| |#1| (-37 (-388 (-530)))) ((-109 |#1| |#1|) . T) ((-109 $ $) -1461 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432)) (|has| |#1| (-162))) ((-128) . T) ((-138) |has| |#1| (-138)) ((-140) |has| |#1| (-140)) ((-571 (-804)) . T) ((-162) -1461 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432)) (|has| |#1| (-162))) ((-572 (-506)) -12 (|has| |#1| (-572 (-506))) (|has| |#3| (-572 (-506)))) ((-572 (-833 (-360))) -12 (|has| |#1| (-572 (-833 (-360)))) (|has| |#3| (-572 (-833 (-360))))) ((-572 (-833 (-530))) -12 (|has| |#1| (-572 (-833 (-530)))) (|has| |#3| (-572 (-833 (-530))))) ((-214 |#1|) . T) ((-216) |has| |#1| (-216)) ((-272) -1461 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-291 $) . T) ((-307 |#1| |#4|) . T) ((-358 |#1|) . T) ((-392 |#1|) . T) ((-432) -1461 (|has| |#1| (-850)) (|has| |#1| (-432))) ((-491 |#2| |#1|) |has| |#1| (-216)) ((-491 |#2| $) |has| |#1| (-216)) ((-491 |#3| |#1|) . T) ((-491 |#3| $) . T) ((-491 $ $) . T) ((-522) -1461 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-599 #0#) |has| |#1| (-37 (-388 (-530)))) ((-599 |#1|) . T) ((-599 $) . T) ((-593 (-530)) |has| |#1| (-593 (-530))) ((-593 |#1|) . T) ((-666 #0#) |has| |#1| (-37 (-388 (-530)))) ((-666 |#1|) |has| |#1| (-162)) ((-666 $) -1461 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432))) ((-675) . T) ((-795) |has| |#1| (-795)) ((-841 (-1099)) |has| |#1| (-841 (-1099))) ((-841 |#3|) . T) ((-827 (-360)) -12 (|has| |#1| (-827 (-360))) (|has| |#3| (-827 (-360)))) ((-827 (-530)) -12 (|has| |#1| (-827 (-530))) (|has| |#3| (-827 (-530)))) ((-890 |#1| |#4| |#3|) . T) ((-850) |has| |#1| (-850)) ((-975 (-388 (-530))) |has| |#1| (-975 (-388 (-530)))) ((-975 (-530)) |has| |#1| (-975 (-530))) ((-975 |#1|) . T) ((-975 |#2|) . T) ((-975 |#3|) . T) ((-990 #0#) |has| |#1| (-37 (-388 (-530)))) ((-990 |#1|) . T) ((-990 $) -1461 (|has| |#1| (-850)) (|has| |#1| (-522)) (|has| |#1| (-432)) (|has| |#1| (-162))) ((-984) . T) ((-991) . T) ((-1039) . T) ((-1027) . T) ((-1139) |has| |#1| (-850))) +((-2352 (((-110) $ $) 19 (|has| |#1| (-1027)))) (-3468 ((|#1| $) 54)) (-1598 ((|#1| $) 44)) (-3186 (((-110) $ (-719)) 8)) (-2350 (($) 7 T CONST)) (-1907 (($ $) 60)) (-1337 (($ $) 48)) (-3684 ((|#1| |#1| $) 46)) (-2176 ((|#1| $) 45)) (-3779 (((-597 |#1|) $) 30 (|has| $ (-6 -4269)))) (-4027 (((-110) $ (-719)) 9)) (-2395 (((-597 |#1|) $) 29 (|has| $ (-6 -4269)))) (-4197 (((-110) |#1| $) 27 (-12 (|has| |#1| (-1027)) (|has| $ (-6 -4269))))) (-3583 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4270)))) (-3217 (($ (-1 |#1| |#1|) $) 35)) (-2763 (((-110) $ (-719)) 10)) (-4109 (((-719) $) 61)) (-1424 (((-1082) $) 22 (|has| |#1| (-1027)))) (-1723 ((|#1| $) 39)) (-1260 ((|#1| |#1| $) 52)) (-1848 ((|#1| |#1| $) 51)) (-2441 (($ |#1| $) 40)) (-4156 (((-719) $) 55)) (-2624 (((-1046) $) 21 (|has| |#1| (-1027)))) (-3288 ((|#1| $) 62)) (-1458 ((|#1| $) 50)) (-3083 ((|#1| $) 49)) (-2738 ((|#1| $) 41)) (-1533 (((-110) (-1 (-110) |#1|) $) 32 (|has| $ (-6 -4269)))) (-4098 (($ $ (-597 (-276 |#1|))) 26 (-12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (($ $ (-276 |#1|)) 25 (-12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027)))) (($ $ (-597 |#1|) (-597 |#1|)) 23 (-12 (|has| |#1| (-291 |#1|)) (|has| |#1| (-1027))))) (-2391 (((-110) $ $) 14)) (-3203 ((|#1| |#1| $) 58)) (-3250 (((-110) $) 11)) (-3958 (($) 12)) (-1540 ((|#1| $) 59)) (-1909 (($) 57) (($ (-597 |#1|)) 56)) (-4218 (((-719) $) 43)) (-2632 (((-719) (-1 (-110) |#1|) $) 31 (|has| $ (-6 -4269))) (((-719) |#1| $) 28 (-12 (|has| |#1| (-1027)) (|has| $ (-6 -4269))))) (-2579 (($ $) 13)) (-2366 (((-804) $) 18 (|has| |#1| (-571 (-804))))) (-3871 ((|#1| $) 53)) (-2242 (($ (-597 |#1|)) 42)) (-1371 ((|#1| $) 63)) (-3889 (((-110) (-1 (-110) |#1|) $) 33 (|has| $ (-6 -4269)))) (-2248 (((-110) $ $) 20 (|has| |#1| (-1027)))) (-2267 (((-719) $) 6 (|has| $ (-6 -4269))))) (((-236 |#1|) (-133) (-1135)) (T -236)) -((-4043 (*1 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135)))) (-4043 (*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1135)) (-4 *1 (-236 *3)))) (-4150 (*1 *2 *1) (-12 (-4 *1 (-236 *3)) (-4 *3 (-1135)) (-5 *2 (-719)))) (-4033 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135)))) (-4023 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135)))) (-4012 (*1 *2 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135)))) (-4003 (*1 *2 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135)))) (-3992 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135)))) (-3983 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135)))) (-1389 (*1 *1 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135))))) -(-13 (-1047 |t#1|) (-934 |t#1|) (-10 -8 (-15 -4043 ($)) (-15 -4043 ($ (-597 |t#1|))) (-15 -4150 ((-719) $)) (-15 -4033 (|t#1| $)) (-15 -4023 (|t#1| $)) (-15 -4012 (|t#1| |t#1| $)) (-15 -4003 (|t#1| |t#1| $)) (-15 -3992 (|t#1| $)) (-15 -3983 (|t#1| $)) (-15 -1389 ($ $)))) -(((-33) . 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(-349) (-572 (-530)) (-1075)) (-862)) (T -1207)) NIL (-13 (-162) (-349) (-572 (-530)) (-1075)) @@ -4959,4 +4959,4 @@ NIL NIL NIL NIL -((-3 3152487 3152492 3152497 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3152472 3152477 3152482 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3152457 3152462 3152467 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3152442 3152447 3152452 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1207 3151572 3152317 3152394 "ZMOD" 3152399 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1206 3150682 3150846 3151055 "ZLINDEP" 3151404 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1205 3140086 3141831 3143783 "ZDSOLVE" 3148831 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1204 3139332 3139473 3139662 "YSTREAM" 3139932 NIL YSTREAM (NIL T) -7 NIL NIL) (-1203 3137101 3138637 3138840 "XRPOLY" 3139175 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1202 3133563 3134892 3135474 "XPR" 3136565 NIL XPR (NIL T T) -8 NIL NIL) (-1201 3131277 3132898 3133101 "XPOLY" 3133394 NIL XPOLY (NIL T) -8 NIL NIL) (-1200 3129091 3130469 3130523 "XPOLYC" 3130808 NIL 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T) -9 NIL 3100410) (-1187 3099572 3099599 3099690 "VSPACE-" 3099695 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1186 3099318 3099361 3099432 "VOID" 3099523 T VOID (NIL) -8 NIL NIL) (-1185 3097454 3097813 3098219 "VIEW" 3098934 T VIEW (NIL) -7 NIL NIL) (-1184 3093879 3094517 3095254 "VIEWDEF" 3096739 T VIEWDEF (NIL) -7 NIL NIL) (-1183 3083217 3085427 3087600 "VIEW3D" 3091728 T VIEW3D (NIL) -8 NIL NIL) (-1182 3075499 3077128 3078707 "VIEW2D" 3081660 T VIEW2D (NIL) -8 NIL NIL) (-1181 3070908 3075269 3075361 "VECTOR" 3075442 NIL VECTOR (NIL T) -8 NIL NIL) (-1180 3069485 3069744 3070062 "VECTOR2" 3070638 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1179 3063025 3067277 3067320 "VECTCAT" 3068308 NIL VECTCAT (NIL T) -9 NIL 3068892) (-1178 3062039 3062293 3062683 "VECTCAT-" 3062688 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1177 3061520 3061690 3061810 "VARIABLE" 3061954 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1176 3061453 3061458 3061488 "UTYPE" 3061493 T UTYPE (NIL) -9 NIL NIL) (-1175 3060288 3060442 3060703 "UTSODETL" 3061279 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1174 3057728 3058188 3058712 "UTSODE" 3059829 NIL UTSODE (NIL T T) -7 NIL NIL) (-1173 3049572 3055368 3055856 "UTS" 3057297 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1172 3040917 3046282 3046324 "UTSCAT" 3047425 NIL UTSCAT (NIL T) -9 NIL 3048182) (-1171 3038272 3038988 3039976 "UTSCAT-" 3039981 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1170 3037903 3037946 3038077 "UTS2" 3038223 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1169 3032179 3034744 3034787 "URAGG" 3036857 NIL URAGG (NIL T) -9 NIL 3037579) (-1168 3029118 3029981 3031104 "URAGG-" 3031109 NIL URAGG- (NIL T T) -8 NIL NIL) (-1167 3024804 3027735 3028206 "UPXSSING" 3028782 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1166 3016695 3023925 3024205 "UPXS" 3024581 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1165 3009724 3016600 3016671 "UPXSCONS" 3016676 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1164 3000013 3006843 3006904 "UPXSCCA" 3007553 NIL UPXSCCA (NIL T T) -9 NIL 3007794) (-1163 2999652 2999737 2999910 "UPXSCCA-" 2999915 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1162 2989863 2996466 2996508 "UPXSCAT" 2997151 NIL UPXSCAT (NIL T) -9 NIL 2997759) (-1161 2989297 2989376 2989553 "UPXS2" 2989778 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1160 2987951 2988204 2988555 "UPSQFREE" 2989040 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1159 2981842 2984897 2984951 "UPSCAT" 2986100 NIL UPSCAT (NIL T T) -9 NIL 2986874) (-1158 2981047 2981254 2981580 "UPSCAT-" 2981585 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1157 2967133 2975170 2975212 "UPOLYC" 2977290 NIL UPOLYC (NIL T) -9 NIL 2978511) (-1156 2958463 2960888 2964034 "UPOLYC-" 2964039 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1155 2958094 2958137 2958268 "UPOLYC2" 2958414 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1154 2949513 2957663 2957800 "UP" 2958004 NIL UP (NIL NIL T) -8 NIL NIL) (-1153 2948856 2948963 2949126 "UPMP" 2949402 NIL UPMP (NIL T T) -7 NIL NIL) (-1152 2948409 2948490 2948629 "UPDIVP" 2948769 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1151 2946977 2947226 2947542 "UPDECOMP" 2948158 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1150 2946212 2946324 2946509 "UPCDEN" 2946861 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1149 2945735 2945804 2945951 "UP2" 2946137 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1148 2944252 2944939 2945216 "UNISEG" 2945493 NIL UNISEG (NIL T) -8 NIL NIL) (-1147 2943467 2943594 2943799 "UNISEG2" 2944095 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1146 2942527 2942707 2942933 "UNIFACT" 2943283 NIL UNIFACT (NIL T) -7 NIL NIL) (-1145 2926423 2941708 2941958 "ULS" 2942334 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1144 2914388 2926328 2926399 "ULSCONS" 2926404 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1143 2897138 2909151 2909212 "ULSCCAT" 2909924 NIL ULSCCAT (NIL T T) -9 NIL 2910220) (-1142 2896189 2896434 2896821 "ULSCCAT-" 2896826 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1141 2886179 2892696 2892738 "ULSCAT" 2893594 NIL ULSCAT (NIL T) -9 NIL 2894324) (-1140 2885613 2885692 2885869 "ULS2" 2886094 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1139 2884011 2884978 2885008 "UFD" 2885220 T UFD (NIL) -9 NIL 2885334) (-1138 2883805 2883851 2883946 "UFD-" 2883951 NIL UFD- (NIL T) -8 NIL NIL) (-1137 2882887 2883070 2883286 "UDVO" 2883611 T UDVO (NIL) -7 NIL NIL) (-1136 2880703 2881112 2881583 "UDPO" 2882451 NIL UDPO (NIL T) -7 NIL NIL) (-1135 2880636 2880641 2880671 "TYPE" 2880676 T TYPE (NIL) -9 NIL NIL) (-1134 2879607 2879809 2880049 "TWOFACT" 2880430 NIL TWOFACT (NIL T) -7 NIL NIL) (-1133 2878545 2878882 2879145 "TUPLE" 2879379 NIL TUPLE (NIL T) -8 NIL NIL) (-1132 2876236 2876755 2877294 "TUBETOOL" 2878028 T TUBETOOL (NIL) -7 NIL NIL) (-1131 2875085 2875290 2875531 "TUBE" 2876029 NIL TUBE (NIL T) -8 NIL NIL) (-1130 2869809 2874063 2874345 "TS" 2874837 NIL TS (NIL T) -8 NIL NIL) (-1129 2858513 2862605 2862701 "TSETCAT" 2867935 NIL TSETCAT (NIL T T T T) -9 NIL 2869466) (-1128 2853248 2854846 2856736 "TSETCAT-" 2856741 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1127 2847511 2848357 2849299 "TRMANIP" 2852384 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1126 2846952 2847015 2847178 "TRIMAT" 2847443 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1125 2844758 2844995 2845358 "TRIGMNIP" 2846701 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1124 2844278 2844391 2844421 "TRIGCAT" 2844634 T TRIGCAT (NIL) -9 NIL NIL) (-1123 2843947 2844026 2844167 "TRIGCAT-" 2844172 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1122 2840846 2842807 2843087 "TREE" 2843702 NIL TREE (NIL T) -8 NIL NIL) (-1121 2840120 2840648 2840678 "TRANFUN" 2840713 T TRANFUN (NIL) -9 NIL 2840779) (-1120 2839399 2839590 2839870 "TRANFUN-" 2839875 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1119 2839203 2839235 2839296 "TOPSP" 2839360 T TOPSP (NIL) -7 NIL NIL) (-1118 2838555 2838670 2838823 "TOOLSIGN" 2839084 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1117 2837216 2837732 2837971 "TEXTFILE" 2838338 T TEXTFILE (NIL) -8 NIL NIL) (-1116 2835081 2835595 2836033 "TEX" 2836800 T TEX (NIL) -8 NIL NIL) (-1115 2834862 2834893 2834965 "TEX1" 2835044 NIL TEX1 (NIL T) -7 NIL NIL) (-1114 2834510 2834573 2834663 "TEMUTL" 2834794 T TEMUTL (NIL) -7 NIL NIL) (-1113 2832664 2832944 2833269 "TBCMPPK" 2834233 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1112 2824553 2830825 2830881 "TBAGG" 2831281 NIL TBAGG (NIL T T) -9 NIL 2831492) (-1111 2819623 2821111 2822865 "TBAGG-" 2822870 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1110 2819007 2819114 2819259 "TANEXP" 2819512 NIL TANEXP (NIL T) -7 NIL NIL) (-1109 2812508 2818864 2818957 "TABLE" 2818962 NIL TABLE (NIL T T) -8 NIL NIL) (-1108 2811920 2812019 2812157 "TABLEAU" 2812405 NIL TABLEAU (NIL T) -8 NIL NIL) (-1107 2806528 2807748 2808996 "TABLBUMP" 2810706 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1106 2805956 2806056 2806184 "SYSTEM" 2806422 T SYSTEM (NIL) -7 NIL NIL) (-1105 2802419 2803114 2803897 "SYSSOLP" 2805207 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1104 2798710 2799418 2800152 "SYNTAX" 2801707 T SYNTAX (NIL) -8 NIL NIL) (-1103 2795844 2796452 2797090 "SYMTAB" 2798094 T SYMTAB (NIL) -8 NIL NIL) (-1102 2791093 2791995 2792978 "SYMS" 2794883 T SYMS (NIL) -8 NIL NIL) (-1101 2788326 2790553 2790782 "SYMPOLY" 2790898 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1100 2787846 2787921 2788043 "SYMFUNC" 2788238 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1099 2783823 2785083 2785905 "SYMBOL" 2787046 T SYMBOL (NIL) -8 NIL NIL) (-1098 2777362 2779051 2780771 "SWITCH" 2782125 T SWITCH (NIL) -8 NIL NIL) (-1097 2770592 2776189 2776491 "SUTS" 2777117 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1096 2762482 2769713 2769993 "SUPXS" 2770369 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1095 2753974 2762103 2762228 "SUP" 2762391 NIL SUP (NIL T) -8 NIL NIL) (-1094 2753133 2753260 2753477 "SUPFRACF" 2753842 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1093 2752758 2752817 2752928 "SUP2" 2753068 NIL SUP2 (NIL T T) -7 NIL NIL) (-1092 2751176 2751450 2751812 "SUMRF" 2752457 NIL SUMRF (NIL T) -7 NIL NIL) (-1091 2750493 2750559 2750757 "SUMFS" 2751097 NIL SUMFS (NIL T T) -7 NIL NIL) (-1090 2734429 2749674 2749924 "SULS" 2750300 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1089 2733751 2733954 2734094 "SUCH" 2734337 NIL SUCH (NIL T T) -8 NIL NIL) (-1088 2727678 2728690 2729648 "SUBSPACE" 2732839 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1087 2727108 2727198 2727362 "SUBRESP" 2727566 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1086 2720477 2721773 2723084 "STTF" 2725844 NIL STTF (NIL T) -7 NIL NIL) (-1085 2714650 2715770 2716917 "STTFNC" 2719377 NIL STTFNC (NIL T) -7 NIL NIL) (-1084 2706001 2707868 2709661 "STTAYLOR" 2712891 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1083 2699245 2705865 2705948 "STRTBL" 2705953 NIL STRTBL (NIL T) -8 NIL NIL) (-1082 2694636 2699200 2699231 "STRING" 2699236 T STRING (NIL) -8 NIL NIL) (-1081 2689525 2694010 2694040 "STRICAT" 2694099 T STRICAT (NIL) -9 NIL 2694161) (-1080 2682239 2687048 2687668 "STREAM" 2688940 NIL STREAM (NIL T) -8 NIL NIL) (-1079 2681749 2681826 2681970 "STREAM3" 2682156 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1078 2680731 2680914 2681149 "STREAM2" 2681562 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1077 2680419 2680471 2680564 "STREAM1" 2680673 NIL STREAM1 (NIL T) -7 NIL NIL) (-1076 2679435 2679616 2679847 "STINPROD" 2680235 NIL STINPROD (NIL T) -7 NIL NIL) (-1075 2679014 2679198 2679228 "STEP" 2679308 T STEP (NIL) -9 NIL 2679386) (-1074 2672557 2678913 2678990 "STBL" 2678995 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1073 2667733 2671780 2671823 "STAGG" 2671976 NIL STAGG (NIL T) -9 NIL 2672065) (-1072 2665435 2666037 2666909 "STAGG-" 2666914 NIL STAGG- (NIL T T) -8 NIL NIL) (-1071 2663630 2665205 2665297 "STACK" 2665378 NIL STACK (NIL T) -8 NIL NIL) (-1070 2656361 2661777 2662232 "SREGSET" 2663260 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1069 2648801 2650169 2651681 "SRDCMPK" 2654967 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1068 2641769 2646242 2646272 "SRAGG" 2647575 T SRAGG (NIL) -9 NIL 2648183) (-1067 2640786 2641041 2641420 "SRAGG-" 2641425 NIL SRAGG- (NIL T) -8 NIL NIL) (-1066 2635235 2639705 2640132 "SQMATRIX" 2640405 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1065 2628987 2631955 2632681 "SPLTREE" 2634581 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1064 2624977 2625643 2626289 "SPLNODE" 2628413 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1063 2624024 2624257 2624287 "SPFCAT" 2624731 T SPFCAT (NIL) -9 NIL NIL) (-1062 2622761 2622971 2623235 "SPECOUT" 2623782 T SPECOUT (NIL) -7 NIL NIL) (-1061 2622522 2622562 2622631 "SPADPRSR" 2622714 T SPADPRSR (NIL) -7 NIL NIL) (-1060 2614545 2616292 2616334 "SPACEC" 2620657 NIL SPACEC (NIL T) -9 NIL 2622473) (-1059 2612717 2614478 2614526 "SPACE3" 2614531 NIL SPACE3 (NIL T) -8 NIL NIL) (-1058 2611469 2611640 2611931 "SORTPAK" 2612522 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1057 2609525 2609828 2610246 "SOLVETRA" 2611133 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1056 2608536 2608758 2609032 "SOLVESER" 2609298 NIL SOLVESER (NIL T) -7 NIL NIL) (-1055 2603756 2604637 2605639 "SOLVERAD" 2607588 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1054 2599571 2600180 2600909 "SOLVEFOR" 2603123 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1053 2593870 2598922 2599018 "SNTSCAT" 2599023 NIL SNTSCAT (NIL T T T T) -9 NIL 2599093) (-1052 2587974 2592201 2592591 "SMTS" 2593560 NIL SMTS (NIL T T T) -8 NIL NIL) (-1051 2582384 2587863 2587939 "SMP" 2587944 NIL SMP (NIL T T) -8 NIL NIL) (-1050 2580543 2580844 2581242 "SMITH" 2582081 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1049 2573508 2577704 2577806 "SMATCAT" 2579146 NIL SMATCAT (NIL NIL T T T) -9 NIL 2579695) (-1048 2570449 2571272 2572449 "SMATCAT-" 2572454 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1047 2568163 2569686 2569729 "SKAGG" 2569990 NIL SKAGG (NIL T) -9 NIL 2570125) (-1046 2564221 2567267 2567545 "SINT" 2567907 T SINT (NIL) -8 NIL NIL) (-1045 2563993 2564031 2564097 "SIMPAN" 2564177 T SIMPAN (NIL) -7 NIL NIL) (-1044 2563509 2563695 2563794 "SIG" 2563916 T SIG (NIL) -8 NIL NIL) (-1043 2562347 2562568 2562843 "SIGNRF" 2563268 NIL SIGNRF (NIL T) -7 NIL NIL) (-1042 2561156 2561307 2561597 "SIGNEF" 2562176 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1041 2558846 2559300 2559806 "SHP" 2560697 NIL SHP (NIL T NIL) -7 NIL NIL) (-1040 2552699 2558747 2558823 "SHDP" 2558828 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1039 2552189 2552381 2552411 "SGROUP" 2552563 T SGROUP (NIL) -9 NIL 2552650) (-1038 2551959 2552011 2552115 "SGROUP-" 2552120 NIL SGROUP- (NIL T) -8 NIL NIL) (-1037 2548795 2549492 2550215 "SGCF" 2551258 T SGCF (NIL) -7 NIL NIL) (-1036 2543192 2548244 2548340 "SFRTCAT" 2548345 NIL SFRTCAT (NIL T T T T) -9 NIL 2548384) (-1035 2536634 2537649 2538784 "SFRGCD" 2542175 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1034 2529781 2530852 2532037 "SFQCMPK" 2535567 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1033 2529403 2529492 2529602 "SFORT" 2529722 NIL SFORT (NIL T T) -8 NIL NIL) (-1032 2528548 2529243 2529364 "SEXOF" 2529369 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1031 2527682 2528429 2528497 "SEX" 2528502 T SEX (NIL) -8 NIL NIL) (-1030 2522459 2523148 2523243 "SEXCAT" 2527014 NIL SEXCAT (NIL T T T T T) -9 NIL 2527633) (-1029 2519639 2522393 2522441 "SET" 2522446 NIL SET (NIL T) -8 NIL NIL) (-1028 2517890 2518352 2518657 "SETMN" 2519380 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1027 2517498 2517624 2517654 "SETCAT" 2517771 T SETCAT (NIL) -9 NIL 2517855) (-1026 2517278 2517330 2517429 "SETCAT-" 2517434 NIL SETCAT- (NIL T) -8 NIL NIL) (-1025 2513666 2515740 2515783 "SETAGG" 2516653 NIL SETAGG (NIL T) -9 NIL 2516993) (-1024 2513124 2513240 2513477 "SETAGG-" 2513482 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1023 2512328 2512621 2512682 "SEGXCAT" 2512968 NIL SEGXCAT (NIL T T) -9 NIL 2513088) (-1022 2511384 2511994 2512176 "SEG" 2512181 NIL SEG (NIL T) -8 NIL NIL) (-1021 2510291 2510504 2510547 "SEGCAT" 2511129 NIL SEGCAT (NIL T) -9 NIL 2511367) (-1020 2509340 2509670 2509870 "SEGBIND" 2510126 NIL SEGBIND (NIL T) -8 NIL NIL) (-1019 2508961 2509020 2509133 "SEGBIND2" 2509275 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1018 2508180 2508306 2508510 "SEG2" 2508805 NIL SEG2 (NIL T T) -7 NIL NIL) (-1017 2507617 2508115 2508162 "SDVAR" 2508167 NIL SDVAR (NIL T) -8 NIL NIL) (-1016 2499869 2507390 2507518 "SDPOL" 2507523 NIL SDPOL (NIL T) -8 NIL NIL) (-1015 2498462 2498728 2499047 "SCPKG" 2499584 NIL SCPKG (NIL T) -7 NIL NIL) (-1014 2497598 2497778 2497978 "SCOPE" 2498284 T SCOPE (NIL) -8 NIL NIL) (-1013 2496819 2496952 2497131 "SCACHE" 2497453 NIL SCACHE (NIL T) -7 NIL NIL) (-1012 2496258 2496579 2496664 "SAOS" 2496756 T SAOS (NIL) -8 NIL NIL) (-1011 2495823 2495858 2496031 "SAERFFC" 2496217 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1010 2489717 2495720 2495800 "SAE" 2495805 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1009 2489310 2489345 2489504 "SAEFACT" 2489676 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1008 2487631 2487945 2488346 "RURPK" 2488976 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1007 2486271 2486550 2486861 "RULESET" 2487465 NIL RULESET (NIL T T T) -8 NIL NIL) (-1006 2483469 2483972 2484435 "RULE" 2485953 NIL RULE (NIL T T T) -8 NIL NIL) (-1005 2483108 2483263 2483346 "RULECOLD" 2483421 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1004 2477971 2478765 2479684 "RSETGCD" 2482307 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1003 2467257 2472309 2472405 "RSETCAT" 2476497 NIL RSETCAT (NIL T T T T) -9 NIL 2477594) (-1002 2465185 2465724 2466547 "RSETCAT-" 2466552 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1001 2457586 2458961 2460480 "RSDCMPK" 2463784 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1000 2455592 2456033 2456107 "RRCC" 2457193 NIL RRCC (NIL T T) -9 NIL 2457537) (-999 2454945 2455119 2455396 "RRCC-" 2455401 NIL RRCC- (NIL T T T) -8 NIL NIL) (-998 2429312 2438937 2439001 "RPOLCAT" 2449503 NIL RPOLCAT (NIL T T T) -9 NIL 2452661) (-997 2420816 2423154 2426272 "RPOLCAT-" 2426277 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-996 2411882 2419046 2419526 "ROUTINE" 2420356 T ROUTINE (NIL) -8 NIL NIL) (-995 2408587 2411438 2411585 "ROMAN" 2411755 T ROMAN (NIL) -8 NIL NIL) (-994 2406871 2407456 2407714 "ROIRC" 2408392 NIL ROIRC (NIL T T) -8 NIL NIL) (-993 2403276 2405580 2405608 "RNS" 2405904 T RNS (NIL) -9 NIL 2406174) (-992 2401790 2402173 2402704 "RNS-" 2402777 NIL RNS- (NIL T) -8 NIL NIL) (-991 2401216 2401624 2401652 "RNG" 2401657 T RNG (NIL) -9 NIL 2401678) (-990 2400614 2400976 2401016 "RMODULE" 2401076 NIL RMODULE (NIL T) -9 NIL 2401118) (-989 2399466 2399560 2399890 "RMCAT2" 2400515 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-988 2396180 2398649 2398970 "RMATRIX" 2399201 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-987 2389177 2391411 2391523 "RMATCAT" 2394832 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2395814) (-986 2388556 2388703 2389006 "RMATCAT-" 2389011 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-985 2388126 2388201 2388327 "RINTERP" 2388475 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-984 2387177 2387741 2387769 "RING" 2387879 T RING (NIL) -9 NIL 2387973) (-983 2386972 2387016 2387110 "RING-" 2387115 NIL RING- (NIL T) -8 NIL NIL) (-982 2385820 2386057 2386313 "RIDIST" 2386736 T RIDIST (NIL) -7 NIL NIL) (-981 2377140 2385292 2385496 "RGCHAIN" 2385668 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-980 2374145 2374759 2375427 "RF" 2376504 NIL RF (NIL T) -7 NIL NIL) (-979 2373794 2373857 2373958 "RFFACTOR" 2374076 NIL RFFACTOR (NIL T) -7 NIL NIL) (-978 2373522 2373557 2373652 "RFFACT" 2373753 NIL RFFACT (NIL T) -7 NIL NIL) (-977 2371652 2372016 2372396 "RFDIST" 2373162 T RFDIST (NIL) -7 NIL NIL) (-976 2371110 2371202 2371362 "RETSOL" 2371554 NIL RETSOL (NIL T T) -7 NIL NIL) (-975 2370703 2370783 2370824 "RETRACT" 2371014 NIL RETRACT (NIL T) -9 NIL NIL) (-974 2370555 2370580 2370664 "RETRACT-" 2370669 NIL RETRACT- (NIL T T) -8 NIL NIL) (-973 2363413 2370212 2370337 "RESULT" 2370450 T RESULT (NIL) -8 NIL NIL) (-972 2361998 2362687 2362884 "RESRING" 2363316 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-971 2361638 2361687 2361783 "RESLATC" 2361935 NIL RESLATC (NIL T) -7 NIL NIL) (-970 2361347 2361381 2361486 "REPSQ" 2361597 NIL REPSQ (NIL T) -7 NIL NIL) (-969 2358778 2359358 2359958 "REP" 2360767 T REP (NIL) -7 NIL NIL) (-968 2358479 2358513 2358622 "REPDB" 2358737 NIL REPDB (NIL T) -7 NIL NIL) (-967 2352424 2353803 2355023 "REP2" 2357291 NIL REP2 (NIL T) -7 NIL NIL) (-966 2348830 2349511 2350316 "REP1" 2351651 NIL REP1 (NIL T) -7 NIL NIL) (-965 2341574 2346989 2347442 "REGSET" 2348460 NIL REGSET (NIL T T T T) -8 NIL NIL) (-964 2340395 2340730 2340978 "REF" 2341359 NIL REF (NIL T) -8 NIL NIL) (-963 2339776 2339879 2340044 "REDORDER" 2340279 NIL REDORDER (NIL T T) -7 NIL NIL) (-962 2335745 2339010 2339231 "RECLOS" 2339607 NIL RECLOS (NIL T) -8 NIL NIL) (-961 2334802 2334983 2335196 "REALSOLV" 2335552 T REALSOLV (NIL) -7 NIL NIL) (-960 2334650 2334691 2334719 "REAL" 2334724 T REAL (NIL) -9 NIL 2334759) (-959 2331141 2331943 2332825 "REAL0Q" 2333815 NIL REAL0Q (NIL T) -7 NIL NIL) (-958 2326752 2327740 2328799 "REAL0" 2330122 NIL REAL0 (NIL T) -7 NIL NIL) (-957 2326160 2326232 2326437 "RDIV" 2326674 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-956 2325233 2325407 2325618 "RDIST" 2325982 NIL RDIST (NIL T) -7 NIL NIL) (-955 2323837 2324124 2324493 "RDETRS" 2324941 NIL RDETRS (NIL T T) -7 NIL NIL) (-954 2321658 2322112 2322647 "RDETR" 2323379 NIL RDETR (NIL T T) -7 NIL NIL) (-953 2320274 2320552 2320953 "RDEEFS" 2321374 NIL RDEEFS (NIL T T) -7 NIL NIL) (-952 2318774 2319080 2319509 "RDEEF" 2319962 NIL RDEEF (NIL T T) -7 NIL NIL) (-951 2313059 2315991 2316019 "RCFIELD" 2317296 T RCFIELD (NIL) -9 NIL 2318026) (-950 2311128 2311632 2312325 "RCFIELD-" 2312398 NIL RCFIELD- (NIL T) -8 NIL NIL) (-949 2307460 2309245 2309286 "RCAGG" 2310357 NIL RCAGG (NIL T) -9 NIL 2310822) (-948 2307091 2307185 2307345 "RCAGG-" 2307350 NIL RCAGG- (NIL T T) -8 NIL NIL) (-947 2306435 2306547 2306709 "RATRET" 2306975 NIL RATRET (NIL T) -7 NIL NIL) (-946 2305992 2306059 2306178 "RATFACT" 2306363 NIL RATFACT (NIL T) -7 NIL NIL) (-945 2305307 2305427 2305577 "RANDSRC" 2305862 T RANDSRC (NIL) -7 NIL NIL) (-944 2305044 2305088 2305159 "RADUTIL" 2305256 T RADUTIL (NIL) -7 NIL NIL) (-943 2298051 2303787 2304104 "RADIX" 2304759 NIL RADIX (NIL NIL) -8 NIL NIL) (-942 2289620 2297895 2298023 "RADFF" 2298028 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-941 2289272 2289347 2289375 "RADCAT" 2289532 T RADCAT (NIL) -9 NIL NIL) (-940 2289057 2289105 2289202 "RADCAT-" 2289207 NIL RADCAT- (NIL T) -8 NIL NIL) (-939 2287208 2288832 2288921 "QUEUE" 2289001 NIL QUEUE (NIL T) -8 NIL NIL) (-938 2283705 2287145 2287190 "QUAT" 2287195 NIL QUAT (NIL T) -8 NIL NIL) (-937 2283343 2283386 2283513 "QUATCT2" 2283656 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-936 2277137 2280517 2280557 "QUATCAT" 2281336 NIL QUATCAT (NIL T) -9 NIL 2282101) (-935 2273281 2274318 2275705 "QUATCAT-" 2275799 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-934 2270802 2272366 2272407 "QUAGG" 2272782 NIL QUAGG (NIL T) -9 NIL 2272957) (-933 2269727 2270200 2270372 "QFORM" 2270674 NIL QFORM (NIL NIL T) -8 NIL NIL) (-932 2261024 2266282 2266322 "QFCAT" 2266980 NIL QFCAT (NIL T) -9 NIL 2267973) (-931 2256596 2257797 2259388 "QFCAT-" 2259482 NIL QFCAT- (NIL T T) -8 NIL NIL) (-930 2256234 2256277 2256404 "QFCAT2" 2256547 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-929 2255694 2255804 2255934 "QEQUAT" 2256124 T QEQUAT (NIL) -8 NIL NIL) (-928 2248861 2249932 2251115 "QCMPACK" 2254627 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-927 2246437 2246858 2247286 "QALGSET" 2248516 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-926 2245682 2245856 2246088 "QALGSET2" 2246257 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-925 2244373 2244596 2244913 "PWFFINTB" 2245455 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-924 2242561 2242729 2243082 "PUSHVAR" 2244187 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-923 2238479 2239533 2239574 "PTRANFN" 2241458 NIL PTRANFN (NIL T) -9 NIL NIL) (-922 2236891 2237182 2237503 "PTPACK" 2238190 NIL PTPACK (NIL T) -7 NIL NIL) (-921 2236527 2236584 2236691 "PTFUNC2" 2236828 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-920 2231004 2235345 2235385 "PTCAT" 2235753 NIL PTCAT (NIL T) -9 NIL 2235915) (-919 2230662 2230697 2230821 "PSQFR" 2230963 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-918 2229257 2229555 2229889 "PSEUDLIN" 2230360 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-917 2216064 2218429 2220752 "PSETPK" 2227017 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-916 2209151 2211865 2211959 "PSETCAT" 2214940 NIL PSETCAT (NIL T T T T) -9 NIL 2215754) (-915 2206989 2207623 2208442 "PSETCAT-" 2208447 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-914 2206338 2206503 2206531 "PSCURVE" 2206799 T PSCURVE (NIL) -9 NIL 2206966) (-913 2202790 2204316 2204380 "PSCAT" 2205216 NIL PSCAT (NIL T T T) -9 NIL 2205456) (-912 2201854 2202070 2202469 "PSCAT-" 2202474 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-911 2200506 2201139 2201353 "PRTITION" 2201660 T PRTITION (NIL) -8 NIL NIL) (-910 2189604 2191810 2193998 "PRS" 2198368 NIL PRS (NIL T T) -7 NIL NIL) (-909 2187463 2188955 2188995 "PRQAGG" 2189178 NIL PRQAGG (NIL T) -9 NIL 2189280) (-908 2187034 2187136 2187164 "PROPLOG" 2187349 T PROPLOG (NIL) -9 NIL NIL) (-907 2184157 2184722 2185249 "PROPFRML" 2186539 NIL PROPFRML (NIL T) -8 NIL NIL) (-906 2183617 2183727 2183857 "PROPERTY" 2184047 T PROPERTY (NIL) -8 NIL NIL) (-905 2177391 2181783 2182603 "PRODUCT" 2182843 NIL PRODUCT (NIL T T) -8 NIL NIL) (-904 2174667 2176851 2177084 "PR" 2177202 NIL PR (NIL T T) -8 NIL NIL) (-903 2174463 2174495 2174554 "PRINT" 2174628 T PRINT (NIL) -7 NIL NIL) (-902 2173803 2173920 2174072 "PRIMES" 2174343 NIL PRIMES (NIL T) -7 NIL NIL) (-901 2171868 2172269 2172735 "PRIMELT" 2173382 NIL PRIMELT (NIL T) -7 NIL NIL) (-900 2171597 2171646 2171674 "PRIMCAT" 2171798 T PRIMCAT (NIL) -9 NIL NIL) (-899 2167758 2171535 2171580 "PRIMARR" 2171585 NIL PRIMARR (NIL T) -8 NIL NIL) (-898 2166765 2166943 2167171 "PRIMARR2" 2167576 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-897 2166408 2166464 2166575 "PREASSOC" 2166703 NIL PREASSOC (NIL T T) -7 NIL NIL) (-896 2165883 2166016 2166044 "PPCURVE" 2166249 T PPCURVE (NIL) -9 NIL 2166385) (-895 2165505 2165678 2165761 "PORTNUM" 2165820 T PORTNUM (NIL) -8 NIL NIL) (-894 2162864 2163263 2163855 "POLYROOT" 2165086 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-893 2156770 2162470 2162629 "POLY" 2162737 NIL POLY (NIL T) -8 NIL NIL) (-892 2156155 2156213 2156446 "POLYLIFT" 2156706 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-891 2152440 2152889 2153517 "POLYCATQ" 2155700 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-890 2139481 2144878 2144942 "POLYCAT" 2148427 NIL POLYCAT (NIL T T T) -9 NIL 2150354) (-889 2132932 2134793 2137176 "POLYCAT-" 2137181 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-888 2132521 2132589 2132708 "POLY2UP" 2132858 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-887 2132157 2132214 2132321 "POLY2" 2132458 NIL POLY2 (NIL T T) -7 NIL NIL) (-886 2130842 2131081 2131357 "POLUTIL" 2131931 NIL POLUTIL (NIL T T) -7 NIL NIL) (-885 2129204 2129481 2129811 "POLTOPOL" 2130564 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-884 2124727 2129141 2129186 "POINT" 2129191 NIL POINT (NIL T) -8 NIL NIL) (-883 2122914 2123271 2123646 "PNTHEORY" 2124372 T PNTHEORY (NIL) -7 NIL NIL) (-882 2121342 2121639 2122048 "PMTOOLS" 2122612 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-881 2120935 2121013 2121130 "PMSYM" 2121258 NIL PMSYM (NIL T) -7 NIL NIL) (-880 2120445 2120514 2120688 "PMQFCAT" 2120860 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-879 2119800 2119910 2120066 "PMPRED" 2120322 NIL PMPRED (NIL T) -7 NIL NIL) (-878 2119196 2119282 2119443 "PMPREDFS" 2119701 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-877 2117842 2118050 2118434 "PMPLCAT" 2118958 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-876 2117374 2117453 2117605 "PMLSAGG" 2117757 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-875 2116851 2116927 2117107 "PMKERNEL" 2117292 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-874 2116468 2116543 2116656 "PMINS" 2116770 NIL PMINS (NIL T) -7 NIL NIL) (-873 2115898 2115967 2116182 "PMFS" 2116393 NIL PMFS (NIL T T T) -7 NIL NIL) (-872 2115129 2115247 2115451 "PMDOWN" 2115775 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-871 2114292 2114451 2114633 "PMASS" 2114967 T PMASS (NIL) -7 NIL NIL) (-870 2113566 2113677 2113840 "PMASSFS" 2114178 NIL PMASSFS (NIL T T) -7 NIL NIL) (-869 2113221 2113289 2113383 "PLOTTOOL" 2113492 T PLOTTOOL (NIL) -7 NIL NIL) (-868 2107843 2109032 2110180 "PLOT" 2112093 T PLOT (NIL) -8 NIL NIL) (-867 2103657 2104691 2105612 "PLOT3D" 2106942 T PLOT3D (NIL) -8 NIL NIL) (-866 2102569 2102746 2102981 "PLOT1" 2103461 NIL PLOT1 (NIL T) -7 NIL NIL) (-865 2077963 2082635 2087486 "PLEQN" 2097835 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-864 2077281 2077403 2077583 "PINTERP" 2077828 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-863 2076974 2077021 2077124 "PINTERPA" 2077228 NIL PINTERPA (NIL T T) -7 NIL NIL) (-862 2076213 2076780 2076867 "PI" 2076907 T PI (NIL) -8 NIL NIL) (-861 2074605 2075590 2075618 "PID" 2075800 T PID (NIL) -9 NIL 2075934) (-860 2074330 2074367 2074455 "PICOERCE" 2074562 NIL PICOERCE (NIL T) -7 NIL NIL) (-859 2073650 2073789 2073965 "PGROEB" 2074186 NIL PGROEB (NIL T) -7 NIL NIL) (-858 2069237 2070051 2070956 "PGE" 2072765 T PGE (NIL) -7 NIL NIL) (-857 2067361 2067607 2067973 "PGCD" 2068954 NIL PGCD (NIL T T T T) -7 NIL NIL) (-856 2066699 2066802 2066963 "PFRPAC" 2067245 NIL PFRPAC (NIL T) -7 NIL NIL) (-855 2063314 2065247 2065600 "PFR" 2066378 NIL PFR (NIL T) -8 NIL NIL) (-854 2061703 2061947 2062272 "PFOTOOLS" 2063061 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-853 2060236 2060475 2060826 "PFOQ" 2061460 NIL PFOQ (NIL T T T) -7 NIL NIL) (-852 2058713 2058925 2059287 "PFO" 2060020 NIL PFO (NIL T T T T T) -7 NIL NIL) (-851 2055236 2058602 2058671 "PF" 2058676 NIL PF (NIL NIL) -8 NIL NIL) (-850 2052665 2053946 2053974 "PFECAT" 2054559 T PFECAT (NIL) -9 NIL 2054943) (-849 2052110 2052264 2052478 "PFECAT-" 2052483 NIL PFECAT- (NIL T) -8 NIL NIL) (-848 2050714 2050965 2051266 "PFBRU" 2051859 NIL PFBRU (NIL T T) -7 NIL NIL) (-847 2048581 2048932 2049364 "PFBR" 2050365 NIL PFBR (NIL T T T T) -7 NIL NIL) (-846 2044432 2045957 2046633 "PERM" 2047938 NIL PERM (NIL T) -8 NIL NIL) (-845 2039698 2040639 2041509 "PERMGRP" 2043595 NIL PERMGRP (NIL T) -8 NIL NIL) (-844 2037769 2038762 2038803 "PERMCAT" 2039249 NIL PERMCAT (NIL T) -9 NIL 2039554) (-843 2037424 2037465 2037588 "PERMAN" 2037722 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-842 2034864 2036993 2037124 "PENDTREE" 2037326 NIL PENDTREE (NIL T) -8 NIL NIL) (-841 2032937 2033715 2033756 "PDRING" 2034413 NIL PDRING (NIL T) -9 NIL 2034698) (-840 2032040 2032258 2032620 "PDRING-" 2032625 NIL PDRING- (NIL T T) -8 NIL NIL) (-839 2029181 2029932 2030623 "PDEPROB" 2031369 T PDEPROB (NIL) -8 NIL NIL) (-838 2026752 2027248 2027797 "PDEPACK" 2028652 T PDEPACK (NIL) -7 NIL NIL) (-837 2025664 2025854 2026105 "PDECOMP" 2026551 NIL PDECOMP (NIL T T) -7 NIL NIL) (-836 2023276 2024091 2024119 "PDECAT" 2024904 T PDECAT (NIL) -9 NIL 2025615) (-835 2023029 2023062 2023151 "PCOMP" 2023237 NIL PCOMP (NIL T T) -7 NIL NIL) (-834 2021236 2021832 2022128 "PBWLB" 2022759 NIL PBWLB (NIL T) -8 NIL NIL) (-833 2013744 2015313 2016649 "PATTERN" 2019921 NIL PATTERN (NIL T) -8 NIL NIL) (-832 2013376 2013433 2013542 "PATTERN2" 2013681 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-831 2011133 2011521 2011978 "PATTERN1" 2012965 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-830 2008528 2009082 2009563 "PATRES" 2010698 NIL PATRES (NIL T T) -8 NIL NIL) (-829 2008092 2008159 2008291 "PATRES2" 2008455 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-828 2005989 2006389 2006794 "PATMATCH" 2007761 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-827 2005526 2005709 2005750 "PATMAB" 2005857 NIL PATMAB (NIL T) -9 NIL 2005940) (-826 2004071 2004380 2004638 "PATLRES" 2005331 NIL PATLRES (NIL T T T) -8 NIL NIL) (-825 2003617 2003740 2003781 "PATAB" 2003786 NIL PATAB (NIL T) -9 NIL 2003958) (-824 2001098 2001630 2002203 "PARTPERM" 2003064 T PARTPERM (NIL) -7 NIL NIL) (-823 2000719 2000782 2000884 "PARSURF" 2001029 NIL PARSURF (NIL T) -8 NIL NIL) (-822 2000351 2000408 2000517 "PARSU2" 2000656 NIL PARSU2 (NIL T T) -7 NIL NIL) (-821 2000115 2000155 2000222 "PARSER" 2000304 T PARSER (NIL) -7 NIL NIL) (-820 1999736 1999799 1999901 "PARSCURV" 2000046 NIL PARSCURV (NIL T) -8 NIL NIL) (-819 1999368 1999425 1999534 "PARSC2" 1999673 NIL PARSC2 (NIL T T) -7 NIL NIL) (-818 1999007 1999065 1999162 "PARPCURV" 1999304 NIL PARPCURV (NIL T) -8 NIL NIL) (-817 1998639 1998696 1998805 "PARPC2" 1998944 NIL PARPC2 (NIL T T) -7 NIL NIL) (-816 1998159 1998245 1998364 "PAN2EXPR" 1998540 T PAN2EXPR (NIL) -7 NIL NIL) (-815 1996965 1997280 1997508 "PALETTE" 1997951 T PALETTE (NIL) -8 NIL NIL) (-814 1995433 1995970 1996330 "PAIR" 1996651 NIL PAIR (NIL T T) -8 NIL NIL) (-813 1989283 1994692 1994886 "PADICRC" 1995288 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-812 1982491 1988629 1988813 "PADICRAT" 1989131 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-811 1980795 1982428 1982473 "PADIC" 1982478 NIL PADIC (NIL NIL) -8 NIL NIL) (-810 1978000 1979574 1979614 "PADICCT" 1980195 NIL PADICCT (NIL NIL) -9 NIL 1980477) (-809 1976957 1977157 1977425 "PADEPAC" 1977787 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-808 1976169 1976302 1976508 "PADE" 1976819 NIL PADE (NIL T T T) -7 NIL NIL) (-807 1974180 1975012 1975327 "OWP" 1975937 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-806 1973289 1973785 1973957 "OVAR" 1974048 NIL OVAR (NIL NIL) -8 NIL NIL) (-805 1972553 1972674 1972835 "OUT" 1973148 T OUT (NIL) -7 NIL NIL) (-804 1961607 1963778 1965948 "OUTFORM" 1970403 T OUTFORM (NIL) -8 NIL NIL) (-803 1961015 1961336 1961425 "OSI" 1961538 T OSI (NIL) -8 NIL NIL) (-802 1960546 1960884 1960912 "OSGROUP" 1960917 T OSGROUP (NIL) -9 NIL 1960939) (-801 1959291 1959518 1959803 "ORTHPOL" 1960293 NIL ORTHPOL (NIL T) -7 NIL NIL) (-800 1956662 1958952 1959090 "OREUP" 1959234 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-799 1954058 1956355 1956481 "ORESUP" 1956604 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-798 1951593 1952093 1952653 "OREPCTO" 1953547 NIL OREPCTO (NIL T T) -7 NIL NIL) (-797 1945503 1947709 1947749 "OREPCAT" 1950070 NIL OREPCAT (NIL T) -9 NIL 1951173) (-796 1942651 1943433 1944490 "OREPCAT-" 1944495 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-795 1941829 1942101 1942129 "ORDSET" 1942438 T ORDSET (NIL) -9 NIL 1942602) (-794 1941348 1941470 1941663 "ORDSET-" 1941668 NIL ORDSET- (NIL T) -8 NIL NIL) (-793 1939962 1940763 1940791 "ORDRING" 1940993 T ORDRING (NIL) -9 NIL 1941117) (-792 1939607 1939701 1939845 "ORDRING-" 1939850 NIL ORDRING- (NIL T) -8 NIL NIL) (-791 1938970 1939451 1939479 "ORDMON" 1939484 T ORDMON (NIL) -9 NIL 1939505) (-790 1938132 1938279 1938474 "ORDFUNS" 1938819 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-789 1937644 1938003 1938031 "ORDFIN" 1938036 T ORDFIN (NIL) -9 NIL 1938057) (-788 1934156 1936230 1936639 "ORDCOMP" 1937268 NIL ORDCOMP (NIL T) -8 NIL NIL) (-787 1933422 1933549 1933735 "ORDCOMP2" 1934016 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-786 1929929 1930812 1931649 "OPTPROB" 1932605 T OPTPROB (NIL) -8 NIL NIL) (-785 1926771 1927400 1928094 "OPTPACK" 1929255 T OPTPACK (NIL) -7 NIL NIL) (-784 1924497 1925233 1925261 "OPTCAT" 1926076 T OPTCAT (NIL) -9 NIL 1926722) (-783 1924265 1924304 1924370 "OPQUERY" 1924451 T OPQUERY (NIL) -7 NIL NIL) (-782 1921401 1922592 1923092 "OP" 1923797 NIL OP (NIL T) -8 NIL NIL) (-781 1918166 1920198 1920567 "ONECOMP" 1921065 NIL ONECOMP (NIL T) -8 NIL NIL) (-780 1917471 1917586 1917760 "ONECOMP2" 1918038 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-779 1916890 1916996 1917126 "OMSERVER" 1917361 T OMSERVER (NIL) -7 NIL NIL) (-778 1913779 1916331 1916371 "OMSAGG" 1916432 NIL OMSAGG (NIL T) -9 NIL 1916496) (-777 1912402 1912665 1912947 "OMPKG" 1913517 T OMPKG (NIL) -7 NIL NIL) (-776 1911832 1911935 1911963 "OM" 1912262 T OM (NIL) -9 NIL NIL) (-775 1910371 1911384 1911552 "OMLO" 1911713 NIL OMLO (NIL T T) -8 NIL NIL) (-774 1909301 1909448 1909674 "OMEXPR" 1910197 NIL OMEXPR (NIL T) -7 NIL NIL) (-773 1908619 1908847 1908983 "OMERR" 1909185 T OMERR (NIL) -8 NIL NIL) (-772 1907797 1908040 1908200 "OMERRK" 1908479 T OMERRK (NIL) -8 NIL NIL) (-771 1907275 1907474 1907582 "OMENC" 1907709 T OMENC (NIL) -8 NIL NIL) (-770 1901170 1902355 1903526 "OMDEV" 1906124 T OMDEV (NIL) -8 NIL NIL) (-769 1900239 1900410 1900604 "OMCONN" 1900996 T OMCONN (NIL) -8 NIL NIL) (-768 1898855 1899841 1899869 "OINTDOM" 1899874 T OINTDOM (NIL) -9 NIL 1899895) (-767 1894617 1895847 1896562 "OFMONOID" 1898172 NIL OFMONOID (NIL T) -8 NIL NIL) (-766 1894055 1894554 1894599 "ODVAR" 1894604 NIL ODVAR (NIL T) -8 NIL NIL) (-765 1891180 1893552 1893737 "ODR" 1893930 NIL ODR (NIL T T NIL) -8 NIL NIL) (-764 1883486 1890959 1891083 "ODPOL" 1891088 NIL ODPOL (NIL T) -8 NIL NIL) (-763 1877309 1883358 1883463 "ODP" 1883468 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-762 1876075 1876290 1876565 "ODETOOLS" 1877083 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-761 1873044 1873700 1874416 "ODESYS" 1875408 NIL ODESYS (NIL T T) -7 NIL NIL) (-760 1867948 1868856 1869879 "ODERTRIC" 1872119 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-759 1867374 1867456 1867650 "ODERED" 1867860 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-758 1864276 1864824 1865499 "ODERAT" 1866797 NIL ODERAT (NIL T T) -7 NIL NIL) (-757 1861244 1861708 1862304 "ODEPRRIC" 1863805 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-756 1859113 1859682 1860191 "ODEPROB" 1860755 T ODEPROB (NIL) -8 NIL NIL) (-755 1855645 1856128 1856774 "ODEPRIM" 1858592 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-754 1854898 1855000 1855258 "ODEPAL" 1855537 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-753 1851100 1851881 1852735 "ODEPACK" 1854064 T ODEPACK (NIL) -7 NIL NIL) (-752 1850137 1850244 1850472 "ODEINT" 1850989 NIL ODEINT (NIL T T) -7 NIL NIL) (-751 1844238 1845663 1847110 "ODEIFTBL" 1848710 T ODEIFTBL (NIL) -8 NIL NIL) (-750 1839582 1840368 1841326 "ODEEF" 1843397 NIL ODEEF (NIL T T) -7 NIL NIL) (-749 1838919 1839008 1839237 "ODECONST" 1839487 NIL ODECONST (NIL T T T) -7 NIL NIL) (-748 1837077 1837710 1837738 "ODECAT" 1838341 T ODECAT (NIL) -9 NIL 1838870) (-747 1833949 1836789 1836908 "OCT" 1836990 NIL OCT (NIL T) -8 NIL NIL) (-746 1833587 1833630 1833757 "OCTCT2" 1833900 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-745 1828421 1830859 1830899 "OC" 1831995 NIL OC (NIL T) -9 NIL 1832852) (-744 1825648 1826396 1827386 "OC-" 1827480 NIL OC- (NIL T T) -8 NIL NIL) (-743 1825027 1825469 1825497 "OCAMON" 1825502 T OCAMON (NIL) -9 NIL 1825523) (-742 1824585 1824900 1824928 "OASGP" 1824933 T OASGP (NIL) -9 NIL 1824953) (-741 1823873 1824336 1824364 "OAMONS" 1824404 T OAMONS (NIL) -9 NIL 1824447) (-740 1823314 1823721 1823749 "OAMON" 1823754 T OAMON (NIL) -9 NIL 1823774) (-739 1822619 1823111 1823139 "OAGROUP" 1823144 T OAGROUP (NIL) -9 NIL 1823164) (-738 1822309 1822359 1822447 "NUMTUBE" 1822563 NIL NUMTUBE (NIL T) -7 NIL NIL) (-737 1815882 1817400 1818936 "NUMQUAD" 1820793 T NUMQUAD (NIL) -7 NIL NIL) (-736 1811638 1812626 1813651 "NUMODE" 1814877 T NUMODE (NIL) -7 NIL NIL) (-735 1809042 1809888 1809916 "NUMINT" 1810833 T NUMINT (NIL) -9 NIL 1811589) (-734 1807990 1808187 1808405 "NUMFMT" 1808844 T NUMFMT (NIL) -7 NIL NIL) (-733 1794369 1797306 1799836 "NUMERIC" 1805499 NIL NUMERIC (NIL T) -7 NIL NIL) (-732 1788768 1793820 1793914 "NTSCAT" 1793919 NIL NTSCAT (NIL T T T T) -9 NIL 1793958) (-731 1787962 1788127 1788320 "NTPOLFN" 1788607 NIL NTPOLFN (NIL T) -7 NIL NIL) (-730 1775778 1784804 1785614 "NSUP" 1787184 NIL NSUP (NIL T) -8 NIL NIL) (-729 1775414 1775471 1775578 "NSUP2" 1775715 NIL NSUP2 (NIL T T) -7 NIL NIL) (-728 1765376 1775193 1775323 "NSMP" 1775328 NIL NSMP (NIL T T) -8 NIL NIL) (-727 1763808 1764109 1764466 "NREP" 1765064 NIL NREP (NIL T) -7 NIL NIL) (-726 1762399 1762651 1763009 "NPCOEF" 1763551 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-725 1761465 1761580 1761796 "NORMRETR" 1762280 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-724 1759512 1759802 1760210 "NORMPK" 1761173 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-723 1759197 1759225 1759349 "NORMMA" 1759478 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-722 1759024 1759154 1759183 "NONE" 1759188 T NONE (NIL) -8 NIL NIL) (-721 1758813 1758842 1758911 "NONE1" 1758988 NIL NONE1 (NIL T) -7 NIL NIL) (-720 1758298 1758360 1758545 "NODE1" 1758745 NIL NODE1 (NIL T T) -7 NIL NIL) (-719 1756592 1757461 1757716 "NNI" 1758063 T NNI (NIL) -8 NIL NIL) (-718 1755012 1755325 1755689 "NLINSOL" 1756260 NIL NLINSOL (NIL T) -7 NIL NIL) (-717 1751179 1752147 1753069 "NIPROB" 1754110 T NIPROB (NIL) -8 NIL NIL) (-716 1749936 1750170 1750472 "NFINTBAS" 1750941 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-715 1748644 1748875 1749156 "NCODIV" 1749704 NIL NCODIV (NIL T T) -7 NIL NIL) (-714 1748406 1748443 1748518 "NCNTFRAC" 1748601 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-713 1746586 1746950 1747370 "NCEP" 1748031 NIL NCEP (NIL T) -7 NIL NIL) (-712 1745498 1746237 1746265 "NASRING" 1746375 T NASRING (NIL) -9 NIL 1746449) (-711 1745293 1745337 1745431 "NASRING-" 1745436 NIL NASRING- (NIL T) -8 NIL NIL) (-710 1744447 1744946 1744974 "NARNG" 1745091 T NARNG (NIL) -9 NIL 1745182) (-709 1744139 1744206 1744340 "NARNG-" 1744345 NIL NARNG- (NIL T) -8 NIL NIL) (-708 1743018 1743225 1743460 "NAGSP" 1743924 T NAGSP (NIL) -7 NIL NIL) (-707 1734442 1736088 1737723 "NAGS" 1741403 T NAGS (NIL) -7 NIL NIL) (-706 1733006 1733310 1733637 "NAGF07" 1734135 T NAGF07 (NIL) -7 NIL NIL) (-705 1727588 1728868 1730164 "NAGF04" 1731730 T NAGF04 (NIL) -7 NIL NIL) (-704 1720620 1722218 1723835 "NAGF02" 1725991 T NAGF02 (NIL) -7 NIL NIL) (-703 1715884 1716974 1718081 "NAGF01" 1719533 T NAGF01 (NIL) -7 NIL NIL) (-702 1709544 1711102 1712679 "NAGE04" 1714327 T NAGE04 (NIL) -7 NIL NIL) (-701 1700785 1702888 1705000 "NAGE02" 1707452 T NAGE02 (NIL) -7 NIL NIL) (-700 1696778 1697715 1698669 "NAGE01" 1699851 T NAGE01 (NIL) -7 NIL NIL) (-699 1694585 1695116 1695671 "NAGD03" 1696243 T NAGD03 (NIL) -7 NIL NIL) (-698 1686371 1688290 1690235 "NAGD02" 1692660 T NAGD02 (NIL) -7 NIL NIL) (-697 1680230 1681643 1683071 "NAGD01" 1684963 T NAGD01 (NIL) -7 NIL NIL) (-696 1676487 1677297 1678122 "NAGC06" 1679425 T NAGC06 (NIL) -7 NIL NIL) (-695 1674964 1675293 1675646 "NAGC05" 1676154 T NAGC05 (NIL) -7 NIL NIL) (-694 1674348 1674465 1674607 "NAGC02" 1674842 T NAGC02 (NIL) -7 NIL NIL) (-693 1673410 1673967 1674007 "NAALG" 1674086 NIL NAALG (NIL T) -9 NIL 1674147) (-692 1673245 1673274 1673364 "NAALG-" 1673369 NIL NAALG- (NIL T T) -8 NIL NIL) (-691 1667195 1668303 1669490 "MULTSQFR" 1672141 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-690 1666514 1666589 1666773 "MULTFACT" 1667107 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-689 1659708 1663619 1663671 "MTSCAT" 1664731 NIL MTSCAT (NIL T T) -9 NIL 1665245) (-688 1659420 1659474 1659566 "MTHING" 1659648 NIL MTHING (NIL T) -7 NIL NIL) (-687 1659212 1659245 1659305 "MSYSCMD" 1659380 T MSYSCMD (NIL) -7 NIL NIL) (-686 1655324 1657967 1658287 "MSET" 1658925 NIL MSET (NIL T) -8 NIL NIL) (-685 1652420 1654886 1654927 "MSETAGG" 1654932 NIL MSETAGG (NIL T) -9 NIL 1654966) (-684 1648276 1649818 1650559 "MRING" 1651723 NIL MRING (NIL T T) -8 NIL NIL) (-683 1647846 1647913 1648042 "MRF2" 1648203 NIL MRF2 (NIL T T T) -7 NIL NIL) (-682 1647464 1647499 1647643 "MRATFAC" 1647805 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-681 1645076 1645371 1645802 "MPRFF" 1647169 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-680 1639096 1644931 1645027 "MPOLY" 1645032 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-679 1638586 1638621 1638829 "MPCPF" 1639055 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-678 1638102 1638145 1638328 "MPC3" 1638537 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-677 1637303 1637384 1637603 "MPC2" 1638017 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-676 1635604 1635941 1636331 "MONOTOOL" 1636963 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-675 1634729 1635064 1635092 "MONOID" 1635369 T MONOID (NIL) -9 NIL 1635541) (-674 1634107 1634270 1634513 "MONOID-" 1634518 NIL MONOID- (NIL T) -8 NIL NIL) (-673 1625088 1631074 1631133 "MONOGEN" 1631807 NIL MONOGEN (NIL T T) -9 NIL 1632263) (-672 1622306 1623041 1624041 "MONOGEN-" 1624160 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-671 1621166 1621586 1621614 "MONADWU" 1622006 T MONADWU (NIL) -9 NIL 1622244) (-670 1620538 1620697 1620945 "MONADWU-" 1620950 NIL MONADWU- (NIL T) -8 NIL NIL) (-669 1619924 1620142 1620170 "MONAD" 1620377 T MONAD (NIL) -9 NIL 1620489) (-668 1619609 1619687 1619819 "MONAD-" 1619824 NIL MONAD- (NIL T) -8 NIL NIL) (-667 1617860 1618522 1618801 "MOEBIUS" 1619362 NIL MOEBIUS (NIL T) -8 NIL NIL) (-666 1617254 1617632 1617672 "MODULE" 1617677 NIL MODULE (NIL T) -9 NIL 1617703) (-665 1616822 1616918 1617108 "MODULE-" 1617113 NIL MODULE- (NIL T T) -8 NIL NIL) (-664 1614493 1615188 1615514 "MODRING" 1616647 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-663 1611449 1612614 1613131 "MODOP" 1614025 NIL MODOP (NIL T T) -8 NIL NIL) (-662 1609636 1610088 1610429 "MODMONOM" 1611248 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-661 1599315 1607840 1608262 "MODMON" 1609264 NIL MODMON (NIL T T) -8 NIL NIL) (-660 1596441 1598159 1598435 "MODFIELD" 1599190 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-659 1595445 1595722 1595912 "MMLFORM" 1596271 T MMLFORM (NIL) -8 NIL NIL) (-658 1594971 1595014 1595193 "MMAP" 1595396 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-657 1593208 1593985 1594025 "MLO" 1594442 NIL MLO (NIL T) -9 NIL 1594683) (-656 1590575 1591090 1591692 "MLIFT" 1592689 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-655 1589966 1590050 1590204 "MKUCFUNC" 1590486 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-654 1589565 1589635 1589758 "MKRECORD" 1589889 NIL MKRECORD (NIL T T) -7 NIL NIL) (-653 1588613 1588774 1589002 "MKFUNC" 1589376 NIL MKFUNC (NIL T) -7 NIL NIL) (-652 1588001 1588105 1588261 "MKFLCFN" 1588496 NIL MKFLCFN (NIL T) -7 NIL NIL) (-651 1587427 1587794 1587883 "MKCHSET" 1587945 NIL MKCHSET (NIL T) -8 NIL NIL) (-650 1586704 1586806 1586991 "MKBCFUNC" 1587320 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-649 1583388 1586258 1586394 "MINT" 1586588 T MINT (NIL) -8 NIL NIL) (-648 1582200 1582443 1582720 "MHROWRED" 1583143 NIL MHROWRED (NIL T) -7 NIL NIL) (-647 1577471 1580645 1581069 "MFLOAT" 1581796 T MFLOAT (NIL) -8 NIL NIL) (-646 1576828 1576904 1577075 "MFINFACT" 1577383 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-645 1573143 1573991 1574875 "MESH" 1575964 T MESH (NIL) -7 NIL NIL) (-644 1571533 1571845 1572198 "MDDFACT" 1572830 NIL MDDFACT (NIL T) -7 NIL NIL) (-643 1568376 1570693 1570734 "MDAGG" 1570989 NIL MDAGG (NIL T) -9 NIL 1571132) (-642 1558074 1567669 1567876 "MCMPLX" 1568189 T MCMPLX (NIL) -8 NIL NIL) (-641 1557215 1557361 1557561 "MCDEN" 1557923 NIL MCDEN (NIL T T) -7 NIL NIL) (-640 1555105 1555375 1555755 "MCALCFN" 1556945 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-639 1554016 1554189 1554430 "MAYBE" 1554903 NIL MAYBE (NIL T) -8 NIL NIL) (-638 1551638 1552161 1552722 "MATSTOR" 1553487 NIL MATSTOR (NIL T) -7 NIL NIL) (-637 1547647 1551013 1551260 "MATRIX" 1551423 NIL MATRIX (NIL T) -8 NIL NIL) (-636 1543416 1544120 1544856 "MATLIN" 1547004 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-635 1533614 1536752 1536828 "MATCAT" 1541666 NIL MATCAT (NIL T T T) -9 NIL 1543083) (-634 1529979 1530992 1532347 "MATCAT-" 1532352 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-633 1528581 1528734 1529065 "MATCAT2" 1529814 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-632 1526693 1527017 1527401 "MAPPKG3" 1528256 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-631 1525674 1525847 1526069 "MAPPKG2" 1526517 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-630 1524173 1524457 1524784 "MAPPKG1" 1525380 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-629 1523784 1523842 1523965 "MAPHACK3" 1524109 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-628 1523376 1523437 1523551 "MAPHACK2" 1523716 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-627 1522814 1522917 1523059 "MAPHACK1" 1523267 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-626 1520922 1521516 1521819 "MAGMA" 1522543 NIL MAGMA (NIL T) -8 NIL NIL) (-625 1517397 1519166 1519626 "M3D" 1520495 NIL M3D (NIL T) -8 NIL NIL) (-624 1511553 1515768 1515809 "LZSTAGG" 1516591 NIL LZSTAGG (NIL T) -9 NIL 1516886) (-623 1507526 1508684 1510141 "LZSTAGG-" 1510146 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-622 1504642 1505419 1505905 "LWORD" 1507072 NIL LWORD (NIL T) -8 NIL NIL) (-621 1497802 1504413 1504547 "LSQM" 1504552 NIL LSQM (NIL NIL T) -8 NIL NIL) (-620 1497026 1497165 1497393 "LSPP" 1497657 NIL LSPP (NIL T T T T) -7 NIL NIL) (-619 1494838 1495139 1495595 "LSMP" 1496715 NIL LSMP (NIL T T T T) -7 NIL NIL) (-618 1491617 1492291 1493021 "LSMP1" 1494140 NIL LSMP1 (NIL T) -7 NIL NIL) (-617 1485544 1490786 1490827 "LSAGG" 1490889 NIL LSAGG (NIL T) -9 NIL 1490967) (-616 1482239 1483163 1484376 "LSAGG-" 1484381 NIL LSAGG- (NIL T T) -8 NIL NIL) (-615 1479865 1481383 1481632 "LPOLY" 1482034 NIL LPOLY (NIL T T) -8 NIL NIL) (-614 1479447 1479532 1479655 "LPEFRAC" 1479774 NIL LPEFRAC (NIL T) -7 NIL NIL) (-613 1477794 1478541 1478794 "LO" 1479279 NIL LO (NIL T T T) -8 NIL NIL) (-612 1477448 1477560 1477588 "LOGIC" 1477699 T LOGIC (NIL) -9 NIL 1477779) (-611 1477310 1477333 1477404 "LOGIC-" 1477409 NIL LOGIC- (NIL T) -8 NIL NIL) (-610 1476503 1476643 1476836 "LODOOPS" 1477166 NIL LODOOPS (NIL T T) -7 NIL NIL) (-609 1473921 1476420 1476485 "LODO" 1476490 NIL LODO (NIL T NIL) -8 NIL NIL) (-608 1472467 1472702 1473053 "LODOF" 1473668 NIL LODOF (NIL T T) -7 NIL NIL) (-607 1468887 1471323 1471363 "LODOCAT" 1471795 NIL LODOCAT (NIL T) -9 NIL 1472006) (-606 1468621 1468679 1468805 "LODOCAT-" 1468810 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-605 1465935 1468462 1468580 "LODO2" 1468585 NIL LODO2 (NIL T T) -8 NIL NIL) (-604 1463364 1465872 1465917 "LODO1" 1465922 NIL LODO1 (NIL T) -8 NIL NIL) (-603 1462227 1462392 1462703 "LODEEF" 1463187 NIL LODEEF (NIL T T T) -7 NIL NIL) (-602 1457514 1460358 1460399 "LNAGG" 1461346 NIL LNAGG (NIL T) -9 NIL 1461790) (-601 1456661 1456875 1457217 "LNAGG-" 1457222 NIL LNAGG- (NIL T T) -8 NIL NIL) (-600 1452826 1453588 1454226 "LMOPS" 1456077 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-599 1452224 1452586 1452626 "LMODULE" 1452686 NIL LMODULE (NIL T) -9 NIL 1452728) (-598 1449470 1451869 1451992 "LMDICT" 1452134 NIL LMDICT (NIL T) -8 NIL NIL) (-597 1442697 1448416 1448714 "LIST" 1449205 NIL LIST (NIL T) -8 NIL NIL) (-596 1442222 1442296 1442435 "LIST3" 1442617 NIL LIST3 (NIL T T T) -7 NIL NIL) (-595 1441229 1441407 1441635 "LIST2" 1442040 NIL LIST2 (NIL T T) -7 NIL NIL) (-594 1439363 1439675 1440074 "LIST2MAP" 1440876 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-593 1438076 1438756 1438796 "LINEXP" 1439049 NIL LINEXP (NIL T) -9 NIL 1439197) (-592 1436723 1436983 1437280 "LINDEP" 1437828 NIL LINDEP (NIL T T) -7 NIL NIL) (-591 1433490 1434209 1434986 "LIMITRF" 1435978 NIL LIMITRF (NIL T) -7 NIL NIL) (-590 1431770 1432065 1432480 "LIMITPS" 1433185 NIL LIMITPS (NIL T T) -7 NIL NIL) (-589 1426225 1431281 1431509 "LIE" 1431591 NIL LIE (NIL T T) -8 NIL NIL) (-588 1425276 1425719 1425759 "LIECAT" 1425899 NIL LIECAT (NIL T) -9 NIL 1426050) (-587 1425117 1425144 1425232 "LIECAT-" 1425237 NIL LIECAT- (NIL T T) -8 NIL NIL) (-586 1417729 1424566 1424731 "LIB" 1424972 T LIB (NIL) -8 NIL NIL) (-585 1413366 1414247 1415182 "LGROBP" 1416846 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-584 1411232 1411506 1411868 "LF" 1413087 NIL LF (NIL T T) -7 NIL NIL) (-583 1410072 1410764 1410792 "LFCAT" 1410999 T LFCAT (NIL) -9 NIL 1411138) (-582 1406984 1407610 1408296 "LEXTRIPK" 1409438 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-581 1403690 1404554 1405057 "LEXP" 1406564 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-580 1402088 1402401 1402802 "LEADCDET" 1403372 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-579 1401281 1401355 1401583 "LAZM3PK" 1402009 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-578 1396198 1399360 1399897 "LAUPOL" 1400794 NIL LAUPOL (NIL T T) -8 NIL NIL) (-577 1395765 1395809 1395976 "LAPLACE" 1396148 NIL LAPLACE (NIL T T) -7 NIL NIL) (-576 1393693 1394866 1395117 "LA" 1395598 NIL LA (NIL T T T) -8 NIL NIL) (-575 1392756 1393350 1393390 "LALG" 1393451 NIL LALG (NIL T) -9 NIL 1393509) (-574 1392471 1392530 1392665 "LALG-" 1392670 NIL LALG- (NIL T T) -8 NIL NIL) (-573 1391381 1391568 1391865 "KOVACIC" 1392271 NIL KOVACIC (NIL T T) -7 NIL NIL) (-572 1391216 1391240 1391281 "KONVERT" 1391343 NIL KONVERT (NIL T) -9 NIL NIL) (-571 1391051 1391075 1391116 "KOERCE" 1391178 NIL KOERCE (NIL T) -9 NIL NIL) (-570 1388785 1389545 1389938 "KERNEL" 1390690 NIL KERNEL (NIL T) -8 NIL NIL) (-569 1388287 1388368 1388498 "KERNEL2" 1388699 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-568 1382139 1386827 1386881 "KDAGG" 1387258 NIL KDAGG (NIL T T) -9 NIL 1387464) (-567 1381668 1381792 1381997 "KDAGG-" 1382002 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-566 1374843 1381329 1381484 "KAFILE" 1381546 NIL KAFILE (NIL T) -8 NIL NIL) (-565 1369298 1374354 1374582 "JORDAN" 1374664 NIL JORDAN (NIL T T) -8 NIL NIL) (-564 1369027 1369086 1369173 "JAVACODE" 1369231 T JAVACODE (NIL) -8 NIL NIL) (-563 1365327 1367233 1367287 "IXAGG" 1368216 NIL IXAGG (NIL T T) -9 NIL 1368675) (-562 1364246 1364552 1364971 "IXAGG-" 1364976 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-561 1359831 1364168 1364227 "IVECTOR" 1364232 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-560 1358597 1358834 1359100 "ITUPLE" 1359598 NIL ITUPLE (NIL T) -8 NIL NIL) (-559 1357033 1357210 1357516 "ITRIGMNP" 1358419 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-558 1355778 1355982 1356265 "ITFUN3" 1356809 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-557 1355410 1355467 1355576 "ITFUN2" 1355715 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-556 1353212 1354283 1354580 "ITAYLOR" 1355145 NIL ITAYLOR (NIL T) -8 NIL NIL) (-555 1342200 1347398 1348557 "ISUPS" 1352085 NIL ISUPS (NIL T) -8 NIL NIL) (-554 1341304 1341444 1341680 "ISUMP" 1342047 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-553 1336568 1341105 1341184 "ISTRING" 1341257 NIL ISTRING (NIL NIL) -8 NIL NIL) (-552 1335781 1335862 1336077 "IRURPK" 1336482 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-551 1334717 1334918 1335158 "IRSN" 1335561 T IRSN (NIL) -7 NIL NIL) (-550 1332752 1333107 1333542 "IRRF2F" 1334355 NIL IRRF2F (NIL T) -7 NIL NIL) (-549 1332499 1332537 1332613 "IRREDFFX" 1332708 NIL IRREDFFX (NIL T) -7 NIL NIL) (-548 1331114 1331373 1331672 "IROOT" 1332232 NIL IROOT (NIL T) -7 NIL NIL) (-547 1327752 1328803 1329493 "IR" 1330456 NIL IR (NIL T) -8 NIL NIL) (-546 1325365 1325860 1326426 "IR2" 1327230 NIL IR2 (NIL T T) -7 NIL NIL) (-545 1324441 1324554 1324774 "IR2F" 1325248 NIL IR2F (NIL T T) -7 NIL NIL) (-544 1324232 1324266 1324326 "IPRNTPK" 1324401 T IPRNTPK (NIL) -7 NIL NIL) (-543 1320786 1324121 1324190 "IPF" 1324195 NIL IPF (NIL NIL) -8 NIL NIL) (-542 1319103 1320711 1320768 "IPADIC" 1320773 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-541 1318602 1318660 1318849 "INVLAPLA" 1319039 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-540 1308251 1310604 1312990 "INTTR" 1316266 NIL INTTR (NIL T T) -7 NIL NIL) (-539 1304599 1305340 1306203 "INTTOOLS" 1307437 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-538 1304185 1304276 1304393 "INTSLPE" 1304502 T INTSLPE (NIL) -7 NIL NIL) (-537 1302135 1304108 1304167 "INTRVL" 1304172 NIL INTRVL (NIL T) -8 NIL NIL) (-536 1299742 1300254 1300828 "INTRF" 1301620 NIL INTRF (NIL T) -7 NIL NIL) (-535 1299157 1299254 1299395 "INTRET" 1299640 NIL INTRET (NIL T) -7 NIL NIL) (-534 1297159 1297548 1298017 "INTRAT" 1298765 NIL INTRAT (NIL T T) -7 NIL NIL) (-533 1294392 1294975 1295600 "INTPM" 1296644 NIL INTPM (NIL T T) -7 NIL NIL) (-532 1291101 1291700 1292444 "INTPAF" 1293778 NIL INTPAF (NIL T T T) -7 NIL NIL) (-531 1286344 1287290 1288325 "INTPACK" 1290086 T INTPACK (NIL) -7 NIL NIL) (-530 1283198 1286073 1286200 "INT" 1286237 T INT (NIL) -8 NIL NIL) (-529 1282450 1282602 1282810 "INTHERTR" 1283040 NIL INTHERTR (NIL T T) -7 NIL NIL) (-528 1281889 1281969 1282157 "INTHERAL" 1282364 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-527 1279735 1280178 1280635 "INTHEORY" 1281452 T INTHEORY (NIL) -7 NIL NIL) (-526 1271057 1272678 1274456 "INTG0" 1278087 NIL INTG0 (NIL T T T) -7 NIL NIL) (-525 1251630 1256420 1261230 "INTFTBL" 1266267 T INTFTBL (NIL) -8 NIL NIL) (-524 1250879 1251017 1251190 "INTFACT" 1251489 NIL INTFACT (NIL T) -7 NIL NIL) (-523 1248270 1248716 1249279 "INTEF" 1250433 NIL INTEF (NIL T T) -7 NIL NIL) (-522 1246732 1247481 1247509 "INTDOM" 1247810 T INTDOM (NIL) -9 NIL 1248017) (-521 1246101 1246275 1246517 "INTDOM-" 1246522 NIL INTDOM- (NIL T) -8 NIL NIL) (-520 1242594 1244526 1244580 "INTCAT" 1245379 NIL INTCAT (NIL T) -9 NIL 1245698) (-519 1242067 1242169 1242297 "INTBIT" 1242486 T INTBIT (NIL) -7 NIL NIL) (-518 1240742 1240896 1241209 "INTALG" 1241912 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-517 1240199 1240289 1240459 "INTAF" 1240646 NIL INTAF (NIL T T) -7 NIL NIL) (-516 1233653 1240009 1240149 "INTABL" 1240154 NIL INTABL (NIL T T T) -8 NIL NIL) (-515 1228604 1231333 1231361 "INS" 1232329 T INS (NIL) -9 NIL 1233010) (-514 1225844 1226615 1227589 "INS-" 1227662 NIL INS- (NIL T) -8 NIL NIL) (-513 1224623 1224850 1225147 "INPSIGN" 1225597 NIL INPSIGN (NIL T T) -7 NIL NIL) (-512 1223741 1223858 1224055 "INPRODPF" 1224503 NIL INPRODPF (NIL T T) -7 NIL NIL) (-511 1222635 1222752 1222989 "INPRODFF" 1223621 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-510 1221635 1221787 1222047 "INNMFACT" 1222471 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-509 1220832 1220929 1221117 "INMODGCD" 1221534 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-508 1219341 1219585 1219909 "INFSP" 1220577 NIL INFSP (NIL T T T) -7 NIL NIL) (-507 1218525 1218642 1218825 "INFPROD0" 1219221 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-506 1215536 1216694 1217185 "INFORM" 1218042 T INFORM (NIL) -8 NIL NIL) (-505 1215146 1215206 1215304 "INFORM1" 1215471 NIL INFORM1 (NIL T) -7 NIL NIL) (-504 1214669 1214758 1214872 "INFINITY" 1215052 T INFINITY (NIL) -7 NIL NIL) (-503 1213286 1213535 1213856 "INEP" 1214417 NIL INEP (NIL T T T) -7 NIL NIL) (-502 1212562 1213183 1213248 "INDE" 1213253 NIL INDE (NIL T) -8 NIL NIL) (-501 1212126 1212194 1212311 "INCRMAPS" 1212489 NIL INCRMAPS (NIL T) -7 NIL NIL) (-500 1207437 1208362 1209306 "INBFF" 1211214 NIL INBFF (NIL T) -7 NIL NIL) (-499 1203932 1207282 1207385 "IMATRIX" 1207390 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-498 1202644 1202767 1203082 "IMATQF" 1203788 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-497 1200864 1201091 1201428 "IMATLIN" 1202400 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-496 1195490 1200788 1200846 "ILIST" 1200851 NIL ILIST (NIL T NIL) -8 NIL NIL) (-495 1193443 1195350 1195463 "IIARRAY2" 1195468 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-494 1188811 1193354 1193418 "IFF" 1193423 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-493 1183854 1188103 1188291 "IFARRAY" 1188668 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-492 1183061 1183758 1183831 "IFAMON" 1183836 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-491 1182645 1182710 1182764 "IEVALAB" 1182971 NIL IEVALAB (NIL T T) -9 NIL NIL) (-490 1182320 1182388 1182548 "IEVALAB-" 1182553 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-489 1181978 1182234 1182297 "IDPO" 1182302 NIL IDPO (NIL T T) -8 NIL NIL) (-488 1181255 1181867 1181942 "IDPOAMS" 1181947 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-487 1180589 1181144 1181219 "IDPOAM" 1181224 NIL IDPOAM (NIL T T) -8 NIL NIL) (-486 1179675 1179925 1179978 "IDPC" 1180391 NIL IDPC (NIL T T) -9 NIL 1180540) (-485 1179171 1179567 1179640 "IDPAM" 1179645 NIL IDPAM (NIL T T) -8 NIL NIL) (-484 1178574 1179063 1179136 "IDPAG" 1179141 NIL IDPAG (NIL T T) -8 NIL NIL) (-483 1174829 1175677 1176572 "IDECOMP" 1177731 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-482 1167702 1168752 1169799 "IDEAL" 1173865 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-481 1166866 1166978 1167177 "ICDEN" 1167586 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-480 1165965 1166346 1166493 "ICARD" 1166739 T ICARD (NIL) -8 NIL NIL) (-479 1164037 1164350 1164753 "IBPTOOLS" 1165642 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-478 1159671 1163657 1163770 "IBITS" 1163956 NIL IBITS (NIL NIL) -8 NIL NIL) (-477 1156394 1156970 1157665 "IBATOOL" 1159088 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-476 1154174 1154635 1155168 "IBACHIN" 1155929 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-475 1152051 1154020 1154123 "IARRAY2" 1154128 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-474 1148204 1151977 1152034 "IARRAY1" 1152039 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-473 1142142 1146622 1147100 "IAN" 1147746 T IAN (NIL) -8 NIL NIL) (-472 1141653 1141710 1141883 "IALGFACT" 1142079 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-471 1141181 1141294 1141322 "HYPCAT" 1141529 T HYPCAT (NIL) -9 NIL NIL) (-470 1140719 1140836 1141022 "HYPCAT-" 1141027 NIL HYPCAT- (NIL T) -8 NIL NIL) (-469 1140341 1140514 1140597 "HOSTNAME" 1140656 T HOSTNAME (NIL) -8 NIL NIL) (-468 1137021 1138352 1138393 "HOAGG" 1139374 NIL HOAGG (NIL T) -9 NIL 1140053) (-467 1135615 1136014 1136540 "HOAGG-" 1136545 NIL HOAGG- (NIL T T) -8 NIL NIL) (-466 1129445 1135056 1135222 "HEXADEC" 1135469 T HEXADEC (NIL) -8 NIL NIL) (-465 1128193 1128415 1128678 "HEUGCD" 1129222 NIL HEUGCD (NIL T) -7 NIL NIL) (-464 1127296 1128030 1128160 "HELLFDIV" 1128165 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-463 1125524 1127073 1127161 "HEAP" 1127240 NIL HEAP (NIL T) -8 NIL NIL) (-462 1124863 1125103 1125231 "HEADAST" 1125416 T HEADAST (NIL) -8 NIL NIL) (-461 1118730 1124778 1124840 "HDP" 1124845 NIL HDP (NIL NIL T) -8 NIL NIL) (-460 1112442 1118367 1118518 "HDMP" 1118631 NIL HDMP (NIL NIL T) -8 NIL NIL) (-459 1111767 1111906 1112070 "HB" 1112298 T HB (NIL) -7 NIL NIL) (-458 1105264 1111613 1111717 "HASHTBL" 1111722 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-457 1103017 1104892 1105071 "HACKPI" 1105105 T HACKPI (NIL) -8 NIL NIL) (-456 1098713 1102871 1102983 "GTSET" 1102988 NIL GTSET (NIL T T T T) -8 NIL NIL) (-455 1092239 1098591 1098689 "GSTBL" 1098694 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-454 1084472 1091275 1091539 "GSERIES" 1092030 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-453 1083495 1083948 1083976 "GROUP" 1084237 T GROUP (NIL) -9 NIL 1084396) (-452 1082611 1082834 1083178 "GROUP-" 1083183 NIL GROUP- (NIL T) -8 NIL NIL) (-451 1080980 1081299 1081686 "GROEBSOL" 1082288 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-450 1079921 1080183 1080234 "GRMOD" 1080763 NIL GRMOD (NIL T T) -9 NIL 1080931) (-449 1079689 1079725 1079853 "GRMOD-" 1079858 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-448 1075014 1076043 1077043 "GRIMAGE" 1078709 T GRIMAGE (NIL) -8 NIL NIL) (-447 1073481 1073741 1074065 "GRDEF" 1074710 T GRDEF (NIL) -7 NIL NIL) (-446 1072925 1073041 1073182 "GRAY" 1073360 T GRAY (NIL) -7 NIL NIL) (-445 1072159 1072539 1072590 "GRALG" 1072743 NIL GRALG (NIL T T) -9 NIL 1072835) (-444 1071820 1071893 1072056 "GRALG-" 1072061 NIL GRALG- (NIL T T T) -8 NIL NIL) (-443 1068628 1071409 1071585 "GPOLSET" 1071727 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-442 1067984 1068041 1068298 "GOSPER" 1068565 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-441 1063743 1064422 1064948 "GMODPOL" 1067683 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-440 1062748 1062932 1063170 "GHENSEL" 1063555 NIL GHENSEL (NIL T T) -7 NIL NIL) (-439 1056814 1057657 1058683 "GENUPS" 1061832 NIL GENUPS (NIL T T) -7 NIL NIL) (-438 1056511 1056562 1056651 "GENUFACT" 1056757 NIL GENUFACT (NIL T) -7 NIL NIL) (-437 1055923 1056000 1056165 "GENPGCD" 1056429 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-436 1055397 1055432 1055645 "GENMFACT" 1055882 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-435 1053965 1054220 1054527 "GENEEZ" 1055140 NIL GENEEZ (NIL T T) -7 NIL NIL) (-434 1047839 1053578 1053739 "GDMP" 1053888 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-433 1037216 1041610 1042716 "GCNAALG" 1046822 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-432 1035638 1036510 1036538 "GCDDOM" 1036793 T GCDDOM (NIL) -9 NIL 1036950) (-431 1035108 1035235 1035450 "GCDDOM-" 1035455 NIL GCDDOM- (NIL T) -8 NIL NIL) (-430 1033780 1033965 1034269 "GB" 1034887 NIL GB (NIL T T T T) -7 NIL NIL) (-429 1022400 1024726 1027118 "GBINTERN" 1031471 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-428 1020237 1020529 1020950 "GBF" 1022075 NIL GBF (NIL T T T T) -7 NIL NIL) (-427 1019018 1019183 1019450 "GBEUCLID" 1020053 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-426 1018367 1018492 1018641 "GAUSSFAC" 1018889 T GAUSSFAC (NIL) -7 NIL NIL) (-425 1016744 1017046 1017359 "GALUTIL" 1018086 NIL GALUTIL (NIL T) -7 NIL NIL) (-424 1015061 1015335 1015658 "GALPOLYU" 1016471 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-423 1012450 1012740 1013145 "GALFACTU" 1014758 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-422 1004256 1005755 1007363 "GALFACT" 1010882 NIL GALFACT (NIL T) -7 NIL NIL) (-421 1001644 1002302 1002330 "FVFUN" 1003486 T FVFUN (NIL) -9 NIL 1004206) (-420 1000910 1001092 1001120 "FVC" 1001411 T FVC (NIL) -9 NIL 1001594) (-419 1000552 1000707 1000788 "FUNCTION" 1000862 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-418 998222 998773 999262 "FT" 1000083 T FT (NIL) -8 NIL NIL) (-417 997040 997523 997726 "FTEM" 998039 T FTEM (NIL) -8 NIL NIL) (-416 995305 995593 995995 "FSUPFACT" 996732 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-415 993702 993991 994323 "FST" 994993 T FST (NIL) -8 NIL NIL) (-414 992877 992983 993177 "FSRED" 993584 NIL FSRED (NIL T T) -7 NIL NIL) (-413 991556 991811 992165 "FSPRMELT" 992592 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-412 988641 989079 989578 "FSPECF" 991119 NIL FSPECF (NIL T T) -7 NIL NIL) (-411 971015 979572 979612 "FS" 983450 NIL FS (NIL T) -9 NIL 985732) (-410 959665 962655 966711 "FS-" 967008 NIL FS- (NIL T T) -8 NIL NIL) (-409 959181 959235 959411 "FSINT" 959606 NIL FSINT (NIL T T) -7 NIL NIL) (-408 957462 958174 958477 "FSERIES" 958960 NIL FSERIES (NIL T T) -8 NIL NIL) (-407 956480 956596 956826 "FSCINT" 957342 NIL FSCINT (NIL T T) -7 NIL NIL) (-406 952715 955425 955466 "FSAGG" 955836 NIL FSAGG (NIL T) -9 NIL 956095) (-405 950477 951078 951874 "FSAGG-" 951969 NIL FSAGG- (NIL T T) -8 NIL NIL) (-404 949519 949662 949889 "FSAGG2" 950330 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-403 947178 947457 948010 "FS2UPS" 949237 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-402 946764 946807 946960 "FS2" 947129 NIL FS2 (NIL T T T T) -7 NIL NIL) (-401 945624 945795 946103 "FS2EXPXP" 946589 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-400 945050 945165 945317 "FRUTIL" 945504 NIL FRUTIL (NIL T) -7 NIL NIL) (-399 936470 940549 941905 "FR" 943726 NIL FR (NIL T) -8 NIL NIL) (-398 931547 934190 934230 "FRNAALG" 935626 NIL FRNAALG (NIL T) -9 NIL 936233) (-397 927225 928296 929571 "FRNAALG-" 930321 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-396 926863 926906 927033 "FRNAAF2" 927176 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-395 925228 925720 926014 "FRMOD" 926676 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-394 922950 923619 923935 "FRIDEAL" 925019 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-393 922149 922236 922523 "FRIDEAL2" 922857 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-392 921407 921815 921856 "FRETRCT" 921861 NIL FRETRCT (NIL T) -9 NIL 922032) (-391 920519 920750 921101 "FRETRCT-" 921106 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-390 917729 918949 919008 "FRAMALG" 919890 NIL FRAMALG (NIL T T) -9 NIL 920182) (-389 915863 916318 916948 "FRAMALG-" 917171 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-388 909765 915338 915614 "FRAC" 915619 NIL FRAC (NIL T) -8 NIL NIL) (-387 909401 909458 909565 "FRAC2" 909702 NIL FRAC2 (NIL T T) -7 NIL NIL) (-386 909037 909094 909201 "FR2" 909338 NIL FR2 (NIL T T) -7 NIL NIL) (-385 903711 906624 906652 "FPS" 907771 T FPS (NIL) -9 NIL 908327) (-384 903160 903269 903433 "FPS-" 903579 NIL FPS- (NIL T) -8 NIL NIL) (-383 900609 902306 902334 "FPC" 902559 T FPC (NIL) -9 NIL 902701) (-382 900402 900442 900539 "FPC-" 900544 NIL FPC- (NIL T) -8 NIL NIL) (-381 899281 899891 899932 "FPATMAB" 899937 NIL FPATMAB (NIL T) -9 NIL 900089) (-380 896981 897457 897883 "FPARFRAC" 898918 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-379 892374 892873 893555 "FORTRAN" 896413 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-378 890090 890590 891129 "FORT" 891855 T FORT (NIL) -7 NIL NIL) (-377 887766 888328 888356 "FORTFN" 889416 T FORTFN (NIL) -9 NIL 890040) (-376 887530 887580 887608 "FORTCAT" 887667 T FORTCAT (NIL) -9 NIL 887729) (-375 885590 886073 886472 "FORMULA" 887151 T FORMULA (NIL) -8 NIL NIL) (-374 885378 885408 885477 "FORMULA1" 885554 NIL FORMULA1 (NIL T) -7 NIL NIL) (-373 884901 884953 885126 "FORDER" 885320 NIL FORDER (NIL T T T T) -7 NIL NIL) (-372 883997 884161 884354 "FOP" 884728 T FOP (NIL) -7 NIL NIL) (-371 882605 883277 883451 "FNLA" 883879 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-370 881274 881663 881691 "FNCAT" 882263 T FNCAT (NIL) -9 NIL 882556) (-369 880840 881233 881261 "FNAME" 881266 T FNAME (NIL) -8 NIL NIL) (-368 879500 880473 880501 "FMTC" 880506 T FMTC (NIL) -9 NIL 880541) (-367 875818 877025 877653 "FMONOID" 878905 NIL FMONOID (NIL T) -8 NIL NIL) (-366 875038 875561 875709 "FM" 875714 NIL FM (NIL T T) -8 NIL NIL) (-365 872462 873108 873136 "FMFUN" 874280 T FMFUN (NIL) -9 NIL 874988) (-364 871731 871912 871940 "FMC" 872230 T FMC (NIL) -9 NIL 872412) (-363 868961 869795 869848 "FMCAT" 871030 NIL FMCAT (NIL T T) -9 NIL 871524) (-362 867856 868729 868828 "FM1" 868906 NIL FM1 (NIL T T) -8 NIL NIL) (-361 865630 866046 866540 "FLOATRP" 867407 NIL FLOATRP (NIL T) -7 NIL NIL) (-360 859116 863286 863916 "FLOAT" 865020 T FLOAT (NIL) -8 NIL NIL) (-359 856554 857054 857632 "FLOATCP" 858583 NIL FLOATCP (NIL T) -7 NIL NIL) (-358 855343 856191 856231 "FLINEXP" 856236 NIL FLINEXP (NIL T) -9 NIL 856329) (-357 854498 854733 855060 "FLINEXP-" 855065 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-356 853574 853718 853942 "FLASORT" 854350 NIL FLASORT (NIL T T) -7 NIL NIL) (-355 850793 851635 851687 "FLALG" 852914 NIL FLALG (NIL T T) -9 NIL 853381) (-354 844578 848280 848321 "FLAGG" 849583 NIL FLAGG (NIL T) -9 NIL 850235) (-353 843304 843643 844133 "FLAGG-" 844138 NIL FLAGG- (NIL T T) -8 NIL NIL) (-352 842346 842489 842716 "FLAGG2" 843157 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-351 839319 840337 840396 "FINRALG" 841524 NIL FINRALG (NIL T T) -9 NIL 842032) (-350 838479 838708 839047 "FINRALG-" 839052 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-349 837886 838099 838127 "FINITE" 838323 T FINITE (NIL) -9 NIL 838430) (-348 830346 832507 832547 "FINAALG" 836214 NIL FINAALG (NIL T) -9 NIL 837667) (-347 825687 826728 827872 "FINAALG-" 829251 NIL FINAALG- (NIL T T) -8 NIL NIL) (-346 825082 825442 825545 "FILE" 825617 NIL FILE (NIL T) -8 NIL NIL) (-345 823767 824079 824133 "FILECAT" 824817 NIL FILECAT (NIL T T) -9 NIL 825033) (-344 821630 823186 823214 "FIELD" 823254 T FIELD (NIL) -9 NIL 823334) (-343 820250 820635 821146 "FIELD-" 821151 NIL FIELD- (NIL T) -8 NIL NIL) (-342 818065 818887 819233 "FGROUP" 819937 NIL FGROUP (NIL T) -8 NIL NIL) (-341 817155 817319 817539 "FGLMICPK" 817897 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-340 812957 817080 817137 "FFX" 817142 NIL FFX (NIL T NIL) -8 NIL NIL) (-339 812558 812619 812754 "FFSLPE" 812890 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-338 808551 809330 810126 "FFPOLY" 811794 NIL FFPOLY (NIL T) -7 NIL NIL) (-337 808055 808091 808300 "FFPOLY2" 808509 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-336 803876 807974 808037 "FFP" 808042 NIL FFP (NIL T NIL) -8 NIL NIL) (-335 799244 803787 803851 "FF" 803856 NIL FF (NIL NIL NIL) -8 NIL NIL) (-334 794340 798587 798777 "FFNBX" 799098 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-333 789249 793475 793733 "FFNBP" 794194 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-332 783852 788533 788744 "FFNB" 789082 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-331 782684 782882 783197 "FFINTBAS" 783649 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-330 778908 781148 781176 "FFIELDC" 781796 T FFIELDC (NIL) -9 NIL 782172) (-329 777571 777941 778438 "FFIELDC-" 778443 NIL FFIELDC- (NIL T) -8 NIL NIL) (-328 777141 777186 777310 "FFHOM" 777513 NIL FFHOM (NIL T T T) -7 NIL NIL) (-327 774839 775323 775840 "FFF" 776656 NIL FFF (NIL T) -7 NIL NIL) (-326 770427 774581 774682 "FFCGX" 774782 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-325 766029 770159 770266 "FFCGP" 770370 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-324 761182 765756 765864 "FFCG" 765965 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-323 743128 752251 752337 "FFCAT" 757502 NIL FFCAT (NIL T T T) -9 NIL 758989) (-322 738326 739373 740687 "FFCAT-" 741917 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-321 737737 737780 738015 "FFCAT2" 738277 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-320 726937 730727 731944 "FEXPR" 736592 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-319 725937 726372 726413 "FEVALAB" 726497 NIL FEVALAB (NIL T) -9 NIL 726758) (-318 725096 725306 725644 "FEVALAB-" 725649 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-317 723689 724479 724682 "FDIV" 724995 NIL FDIV (NIL T T T T) -8 NIL NIL) (-316 720756 721471 721586 "FDIVCAT" 723154 NIL FDIVCAT (NIL T T T T) -9 NIL 723591) (-315 720518 720545 720715 "FDIVCAT-" 720720 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-314 719738 719825 720102 "FDIV2" 720425 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-313 718424 718683 718972 "FCPAK1" 719469 T FCPAK1 (NIL) -7 NIL NIL) (-312 717552 717924 718065 "FCOMP" 718315 NIL FCOMP (NIL T) -8 NIL NIL) (-311 701187 704601 708162 "FC" 714011 T FC (NIL) -8 NIL NIL) (-310 693783 697829 697869 "FAXF" 699671 NIL FAXF (NIL T) -9 NIL 700362) (-309 691062 691717 692542 "FAXF-" 693007 NIL FAXF- (NIL T T) -8 NIL NIL) (-308 686162 690438 690614 "FARRAY" 690919 NIL FARRAY (NIL T) -8 NIL NIL) (-307 681553 683624 683676 "FAMR" 684688 NIL FAMR (NIL T T) -9 NIL 685148) (-306 680444 680746 681180 "FAMR-" 681185 NIL FAMR- (NIL T T T) -8 NIL NIL) (-305 679640 680366 680419 "FAMONOID" 680424 NIL FAMONOID (NIL T) -8 NIL NIL) (-304 677473 678157 678210 "FAMONC" 679151 NIL FAMONC (NIL T T) -9 NIL 679536) (-303 676165 677227 677364 "FAGROUP" 677369 NIL FAGROUP (NIL T) -8 NIL NIL) (-302 673968 674287 674689 "FACUTIL" 675846 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-301 673067 673252 673474 "FACTFUNC" 673778 NIL FACTFUNC (NIL T) -7 NIL NIL) (-300 665387 672318 672530 "EXPUPXS" 672923 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-299 662870 663410 663996 "EXPRTUBE" 664821 T EXPRTUBE (NIL) -7 NIL NIL) (-298 659064 659656 660393 "EXPRODE" 662209 NIL EXPRODE (NIL T T) -7 NIL NIL) (-297 644223 657723 658149 "EXPR" 658670 NIL EXPR (NIL T) -8 NIL NIL) (-296 638651 639238 640050 "EXPR2UPS" 643521 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-295 638287 638344 638451 "EXPR2" 638588 NIL EXPR2 (NIL T T) -7 NIL NIL) (-294 629641 637424 637719 "EXPEXPAN" 638125 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-293 629468 629598 629627 "EXIT" 629632 T EXIT (NIL) -8 NIL NIL) (-292 629095 629157 629270 "EVALCYC" 629400 NIL EVALCYC (NIL T) -7 NIL NIL) (-291 628636 628754 628795 "EVALAB" 628965 NIL EVALAB (NIL T) -9 NIL 629069) (-290 628117 628239 628460 "EVALAB-" 628465 NIL EVALAB- (NIL T T) -8 NIL NIL) (-289 625580 626892 626920 "EUCDOM" 627475 T EUCDOM (NIL) -9 NIL 627825) (-288 623985 624427 625017 "EUCDOM-" 625022 NIL EUCDOM- (NIL T) -8 NIL NIL) (-287 611563 614311 617051 "ESTOOLS" 621265 T ESTOOLS (NIL) -7 NIL NIL) (-286 611199 611256 611363 "ESTOOLS2" 611500 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-285 610950 610992 611072 "ESTOOLS1" 611151 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-284 604888 606612 606640 "ES" 609404 T ES (NIL) -9 NIL 610810) (-283 599835 601122 602939 "ES-" 603103 NIL ES- (NIL T) -8 NIL NIL) (-282 596210 596970 597750 "ESCONT" 599075 T ESCONT (NIL) -7 NIL NIL) (-281 595955 595987 596069 "ESCONT1" 596172 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-280 595630 595680 595780 "ES2" 595899 NIL ES2 (NIL T T) -7 NIL NIL) (-279 595260 595318 595427 "ES1" 595566 NIL ES1 (NIL T T) -7 NIL NIL) (-278 594476 594605 594781 "ERROR" 595104 T ERROR (NIL) -7 NIL NIL) (-277 587979 594335 594426 "EQTBL" 594431 NIL EQTBL (NIL T T) -8 NIL NIL) (-276 580416 583297 584744 "EQ" 586565 NIL -3806 (NIL T) -8 NIL NIL) (-275 580048 580105 580214 "EQ2" 580353 NIL EQ2 (NIL T T) -7 NIL NIL) (-274 575340 576386 577479 "EP" 578987 NIL EP (NIL T) -7 NIL NIL) (-273 573922 574223 574540 "ENV" 575043 T ENV (NIL) -8 NIL NIL) (-272 573082 573646 573674 "ENTIRER" 573679 T ENTIRER (NIL) -9 NIL 573724) (-271 569538 571037 571407 "EMR" 572881 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-270 568682 568867 568921 "ELTAGG" 569301 NIL ELTAGG (NIL T T) -9 NIL 569512) (-269 568401 568463 568604 "ELTAGG-" 568609 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-268 568190 568219 568273 "ELTAB" 568357 NIL ELTAB (NIL T T) -9 NIL NIL) (-267 567316 567462 567661 "ELFUTS" 568041 NIL ELFUTS (NIL T T) -7 NIL NIL) (-266 567058 567114 567142 "ELEMFUN" 567247 T ELEMFUN (NIL) -9 NIL NIL) (-265 566928 566949 567017 "ELEMFUN-" 567022 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-264 561820 565029 565070 "ELAGG" 566010 NIL ELAGG (NIL T) -9 NIL 566473) (-263 560105 560539 561202 "ELAGG-" 561207 NIL ELAGG- (NIL T T) -8 NIL NIL) (-262 558762 559042 559337 "ELABEXPR" 559830 T ELABEXPR (NIL) -8 NIL NIL) (-261 551628 553429 554256 "EFUPXS" 558038 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-260 545078 546879 547689 "EFULS" 550904 NIL EFULS (NIL T T T) -8 NIL NIL) (-259 542509 542867 543345 "EFSTRUC" 544710 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-258 531581 533146 534706 "EF" 541024 NIL EF (NIL T T) -7 NIL NIL) (-257 530682 531066 531215 "EAB" 531452 T EAB (NIL) -8 NIL NIL) (-256 529895 530641 530669 "E04UCFA" 530674 T E04UCFA (NIL) -8 NIL NIL) (-255 529108 529854 529882 "E04NAFA" 529887 T E04NAFA (NIL) -8 NIL NIL) (-254 528321 529067 529095 "E04MBFA" 529100 T E04MBFA (NIL) -8 NIL NIL) (-253 527534 528280 528308 "E04JAFA" 528313 T E04JAFA (NIL) -8 NIL NIL) (-252 526749 527493 527521 "E04GCFA" 527526 T E04GCFA (NIL) -8 NIL NIL) (-251 525964 526708 526736 "E04FDFA" 526741 T E04FDFA (NIL) -8 NIL NIL) (-250 525177 525923 525951 "E04DGFA" 525956 T E04DGFA (NIL) -8 NIL NIL) (-249 519362 520707 522069 "E04AGNT" 523835 T E04AGNT (NIL) -7 NIL NIL) (-248 518089 518569 518609 "DVARCAT" 519084 NIL DVARCAT (NIL T) -9 NIL 519282) (-247 517293 517505 517819 "DVARCAT-" 517824 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-246 510155 517095 517222 "DSMP" 517227 NIL DSMP (NIL T T T) -8 NIL NIL) (-245 504965 506100 507168 "DROPT" 509107 T DROPT (NIL) -8 NIL NIL) (-244 504630 504689 504787 "DROPT1" 504900 NIL DROPT1 (NIL T) -7 NIL NIL) (-243 499745 500871 502008 "DROPT0" 503513 T DROPT0 (NIL) -7 NIL NIL) (-242 498090 498415 498801 "DRAWPT" 499379 T DRAWPT (NIL) -7 NIL NIL) (-241 492677 493600 494679 "DRAW" 497064 NIL DRAW (NIL T) -7 NIL NIL) (-240 492310 492363 492481 "DRAWHACK" 492618 NIL DRAWHACK (NIL T) -7 NIL NIL) (-239 491041 491310 491601 "DRAWCX" 492039 T DRAWCX (NIL) -7 NIL NIL) (-238 490559 490627 490777 "DRAWCURV" 490967 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-237 481030 482989 485104 "DRAWCFUN" 488464 T DRAWCFUN (NIL) -7 NIL NIL) (-236 477844 479726 479767 "DQAGG" 480396 NIL DQAGG (NIL T) -9 NIL 480669) (-235 466351 473089 473171 "DPOLCAT" 475009 NIL DPOLCAT (NIL T T T T) -9 NIL 475553) (-234 461191 462537 464494 "DPOLCAT-" 464499 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-233 453987 461053 461150 "DPMO" 461155 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-232 446686 453768 453934 "DPMM" 453939 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-231 446106 446309 446423 "DOMAIN" 446592 T DOMAIN (NIL) -8 NIL NIL) (-230 439818 445743 445894 "DMP" 446007 NIL DMP (NIL NIL T) -8 NIL NIL) (-229 439418 439474 439618 "DLP" 439756 NIL DLP (NIL T) -7 NIL NIL) (-228 433062 438519 438746 "DLIST" 439223 NIL DLIST (NIL T) -8 NIL NIL) (-227 429909 431918 431959 "DLAGG" 432509 NIL DLAGG (NIL T) -9 NIL 432738) (-226 428619 429311 429339 "DIVRING" 429489 T DIVRING (NIL) -9 NIL 429597) (-225 427607 427860 428253 "DIVRING-" 428258 NIL DIVRING- (NIL T) -8 NIL NIL) (-224 425709 426066 426472 "DISPLAY" 427221 T DISPLAY (NIL) -7 NIL NIL) (-223 419598 425623 425686 "DIRPROD" 425691 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-222 418446 418649 418914 "DIRPROD2" 419391 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-221 407965 413970 414023 "DIRPCAT" 414431 NIL DIRPCAT (NIL NIL T) -9 NIL 415270) (-220 405291 405933 406814 "DIRPCAT-" 407151 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-219 404578 404738 404924 "DIOSP" 405125 T DIOSP (NIL) -7 NIL NIL) (-218 401281 403491 403532 "DIOPS" 403966 NIL DIOPS (NIL T) -9 NIL 404195) (-217 400830 400944 401135 "DIOPS-" 401140 NIL DIOPS- (NIL T T) -8 NIL NIL) (-216 399702 400340 400368 "DIFRING" 400555 T DIFRING (NIL) -9 NIL 400664) (-215 399348 399425 399577 "DIFRING-" 399582 NIL DIFRING- (NIL T) -8 NIL NIL) (-214 397138 398420 398460 "DIFEXT" 398819 NIL DIFEXT (NIL T) -9 NIL 399112) (-213 395424 395852 396517 "DIFEXT-" 396522 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-212 392747 394957 394998 "DIAGG" 395003 NIL DIAGG (NIL T) -9 NIL 395023) (-211 392131 392288 392540 "DIAGG-" 392545 NIL DIAGG- (NIL T T) -8 NIL NIL) (-210 387596 391090 391367 "DHMATRIX" 391900 NIL DHMATRIX (NIL T) -8 NIL NIL) (-209 383208 384117 385127 "DFSFUN" 386606 T DFSFUN (NIL) -7 NIL NIL) (-208 377994 381922 382287 "DFLOAT" 382863 T DFLOAT (NIL) -8 NIL NIL) (-207 376227 376508 376903 "DFINTTLS" 377702 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-206 373260 374262 374660 "DERHAM" 375894 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-205 371109 373035 373124 "DEQUEUE" 373204 NIL DEQUEUE (NIL T) -8 NIL NIL) (-204 370327 370460 370655 "DEGRED" 370971 NIL DEGRED (NIL T T) -7 NIL NIL) (-203 366727 367472 368324 "DEFINTRF" 369555 NIL DEFINTRF (NIL T) -7 NIL NIL) (-202 364258 364727 365325 "DEFINTEF" 366246 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-201 358088 363699 363865 "DECIMAL" 364112 T DECIMAL (NIL) -8 NIL NIL) (-200 355600 356058 356564 "DDFACT" 357632 NIL DDFACT (NIL T T) -7 NIL NIL) (-199 355196 355239 355390 "DBLRESP" 355551 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-198 352906 353240 353609 "DBASE" 354954 NIL DBASE (NIL T) -8 NIL NIL) (-197 352175 352386 352532 "DATABUF" 352805 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-196 351310 352134 352162 "D03FAFA" 352167 T D03FAFA (NIL) -8 NIL NIL) (-195 350446 351269 351297 "D03EEFA" 351302 T D03EEFA (NIL) -8 NIL NIL) (-194 348396 348862 349351 "D03AGNT" 349977 T D03AGNT (NIL) -7 NIL NIL) (-193 347714 348355 348383 "D02EJFA" 348388 T D02EJFA (NIL) -8 NIL NIL) (-192 347032 347673 347701 "D02CJFA" 347706 T D02CJFA (NIL) -8 NIL NIL) (-191 346350 346991 347019 "D02BHFA" 347024 T D02BHFA (NIL) -8 NIL NIL) (-190 345668 346309 346337 "D02BBFA" 346342 T D02BBFA (NIL) -8 NIL NIL) (-189 338866 340454 342060 "D02AGNT" 344082 T D02AGNT (NIL) -7 NIL NIL) (-188 336635 337157 337703 "D01WGTS" 338340 T D01WGTS (NIL) -7 NIL NIL) (-187 335738 336594 336622 "D01TRNS" 336627 T D01TRNS (NIL) -8 NIL NIL) (-186 334841 335697 335725 "D01GBFA" 335730 T D01GBFA (NIL) -8 NIL NIL) (-185 333944 334800 334828 "D01FCFA" 334833 T D01FCFA (NIL) -8 NIL NIL) (-184 333047 333903 333931 "D01ASFA" 333936 T D01ASFA (NIL) -8 NIL NIL) (-183 332150 333006 333034 "D01AQFA" 333039 T D01AQFA (NIL) -8 NIL NIL) (-182 331253 332109 332137 "D01APFA" 332142 T D01APFA (NIL) -8 NIL NIL) (-181 330356 331212 331240 "D01ANFA" 331245 T D01ANFA (NIL) -8 NIL NIL) (-180 329459 330315 330343 "D01AMFA" 330348 T D01AMFA (NIL) -8 NIL NIL) (-179 328562 329418 329446 "D01ALFA" 329451 T D01ALFA (NIL) -8 NIL NIL) (-178 327665 328521 328549 "D01AKFA" 328554 T D01AKFA (NIL) -8 NIL NIL) (-177 326768 327624 327652 "D01AJFA" 327657 T D01AJFA (NIL) -8 NIL NIL) (-176 320072 321621 323180 "D01AGNT" 325229 T D01AGNT (NIL) -7 NIL NIL) (-175 319409 319537 319689 "CYCLOTOM" 319940 T CYCLOTOM (NIL) -7 NIL NIL) (-174 316144 316857 317584 "CYCLES" 318702 T CYCLES (NIL) -7 NIL NIL) (-173 315456 315590 315761 "CVMP" 316005 NIL CVMP (NIL T) -7 NIL NIL) (-172 313237 313495 313870 "CTRIGMNP" 315184 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-171 312748 312937 313036 "CTORCALL" 313158 T CTORCALL (NIL) -8 NIL NIL) (-170 312122 312221 312374 "CSTTOOLS" 312645 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-169 307921 308578 309336 "CRFP" 311434 NIL CRFP (NIL T T) -7 NIL NIL) (-168 306968 307153 307381 "CRAPACK" 307725 NIL CRAPACK (NIL T) -7 NIL NIL) (-167 306352 306453 306657 "CPMATCH" 306844 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-166 306077 306105 306211 "CPIMA" 306318 NIL CPIMA (NIL T T T) -7 NIL NIL) (-165 302441 303113 303831 "COORDSYS" 305412 NIL COORDSYS (NIL T) -7 NIL NIL) (-164 301825 301954 302104 "CONTOUR" 302311 T CONTOUR (NIL) -8 NIL NIL) (-163 297686 299828 300320 "CONTFRAC" 301365 NIL CONTFRAC (NIL T) -8 NIL NIL) (-162 296840 297404 297432 "COMRING" 297437 T COMRING (NIL) -9 NIL 297488) (-161 295921 296198 296382 "COMPPROP" 296676 T COMPPROP (NIL) -8 NIL NIL) (-160 295582 295617 295745 "COMPLPAT" 295880 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-159 285563 295391 295500 "COMPLEX" 295505 NIL COMPLEX (NIL T) -8 NIL NIL) (-158 285199 285256 285363 "COMPLEX2" 285500 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-157 284917 284952 285050 "COMPFACT" 285158 NIL COMPFACT (NIL T T) -7 NIL NIL) (-156 269252 279546 279586 "COMPCAT" 280588 NIL COMPCAT (NIL T) -9 NIL 281981) (-155 258767 261691 265318 "COMPCAT-" 265674 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-154 258498 258526 258628 "COMMUPC" 258733 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-153 258293 258326 258385 "COMMONOP" 258459 T COMMONOP (NIL) -7 NIL NIL) (-152 257876 258044 258131 "COMM" 258226 T COMM (NIL) -8 NIL NIL) (-151 257125 257319 257347 "COMBOPC" 257685 T COMBOPC (NIL) -9 NIL 257860) (-150 256021 256231 256473 "COMBINAT" 256915 NIL COMBINAT (NIL T) -7 NIL NIL) (-149 252219 252792 253432 "COMBF" 255443 NIL COMBF (NIL T T) -7 NIL NIL) (-148 251005 251335 251570 "COLOR" 252004 T COLOR (NIL) -8 NIL NIL) (-147 250645 250692 250817 "CMPLXRT" 250952 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-146 246147 247175 248255 "CLIP" 249585 T CLIP (NIL) -7 NIL NIL) (-145 244485 245255 245493 "CLIF" 245975 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-144 240708 242632 242673 "CLAGG" 243602 NIL CLAGG (NIL T) -9 NIL 244138) (-143 239130 239587 240170 "CLAGG-" 240175 NIL CLAGG- (NIL T T) -8 NIL NIL) (-142 238674 238759 238899 "CINTSLPE" 239039 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-141 236175 236646 237194 "CHVAR" 238202 NIL CHVAR (NIL T T T) -7 NIL NIL) (-140 235398 235962 235990 "CHARZ" 235995 T CHARZ (NIL) -9 NIL 236009) (-139 235152 235192 235270 "CHARPOL" 235352 NIL CHARPOL (NIL T) -7 NIL NIL) (-138 234259 234856 234884 "CHARNZ" 234931 T CHARNZ (NIL) -9 NIL 234986) (-137 232284 232949 233284 "CHAR" 233944 T CHAR (NIL) -8 NIL NIL) (-136 232010 232071 232099 "CFCAT" 232210 T CFCAT (NIL) -9 NIL NIL) (-135 231255 231366 231548 "CDEN" 231894 NIL CDEN (NIL T T T) -7 NIL NIL) (-134 227247 230408 230688 "CCLASS" 230995 T CCLASS (NIL) -8 NIL NIL) (-133 227166 227192 227227 "CATEGORY" 227232 T -10 (NIL) -8 NIL NIL) (-132 222218 223195 223948 "CARTEN" 226469 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-131 221326 221474 221695 "CARTEN2" 222065 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-130 219624 220478 220734 "CARD" 221090 T CARD (NIL) -8 NIL NIL) (-129 218997 219325 219353 "CACHSET" 219485 T CACHSET (NIL) -9 NIL 219562) (-128 218494 218790 218818 "CABMON" 218868 T CABMON (NIL) -9 NIL 218924) (-127 217662 218041 218184 "BYTE" 218371 T BYTE (NIL) -8 NIL NIL) (-126 213610 217609 217643 "BYTEARY" 217648 T BYTEARY (NIL) -8 NIL NIL) (-125 211167 213302 213409 "BTREE" 213536 NIL BTREE (NIL T) -8 NIL NIL) (-124 208665 210815 210937 "BTOURN" 211077 NIL BTOURN (NIL T) -8 NIL NIL) (-123 206084 208137 208178 "BTCAT" 208246 NIL BTCAT (NIL T) -9 NIL 208323) (-122 205751 205831 205980 "BTCAT-" 205985 NIL BTCAT- (NIL T T) -8 NIL NIL) (-121 201044 204895 204923 "BTAGG" 205145 T BTAGG (NIL) -9 NIL 205306) (-120 200534 200659 200865 "BTAGG-" 200870 NIL BTAGG- (NIL T) -8 NIL NIL) (-119 197578 199812 200027 "BSTREE" 200351 NIL BSTREE (NIL T) -8 NIL NIL) (-118 196716 196842 197026 "BRILL" 197434 NIL BRILL (NIL T) -7 NIL NIL) (-117 193418 195445 195486 "BRAGG" 196135 NIL BRAGG (NIL T) -9 NIL 196392) (-116 191947 192353 192908 "BRAGG-" 192913 NIL BRAGG- (NIL T T) -8 NIL NIL) (-115 185155 191293 191477 "BPADICRT" 191795 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-114 183459 185092 185137 "BPADIC" 185142 NIL BPADIC (NIL NIL) -8 NIL NIL) (-113 183159 183189 183302 "BOUNDZRO" 183423 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-112 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL) (-111 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL) (-110 175019 175705 175905 "BOOLEAN" 176115 T BOOLEAN (NIL) -8 NIL NIL) (-109 174386 174764 174816 "BMODULE" 174821 NIL BMODULE (NIL T T) -9 NIL 174885) (-108 170216 174184 174257 "BITS" 174333 T BITS (NIL) -8 NIL NIL) (-107 169313 169748 169900 "BINFILE" 170084 T BINFILE (NIL) -8 NIL NIL) (-106 168725 168847 168989 "BINDING" 169191 T BINDING (NIL) -8 NIL NIL) (-105 162559 168169 168334 "BINARY" 168580 T BINARY (NIL) -8 NIL NIL) (-104 160387 161815 161856 "BGAGG" 162116 NIL BGAGG (NIL T) -9 NIL 162253) (-103 160218 160250 160341 "BGAGG-" 160346 NIL BGAGG- (NIL T T) -8 NIL NIL) (-102 159316 159602 159807 "BFUNCT" 160033 T BFUNCT (NIL) -8 NIL NIL) (-101 158011 158189 158476 "BEZOUT" 159140 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-100 154528 156863 157193 "BBTREE" 157714 NIL BBTREE (NIL T) -8 NIL NIL) (-99 154266 154319 154345 "BASTYPE" 154462 T BASTYPE (NIL) -9 NIL NIL) (-98 154121 154150 154220 "BASTYPE-" 154225 NIL BASTYPE- (NIL T) -8 NIL NIL) (-97 153559 153635 153785 "BALFACT" 154032 NIL BALFACT (NIL T T) -7 NIL NIL) (-96 152381 152978 153163 "AUTOMOR" 153404 NIL AUTOMOR (NIL T) -8 NIL NIL) (-95 152107 152112 152138 "ATTREG" 152143 T ATTREG (NIL) -9 NIL NIL) (-94 150386 150804 151156 "ATTRBUT" 151773 T ATTRBUT (NIL) -8 NIL NIL) (-93 149922 150035 150061 "ATRIG" 150262 T ATRIG (NIL) -9 NIL NIL) (-92 149731 149772 149859 "ATRIG-" 149864 NIL ATRIG- (NIL T) -8 NIL NIL) (-91 149457 149600 149626 "ASTCAT" 149631 T ASTCAT (NIL) -9 NIL 149661) (-90 149254 149297 149389 "ASTCAT-" 149394 NIL ASTCAT- (NIL T) -8 NIL NIL) (-89 147451 149030 149118 "ASTACK" 149197 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145956 146253 146618 "ASSOCEQ" 147133 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144988 145615 145739 "ASP9" 145863 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144752 144936 144975 "ASP8" 144980 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143621 144357 144499 "ASP80" 144641 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142520 143256 143388 "ASP7" 143520 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141474 142197 142315 "ASP78" 142433 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140443 141154 141271 "ASP77" 141388 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139355 140081 140212 "ASP74" 140343 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138255 138990 139122 "ASP73" 139254 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137210 137932 138050 "ASP6" 138168 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136158 136887 137005 "ASP55" 137123 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135108 135832 135951 "ASP50" 136070 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134196 134809 134919 "ASP4" 135029 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133284 133897 134007 "ASP49" 134117 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132069 132823 132991 "ASP42" 133173 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130846 131602 131772 "ASP41" 131956 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129796 130523 130641 "ASP35" 130759 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129561 129744 129783 "ASP34" 129788 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129298 129365 129441 "ASP33" 129516 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128193 128933 129065 "ASP31" 129197 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127958 128141 128180 "ASP30" 128185 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127693 127762 127838 "ASP29" 127913 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127458 127641 127680 "ASP28" 127685 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127223 127406 127445 "ASP27" 127450 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126307 126921 127032 "ASP24" 127143 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125223 125948 126078 "ASP20" 126208 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124311 124924 125034 "ASP1" 125144 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123255 123985 124104 "ASP19" 124223 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122992 123059 123135 "ASP12" 123210 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121844 122591 122735 "ASP10" 122879 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119743 121688 121779 "ARRAY2" 121784 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115559 119391 119505 "ARRAY1" 119660 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114591 114764 114985 "ARRAY12" 115382 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108951 110822 110897 "ARR2CAT" 113527 NIL ARR2CAT (NIL T T T) -9 NIL 114285) (-54 106385 107129 108083 "ARR2CAT-" 108088 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105137 105289 105594 "APPRULE" 106221 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 3138561 3138566 3138571 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3138546 3138551 3138556 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3138531 3138536 3138541 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3138516 3138521 3138526 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1207 3137692 3138391 3138468 "ZMOD" 3138473 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1206 3136802 3136966 3137175 "ZLINDEP" 3137524 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1205 3126206 3127951 3129903 "ZDSOLVE" 3134951 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1204 3125452 3125593 3125782 "YSTREAM" 3126052 NIL YSTREAM (NIL T) -7 NIL NIL) (-1203 3123267 3124757 3124960 "XRPOLY" 3125295 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1202 3119775 3121058 3121640 "XPR" 3122731 NIL XPR (NIL T T) -8 NIL NIL) (-1201 3117535 3119110 3119313 "XPOLY" 3119606 NIL XPOLY (NIL T) -8 NIL NIL) (-1200 3115393 3116727 3116781 "XPOLYC" 3117066 NIL XPOLYC (NIL T T) -9 NIL 3117179) (-1199 3111811 3113910 3114298 "XPBWPOLY" 3115051 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1198 3107804 3110052 3110094 "XF" 3110715 NIL XF (NIL T) -9 NIL 3111114) (-1197 3107425 3107513 3107682 "XF-" 3107687 NIL XF- (NIL T T) -8 NIL NIL) (-1196 3102849 3104104 3104158 "XFALG" 3106306 NIL XFALG (NIL T T) -9 NIL 3107093) (-1195 3101986 3102090 3102294 "XEXPPKG" 3102741 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1194 3100131 3101837 3101932 "XDPOLY" 3101937 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1193 3099054 3099620 3099662 "XALG" 3099724 NIL XALG (NIL T) -9 NIL 3099843) (-1192 3092530 3097038 3097531 "WUTSET" 3098646 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1191 3090388 3091149 3091500 "WP" 3092312 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1190 3089274 3089472 3089767 "WFFINTBS" 3090185 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1189 3087178 3087605 3088067 "WEIER" 3088846 NIL WEIER (NIL T) -7 NIL NIL) (-1188 3086327 3086751 3086793 "VSPACE" 3086929 NIL VSPACE (NIL T) -9 NIL 3087003) (-1187 3086165 3086192 3086283 "VSPACE-" 3086288 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1186 3085911 3085954 3086025 "VOID" 3086116 T VOID (NIL) -8 NIL NIL) (-1185 3084047 3084406 3084812 "VIEW" 3085527 T VIEW (NIL) -7 NIL NIL) (-1184 3080472 3081110 3081847 "VIEWDEF" 3083332 T VIEWDEF (NIL) -7 NIL NIL) (-1183 3069810 3072020 3074193 "VIEW3D" 3078321 T VIEW3D (NIL) -8 NIL NIL) (-1182 3062092 3063721 3065300 "VIEW2D" 3068253 T VIEW2D (NIL) -8 NIL NIL) (-1181 3057501 3061862 3061954 "VECTOR" 3062035 NIL VECTOR (NIL T) -8 NIL NIL) (-1180 3056078 3056337 3056655 "VECTOR2" 3057231 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1179 3049618 3053870 3053913 "VECTCAT" 3054901 NIL VECTCAT (NIL T) -9 NIL 3055485) (-1178 3048632 3048886 3049276 "VECTCAT-" 3049281 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1177 3048113 3048283 3048403 "VARIABLE" 3048547 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1176 3048046 3048051 3048081 "UTYPE" 3048086 T UTYPE (NIL) -9 NIL NIL) (-1175 3046881 3047035 3047296 "UTSODETL" 3047872 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1174 3044321 3044781 3045305 "UTSODE" 3046422 NIL UTSODE (NIL T T) -7 NIL NIL) (-1173 3036211 3041961 3042449 "UTS" 3043890 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1172 3027602 3032921 3032963 "UTSCAT" 3034064 NIL UTSCAT (NIL T) -9 NIL 3034821) (-1171 3024957 3025673 3026661 "UTSCAT-" 3026666 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1170 3024588 3024631 3024762 "UTS2" 3024908 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1169 3018864 3021429 3021472 "URAGG" 3023542 NIL URAGG (NIL T) -9 NIL 3024264) (-1168 3015803 3016666 3017789 "URAGG-" 3017794 NIL URAGG- (NIL T T) -8 NIL NIL) (-1167 3011535 3014420 3014891 "UPXSSING" 3015467 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1166 3003511 3010656 3010936 "UPXS" 3011312 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1165 2996625 3003416 3003487 "UPXSCONS" 3003492 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1164 2986999 2993744 2993805 "UPXSCCA" 2994454 NIL UPXSCCA (NIL T T) -9 NIL 2994695) (-1163 2986638 2986723 2986896 "UPXSCCA-" 2986901 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1162 2976934 2983452 2983494 "UPXSCAT" 2984137 NIL UPXSCAT (NIL T) -9 NIL 2984745) (-1161 2976368 2976447 2976624 "UPXS2" 2976849 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1160 2975022 2975275 2975626 "UPSQFREE" 2976111 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1159 2968959 2971968 2972022 "UPSCAT" 2973171 NIL UPSCAT (NIL T T) -9 NIL 2973945) (-1158 2968164 2968371 2968697 "UPSCAT-" 2968702 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1157 2954296 2962287 2962329 "UPOLYC" 2964407 NIL UPOLYC (NIL T) -9 NIL 2965628) (-1156 2945626 2948051 2951197 "UPOLYC-" 2951202 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1155 2945257 2945300 2945431 "UPOLYC2" 2945577 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1154 2936722 2944826 2944963 "UP" 2945167 NIL UP (NIL NIL T) -8 NIL NIL) (-1153 2936065 2936172 2936335 "UPMP" 2936611 NIL UPMP (NIL T T) -7 NIL NIL) (-1152 2935618 2935699 2935838 "UPDIVP" 2935978 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1151 2934186 2934435 2934751 "UPDECOMP" 2935367 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1150 2933421 2933533 2933718 "UPCDEN" 2934070 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1149 2932944 2933013 2933160 "UP2" 2933346 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1148 2931461 2932148 2932425 "UNISEG" 2932702 NIL UNISEG (NIL T) -8 NIL NIL) (-1147 2930676 2930803 2931008 "UNISEG2" 2931304 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1146 2929736 2929916 2930142 "UNIFACT" 2930492 NIL UNIFACT (NIL T) -7 NIL NIL) (-1145 2913717 2928917 2929167 "ULS" 2929543 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1144 2901767 2913622 2913693 "ULSCONS" 2913698 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1143 2884602 2896530 2896591 "ULSCCAT" 2897303 NIL ULSCCAT (NIL T T) -9 NIL 2897599) (-1142 2883653 2883898 2884285 "ULSCCAT-" 2884290 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1141 2873728 2880160 2880202 "ULSCAT" 2881058 NIL ULSCAT (NIL T) -9 NIL 2881788) (-1140 2873162 2873241 2873418 "ULS2" 2873643 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1139 2871604 2872527 2872557 "UFD" 2872769 T UFD (NIL) -9 NIL 2872883) (-1138 2871398 2871444 2871539 "UFD-" 2871544 NIL UFD- (NIL T) -8 NIL NIL) (-1137 2870480 2870663 2870879 "UDVO" 2871204 T UDVO (NIL) -7 NIL NIL) (-1136 2868296 2868705 2869176 "UDPO" 2870044 NIL UDPO (NIL T) -7 NIL NIL) (-1135 2868229 2868234 2868264 "TYPE" 2868269 T TYPE (NIL) -9 NIL NIL) (-1134 2867200 2867402 2867642 "TWOFACT" 2868023 NIL TWOFACT (NIL T) -7 NIL NIL) (-1133 2866138 2866475 2866738 "TUPLE" 2866972 NIL TUPLE (NIL T) -8 NIL NIL) (-1132 2863829 2864348 2864887 "TUBETOOL" 2865621 T TUBETOOL (NIL) -7 NIL NIL) (-1131 2862678 2862883 2863124 "TUBE" 2863622 NIL TUBE (NIL T) -8 NIL NIL) (-1130 2857448 2861656 2861938 "TS" 2862430 NIL TS (NIL T) -8 NIL NIL) (-1129 2846152 2850244 2850340 "TSETCAT" 2855574 NIL TSETCAT (NIL T T T T) -9 NIL 2857105) (-1128 2840887 2842485 2844375 "TSETCAT-" 2844380 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1127 2835150 2835996 2836938 "TRMANIP" 2840023 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1126 2834591 2834654 2834817 "TRIMAT" 2835082 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1125 2832397 2832634 2832997 "TRIGMNIP" 2834340 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1124 2831917 2832030 2832060 "TRIGCAT" 2832273 T TRIGCAT (NIL) -9 NIL NIL) (-1123 2831586 2831665 2831806 "TRIGCAT-" 2831811 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1122 2828485 2830446 2830726 "TREE" 2831341 NIL TREE (NIL T) -8 NIL NIL) (-1121 2827759 2828287 2828317 "TRANFUN" 2828352 T TRANFUN (NIL) -9 NIL 2828418) (-1120 2827038 2827229 2827509 "TRANFUN-" 2827514 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1119 2826842 2826874 2826935 "TOPSP" 2826999 T TOPSP (NIL) -7 NIL NIL) (-1118 2826194 2826309 2826462 "TOOLSIGN" 2826723 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1117 2824855 2825371 2825610 "TEXTFILE" 2825977 T TEXTFILE (NIL) -8 NIL NIL) (-1116 2822720 2823234 2823672 "TEX" 2824439 T TEX (NIL) -8 NIL NIL) (-1115 2822501 2822532 2822604 "TEX1" 2822683 NIL TEX1 (NIL T) -7 NIL NIL) (-1114 2822149 2822212 2822302 "TEMUTL" 2822433 T TEMUTL (NIL) -7 NIL NIL) (-1113 2820303 2820583 2820908 "TBCMPPK" 2821872 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1112 2812192 2818464 2818520 "TBAGG" 2818920 NIL TBAGG (NIL T T) -9 NIL 2819131) (-1111 2807262 2808750 2810504 "TBAGG-" 2810509 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1110 2806646 2806753 2806898 "TANEXP" 2807151 NIL TANEXP (NIL T) -7 NIL NIL) (-1109 2800147 2806503 2806596 "TABLE" 2806601 NIL TABLE (NIL T T) -8 NIL NIL) (-1108 2799559 2799658 2799796 "TABLEAU" 2800044 NIL TABLEAU (NIL T) -8 NIL NIL) (-1107 2794167 2795387 2796635 "TABLBUMP" 2798345 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1106 2793595 2793695 2793823 "SYSTEM" 2794061 T SYSTEM (NIL) -7 NIL NIL) (-1105 2790058 2790753 2791536 "SYSSOLP" 2792846 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1104 2786349 2787057 2787791 "SYNTAX" 2789346 T SYNTAX (NIL) -8 NIL NIL) (-1103 2783483 2784091 2784729 "SYMTAB" 2785733 T SYMTAB (NIL) -8 NIL NIL) (-1102 2778732 2779634 2780617 "SYMS" 2782522 T SYMS (NIL) -8 NIL NIL) (-1101 2776011 2778192 2778421 "SYMPOLY" 2778537 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1100 2775531 2775606 2775728 "SYMFUNC" 2775923 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1099 2771508 2772768 2773590 "SYMBOL" 2774731 T SYMBOL (NIL) -8 NIL NIL) (-1098 2765047 2766736 2768456 "SWITCH" 2769810 T SWITCH (NIL) -8 NIL NIL) (-1097 2758323 2763874 2764176 "SUTS" 2764802 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1096 2750298 2757444 2757724 "SUPXS" 2758100 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1095 2741835 2749919 2750044 "SUP" 2750207 NIL SUP (NIL T) -8 NIL NIL) (-1094 2740994 2741121 2741338 "SUPFRACF" 2741703 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1093 2740619 2740678 2740789 "SUP2" 2740929 NIL SUP2 (NIL T T) -7 NIL NIL) (-1092 2739037 2739311 2739673 "SUMRF" 2740318 NIL SUMRF (NIL T) -7 NIL NIL) (-1091 2738354 2738420 2738618 "SUMFS" 2738958 NIL SUMFS (NIL T T) -7 NIL NIL) (-1090 2722375 2737535 2737785 "SULS" 2738161 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1089 2721697 2721900 2722040 "SUCH" 2722283 NIL SUCH (NIL T T) -8 NIL NIL) (-1088 2715624 2716636 2717594 "SUBSPACE" 2720785 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1087 2715054 2715144 2715308 "SUBRESP" 2715512 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1086 2708423 2709719 2711030 "STTF" 2713790 NIL STTF (NIL T) -7 NIL NIL) (-1085 2702596 2703716 2704863 "STTFNC" 2707323 NIL STTFNC (NIL T) -7 NIL NIL) (-1084 2693947 2695814 2697607 "STTAYLOR" 2700837 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1083 2687191 2693811 2693894 "STRTBL" 2693899 NIL STRTBL (NIL T) -8 NIL NIL) (-1082 2682582 2687146 2687177 "STRING" 2687182 T STRING (NIL) -8 NIL NIL) (-1081 2677471 2681956 2681986 "STRICAT" 2682045 T STRICAT (NIL) -9 NIL 2682107) (-1080 2670185 2674994 2675614 "STREAM" 2676886 NIL STREAM (NIL T) -8 NIL NIL) (-1079 2669695 2669772 2669916 "STREAM3" 2670102 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1078 2668677 2668860 2669095 "STREAM2" 2669508 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1077 2668365 2668417 2668510 "STREAM1" 2668619 NIL STREAM1 (NIL T) -7 NIL NIL) (-1076 2667381 2667562 2667793 "STINPROD" 2668181 NIL STINPROD (NIL T) -7 NIL NIL) (-1075 2666960 2667144 2667174 "STEP" 2667254 T STEP (NIL) -9 NIL 2667332) (-1074 2660503 2666859 2666936 "STBL" 2666941 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1073 2655679 2659726 2659769 "STAGG" 2659922 NIL STAGG (NIL T) -9 NIL 2660011) (-1072 2653381 2653983 2654855 "STAGG-" 2654860 NIL STAGG- (NIL T T) -8 NIL NIL) (-1071 2651576 2653151 2653243 "STACK" 2653324 NIL STACK (NIL T) -8 NIL NIL) (-1070 2644307 2649723 2650178 "SREGSET" 2651206 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1069 2636747 2638115 2639627 "SRDCMPK" 2642913 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1068 2629715 2634188 2634218 "SRAGG" 2635521 T SRAGG (NIL) -9 NIL 2636129) (-1067 2628732 2628987 2629366 "SRAGG-" 2629371 NIL SRAGG- (NIL T) -8 NIL NIL) (-1066 2623227 2627651 2628078 "SQMATRIX" 2628351 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1065 2616979 2619947 2620673 "SPLTREE" 2622573 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1064 2612969 2613635 2614281 "SPLNODE" 2616405 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1063 2612016 2612249 2612279 "SPFCAT" 2612723 T SPFCAT (NIL) -9 NIL NIL) (-1062 2610753 2610963 2611227 "SPECOUT" 2611774 T SPECOUT (NIL) -7 NIL NIL) (-1061 2610514 2610554 2610623 "SPADPRSR" 2610706 T SPADPRSR (NIL) -7 NIL NIL) (-1060 2602537 2604284 2604326 "SPACEC" 2608649 NIL SPACEC (NIL T) -9 NIL 2610465) (-1059 2600709 2602470 2602518 "SPACE3" 2602523 NIL SPACE3 (NIL T) -8 NIL NIL) (-1058 2599461 2599632 2599923 "SORTPAK" 2600514 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1057 2597517 2597820 2598238 "SOLVETRA" 2599125 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1056 2596528 2596750 2597024 "SOLVESER" 2597290 NIL SOLVESER (NIL T) -7 NIL NIL) (-1055 2591748 2592629 2593631 "SOLVERAD" 2595580 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1054 2587563 2588172 2588901 "SOLVEFOR" 2591115 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1053 2581862 2586914 2587010 "SNTSCAT" 2587015 NIL SNTSCAT (NIL T T T T) -9 NIL 2587085) (-1052 2576012 2580193 2580583 "SMTS" 2581552 NIL SMTS (NIL T T T) -8 NIL NIL) (-1051 2570468 2575901 2575977 "SMP" 2575982 NIL SMP (NIL T T) -8 NIL NIL) (-1050 2568627 2568928 2569326 "SMITH" 2570165 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1049 2561638 2565788 2565890 "SMATCAT" 2567230 NIL SMATCAT (NIL NIL T T T) -9 NIL 2567779) (-1048 2558579 2559402 2560579 "SMATCAT-" 2560584 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1047 2556293 2557816 2557859 "SKAGG" 2558120 NIL SKAGG (NIL T) -9 NIL 2558255) (-1046 2552397 2555397 2555675 "SINT" 2556037 T SINT (NIL) -8 NIL NIL) (-1045 2552169 2552207 2552273 "SIMPAN" 2552353 T SIMPAN (NIL) -7 NIL NIL) (-1044 2551685 2551871 2551970 "SIG" 2552092 T SIG (NIL) -8 NIL NIL) (-1043 2550523 2550744 2551019 "SIGNRF" 2551444 NIL SIGNRF (NIL T) -7 NIL NIL) (-1042 2549332 2549483 2549773 "SIGNEF" 2550352 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1041 2547022 2547476 2547982 "SHP" 2548873 NIL SHP (NIL T NIL) -7 NIL NIL) (-1040 2540961 2546923 2546999 "SHDP" 2547004 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1039 2540561 2540727 2540757 "SGROUP" 2540850 T SGROUP (NIL) -9 NIL 2540912) (-1038 2540419 2540445 2540518 "SGROUP-" 2540523 NIL SGROUP- (NIL T) -8 NIL NIL) (-1037 2537255 2537952 2538675 "SGCF" 2539718 T SGCF (NIL) -7 NIL NIL) (-1036 2531652 2536704 2536800 "SFRTCAT" 2536805 NIL SFRTCAT (NIL T T T T) -9 NIL 2536844) (-1035 2525094 2526109 2527244 "SFRGCD" 2530635 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1034 2518241 2519312 2520497 "SFQCMPK" 2524027 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1033 2517863 2517952 2518062 "SFORT" 2518182 NIL SFORT (NIL T T) -8 NIL NIL) (-1032 2517008 2517703 2517824 "SEXOF" 2517829 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1031 2516142 2516889 2516957 "SEX" 2516962 T SEX (NIL) -8 NIL NIL) (-1030 2510919 2511608 2511703 "SEXCAT" 2515474 NIL SEXCAT (NIL T T T T T) -9 NIL 2516093) (-1029 2508099 2510853 2510901 "SET" 2510906 NIL SET (NIL T) -8 NIL NIL) (-1028 2506350 2506812 2507117 "SETMN" 2507840 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1027 2505958 2506084 2506114 "SETCAT" 2506231 T SETCAT (NIL) -9 NIL 2506315) (-1026 2505738 2505790 2505889 "SETCAT-" 2505894 NIL SETCAT- (NIL T) -8 NIL NIL) (-1025 2502126 2504200 2504243 "SETAGG" 2505113 NIL SETAGG (NIL T) -9 NIL 2505453) (-1024 2501584 2501700 2501937 "SETAGG-" 2501942 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1023 2500788 2501081 2501142 "SEGXCAT" 2501428 NIL SEGXCAT (NIL T T) -9 NIL 2501548) (-1022 2499844 2500454 2500636 "SEG" 2500641 NIL SEG (NIL T) -8 NIL NIL) (-1021 2498751 2498964 2499007 "SEGCAT" 2499589 NIL SEGCAT (NIL T) -9 NIL 2499827) (-1020 2497800 2498130 2498330 "SEGBIND" 2498586 NIL SEGBIND (NIL T) -8 NIL NIL) (-1019 2497421 2497480 2497593 "SEGBIND2" 2497735 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1018 2496640 2496766 2496970 "SEG2" 2497265 NIL SEG2 (NIL T T) -7 NIL NIL) (-1017 2496077 2496575 2496622 "SDVAR" 2496627 NIL SDVAR (NIL T) -8 NIL NIL) (-1016 2488375 2495850 2495978 "SDPOL" 2495983 NIL SDPOL (NIL T) -8 NIL NIL) (-1015 2486968 2487234 2487553 "SCPKG" 2488090 NIL SCPKG (NIL T) -7 NIL NIL) (-1014 2486104 2486284 2486484 "SCOPE" 2486790 T SCOPE (NIL) -8 NIL NIL) (-1013 2485325 2485458 2485637 "SCACHE" 2485959 NIL SCACHE (NIL T) -7 NIL NIL) (-1012 2484764 2485085 2485170 "SAOS" 2485262 T SAOS (NIL) -8 NIL NIL) (-1011 2484329 2484364 2484537 "SAERFFC" 2484723 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1010 2478308 2484226 2484306 "SAE" 2484311 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1009 2477901 2477936 2478095 "SAEFACT" 2478267 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1008 2476222 2476536 2476937 "RURPK" 2477567 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1007 2474862 2475141 2475452 "RULESET" 2476056 NIL RULESET (NIL T T T) -8 NIL NIL) (-1006 2472060 2472563 2473026 "RULE" 2474544 NIL RULE (NIL T T T) -8 NIL NIL) (-1005 2471699 2471854 2471937 "RULECOLD" 2472012 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1004 2466562 2467356 2468275 "RSETGCD" 2470898 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1003 2455848 2460900 2460996 "RSETCAT" 2465088 NIL RSETCAT (NIL T T T T) -9 NIL 2466185) (-1002 2453776 2454315 2455138 "RSETCAT-" 2455143 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1001 2446177 2447552 2449071 "RSDCMPK" 2452375 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1000 2444183 2444624 2444698 "RRCC" 2445784 NIL RRCC (NIL T T) -9 NIL 2446128) (-999 2443536 2443710 2443987 "RRCC-" 2443992 NIL RRCC- (NIL T T T) -8 NIL NIL) (-998 2417949 2427528 2427592 "RPOLCAT" 2438094 NIL RPOLCAT (NIL T T T) -9 NIL 2441252) (-997 2409453 2411791 2414909 "RPOLCAT-" 2414914 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-996 2400519 2407683 2408163 "ROUTINE" 2408993 T ROUTINE (NIL) -8 NIL NIL) (-995 2397270 2400075 2400222 "ROMAN" 2400392 T ROMAN (NIL) -8 NIL NIL) (-994 2395554 2396139 2396397 "ROIRC" 2397075 NIL ROIRC (NIL T T) -8 NIL NIL) (-993 2392024 2394263 2394291 "RNS" 2394587 T RNS (NIL) -9 NIL 2394857) (-992 2390538 2390921 2391452 "RNS-" 2391525 NIL RNS- (NIL T) -8 NIL NIL) (-991 2389990 2390372 2390400 "RNG" 2390405 T RNG (NIL) -9 NIL 2390426) (-990 2389388 2389750 2389790 "RMODULE" 2389850 NIL RMODULE (NIL T) -9 NIL 2389892) (-989 2388240 2388334 2388664 "RMCAT2" 2389289 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-988 2384954 2387423 2387744 "RMATRIX" 2387975 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-987 2377951 2380185 2380297 "RMATCAT" 2383606 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2384588) (-986 2377330 2377477 2377780 "RMATCAT-" 2377785 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-985 2376900 2376975 2377101 "RINTERP" 2377249 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-984 2375995 2376515 2376543 "RING" 2376653 T RING (NIL) -9 NIL 2376747) (-983 2375790 2375834 2375928 "RING-" 2375933 NIL RING- (NIL T) -8 NIL NIL) (-982 2374638 2374875 2375131 "RIDIST" 2375554 T RIDIST (NIL) -7 NIL NIL) (-981 2365958 2374110 2374314 "RGCHAIN" 2374486 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-980 2362963 2363577 2364245 "RF" 2365322 NIL RF (NIL T) -7 NIL NIL) (-979 2362612 2362675 2362776 "RFFACTOR" 2362894 NIL RFFACTOR (NIL T) -7 NIL NIL) (-978 2362340 2362375 2362470 "RFFACT" 2362571 NIL RFFACT (NIL T) -7 NIL NIL) (-977 2360470 2360834 2361214 "RFDIST" 2361980 T RFDIST (NIL) -7 NIL NIL) (-976 2359928 2360020 2360180 "RETSOL" 2360372 NIL RETSOL (NIL T T) -7 NIL NIL) (-975 2359521 2359601 2359642 "RETRACT" 2359832 NIL RETRACT (NIL T) -9 NIL NIL) (-974 2359373 2359398 2359482 "RETRACT-" 2359487 NIL RETRACT- (NIL T T) -8 NIL NIL) (-973 2352231 2359030 2359155 "RESULT" 2359268 T RESULT (NIL) -8 NIL NIL) (-972 2350862 2351505 2351702 "RESRING" 2352134 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-971 2350502 2350551 2350647 "RESLATC" 2350799 NIL RESLATC (NIL T) -7 NIL NIL) (-970 2350211 2350245 2350350 "REPSQ" 2350461 NIL REPSQ (NIL T) -7 NIL NIL) (-969 2347642 2348222 2348822 "REP" 2349631 T REP (NIL) -7 NIL NIL) (-968 2347343 2347377 2347486 "REPDB" 2347601 NIL REPDB (NIL T) -7 NIL NIL) (-967 2341288 2342667 2343887 "REP2" 2346155 NIL REP2 (NIL T) -7 NIL NIL) (-966 2337694 2338375 2339180 "REP1" 2340515 NIL REP1 (NIL T) -7 NIL NIL) (-965 2330438 2335853 2336306 "REGSET" 2337324 NIL REGSET (NIL T T T T) -8 NIL NIL) (-964 2329259 2329594 2329842 "REF" 2330223 NIL REF (NIL T) -8 NIL NIL) (-963 2328640 2328743 2328908 "REDORDER" 2329143 NIL REDORDER (NIL T T) -7 NIL NIL) (-962 2324674 2327874 2328095 "RECLOS" 2328471 NIL RECLOS (NIL T) -8 NIL NIL) (-961 2323731 2323912 2324125 "REALSOLV" 2324481 T REALSOLV (NIL) -7 NIL NIL) (-960 2323579 2323620 2323648 "REAL" 2323653 T REAL (NIL) -9 NIL 2323688) (-959 2320070 2320872 2321754 "REAL0Q" 2322744 NIL REAL0Q (NIL T) -7 NIL NIL) (-958 2315681 2316669 2317728 "REAL0" 2319051 NIL REAL0 (NIL T) -7 NIL NIL) (-957 2315089 2315161 2315366 "RDIV" 2315603 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-956 2314162 2314336 2314547 "RDIST" 2314911 NIL RDIST (NIL T) -7 NIL NIL) (-955 2312766 2313053 2313422 "RDETRS" 2313870 NIL RDETRS (NIL T T) -7 NIL NIL) (-954 2310587 2311041 2311576 "RDETR" 2312308 NIL RDETR (NIL T T) -7 NIL NIL) (-953 2309203 2309481 2309882 "RDEEFS" 2310303 NIL RDEEFS (NIL T T) -7 NIL NIL) (-952 2307703 2308009 2308438 "RDEEF" 2308891 NIL RDEEF (NIL T T) -7 NIL NIL) (-951 2302053 2304920 2304948 "RCFIELD" 2306225 T RCFIELD (NIL) -9 NIL 2306955) (-950 2300122 2300626 2301319 "RCFIELD-" 2301392 NIL RCFIELD- (NIL T) -8 NIL NIL) (-949 2296454 2298239 2298280 "RCAGG" 2299351 NIL RCAGG (NIL T) -9 NIL 2299816) (-948 2296085 2296179 2296339 "RCAGG-" 2296344 NIL RCAGG- (NIL T T) -8 NIL NIL) (-947 2295429 2295541 2295703 "RATRET" 2295969 NIL RATRET (NIL T) -7 NIL NIL) (-946 2294986 2295053 2295172 "RATFACT" 2295357 NIL RATFACT (NIL T) -7 NIL NIL) (-945 2294301 2294421 2294571 "RANDSRC" 2294856 T RANDSRC (NIL) -7 NIL NIL) (-944 2294038 2294082 2294153 "RADUTIL" 2294250 T RADUTIL (NIL) -7 NIL NIL) (-943 2287110 2292781 2293098 "RADIX" 2293753 NIL RADIX (NIL NIL) -8 NIL NIL) (-942 2278771 2286954 2287082 "RADFF" 2287087 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-941 2278423 2278498 2278526 "RADCAT" 2278683 T RADCAT (NIL) -9 NIL NIL) (-940 2278208 2278256 2278353 "RADCAT-" 2278358 NIL RADCAT- (NIL T) -8 NIL NIL) (-939 2276359 2277983 2278072 "QUEUE" 2278152 NIL QUEUE (NIL T) -8 NIL NIL) (-938 2272941 2276296 2276341 "QUAT" 2276346 NIL QUAT (NIL T) -8 NIL NIL) (-937 2272579 2272622 2272749 "QUATCT2" 2272892 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-936 2266458 2269753 2269793 "QUATCAT" 2270572 NIL QUATCAT (NIL T) -9 NIL 2271337) (-935 2262602 2263639 2265026 "QUATCAT-" 2265120 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-934 2260123 2261687 2261728 "QUAGG" 2262103 NIL QUAGG (NIL T) -9 NIL 2262278) (-933 2259048 2259521 2259693 "QFORM" 2259995 NIL QFORM (NIL NIL T) -8 NIL NIL) (-932 2250407 2255603 2255643 "QFCAT" 2256301 NIL QFCAT (NIL T) -9 NIL 2257294) (-931 2245979 2247180 2248771 "QFCAT-" 2248865 NIL QFCAT- (NIL T T) -8 NIL NIL) (-930 2245617 2245660 2245787 "QFCAT2" 2245930 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-929 2245077 2245187 2245317 "QEQUAT" 2245507 T QEQUAT (NIL) -8 NIL NIL) (-928 2238244 2239315 2240498 "QCMPACK" 2244010 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-927 2235820 2236241 2236669 "QALGSET" 2237899 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-926 2235065 2235239 2235471 "QALGSET2" 2235640 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-925 2233756 2233979 2234296 "PWFFINTB" 2234838 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-924 2231944 2232112 2232465 "PUSHVAR" 2233570 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-923 2227862 2228916 2228957 "PTRANFN" 2230841 NIL PTRANFN (NIL T) -9 NIL NIL) (-922 2226274 2226565 2226886 "PTPACK" 2227573 NIL PTPACK (NIL T) -7 NIL NIL) (-921 2225910 2225967 2226074 "PTFUNC2" 2226211 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-920 2220387 2224728 2224768 "PTCAT" 2225136 NIL PTCAT (NIL T) -9 NIL 2225298) (-919 2220045 2220080 2220204 "PSQFR" 2220346 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-918 2218640 2218938 2219272 "PSEUDLIN" 2219743 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-917 2205447 2207812 2210135 "PSETPK" 2216400 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-916 2198534 2201248 2201342 "PSETCAT" 2204323 NIL PSETCAT (NIL T T T T) -9 NIL 2205137) (-915 2196372 2197006 2197825 "PSETCAT-" 2197830 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-914 2195721 2195886 2195914 "PSCURVE" 2196182 T PSCURVE (NIL) -9 NIL 2196349) (-913 2192217 2193699 2193763 "PSCAT" 2194599 NIL PSCAT (NIL T T T) -9 NIL 2194839) (-912 2191281 2191497 2191896 "PSCAT-" 2191901 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-911 2189933 2190566 2190780 "PRTITION" 2191087 T PRTITION (NIL) -8 NIL NIL) (-910 2179031 2181237 2183425 "PRS" 2187795 NIL PRS (NIL T T) -7 NIL NIL) (-909 2176890 2178382 2178422 "PRQAGG" 2178605 NIL PRQAGG (NIL T) -9 NIL 2178707) (-908 2176461 2176563 2176591 "PROPLOG" 2176776 T PROPLOG (NIL) -9 NIL NIL) (-907 2173584 2174149 2174676 "PROPFRML" 2175966 NIL PROPFRML (NIL T) -8 NIL NIL) (-906 2173044 2173154 2173284 "PROPERTY" 2173474 T PROPERTY (NIL) -8 NIL NIL) (-905 2167129 2171210 2172030 "PRODUCT" 2172270 NIL PRODUCT (NIL T T) -8 NIL NIL) (-904 2164449 2166589 2166822 "PR" 2166940 NIL PR (NIL T T) -8 NIL NIL) (-903 2164245 2164277 2164336 "PRINT" 2164410 T PRINT (NIL) -7 NIL NIL) (-902 2163585 2163702 2163854 "PRIMES" 2164125 NIL PRIMES (NIL T) -7 NIL NIL) (-901 2161650 2162051 2162517 "PRIMELT" 2163164 NIL PRIMELT (NIL T) -7 NIL NIL) (-900 2161379 2161428 2161456 "PRIMCAT" 2161580 T PRIMCAT (NIL) -9 NIL NIL) (-899 2157540 2161317 2161362 "PRIMARR" 2161367 NIL PRIMARR (NIL T) -8 NIL NIL) (-898 2156547 2156725 2156953 "PRIMARR2" 2157358 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-897 2156190 2156246 2156357 "PREASSOC" 2156485 NIL PREASSOC (NIL T T) -7 NIL NIL) (-896 2155665 2155798 2155826 "PPCURVE" 2156031 T PPCURVE (NIL) -9 NIL 2156167) (-895 2155287 2155460 2155543 "PORTNUM" 2155602 T PORTNUM (NIL) -8 NIL NIL) (-894 2152646 2153045 2153637 "POLYROOT" 2154868 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-893 2146598 2152252 2152411 "POLY" 2152519 NIL POLY (NIL T) -8 NIL NIL) (-892 2145983 2146041 2146274 "POLYLIFT" 2146534 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-891 2142268 2142717 2143345 "POLYCATQ" 2145528 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-890 2129355 2134706 2134770 "POLYCAT" 2138255 NIL POLYCAT (NIL T T T) -9 NIL 2140182) (-889 2122806 2124667 2127050 "POLYCAT-" 2127055 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-888 2122395 2122463 2122582 "POLY2UP" 2122732 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-887 2122031 2122088 2122195 "POLY2" 2122332 NIL POLY2 (NIL T T) -7 NIL NIL) (-886 2120716 2120955 2121231 "POLUTIL" 2121805 NIL POLUTIL (NIL T T) -7 NIL NIL) (-885 2119078 2119355 2119685 "POLTOPOL" 2120438 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-884 2114601 2119015 2119060 "POINT" 2119065 NIL POINT (NIL T) -8 NIL NIL) (-883 2112788 2113145 2113520 "PNTHEORY" 2114246 T PNTHEORY (NIL) -7 NIL NIL) (-882 2111216 2111513 2111922 "PMTOOLS" 2112486 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-881 2110809 2110887 2111004 "PMSYM" 2111132 NIL PMSYM (NIL T) -7 NIL NIL) (-880 2110319 2110388 2110562 "PMQFCAT" 2110734 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-879 2109674 2109784 2109940 "PMPRED" 2110196 NIL PMPRED (NIL T) -7 NIL NIL) (-878 2109070 2109156 2109317 "PMPREDFS" 2109575 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-877 2107716 2107924 2108308 "PMPLCAT" 2108832 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-876 2107248 2107327 2107479 "PMLSAGG" 2107631 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-875 2106725 2106801 2106981 "PMKERNEL" 2107166 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-874 2106342 2106417 2106530 "PMINS" 2106644 NIL PMINS (NIL T) -7 NIL NIL) (-873 2105772 2105841 2106056 "PMFS" 2106267 NIL PMFS (NIL T T T) -7 NIL NIL) (-872 2105003 2105121 2105325 "PMDOWN" 2105649 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-871 2104166 2104325 2104507 "PMASS" 2104841 T PMASS (NIL) -7 NIL NIL) (-870 2103440 2103551 2103714 "PMASSFS" 2104052 NIL PMASSFS (NIL T T) -7 NIL NIL) (-869 2103095 2103163 2103257 "PLOTTOOL" 2103366 T PLOTTOOL (NIL) -7 NIL NIL) (-868 2097717 2098906 2100054 "PLOT" 2101967 T PLOT (NIL) -8 NIL NIL) (-867 2093531 2094565 2095486 "PLOT3D" 2096816 T PLOT3D (NIL) -8 NIL NIL) (-866 2092443 2092620 2092855 "PLOT1" 2093335 NIL PLOT1 (NIL T) -7 NIL NIL) (-865 2067837 2072509 2077360 "PLEQN" 2087709 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-864 2067155 2067277 2067457 "PINTERP" 2067702 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-863 2066848 2066895 2066998 "PINTERPA" 2067102 NIL PINTERPA (NIL T T) -7 NIL NIL) (-862 2066133 2066654 2066741 "PI" 2066781 T PI (NIL) -8 NIL NIL) (-861 2064569 2065510 2065538 "PID" 2065720 T PID (NIL) -9 NIL 2065854) (-860 2064294 2064331 2064419 "PICOERCE" 2064526 NIL PICOERCE (NIL T) -7 NIL NIL) (-859 2063614 2063753 2063929 "PGROEB" 2064150 NIL PGROEB (NIL T) -7 NIL NIL) (-858 2059201 2060015 2060920 "PGE" 2062729 T PGE (NIL) -7 NIL NIL) (-857 2057325 2057571 2057937 "PGCD" 2058918 NIL PGCD (NIL T T T T) -7 NIL NIL) (-856 2056663 2056766 2056927 "PFRPAC" 2057209 NIL PFRPAC (NIL T) -7 NIL NIL) (-855 2053343 2055211 2055564 "PFR" 2056342 NIL PFR (NIL T) -8 NIL NIL) (-854 2051732 2051976 2052301 "PFOTOOLS" 2053090 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-853 2050265 2050504 2050855 "PFOQ" 2051489 NIL PFOQ (NIL T T T) -7 NIL NIL) (-852 2048742 2048954 2049316 "PFO" 2050049 NIL PFO (NIL T T T T T) -7 NIL NIL) (-851 2045330 2048631 2048700 "PF" 2048705 NIL PF (NIL NIL) -8 NIL NIL) (-850 2042803 2044040 2044068 "PFECAT" 2044653 T PFECAT (NIL) -9 NIL 2045037) (-849 2042248 2042402 2042616 "PFECAT-" 2042621 NIL PFECAT- (NIL T) -8 NIL NIL) (-848 2040852 2041103 2041404 "PFBRU" 2041997 NIL PFBRU (NIL T T) -7 NIL NIL) (-847 2038719 2039070 2039502 "PFBR" 2040503 NIL PFBR (NIL T T T T) -7 NIL NIL) (-846 2034635 2036095 2036771 "PERM" 2038076 NIL PERM (NIL T) -8 NIL NIL) (-845 2029901 2030842 2031712 "PERMGRP" 2033798 NIL PERMGRP (NIL T) -8 NIL NIL) (-844 2028034 2028965 2029006 "PERMCAT" 2029452 NIL PERMCAT (NIL T) -9 NIL 2029757) (-843 2027689 2027730 2027853 "PERMAN" 2027987 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-842 2025129 2027258 2027389 "PENDTREE" 2027591 NIL PENDTREE (NIL T) -8 NIL NIL) (-841 2023246 2023980 2024021 "PDRING" 2024678 NIL PDRING (NIL T) -9 NIL 2024963) (-840 2022349 2022567 2022929 "PDRING-" 2022934 NIL PDRING- (NIL T T) -8 NIL NIL) (-839 2019490 2020241 2020932 "PDEPROB" 2021678 T PDEPROB (NIL) -8 NIL NIL) (-838 2017061 2017557 2018106 "PDEPACK" 2018961 T PDEPACK (NIL) -7 NIL NIL) (-837 2015973 2016163 2016414 "PDECOMP" 2016860 NIL PDECOMP (NIL T T) -7 NIL NIL) (-836 2013585 2014400 2014428 "PDECAT" 2015213 T PDECAT (NIL) -9 NIL 2015924) (-835 2013338 2013371 2013460 "PCOMP" 2013546 NIL PCOMP (NIL T T) -7 NIL NIL) (-834 2011545 2012141 2012437 "PBWLB" 2013068 NIL PBWLB (NIL T) -8 NIL NIL) (-833 2004053 2005622 2006958 "PATTERN" 2010230 NIL PATTERN (NIL T) -8 NIL NIL) (-832 2003685 2003742 2003851 "PATTERN2" 2003990 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-831 2001442 2001830 2002287 "PATTERN1" 2003274 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-830 1998837 1999391 1999872 "PATRES" 2001007 NIL PATRES (NIL T T) -8 NIL NIL) (-829 1998401 1998468 1998600 "PATRES2" 1998764 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-828 1996298 1996698 1997103 "PATMATCH" 1998070 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-827 1995835 1996018 1996059 "PATMAB" 1996166 NIL PATMAB (NIL T) -9 NIL 1996249) (-826 1994380 1994689 1994947 "PATLRES" 1995640 NIL PATLRES (NIL T T T) -8 NIL NIL) (-825 1993926 1994049 1994090 "PATAB" 1994095 NIL PATAB (NIL T) -9 NIL 1994267) (-824 1991407 1991939 1992512 "PARTPERM" 1993373 T PARTPERM (NIL) -7 NIL NIL) (-823 1991028 1991091 1991193 "PARSURF" 1991338 NIL PARSURF (NIL T) -8 NIL NIL) (-822 1990660 1990717 1990826 "PARSU2" 1990965 NIL PARSU2 (NIL T T) -7 NIL NIL) (-821 1990424 1990464 1990531 "PARSER" 1990613 T PARSER (NIL) -7 NIL NIL) (-820 1990045 1990108 1990210 "PARSCURV" 1990355 NIL PARSCURV (NIL T) -8 NIL NIL) (-819 1989677 1989734 1989843 "PARSC2" 1989982 NIL PARSC2 (NIL T T) -7 NIL NIL) (-818 1989316 1989374 1989471 "PARPCURV" 1989613 NIL PARPCURV (NIL T) -8 NIL NIL) (-817 1988948 1989005 1989114 "PARPC2" 1989253 NIL PARPC2 (NIL T T) -7 NIL NIL) (-816 1988468 1988554 1988673 "PAN2EXPR" 1988849 T PAN2EXPR (NIL) -7 NIL NIL) (-815 1987274 1987589 1987817 "PALETTE" 1988260 T PALETTE (NIL) -8 NIL NIL) (-814 1985742 1986279 1986639 "PAIR" 1986960 NIL PAIR (NIL T T) -8 NIL NIL) (-813 1979657 1985001 1985195 "PADICRC" 1985597 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-812 1972930 1979003 1979187 "PADICRAT" 1979505 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-811 1971280 1972867 1972912 "PADIC" 1972917 NIL PADIC (NIL NIL) -8 NIL NIL) (-810 1968529 1970059 1970099 "PADICCT" 1970680 NIL PADICCT (NIL NIL) -9 NIL 1970962) (-809 1967486 1967686 1967954 "PADEPAC" 1968316 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-808 1966698 1966831 1967037 "PADE" 1967348 NIL PADE (NIL T T T) -7 NIL NIL) (-807 1964755 1965541 1965856 "OWP" 1966466 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-806 1963864 1964360 1964532 "OVAR" 1964623 NIL OVAR (NIL NIL) -8 NIL NIL) (-805 1963128 1963249 1963410 "OUT" 1963723 T OUT (NIL) -7 NIL NIL) (-804 1952182 1954353 1956523 "OUTFORM" 1960978 T OUTFORM (NIL) -8 NIL NIL) (-803 1951590 1951911 1952000 "OSI" 1952113 T OSI (NIL) -8 NIL NIL) (-802 1951147 1951459 1951487 "OSGROUP" 1951492 T OSGROUP (NIL) -9 NIL 1951514) (-801 1949892 1950119 1950404 "ORTHPOL" 1950894 NIL ORTHPOL (NIL T) -7 NIL NIL) (-800 1947309 1949553 1949691 "OREUP" 1949835 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-799 1944751 1947002 1947128 "ORESUP" 1947251 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-798 1942286 1942786 1943346 "OREPCTO" 1944240 NIL OREPCTO (NIL T T) -7 NIL NIL) (-797 1936240 1938402 1938442 "OREPCAT" 1940763 NIL OREPCAT (NIL T) -9 NIL 1941866) (-796 1933388 1934170 1935227 "OREPCAT-" 1935232 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-795 1932566 1932838 1932866 "ORDSET" 1933175 T ORDSET (NIL) -9 NIL 1933339) (-794 1932085 1932207 1932400 "ORDSET-" 1932405 NIL ORDSET- (NIL T) -8 NIL NIL) (-793 1930743 1931500 1931528 "ORDRING" 1931730 T ORDRING (NIL) -9 NIL 1931854) (-792 1930388 1930482 1930626 "ORDRING-" 1930631 NIL ORDRING- (NIL T) -8 NIL NIL) (-791 1929795 1930232 1930260 "ORDMON" 1930265 T ORDMON (NIL) -9 NIL 1930286) (-790 1928957 1929104 1929299 "ORDFUNS" 1929644 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-789 1928469 1928828 1928856 "ORDFIN" 1928861 T ORDFIN (NIL) -9 NIL 1928882) (-788 1925067 1927055 1927464 "ORDCOMP" 1928093 NIL ORDCOMP (NIL T) -8 NIL NIL) (-787 1924333 1924460 1924646 "ORDCOMP2" 1924927 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-786 1920840 1921723 1922560 "OPTPROB" 1923516 T OPTPROB (NIL) -8 NIL NIL) (-785 1917682 1918311 1919005 "OPTPACK" 1920166 T OPTPACK (NIL) -7 NIL NIL) (-784 1915408 1916144 1916172 "OPTCAT" 1916987 T OPTCAT (NIL) -9 NIL 1917633) (-783 1915176 1915215 1915281 "OPQUERY" 1915362 T OPQUERY (NIL) -7 NIL NIL) (-782 1912358 1913503 1914003 "OP" 1914708 NIL OP (NIL T) -8 NIL NIL) (-781 1909209 1911155 1911524 "ONECOMP" 1912022 NIL ONECOMP (NIL T) -8 NIL NIL) (-780 1908514 1908629 1908803 "ONECOMP2" 1909081 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-779 1907933 1908039 1908169 "OMSERVER" 1908404 T OMSERVER (NIL) -7 NIL NIL) (-778 1904822 1907374 1907414 "OMSAGG" 1907475 NIL OMSAGG (NIL T) -9 NIL 1907539) (-777 1903445 1903708 1903990 "OMPKG" 1904560 T OMPKG (NIL) -7 NIL NIL) (-776 1902875 1902978 1903006 "OM" 1903305 T OM (NIL) -9 NIL NIL) (-775 1901460 1902427 1902595 "OMLO" 1902756 NIL OMLO (NIL T T) -8 NIL NIL) (-774 1900390 1900537 1900763 "OMEXPR" 1901286 NIL OMEXPR (NIL T) -7 NIL NIL) (-773 1899708 1899936 1900072 "OMERR" 1900274 T OMERR (NIL) -8 NIL NIL) (-772 1898886 1899129 1899289 "OMERRK" 1899568 T OMERRK (NIL) -8 NIL NIL) (-771 1898364 1898563 1898671 "OMENC" 1898798 T OMENC (NIL) -8 NIL NIL) (-770 1892259 1893444 1894615 "OMDEV" 1897213 T OMDEV (NIL) -8 NIL NIL) (-769 1891328 1891499 1891693 "OMCONN" 1892085 T OMCONN (NIL) -8 NIL NIL) (-768 1889988 1890930 1890958 "OINTDOM" 1890963 T OINTDOM (NIL) -9 NIL 1890984) (-767 1885796 1886980 1887695 "OFMONOID" 1889305 NIL OFMONOID (NIL T) -8 NIL NIL) (-766 1885234 1885733 1885778 "ODVAR" 1885783 NIL ODVAR (NIL T) -8 NIL NIL) (-765 1882444 1884731 1884916 "ODR" 1885109 NIL ODR (NIL T T NIL) -8 NIL NIL) (-764 1874796 1882223 1882347 "ODPOL" 1882352 NIL ODPOL (NIL T) -8 NIL NIL) (-763 1868705 1874668 1874773 "ODP" 1874778 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-762 1867471 1867686 1867961 "ODETOOLS" 1868479 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-761 1864440 1865096 1865812 "ODESYS" 1866804 NIL ODESYS (NIL T T) -7 NIL NIL) (-760 1859344 1860252 1861275 "ODERTRIC" 1863515 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-759 1858770 1858852 1859046 "ODERED" 1859256 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-758 1855672 1856220 1856895 "ODERAT" 1858193 NIL ODERAT (NIL T T) -7 NIL NIL) (-757 1852640 1853104 1853700 "ODEPRRIC" 1855201 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-756 1850509 1851078 1851587 "ODEPROB" 1852151 T ODEPROB (NIL) -8 NIL NIL) (-755 1847041 1847524 1848170 "ODEPRIM" 1849988 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-754 1846294 1846396 1846654 "ODEPAL" 1846933 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-753 1842496 1843277 1844131 "ODEPACK" 1845460 T ODEPACK (NIL) -7 NIL NIL) (-752 1841533 1841640 1841868 "ODEINT" 1842385 NIL ODEINT (NIL T T) -7 NIL NIL) (-751 1835634 1837059 1838506 "ODEIFTBL" 1840106 T ODEIFTBL (NIL) -8 NIL NIL) (-750 1830978 1831764 1832722 "ODEEF" 1834793 NIL ODEEF (NIL T T) -7 NIL NIL) (-749 1830315 1830404 1830633 "ODECONST" 1830883 NIL ODECONST (NIL T T T) -7 NIL NIL) (-748 1828473 1829106 1829134 "ODECAT" 1829737 T ODECAT (NIL) -9 NIL 1830266) (-747 1825391 1828185 1828304 "OCT" 1828386 NIL OCT (NIL T) -8 NIL NIL) (-746 1825029 1825072 1825199 "OCTCT2" 1825342 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-745 1819907 1822301 1822341 "OC" 1823437 NIL OC (NIL T) -9 NIL 1824294) (-744 1817134 1817882 1818872 "OC-" 1818966 NIL OC- (NIL T T) -8 NIL NIL) (-743 1816513 1816955 1816983 "OCAMON" 1816988 T OCAMON (NIL) -9 NIL 1817009) (-742 1816071 1816386 1816414 "OASGP" 1816419 T OASGP (NIL) -9 NIL 1816439) (-741 1815359 1815822 1815850 "OAMONS" 1815890 T OAMONS (NIL) -9 NIL 1815933) (-740 1814800 1815207 1815235 "OAMON" 1815240 T OAMON (NIL) -9 NIL 1815260) (-739 1814105 1814597 1814625 "OAGROUP" 1814630 T OAGROUP (NIL) -9 NIL 1814650) (-738 1813795 1813845 1813933 "NUMTUBE" 1814049 NIL NUMTUBE (NIL T) -7 NIL NIL) (-737 1807368 1808886 1810422 "NUMQUAD" 1812279 T NUMQUAD (NIL) -7 NIL NIL) (-736 1803124 1804112 1805137 "NUMODE" 1806363 T NUMODE (NIL) -7 NIL NIL) (-735 1800528 1801374 1801402 "NUMINT" 1802319 T NUMINT (NIL) -9 NIL 1803075) (-734 1799476 1799673 1799891 "NUMFMT" 1800330 T NUMFMT (NIL) -7 NIL NIL) (-733 1785855 1788792 1791322 "NUMERIC" 1796985 NIL NUMERIC (NIL T) -7 NIL NIL) (-732 1780254 1785306 1785400 "NTSCAT" 1785405 NIL NTSCAT (NIL T T T T) -9 NIL 1785444) (-731 1779448 1779613 1779806 "NTPOLFN" 1780093 NIL NTPOLFN (NIL T) -7 NIL NIL) (-730 1767310 1776290 1777100 "NSUP" 1778670 NIL NSUP (NIL T) -8 NIL NIL) (-729 1766946 1767003 1767110 "NSUP2" 1767247 NIL NSUP2 (NIL T T) -7 NIL NIL) (-728 1756954 1766725 1766855 "NSMP" 1766860 NIL NSMP (NIL T T) -8 NIL NIL) (-727 1755386 1755687 1756044 "NREP" 1756642 NIL NREP (NIL T) -7 NIL NIL) (-726 1753977 1754229 1754587 "NPCOEF" 1755129 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-725 1753043 1753158 1753374 "NORMRETR" 1753858 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-724 1751090 1751380 1751788 "NORMPK" 1752751 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-723 1750775 1750803 1750927 "NORMMA" 1751056 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-722 1750602 1750732 1750761 "NONE" 1750766 T NONE (NIL) -8 NIL NIL) (-721 1750391 1750420 1750489 "NONE1" 1750566 NIL NONE1 (NIL T) -7 NIL NIL) (-720 1749876 1749938 1750123 "NODE1" 1750323 NIL NODE1 (NIL T T) -7 NIL NIL) (-719 1748216 1749039 1749294 "NNI" 1749641 T NNI (NIL) -8 NIL NIL) (-718 1746636 1746949 1747313 "NLINSOL" 1747884 NIL NLINSOL (NIL T) -7 NIL NIL) (-717 1742803 1743771 1744693 "NIPROB" 1745734 T NIPROB (NIL) -8 NIL NIL) (-716 1741560 1741794 1742096 "NFINTBAS" 1742565 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-715 1740268 1740499 1740780 "NCODIV" 1741328 NIL NCODIV (NIL T T) -7 NIL NIL) (-714 1740030 1740067 1740142 "NCNTFRAC" 1740225 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-713 1738210 1738574 1738994 "NCEP" 1739655 NIL NCEP (NIL T) -7 NIL NIL) (-712 1737122 1737861 1737889 "NASRING" 1737999 T NASRING (NIL) -9 NIL 1738073) (-711 1736917 1736961 1737055 "NASRING-" 1737060 NIL NASRING- (NIL T) -8 NIL NIL) (-710 1736071 1736570 1736598 "NARNG" 1736715 T NARNG (NIL) -9 NIL 1736806) (-709 1735763 1735830 1735964 "NARNG-" 1735969 NIL NARNG- (NIL T) -8 NIL NIL) (-708 1734642 1734849 1735084 "NAGSP" 1735548 T NAGSP (NIL) -7 NIL NIL) (-707 1726066 1727712 1729347 "NAGS" 1733027 T NAGS (NIL) -7 NIL NIL) (-706 1724630 1724934 1725261 "NAGF07" 1725759 T NAGF07 (NIL) -7 NIL NIL) (-705 1719212 1720492 1721788 "NAGF04" 1723354 T NAGF04 (NIL) -7 NIL NIL) (-704 1712244 1713842 1715459 "NAGF02" 1717615 T NAGF02 (NIL) -7 NIL NIL) (-703 1707508 1708598 1709705 "NAGF01" 1711157 T NAGF01 (NIL) -7 NIL NIL) (-702 1701168 1702726 1704303 "NAGE04" 1705951 T NAGE04 (NIL) -7 NIL NIL) (-701 1692409 1694512 1696624 "NAGE02" 1699076 T NAGE02 (NIL) -7 NIL NIL) (-700 1688402 1689339 1690293 "NAGE01" 1691475 T NAGE01 (NIL) -7 NIL NIL) (-699 1686209 1686740 1687295 "NAGD03" 1687867 T NAGD03 (NIL) -7 NIL NIL) (-698 1677995 1679914 1681859 "NAGD02" 1684284 T NAGD02 (NIL) -7 NIL NIL) (-697 1671854 1673267 1674695 "NAGD01" 1676587 T NAGD01 (NIL) -7 NIL NIL) (-696 1668111 1668921 1669746 "NAGC06" 1671049 T NAGC06 (NIL) -7 NIL NIL) (-695 1666588 1666917 1667270 "NAGC05" 1667778 T NAGC05 (NIL) -7 NIL NIL) (-694 1665972 1666089 1666231 "NAGC02" 1666466 T NAGC02 (NIL) -7 NIL NIL) (-693 1665034 1665591 1665631 "NAALG" 1665710 NIL NAALG (NIL T) -9 NIL 1665771) (-692 1664869 1664898 1664988 "NAALG-" 1664993 NIL NAALG- (NIL T T) -8 NIL NIL) (-691 1658819 1659927 1661114 "MULTSQFR" 1663765 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-690 1658138 1658213 1658397 "MULTFACT" 1658731 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-689 1651378 1655243 1655295 "MTSCAT" 1656355 NIL MTSCAT (NIL T T) -9 NIL 1656869) (-688 1651090 1651144 1651236 "MTHING" 1651318 NIL MTHING (NIL T) -7 NIL NIL) (-687 1650882 1650915 1650975 "MSYSCMD" 1651050 T MSYSCMD (NIL) -7 NIL NIL) (-686 1646994 1649637 1649957 "MSET" 1650595 NIL MSET (NIL T) -8 NIL NIL) (-685 1644090 1646556 1646597 "MSETAGG" 1646602 NIL MSETAGG (NIL T) -9 NIL 1646636) (-684 1639992 1641488 1642229 "MRING" 1643393 NIL MRING (NIL T T) -8 NIL NIL) (-683 1639562 1639629 1639758 "MRF2" 1639919 NIL MRF2 (NIL T T T) -7 NIL NIL) (-682 1639180 1639215 1639359 "MRATFAC" 1639521 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-681 1636792 1637087 1637518 "MPRFF" 1638885 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-680 1630858 1636647 1636743 "MPOLY" 1636748 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-679 1630348 1630383 1630591 "MPCPF" 1630817 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-678 1629864 1629907 1630090 "MPC3" 1630299 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-677 1629065 1629146 1629365 "MPC2" 1629779 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-676 1627366 1627703 1628093 "MONOTOOL" 1628725 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-675 1626618 1626909 1626937 "MONOID" 1627156 T MONOID (NIL) -9 NIL 1627303) (-674 1626164 1626283 1626464 "MONOID-" 1626469 NIL MONOID- (NIL T) -8 NIL NIL) (-673 1617230 1623131 1623190 "MONOGEN" 1623864 NIL MONOGEN (NIL T T) -9 NIL 1624320) (-672 1614448 1615183 1616183 "MONOGEN-" 1616302 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-671 1613308 1613728 1613756 "MONADWU" 1614148 T MONADWU (NIL) -9 NIL 1614386) (-670 1612680 1612839 1613087 "MONADWU-" 1613092 NIL MONADWU- (NIL T) -8 NIL NIL) (-669 1612066 1612284 1612312 "MONAD" 1612519 T MONAD (NIL) -9 NIL 1612631) (-668 1611751 1611829 1611961 "MONAD-" 1611966 NIL MONAD- (NIL T) -8 NIL NIL) (-667 1610067 1610664 1610943 "MOEBIUS" 1611504 NIL MOEBIUS (NIL T) -8 NIL NIL) (-666 1609461 1609839 1609879 "MODULE" 1609884 NIL MODULE (NIL T) -9 NIL 1609910) (-665 1609029 1609125 1609315 "MODULE-" 1609320 NIL MODULE- (NIL T T) -8 NIL NIL) (-664 1606746 1607395 1607721 "MODRING" 1608854 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-663 1603748 1604867 1605384 "MODOP" 1606278 NIL MODOP (NIL T T) -8 NIL NIL) (-662 1601935 1602387 1602728 "MODMONOM" 1603547 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-661 1591660 1600139 1600561 "MODMON" 1601563 NIL MODMON (NIL T T) -8 NIL NIL) (-660 1588851 1590504 1590780 "MODFIELD" 1591535 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-659 1587855 1588132 1588322 "MMLFORM" 1588681 T MMLFORM (NIL) -8 NIL NIL) (-658 1587381 1587424 1587603 "MMAP" 1587806 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-657 1585662 1586395 1586435 "MLO" 1586852 NIL MLO (NIL T) -9 NIL 1587093) (-656 1583029 1583544 1584146 "MLIFT" 1585143 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-655 1582420 1582504 1582658 "MKUCFUNC" 1582940 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-654 1582019 1582089 1582212 "MKRECORD" 1582343 NIL MKRECORD (NIL T T) -7 NIL NIL) (-653 1581067 1581228 1581456 "MKFUNC" 1581830 NIL MKFUNC (NIL T) -7 NIL NIL) (-652 1580455 1580559 1580715 "MKFLCFN" 1580950 NIL MKFLCFN (NIL T) -7 NIL NIL) (-651 1579881 1580248 1580337 "MKCHSET" 1580399 NIL MKCHSET (NIL T) -8 NIL NIL) (-650 1579158 1579260 1579445 "MKBCFUNC" 1579774 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-649 1575888 1578712 1578848 "MINT" 1579042 T MINT (NIL) -8 NIL NIL) (-648 1574700 1574943 1575220 "MHROWRED" 1575643 NIL MHROWRED (NIL T) -7 NIL NIL) (-647 1570036 1573145 1573569 "MFLOAT" 1574296 T MFLOAT (NIL) -8 NIL NIL) (-646 1569393 1569469 1569640 "MFINFACT" 1569948 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-645 1565708 1566556 1567440 "MESH" 1568529 T MESH (NIL) -7 NIL NIL) (-644 1564098 1564410 1564763 "MDDFACT" 1565395 NIL MDDFACT (NIL T) -7 NIL NIL) (-643 1560941 1563258 1563299 "MDAGG" 1563554 NIL MDAGG (NIL T) -9 NIL 1563697) (-642 1550726 1560234 1560441 "MCMPLX" 1560754 T MCMPLX (NIL) -8 NIL NIL) (-641 1549867 1550013 1550213 "MCDEN" 1550575 NIL MCDEN (NIL T T) -7 NIL NIL) (-640 1547757 1548027 1548407 "MCALCFN" 1549597 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-639 1546668 1546841 1547082 "MAYBE" 1547555 NIL MAYBE (NIL T) -8 NIL NIL) (-638 1544290 1544813 1545374 "MATSTOR" 1546139 NIL MATSTOR (NIL T) -7 NIL NIL) (-637 1540299 1543665 1543912 "MATRIX" 1544075 NIL MATRIX (NIL T) -8 NIL NIL) (-636 1536068 1536772 1537508 "MATLIN" 1539656 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-635 1526266 1529404 1529480 "MATCAT" 1534318 NIL MATCAT (NIL T T T) -9 NIL 1535735) (-634 1522631 1523644 1524999 "MATCAT-" 1525004 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-633 1521233 1521386 1521717 "MATCAT2" 1522466 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-632 1519345 1519669 1520053 "MAPPKG3" 1520908 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-631 1518326 1518499 1518721 "MAPPKG2" 1519169 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-630 1516825 1517109 1517436 "MAPPKG1" 1518032 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-629 1516436 1516494 1516617 "MAPHACK3" 1516761 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-628 1516028 1516089 1516203 "MAPHACK2" 1516368 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-627 1515466 1515569 1515711 "MAPHACK1" 1515919 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-626 1513574 1514168 1514471 "MAGMA" 1515195 NIL MAGMA (NIL T) -8 NIL NIL) (-625 1510049 1511818 1512278 "M3D" 1513147 NIL M3D (NIL T) -8 NIL NIL) (-624 1504205 1508420 1508461 "LZSTAGG" 1509243 NIL LZSTAGG (NIL T) -9 NIL 1509538) (-623 1500178 1501336 1502793 "LZSTAGG-" 1502798 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-622 1497294 1498071 1498557 "LWORD" 1499724 NIL LWORD (NIL T) -8 NIL NIL) (-621 1490500 1497065 1497199 "LSQM" 1497204 NIL LSQM (NIL NIL T) -8 NIL NIL) (-620 1489724 1489863 1490091 "LSPP" 1490355 NIL LSPP (NIL T T T T) -7 NIL NIL) (-619 1487536 1487837 1488293 "LSMP" 1489413 NIL LSMP (NIL T T T T) -7 NIL NIL) (-618 1484315 1484989 1485719 "LSMP1" 1486838 NIL LSMP1 (NIL T) -7 NIL NIL) (-617 1478242 1483484 1483525 "LSAGG" 1483587 NIL LSAGG (NIL T) -9 NIL 1483665) (-616 1474937 1475861 1477074 "LSAGG-" 1477079 NIL LSAGG- (NIL T T) -8 NIL NIL) (-615 1472563 1474081 1474330 "LPOLY" 1474732 NIL LPOLY (NIL T T) -8 NIL NIL) (-614 1472145 1472230 1472353 "LPEFRAC" 1472472 NIL LPEFRAC (NIL T) -7 NIL NIL) (-613 1470492 1471239 1471492 "LO" 1471977 NIL LO (NIL T T T) -8 NIL NIL) (-612 1470146 1470258 1470286 "LOGIC" 1470397 T LOGIC (NIL) -9 NIL 1470477) (-611 1470008 1470031 1470102 "LOGIC-" 1470107 NIL LOGIC- (NIL T) -8 NIL NIL) (-610 1469201 1469341 1469534 "LODOOPS" 1469864 NIL LODOOPS (NIL T T) -7 NIL NIL) (-609 1466665 1469118 1469183 "LODO" 1469188 NIL LODO (NIL T NIL) -8 NIL NIL) (-608 1465211 1465446 1465797 "LODOF" 1466412 NIL LODOF (NIL T T) -7 NIL NIL) (-607 1461675 1464067 1464107 "LODOCAT" 1464539 NIL LODOCAT (NIL T) -9 NIL 1464750) (-606 1461409 1461467 1461593 "LODOCAT-" 1461598 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-605 1458769 1461250 1461368 "LODO2" 1461373 NIL LODO2 (NIL T T) -8 NIL NIL) (-604 1456244 1458706 1458751 "LODO1" 1458756 NIL LODO1 (NIL T) -8 NIL NIL) (-603 1455107 1455272 1455583 "LODEEF" 1456067 NIL LODEEF (NIL T T T) -7 NIL NIL) (-602 1450394 1453238 1453279 "LNAGG" 1454226 NIL LNAGG (NIL T) -9 NIL 1454670) (-601 1449541 1449755 1450097 "LNAGG-" 1450102 NIL LNAGG- (NIL T T) -8 NIL NIL) (-600 1445706 1446468 1447106 "LMOPS" 1448957 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-599 1445104 1445466 1445506 "LMODULE" 1445566 NIL LMODULE (NIL T) -9 NIL 1445608) (-598 1442350 1444749 1444872 "LMDICT" 1445014 NIL LMDICT (NIL T) -8 NIL NIL) (-597 1435577 1441296 1441594 "LIST" 1442085 NIL LIST (NIL T) -8 NIL NIL) (-596 1435102 1435176 1435315 "LIST3" 1435497 NIL LIST3 (NIL T T T) -7 NIL NIL) (-595 1434109 1434287 1434515 "LIST2" 1434920 NIL LIST2 (NIL T T) -7 NIL NIL) (-594 1432243 1432555 1432954 "LIST2MAP" 1433756 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-593 1431000 1431636 1431676 "LINEXP" 1431929 NIL LINEXP (NIL T) -9 NIL 1432077) (-592 1429647 1429907 1430204 "LINDEP" 1430752 NIL LINDEP (NIL T T) -7 NIL NIL) (-591 1426414 1427133 1427910 "LIMITRF" 1428902 NIL LIMITRF (NIL T) -7 NIL NIL) (-590 1424694 1424989 1425404 "LIMITPS" 1426109 NIL LIMITPS (NIL T T) -7 NIL NIL) (-589 1419149 1424205 1424433 "LIE" 1424515 NIL LIE (NIL T T) -8 NIL NIL) (-588 1418200 1418643 1418683 "LIECAT" 1418823 NIL LIECAT (NIL T) -9 NIL 1418974) (-587 1418041 1418068 1418156 "LIECAT-" 1418161 NIL LIECAT- (NIL T T) -8 NIL NIL) (-586 1410653 1417490 1417655 "LIB" 1417896 T LIB (NIL) -8 NIL NIL) (-585 1406290 1407171 1408106 "LGROBP" 1409770 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-584 1404156 1404430 1404792 "LF" 1406011 NIL LF (NIL T T) -7 NIL NIL) (-583 1402996 1403688 1403716 "LFCAT" 1403923 T LFCAT (NIL) -9 NIL 1404062) (-582 1399908 1400534 1401220 "LEXTRIPK" 1402362 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-581 1396679 1397478 1397981 "LEXP" 1399488 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-580 1395077 1395390 1395791 "LEADCDET" 1396361 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-579 1394270 1394344 1394572 "LAZM3PK" 1394998 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-578 1389233 1392349 1392886 "LAUPOL" 1393783 NIL LAUPOL (NIL T T) -8 NIL NIL) (-577 1388800 1388844 1389011 "LAPLACE" 1389183 NIL LAPLACE (NIL T T) -7 NIL NIL) (-576 1386774 1387901 1388152 "LA" 1388633 NIL LA (NIL T T T) -8 NIL NIL) (-575 1385881 1386431 1386471 "LALG" 1386532 NIL LALG (NIL T) -9 NIL 1386590) (-574 1385596 1385655 1385790 "LALG-" 1385795 NIL LALG- (NIL T T) -8 NIL NIL) (-573 1384506 1384693 1384990 "KOVACIC" 1385396 NIL KOVACIC (NIL T T) -7 NIL NIL) (-572 1384341 1384365 1384406 "KONVERT" 1384468 NIL KONVERT (NIL T) -9 NIL NIL) (-571 1384176 1384200 1384241 "KOERCE" 1384303 NIL KOERCE (NIL T) -9 NIL NIL) (-570 1381910 1382670 1383063 "KERNEL" 1383815 NIL KERNEL (NIL T) -8 NIL NIL) (-569 1381412 1381493 1381623 "KERNEL2" 1381824 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-568 1375264 1379952 1380006 "KDAGG" 1380383 NIL KDAGG (NIL T T) -9 NIL 1380589) (-567 1374793 1374917 1375122 "KDAGG-" 1375127 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-566 1367968 1374454 1374609 "KAFILE" 1374671 NIL KAFILE (NIL T) -8 NIL NIL) (-565 1362423 1367479 1367707 "JORDAN" 1367789 NIL JORDAN (NIL T T) -8 NIL NIL) (-564 1362152 1362211 1362298 "JAVACODE" 1362356 T JAVACODE (NIL) -8 NIL NIL) (-563 1358452 1360358 1360412 "IXAGG" 1361341 NIL IXAGG (NIL T T) -9 NIL 1361800) (-562 1357371 1357677 1358096 "IXAGG-" 1358101 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-561 1352956 1357293 1357352 "IVECTOR" 1357357 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-560 1351722 1351959 1352225 "ITUPLE" 1352723 NIL ITUPLE (NIL T) -8 NIL NIL) (-559 1350158 1350335 1350641 "ITRIGMNP" 1351544 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-558 1348903 1349107 1349390 "ITFUN3" 1349934 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-557 1348535 1348592 1348701 "ITFUN2" 1348840 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-556 1346383 1347408 1347705 "ITAYLOR" 1348270 NIL ITAYLOR (NIL T) -8 NIL NIL) (-555 1335417 1340569 1341728 "ISUPS" 1345256 NIL ISUPS (NIL T) -8 NIL NIL) (-554 1334521 1334661 1334897 "ISUMP" 1335264 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-553 1329785 1334322 1334401 "ISTRING" 1334474 NIL ISTRING (NIL NIL) -8 NIL NIL) (-552 1328998 1329079 1329294 "IRURPK" 1329699 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-551 1327934 1328135 1328375 "IRSN" 1328778 T IRSN (NIL) -7 NIL NIL) (-550 1325969 1326324 1326759 "IRRF2F" 1327572 NIL IRRF2F (NIL T) -7 NIL NIL) (-549 1325716 1325754 1325830 "IRREDFFX" 1325925 NIL IRREDFFX (NIL T) -7 NIL NIL) (-548 1324331 1324590 1324889 "IROOT" 1325449 NIL IROOT (NIL T) -7 NIL NIL) (-547 1320969 1322020 1322710 "IR" 1323673 NIL IR (NIL T) -8 NIL NIL) (-546 1318582 1319077 1319643 "IR2" 1320447 NIL IR2 (NIL T T) -7 NIL NIL) (-545 1317658 1317771 1317991 "IR2F" 1318465 NIL IR2F (NIL T T) -7 NIL NIL) (-544 1317449 1317483 1317543 "IPRNTPK" 1317618 T IPRNTPK (NIL) -7 NIL NIL) (-543 1314068 1317338 1317407 "IPF" 1317412 NIL IPF (NIL NIL) -8 NIL NIL) (-542 1312431 1313993 1314050 "IPADIC" 1314055 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-541 1311930 1311988 1312177 "INVLAPLA" 1312367 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-540 1301579 1303932 1306318 "INTTR" 1309594 NIL INTTR (NIL T T) -7 NIL NIL) (-539 1297927 1298668 1299531 "INTTOOLS" 1300765 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-538 1297513 1297604 1297721 "INTSLPE" 1297830 T INTSLPE (NIL) -7 NIL NIL) (-537 1295508 1297436 1297495 "INTRVL" 1297500 NIL INTRVL (NIL T) -8 NIL NIL) (-536 1293115 1293627 1294201 "INTRF" 1294993 NIL INTRF (NIL T) -7 NIL NIL) (-535 1292530 1292627 1292768 "INTRET" 1293013 NIL INTRET (NIL T) -7 NIL NIL) (-534 1290532 1290921 1291390 "INTRAT" 1292138 NIL INTRAT (NIL T T) -7 NIL NIL) (-533 1287765 1288348 1288973 "INTPM" 1290017 NIL INTPM (NIL T T) -7 NIL NIL) (-532 1284474 1285073 1285817 "INTPAF" 1287151 NIL INTPAF (NIL T T T) -7 NIL NIL) (-531 1279717 1280663 1281698 "INTPACK" 1283459 T INTPACK (NIL) -7 NIL NIL) (-530 1276617 1279446 1279573 "INT" 1279610 T INT (NIL) -8 NIL NIL) (-529 1275869 1276021 1276229 "INTHERTR" 1276459 NIL INTHERTR (NIL T T) -7 NIL NIL) (-528 1275308 1275388 1275576 "INTHERAL" 1275783 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-527 1273154 1273597 1274054 "INTHEORY" 1274871 T INTHEORY (NIL) -7 NIL NIL) (-526 1264476 1266097 1267875 "INTG0" 1271506 NIL INTG0 (NIL T T T) -7 NIL NIL) (-525 1245049 1249839 1254649 "INTFTBL" 1259686 T INTFTBL (NIL) -8 NIL NIL) (-524 1244298 1244436 1244609 "INTFACT" 1244908 NIL INTFACT (NIL T) -7 NIL NIL) (-523 1241689 1242135 1242698 "INTEF" 1243852 NIL INTEF (NIL T T) -7 NIL NIL) (-522 1240195 1240900 1240928 "INTDOM" 1241229 T INTDOM (NIL) -9 NIL 1241436) (-521 1239564 1239738 1239980 "INTDOM-" 1239985 NIL INTDOM- (NIL T) -8 NIL NIL) (-520 1236103 1237989 1238043 "INTCAT" 1238842 NIL INTCAT (NIL T) -9 NIL 1239161) (-519 1235576 1235678 1235806 "INTBIT" 1235995 T INTBIT (NIL) -7 NIL NIL) (-518 1234251 1234405 1234718 "INTALG" 1235421 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-517 1233708 1233798 1233968 "INTAF" 1234155 NIL INTAF (NIL T T) -7 NIL NIL) (-516 1227162 1233518 1233658 "INTABL" 1233663 NIL INTABL (NIL T T T) -8 NIL NIL) (-515 1222159 1224842 1224870 "INS" 1225838 T INS (NIL) -9 NIL 1226519) (-514 1219399 1220170 1221144 "INS-" 1221217 NIL INS- (NIL T) -8 NIL NIL) (-513 1218178 1218405 1218702 "INPSIGN" 1219152 NIL INPSIGN (NIL T T) -7 NIL NIL) (-512 1217296 1217413 1217610 "INPRODPF" 1218058 NIL INPRODPF (NIL T T) -7 NIL NIL) (-511 1216190 1216307 1216544 "INPRODFF" 1217176 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-510 1215190 1215342 1215602 "INNMFACT" 1216026 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-509 1214387 1214484 1214672 "INMODGCD" 1215089 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-508 1212896 1213140 1213464 "INFSP" 1214132 NIL INFSP (NIL T T T) -7 NIL NIL) (-507 1212080 1212197 1212380 "INFPROD0" 1212776 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-506 1209091 1210249 1210740 "INFORM" 1211597 T INFORM (NIL) -8 NIL NIL) (-505 1208701 1208761 1208859 "INFORM1" 1209026 NIL INFORM1 (NIL T) -7 NIL NIL) (-504 1208224 1208313 1208427 "INFINITY" 1208607 T INFINITY (NIL) -7 NIL NIL) (-503 1206841 1207090 1207411 "INEP" 1207972 NIL INEP (NIL T T T) -7 NIL NIL) (-502 1206117 1206738 1206803 "INDE" 1206808 NIL INDE (NIL T) -8 NIL NIL) (-501 1205681 1205749 1205866 "INCRMAPS" 1206044 NIL INCRMAPS (NIL T) -7 NIL NIL) (-500 1200992 1201917 1202861 "INBFF" 1204769 NIL INBFF (NIL T) -7 NIL NIL) (-499 1197487 1200837 1200940 "IMATRIX" 1200945 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-498 1196199 1196322 1196637 "IMATQF" 1197343 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-497 1194419 1194646 1194983 "IMATLIN" 1195955 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-496 1189045 1194343 1194401 "ILIST" 1194406 NIL ILIST (NIL T NIL) -8 NIL NIL) (-495 1186998 1188905 1189018 "IIARRAY2" 1189023 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-494 1182431 1186909 1186973 "IFF" 1186978 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-493 1177474 1181723 1181911 "IFARRAY" 1182288 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-492 1176681 1177378 1177451 "IFAMON" 1177456 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-491 1176265 1176330 1176384 "IEVALAB" 1176591 NIL IEVALAB (NIL T T) -9 NIL NIL) (-490 1175940 1176008 1176168 "IEVALAB-" 1176173 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-489 1175598 1175854 1175917 "IDPO" 1175922 NIL IDPO (NIL T T) -8 NIL NIL) (-488 1174875 1175487 1175562 "IDPOAMS" 1175567 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-487 1174209 1174764 1174839 "IDPOAM" 1174844 NIL IDPOAM (NIL T T) -8 NIL NIL) (-486 1173295 1173545 1173598 "IDPC" 1174011 NIL IDPC (NIL T T) -9 NIL 1174160) (-485 1172791 1173187 1173260 "IDPAM" 1173265 NIL IDPAM (NIL T T) -8 NIL NIL) (-484 1172194 1172683 1172756 "IDPAG" 1172761 NIL IDPAG (NIL T T) -8 NIL NIL) (-483 1168449 1169297 1170192 "IDECOMP" 1171351 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-482 1161322 1162372 1163419 "IDEAL" 1167485 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-481 1160486 1160598 1160797 "ICDEN" 1161206 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-480 1159585 1159966 1160113 "ICARD" 1160359 T ICARD (NIL) -8 NIL NIL) (-479 1157657 1157970 1158373 "IBPTOOLS" 1159262 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-478 1153291 1157277 1157390 "IBITS" 1157576 NIL IBITS (NIL NIL) -8 NIL NIL) (-477 1150014 1150590 1151285 "IBATOOL" 1152708 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-476 1147794 1148255 1148788 "IBACHIN" 1149549 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-475 1145671 1147640 1147743 "IARRAY2" 1147748 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-474 1141824 1145597 1145654 "IARRAY1" 1145659 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-473 1135827 1140242 1140720 "IAN" 1141366 T IAN (NIL) -8 NIL NIL) (-472 1135338 1135395 1135568 "IALGFACT" 1135764 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-471 1134866 1134979 1135007 "HYPCAT" 1135214 T HYPCAT (NIL) -9 NIL NIL) (-470 1134404 1134521 1134707 "HYPCAT-" 1134712 NIL HYPCAT- (NIL T) -8 NIL NIL) (-469 1134026 1134199 1134282 "HOSTNAME" 1134341 T HOSTNAME (NIL) -8 NIL NIL) (-468 1130706 1132037 1132078 "HOAGG" 1133059 NIL HOAGG (NIL T) -9 NIL 1133738) (-467 1129300 1129699 1130225 "HOAGG-" 1130230 NIL HOAGG- (NIL T T) -8 NIL NIL) (-466 1123195 1128741 1128907 "HEXADEC" 1129154 T HEXADEC (NIL) -8 NIL NIL) (-465 1121943 1122165 1122428 "HEUGCD" 1122972 NIL HEUGCD (NIL T) -7 NIL NIL) (-464 1121046 1121780 1121910 "HELLFDIV" 1121915 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-463 1119274 1120823 1120911 "HEAP" 1120990 NIL HEAP (NIL T) -8 NIL NIL) (-462 1118613 1118853 1118981 "HEADAST" 1119166 T HEADAST (NIL) -8 NIL NIL) (-461 1112566 1118528 1118590 "HDP" 1118595 NIL HDP (NIL NIL T) -8 NIL NIL) (-460 1106324 1112203 1112354 "HDMP" 1112467 NIL HDMP (NIL NIL T) -8 NIL NIL) (-459 1105649 1105788 1105952 "HB" 1106180 T HB (NIL) -7 NIL NIL) (-458 1099146 1105495 1105599 "HASHTBL" 1105604 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-457 1096964 1098774 1098953 "HACKPI" 1098987 T HACKPI (NIL) -8 NIL NIL) (-456 1092660 1096818 1096930 "GTSET" 1096935 NIL GTSET (NIL T T T T) -8 NIL NIL) (-455 1086186 1092538 1092636 "GSTBL" 1092641 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-454 1078504 1085222 1085486 "GSERIES" 1085977 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-453 1077672 1078063 1078091 "GROUP" 1078294 T GROUP (NIL) -9 NIL 1078428) (-452 1077038 1077197 1077448 "GROUP-" 1077453 NIL GROUP- (NIL T) -8 NIL NIL) (-451 1075407 1075726 1076113 "GROEBSOL" 1076715 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-450 1074348 1074610 1074661 "GRMOD" 1075190 NIL GRMOD (NIL T T) -9 NIL 1075358) (-449 1074116 1074152 1074280 "GRMOD-" 1074285 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-448 1069441 1070470 1071470 "GRIMAGE" 1073136 T GRIMAGE (NIL) -8 NIL NIL) (-447 1067908 1068168 1068492 "GRDEF" 1069137 T GRDEF (NIL) -7 NIL NIL) (-446 1067352 1067468 1067609 "GRAY" 1067787 T GRAY (NIL) -7 NIL NIL) (-445 1066586 1066966 1067017 "GRALG" 1067170 NIL GRALG (NIL T T) -9 NIL 1067262) (-444 1066247 1066320 1066483 "GRALG-" 1066488 NIL GRALG- (NIL T T T) -8 NIL NIL) (-443 1063055 1065836 1066012 "GPOLSET" 1066154 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-442 1062411 1062468 1062725 "GOSPER" 1062992 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-441 1058170 1058849 1059375 "GMODPOL" 1062110 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-440 1057175 1057359 1057597 "GHENSEL" 1057982 NIL GHENSEL (NIL T T) -7 NIL NIL) (-439 1051241 1052084 1053110 "GENUPS" 1056259 NIL GENUPS (NIL T T) -7 NIL NIL) (-438 1050938 1050989 1051078 "GENUFACT" 1051184 NIL GENUFACT (NIL T) -7 NIL NIL) (-437 1050350 1050427 1050592 "GENPGCD" 1050856 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-436 1049824 1049859 1050072 "GENMFACT" 1050309 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-435 1048392 1048647 1048954 "GENEEZ" 1049567 NIL GENEEZ (NIL T T) -7 NIL NIL) (-434 1042312 1048005 1048166 "GDMP" 1048315 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-433 1031689 1036083 1037189 "GCNAALG" 1041295 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-432 1030155 1030983 1031011 "GCDDOM" 1031266 T GCDDOM (NIL) -9 NIL 1031423) (-431 1029625 1029752 1029967 "GCDDOM-" 1029972 NIL GCDDOM- (NIL T) -8 NIL NIL) (-430 1028297 1028482 1028786 "GB" 1029404 NIL GB (NIL T T T T) -7 NIL NIL) (-429 1016917 1019243 1021635 "GBINTERN" 1025988 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-428 1014754 1015046 1015467 "GBF" 1016592 NIL GBF (NIL T T T T) -7 NIL NIL) (-427 1013535 1013700 1013967 "GBEUCLID" 1014570 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-426 1012884 1013009 1013158 "GAUSSFAC" 1013406 T GAUSSFAC (NIL) -7 NIL NIL) (-425 1011261 1011563 1011876 "GALUTIL" 1012603 NIL GALUTIL (NIL T) -7 NIL NIL) (-424 1009578 1009852 1010175 "GALPOLYU" 1010988 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-423 1006967 1007257 1007662 "GALFACTU" 1009275 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-422 998773 1000272 1001880 "GALFACT" 1005399 NIL GALFACT (NIL T) -7 NIL NIL) (-421 996161 996819 996847 "FVFUN" 998003 T FVFUN (NIL) -9 NIL 998723) (-420 995427 995609 995637 "FVC" 995928 T FVC (NIL) -9 NIL 996111) (-419 995069 995224 995305 "FUNCTION" 995379 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-418 992739 993290 993779 "FT" 994600 T FT (NIL) -8 NIL NIL) (-417 991557 992040 992243 "FTEM" 992556 T FTEM (NIL) -8 NIL NIL) (-416 989822 990110 990512 "FSUPFACT" 991249 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-415 988219 988508 988840 "FST" 989510 T FST (NIL) -8 NIL NIL) (-414 987394 987500 987694 "FSRED" 988101 NIL FSRED (NIL T T) -7 NIL NIL) (-413 986073 986328 986682 "FSPRMELT" 987109 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-412 983158 983596 984095 "FSPECF" 985636 NIL FSPECF (NIL T T) -7 NIL NIL) (-411 965687 974089 974129 "FS" 977967 NIL FS (NIL T) -9 NIL 980249) (-410 954337 957327 961383 "FS-" 961680 NIL FS- (NIL T T) -8 NIL NIL) (-409 953853 953907 954083 "FSINT" 954278 NIL FSINT (NIL T T) -7 NIL NIL) (-408 952180 952846 953149 "FSERIES" 953632 NIL FSERIES (NIL T T) -8 NIL NIL) (-407 951198 951314 951544 "FSCINT" 952060 NIL FSCINT (NIL T T) -7 NIL NIL) (-406 947433 950143 950184 "FSAGG" 950554 NIL FSAGG (NIL T) -9 NIL 950813) (-405 945195 945796 946592 "FSAGG-" 946687 NIL FSAGG- (NIL T T) -8 NIL NIL) (-404 944237 944380 944607 "FSAGG2" 945048 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-403 941896 942175 942728 "FS2UPS" 943955 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-402 941482 941525 941678 "FS2" 941847 NIL FS2 (NIL T T T T) -7 NIL NIL) (-401 940342 940513 940821 "FS2EXPXP" 941307 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-400 939768 939883 940035 "FRUTIL" 940222 NIL FRUTIL (NIL T) -7 NIL NIL) (-399 931234 935267 936623 "FR" 938444 NIL FR (NIL T) -8 NIL NIL) (-398 926311 928954 928994 "FRNAALG" 930390 NIL FRNAALG (NIL T) -9 NIL 930997) (-397 921989 923060 924335 "FRNAALG-" 925085 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-396 921627 921670 921797 "FRNAAF2" 921940 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-395 920038 920484 920778 "FRMOD" 921440 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-394 917825 918429 918745 "FRIDEAL" 919829 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-393 917024 917111 917398 "FRIDEAL2" 917732 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-392 916282 916690 916731 "FRETRCT" 916736 NIL FRETRCT (NIL T) -9 NIL 916907) (-391 915394 915625 915976 "FRETRCT-" 915981 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-390 912648 913824 913883 "FRAMALG" 914765 NIL FRAMALG (NIL T T) -9 NIL 915057) (-389 910782 911237 911867 "FRAMALG-" 912090 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-388 904749 910257 910533 "FRAC" 910538 NIL FRAC (NIL T) -8 NIL NIL) (-387 904385 904442 904549 "FRAC2" 904686 NIL FRAC2 (NIL T T) -7 NIL NIL) (-386 904021 904078 904185 "FR2" 904322 NIL FR2 (NIL T T) -7 NIL NIL) (-385 898760 901608 901636 "FPS" 902755 T FPS (NIL) -9 NIL 903311) (-384 898209 898318 898482 "FPS-" 898628 NIL FPS- (NIL T) -8 NIL NIL) (-383 895720 897355 897383 "FPC" 897608 T FPC (NIL) -9 NIL 897750) (-382 895513 895553 895650 "FPC-" 895655 NIL FPC- (NIL T) -8 NIL NIL) (-381 894392 895002 895043 "FPATMAB" 895048 NIL FPATMAB (NIL T) -9 NIL 895200) (-380 892092 892568 892994 "FPARFRAC" 894029 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-379 887485 887984 888666 "FORTRAN" 891524 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-378 885201 885701 886240 "FORT" 886966 T FORT (NIL) -7 NIL NIL) (-377 882877 883439 883467 "FORTFN" 884527 T FORTFN (NIL) -9 NIL 885151) (-376 882641 882691 882719 "FORTCAT" 882778 T FORTCAT (NIL) -9 NIL 882840) (-375 880701 881184 881583 "FORMULA" 882262 T FORMULA (NIL) -8 NIL NIL) (-374 880489 880519 880588 "FORMULA1" 880665 NIL FORMULA1 (NIL T) -7 NIL NIL) (-373 880012 880064 880237 "FORDER" 880431 NIL FORDER (NIL T T T T) -7 NIL NIL) (-372 879108 879272 879465 "FOP" 879839 T FOP (NIL) -7 NIL NIL) (-371 877716 878388 878562 "FNLA" 878990 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-370 876385 876774 876802 "FNCAT" 877374 T FNCAT (NIL) -9 NIL 877667) (-369 875951 876344 876372 "FNAME" 876377 T FNAME (NIL) -8 NIL NIL) (-368 874655 875584 875612 "FMTC" 875617 T FMTC (NIL) -9 NIL 875652) (-367 871019 872180 872808 "FMONOID" 874060 NIL FMONOID (NIL T) -8 NIL NIL) (-366 870239 870762 870910 "FM" 870915 NIL FM (NIL T T) -8 NIL NIL) (-365 867663 868309 868337 "FMFUN" 869481 T FMFUN (NIL) -9 NIL 870189) (-364 866932 867113 867141 "FMC" 867431 T FMC (NIL) -9 NIL 867613) (-363 864162 864996 865049 "FMCAT" 866231 NIL FMCAT (NIL T T) -9 NIL 866725) (-362 863057 863930 864029 "FM1" 864107 NIL FM1 (NIL T T) -8 NIL NIL) (-361 860831 861247 861741 "FLOATRP" 862608 NIL FLOATRP (NIL T) -7 NIL NIL) (-360 854382 858487 859117 "FLOAT" 860221 T FLOAT (NIL) -8 NIL NIL) (-359 851820 852320 852898 "FLOATCP" 853849 NIL FLOATCP (NIL T) -7 NIL NIL) (-358 850653 851457 851497 "FLINEXP" 851502 NIL FLINEXP (NIL T) -9 NIL 851595) (-357 849808 850043 850370 "FLINEXP-" 850375 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-356 848884 849028 849252 "FLASORT" 849660 NIL FLASORT (NIL T T) -7 NIL NIL) (-355 846103 846945 846997 "FLALG" 848224 NIL FLALG (NIL T T) -9 NIL 848691) (-354 839888 843590 843631 "FLAGG" 844893 NIL FLAGG (NIL T) -9 NIL 845545) (-353 838614 838953 839443 "FLAGG-" 839448 NIL FLAGG- (NIL T T) -8 NIL NIL) (-352 837656 837799 838026 "FLAGG2" 838467 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-351 834673 835647 835706 "FINRALG" 836834 NIL FINRALG (NIL T T) -9 NIL 837342) (-350 833833 834062 834401 "FINRALG-" 834406 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-349 833240 833453 833481 "FINITE" 833677 T FINITE (NIL) -9 NIL 833784) (-348 825700 827861 827901 "FINAALG" 831568 NIL FINAALG (NIL T) -9 NIL 833021) (-347 821041 822082 823226 "FINAALG-" 824605 NIL FINAALG- (NIL T T) -8 NIL NIL) (-346 820436 820796 820899 "FILE" 820971 NIL FILE (NIL T) -8 NIL NIL) (-345 819121 819433 819487 "FILECAT" 820171 NIL FILECAT (NIL T T) -9 NIL 820387) (-344 817046 818540 818568 "FIELD" 818608 T FIELD (NIL) -9 NIL 818688) (-343 815666 816051 816562 "FIELD-" 816567 NIL FIELD- (NIL T) -8 NIL NIL) (-342 813546 814303 814649 "FGROUP" 815353 NIL FGROUP (NIL T) -8 NIL NIL) (-341 812636 812800 813020 "FGLMICPK" 813378 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-340 808503 812561 812618 "FFX" 812623 NIL FFX (NIL T NIL) -8 NIL NIL) (-339 808104 808165 808300 "FFSLPE" 808436 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-338 804097 804876 805672 "FFPOLY" 807340 NIL FFPOLY (NIL T) -7 NIL NIL) (-337 803601 803637 803846 "FFPOLY2" 804055 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-336 799487 803520 803583 "FFP" 803588 NIL FFP (NIL T NIL) -8 NIL NIL) (-335 794920 799398 799462 "FF" 799467 NIL FF (NIL NIL NIL) -8 NIL NIL) (-334 790081 794263 794453 "FFNBX" 794774 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-333 785055 789216 789474 "FFNBP" 789935 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-332 779723 784339 784550 "FFNB" 784888 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-331 778555 778753 779068 "FFINTBAS" 779520 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-330 774844 777019 777047 "FFIELDC" 777667 T FFIELDC (NIL) -9 NIL 778043) (-329 773507 773877 774374 "FFIELDC-" 774379 NIL FFIELDC- (NIL T) -8 NIL NIL) (-328 773077 773122 773246 "FFHOM" 773449 NIL FFHOM (NIL T T T) -7 NIL NIL) (-327 770775 771259 771776 "FFF" 772592 NIL FFF (NIL T) -7 NIL NIL) (-326 766428 770517 770618 "FFCGX" 770718 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-325 762095 766160 766267 "FFCGP" 766371 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-324 757313 761822 761930 "FFCG" 762031 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-323 739387 748418 748504 "FFCAT" 753669 NIL FFCAT (NIL T T T) -9 NIL 755120) (-322 734585 735632 736946 "FFCAT-" 738176 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-321 733996 734039 734274 "FFCAT2" 734536 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-320 723242 726986 728203 "FEXPR" 732851 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-319 722242 722677 722718 "FEVALAB" 722802 NIL FEVALAB (NIL T) -9 NIL 723063) (-318 721401 721611 721949 "FEVALAB-" 721954 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-317 719994 720784 720987 "FDIV" 721300 NIL FDIV (NIL T T T T) -8 NIL NIL) (-316 717061 717776 717891 "FDIVCAT" 719459 NIL FDIVCAT (NIL T T T T) -9 NIL 719896) (-315 716823 716850 717020 "FDIVCAT-" 717025 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-314 716043 716130 716407 "FDIV2" 716730 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-313 714729 714988 715277 "FCPAK1" 715774 T FCPAK1 (NIL) -7 NIL NIL) (-312 713857 714229 714370 "FCOMP" 714620 NIL FCOMP (NIL T) -8 NIL NIL) (-311 697492 700906 704467 "FC" 710316 T FC (NIL) -8 NIL NIL) (-310 690153 694134 694174 "FAXF" 695976 NIL FAXF (NIL T) -9 NIL 696667) (-309 687432 688087 688912 "FAXF-" 689377 NIL FAXF- (NIL T T) -8 NIL NIL) (-308 682532 686808 686984 "FARRAY" 687289 NIL FARRAY (NIL T) -8 NIL NIL) (-307 677967 679994 680046 "FAMR" 681058 NIL FAMR (NIL T T) -9 NIL 681518) (-306 676858 677160 677594 "FAMR-" 677599 NIL FAMR- (NIL T T T) -8 NIL NIL) (-305 676054 676780 676833 "FAMONOID" 676838 NIL FAMONOID (NIL T) -8 NIL NIL) (-304 673887 674571 674624 "FAMONC" 675565 NIL FAMONC (NIL T T) -9 NIL 675950) (-303 672579 673641 673778 "FAGROUP" 673783 NIL FAGROUP (NIL T) -8 NIL NIL) (-302 670382 670701 671103 "FACUTIL" 672260 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-301 669481 669666 669888 "FACTFUNC" 670192 NIL FACTFUNC (NIL T) -7 NIL NIL) (-300 661886 668732 668944 "EXPUPXS" 669337 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-299 659369 659909 660495 "EXPRTUBE" 661320 T EXPRTUBE (NIL) -7 NIL NIL) (-298 655563 656155 656892 "EXPRODE" 658708 NIL EXPRODE (NIL T T) -7 NIL NIL) (-297 640999 654222 654648 "EXPR" 655169 NIL EXPR (NIL T) -8 NIL NIL) (-296 635427 636014 636826 "EXPR2UPS" 640297 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-295 635063 635120 635227 "EXPR2" 635364 NIL EXPR2 (NIL T T) -7 NIL NIL) (-294 626482 634200 634495 "EXPEXPAN" 634901 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-293 626309 626439 626468 "EXIT" 626473 T EXIT (NIL) -8 NIL NIL) (-292 625936 625998 626111 "EVALCYC" 626241 NIL EVALCYC (NIL T) -7 NIL NIL) (-291 625477 625595 625636 "EVALAB" 625806 NIL EVALAB (NIL T) -9 NIL 625910) (-290 624958 625080 625301 "EVALAB-" 625306 NIL EVALAB- (NIL T T) -8 NIL NIL) (-289 622465 623733 623761 "EUCDOM" 624316 T EUCDOM (NIL) -9 NIL 624666) (-288 620870 621312 621902 "EUCDOM-" 621907 NIL EUCDOM- (NIL T) -8 NIL NIL) (-287 608448 611196 613936 "ESTOOLS" 618150 T ESTOOLS (NIL) -7 NIL NIL) (-286 608084 608141 608248 "ESTOOLS2" 608385 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-285 607835 607877 607957 "ESTOOLS1" 608036 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-284 601773 603497 603525 "ES" 606289 T ES (NIL) -9 NIL 607695) (-283 596720 598007 599824 "ES-" 599988 NIL ES- (NIL T) -8 NIL NIL) (-282 593095 593855 594635 "ESCONT" 595960 T ESCONT (NIL) -7 NIL NIL) (-281 592840 592872 592954 "ESCONT1" 593057 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-280 592515 592565 592665 "ES2" 592784 NIL ES2 (NIL T T) -7 NIL NIL) (-279 592145 592203 592312 "ES1" 592451 NIL ES1 (NIL T T) -7 NIL NIL) (-278 591361 591490 591666 "ERROR" 591989 T ERROR (NIL) -7 NIL NIL) (-277 584864 591220 591311 "EQTBL" 591316 NIL EQTBL (NIL T T) -8 NIL NIL) (-276 577427 580182 581629 "EQ" 583450 NIL -3805 (NIL T) -8 NIL NIL) (-275 577059 577116 577225 "EQ2" 577364 NIL EQ2 (NIL T T) -7 NIL NIL) (-274 572351 573397 574490 "EP" 575998 NIL EP (NIL T) -7 NIL NIL) (-273 570933 571234 571551 "ENV" 572054 T ENV (NIL) -8 NIL NIL) (-272 570137 570657 570685 "ENTIRER" 570690 T ENTIRER (NIL) -9 NIL 570735) (-271 566639 568092 568462 "EMR" 569936 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-270 565783 565968 566022 "ELTAGG" 566402 NIL ELTAGG (NIL T T) -9 NIL 566613) (-269 565502 565564 565705 "ELTAGG-" 565710 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-268 565291 565320 565374 "ELTAB" 565458 NIL ELTAB (NIL T T) -9 NIL NIL) (-267 564417 564563 564762 "ELFUTS" 565142 NIL ELFUTS (NIL T T) -7 NIL NIL) (-266 564159 564215 564243 "ELEMFUN" 564348 T ELEMFUN (NIL) -9 NIL NIL) (-265 564029 564050 564118 "ELEMFUN-" 564123 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-264 558921 562130 562171 "ELAGG" 563111 NIL ELAGG (NIL T) -9 NIL 563574) (-263 557206 557640 558303 "ELAGG-" 558308 NIL ELAGG- (NIL T T) -8 NIL NIL) (-262 555863 556143 556438 "ELABEXPR" 556931 T ELABEXPR (NIL) -8 NIL NIL) (-261 548729 550530 551357 "EFUPXS" 555139 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-260 542179 543980 544790 "EFULS" 548005 NIL EFULS (NIL T T T) -8 NIL NIL) (-259 539610 539968 540446 "EFSTRUC" 541811 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-258 528682 530247 531807 "EF" 538125 NIL EF (NIL T T) -7 NIL NIL) (-257 527783 528167 528316 "EAB" 528553 T EAB (NIL) -8 NIL NIL) (-256 526996 527742 527770 "E04UCFA" 527775 T E04UCFA (NIL) -8 NIL NIL) (-255 526209 526955 526983 "E04NAFA" 526988 T E04NAFA (NIL) -8 NIL NIL) (-254 525422 526168 526196 "E04MBFA" 526201 T E04MBFA (NIL) -8 NIL NIL) (-253 524635 525381 525409 "E04JAFA" 525414 T E04JAFA (NIL) -8 NIL NIL) (-252 523850 524594 524622 "E04GCFA" 524627 T E04GCFA (NIL) -8 NIL NIL) (-251 523065 523809 523837 "E04FDFA" 523842 T E04FDFA (NIL) -8 NIL NIL) (-250 522278 523024 523052 "E04DGFA" 523057 T E04DGFA (NIL) -8 NIL NIL) (-249 516463 517808 519170 "E04AGNT" 520936 T E04AGNT (NIL) -7 NIL NIL) (-248 515190 515670 515710 "DVARCAT" 516185 NIL DVARCAT (NIL T) -9 NIL 516383) (-247 514394 514606 514920 "DVARCAT-" 514925 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-246 507302 514196 514323 "DSMP" 514328 NIL DSMP (NIL T T T) -8 NIL NIL) (-245 502112 503247 504315 "DROPT" 506254 T DROPT (NIL) -8 NIL NIL) (-244 501777 501836 501934 "DROPT1" 502047 NIL DROPT1 (NIL T) -7 NIL NIL) (-243 496892 498018 499155 "DROPT0" 500660 T DROPT0 (NIL) -7 NIL NIL) (-242 495237 495562 495948 "DRAWPT" 496526 T DRAWPT (NIL) -7 NIL NIL) (-241 489824 490747 491826 "DRAW" 494211 NIL DRAW (NIL T) -7 NIL NIL) (-240 489457 489510 489628 "DRAWHACK" 489765 NIL DRAWHACK (NIL T) -7 NIL NIL) (-239 488188 488457 488748 "DRAWCX" 489186 T DRAWCX (NIL) -7 NIL NIL) (-238 487706 487774 487924 "DRAWCURV" 488114 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-237 478177 480136 482251 "DRAWCFUN" 485611 T DRAWCFUN (NIL) -7 NIL NIL) (-236 474991 476873 476914 "DQAGG" 477543 NIL DQAGG (NIL T) -9 NIL 477816) (-235 463544 470236 470318 "DPOLCAT" 472156 NIL DPOLCAT (NIL T T T T) -9 NIL 472700) (-234 458384 459730 461687 "DPOLCAT-" 461692 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-233 451588 458246 458343 "DPMO" 458348 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-232 444695 451369 451535 "DPMM" 451540 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-231 444115 444318 444432 "DOMAIN" 444601 T DOMAIN (NIL) -8 NIL NIL) (-230 437873 443752 443903 "DMP" 444016 NIL DMP (NIL NIL T) -8 NIL NIL) (-229 437473 437529 437673 "DLP" 437811 NIL DLP (NIL T) -7 NIL NIL) (-228 431117 436574 436801 "DLIST" 437278 NIL DLIST (NIL T) -8 NIL NIL) (-227 427964 429973 430014 "DLAGG" 430564 NIL DLAGG (NIL T) -9 NIL 430793) (-226 426819 427449 427477 "DIVRING" 427569 T DIVRING (NIL) -9 NIL 427652) (-225 426056 426246 426546 "DIVRING-" 426551 NIL DIVRING- (NIL T) -8 NIL NIL) (-224 424158 424515 424921 "DISPLAY" 425670 T DISPLAY (NIL) -7 NIL NIL) (-223 418133 424072 424135 "DIRPROD" 424140 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-222 416981 417184 417449 "DIRPROD2" 417926 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-221 406586 412505 412558 "DIRPCAT" 412966 NIL DIRPCAT (NIL NIL T) -9 NIL 413805) (-220 403912 404554 405435 "DIRPCAT-" 405772 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-219 403199 403359 403545 "DIOSP" 403746 T DIOSP (NIL) -7 NIL NIL) (-218 399902 402112 402153 "DIOPS" 402587 NIL DIOPS (NIL T) -9 NIL 402816) (-217 399451 399565 399756 "DIOPS-" 399761 NIL DIOPS- (NIL T T) -8 NIL NIL) (-216 398367 398961 398989 "DIFRING" 399176 T DIFRING (NIL) -9 NIL 399285) (-215 398013 398090 398242 "DIFRING-" 398247 NIL DIFRING- (NIL T) -8 NIL NIL) (-214 395847 397085 397125 "DIFEXT" 397484 NIL DIFEXT (NIL T) -9 NIL 397777) (-213 394133 394561 395226 "DIFEXT-" 395231 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-212 391456 393666 393707 "DIAGG" 393712 NIL DIAGG (NIL T) -9 NIL 393732) (-211 390840 390997 391249 "DIAGG-" 391254 NIL DIAGG- (NIL T T) -8 NIL NIL) (-210 386305 389799 390076 "DHMATRIX" 390609 NIL DHMATRIX (NIL T) -8 NIL NIL) (-209 381917 382826 383836 "DFSFUN" 385315 T DFSFUN (NIL) -7 NIL NIL) (-208 376768 380631 380996 "DFLOAT" 381572 T DFLOAT (NIL) -8 NIL NIL) (-207 375001 375282 375677 "DFINTTLS" 376476 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-206 372080 373036 373434 "DERHAM" 374668 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-205 369929 371855 371944 "DEQUEUE" 372024 NIL DEQUEUE (NIL T) -8 NIL NIL) (-204 369147 369280 369475 "DEGRED" 369791 NIL DEGRED (NIL T T) -7 NIL NIL) (-203 365547 366292 367144 "DEFINTRF" 368375 NIL DEFINTRF (NIL T) -7 NIL NIL) (-202 363078 363547 364145 "DEFINTEF" 365066 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-201 356973 362519 362685 "DECIMAL" 362932 T DECIMAL (NIL) -8 NIL NIL) (-200 354485 354943 355449 "DDFACT" 356517 NIL DDFACT (NIL T T) -7 NIL NIL) (-199 354081 354124 354275 "DBLRESP" 354436 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-198 351791 352125 352494 "DBASE" 353839 NIL DBASE (NIL T) -8 NIL NIL) (-197 351060 351271 351417 "DATABUF" 351690 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-196 350195 351019 351047 "D03FAFA" 351052 T D03FAFA (NIL) -8 NIL NIL) (-195 349331 350154 350182 "D03EEFA" 350187 T D03EEFA (NIL) -8 NIL NIL) (-194 347281 347747 348236 "D03AGNT" 348862 T D03AGNT (NIL) -7 NIL NIL) (-193 346599 347240 347268 "D02EJFA" 347273 T D02EJFA (NIL) -8 NIL NIL) (-192 345917 346558 346586 "D02CJFA" 346591 T D02CJFA (NIL) -8 NIL NIL) (-191 345235 345876 345904 "D02BHFA" 345909 T D02BHFA (NIL) -8 NIL NIL) (-190 344553 345194 345222 "D02BBFA" 345227 T D02BBFA (NIL) -8 NIL NIL) (-189 337751 339339 340945 "D02AGNT" 342967 T D02AGNT (NIL) -7 NIL NIL) (-188 335520 336042 336588 "D01WGTS" 337225 T D01WGTS (NIL) -7 NIL NIL) (-187 334623 335479 335507 "D01TRNS" 335512 T D01TRNS (NIL) -8 NIL NIL) (-186 333726 334582 334610 "D01GBFA" 334615 T D01GBFA (NIL) -8 NIL NIL) (-185 332829 333685 333713 "D01FCFA" 333718 T D01FCFA (NIL) -8 NIL NIL) (-184 331932 332788 332816 "D01ASFA" 332821 T D01ASFA (NIL) -8 NIL NIL) (-183 331035 331891 331919 "D01AQFA" 331924 T D01AQFA (NIL) -8 NIL NIL) (-182 330138 330994 331022 "D01APFA" 331027 T D01APFA (NIL) -8 NIL NIL) (-181 329241 330097 330125 "D01ANFA" 330130 T D01ANFA (NIL) -8 NIL NIL) (-180 328344 329200 329228 "D01AMFA" 329233 T D01AMFA (NIL) -8 NIL NIL) (-179 327447 328303 328331 "D01ALFA" 328336 T D01ALFA (NIL) -8 NIL NIL) (-178 326550 327406 327434 "D01AKFA" 327439 T D01AKFA (NIL) -8 NIL NIL) (-177 325653 326509 326537 "D01AJFA" 326542 T D01AJFA (NIL) -8 NIL NIL) (-176 318957 320506 322065 "D01AGNT" 324114 T D01AGNT (NIL) -7 NIL NIL) (-175 318294 318422 318574 "CYCLOTOM" 318825 T CYCLOTOM (NIL) -7 NIL NIL) (-174 315029 315742 316469 "CYCLES" 317587 T CYCLES (NIL) -7 NIL NIL) (-173 314341 314475 314646 "CVMP" 314890 NIL CVMP (NIL T) -7 NIL NIL) (-172 312122 312380 312755 "CTRIGMNP" 314069 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-171 311633 311822 311921 "CTORCALL" 312043 T CTORCALL (NIL) -8 NIL NIL) (-170 311007 311106 311259 "CSTTOOLS" 311530 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-169 306806 307463 308221 "CRFP" 310319 NIL CRFP (NIL T T) -7 NIL NIL) (-168 305853 306038 306266 "CRAPACK" 306610 NIL CRAPACK (NIL T) -7 NIL NIL) (-167 305237 305338 305542 "CPMATCH" 305729 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-166 304962 304990 305096 "CPIMA" 305203 NIL CPIMA (NIL T T T) -7 NIL NIL) (-165 301326 301998 302716 "COORDSYS" 304297 NIL COORDSYS (NIL T) -7 NIL NIL) (-164 300710 300839 300989 "CONTOUR" 301196 T CONTOUR (NIL) -8 NIL NIL) (-163 296636 298713 299205 "CONTFRAC" 300250 NIL CONTFRAC (NIL T) -8 NIL NIL) (-162 295834 296354 296382 "COMRING" 296387 T COMRING (NIL) -9 NIL 296438) (-161 294915 295192 295376 "COMPPROP" 295670 T COMPPROP (NIL) -8 NIL NIL) (-160 294576 294611 294739 "COMPLPAT" 294874 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-159 284642 294385 294494 "COMPLEX" 294499 NIL COMPLEX (NIL T) -8 NIL NIL) (-158 284278 284335 284442 "COMPLEX2" 284579 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-157 283996 284031 284129 "COMPFACT" 284237 NIL COMPFACT (NIL T T) -7 NIL NIL) (-156 268416 278625 278665 "COMPCAT" 279667 NIL COMPCAT (NIL T) -9 NIL 281060) (-155 257931 260855 264482 "COMPCAT-" 264838 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-154 257662 257690 257792 "COMMUPC" 257897 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-153 257457 257490 257549 "COMMONOP" 257623 T COMMONOP (NIL) -7 NIL NIL) (-152 257040 257208 257295 "COMM" 257390 T COMM (NIL) -8 NIL NIL) (-151 256289 256483 256511 "COMBOPC" 256849 T COMBOPC (NIL) -9 NIL 257024) (-150 255185 255395 255637 "COMBINAT" 256079 NIL COMBINAT (NIL T) -7 NIL NIL) (-149 251383 251956 252596 "COMBF" 254607 NIL COMBF (NIL T T) -7 NIL NIL) (-148 250169 250499 250734 "COLOR" 251168 T COLOR (NIL) -8 NIL NIL) (-147 249809 249856 249981 "CMPLXRT" 250116 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-146 245311 246339 247419 "CLIP" 248749 T CLIP (NIL) -7 NIL NIL) (-145 243695 244419 244657 "CLIF" 245139 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-144 239918 241842 241883 "CLAGG" 242812 NIL CLAGG (NIL T) -9 NIL 243348) (-143 238340 238797 239380 "CLAGG-" 239385 NIL CLAGG- (NIL T T) -8 NIL NIL) (-142 237884 237969 238109 "CINTSLPE" 238249 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-141 235385 235856 236404 "CHVAR" 237412 NIL CHVAR (NIL T T T) -7 NIL NIL) (-140 234652 235172 235200 "CHARZ" 235205 T CHARZ (NIL) -9 NIL 235219) (-139 234406 234446 234524 "CHARPOL" 234606 NIL CHARPOL (NIL T) -7 NIL NIL) (-138 233557 234110 234138 "CHARNZ" 234185 T CHARNZ (NIL) -9 NIL 234240) (-137 231582 232247 232582 "CHAR" 233242 T CHAR (NIL) -8 NIL NIL) (-136 231308 231369 231397 "CFCAT" 231508 T CFCAT (NIL) -9 NIL NIL) (-135 230553 230664 230846 "CDEN" 231192 NIL CDEN (NIL T T T) -7 NIL NIL) (-134 226545 229706 229986 "CCLASS" 230293 T CCLASS (NIL) -8 NIL NIL) (-133 226464 226490 226525 "CATEGORY" 226530 T -10 (NIL) -8 NIL NIL) (-132 221516 222493 223246 "CARTEN" 225767 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-131 220624 220772 220993 "CARTEN2" 221363 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-130 218968 219776 220032 "CARD" 220388 T CARD (NIL) -8 NIL NIL) (-129 218341 218669 218697 "CACHSET" 218829 T CACHSET (NIL) -9 NIL 218906) (-128 217838 218134 218162 "CABMON" 218212 T CABMON (NIL) -9 NIL 218268) (-127 217006 217385 217528 "BYTE" 217715 T BYTE (NIL) -8 NIL NIL) (-126 212954 216953 216987 "BYTEARY" 216992 T BYTEARY (NIL) -8 NIL NIL) (-125 210511 212646 212753 "BTREE" 212880 NIL BTREE (NIL T) -8 NIL NIL) (-124 208009 210159 210281 "BTOURN" 210421 NIL BTOURN (NIL T) -8 NIL NIL) (-123 205428 207481 207522 "BTCAT" 207590 NIL BTCAT (NIL T) -9 NIL 207667) (-122 205095 205175 205324 "BTCAT-" 205329 NIL BTCAT- (NIL T T) -8 NIL NIL) (-121 200388 204239 204267 "BTAGG" 204489 T BTAGG (NIL) -9 NIL 204650) (-120 199878 200003 200209 "BTAGG-" 200214 NIL BTAGG- (NIL T) -8 NIL NIL) (-119 196922 199156 199371 "BSTREE" 199695 NIL BSTREE (NIL T) -8 NIL NIL) (-118 196060 196186 196370 "BRILL" 196778 NIL BRILL (NIL T) -7 NIL NIL) (-117 192762 194789 194830 "BRAGG" 195479 NIL BRAGG (NIL T) -9 NIL 195736) (-116 191291 191697 192252 "BRAGG-" 192257 NIL BRAGG- (NIL T T) -8 NIL NIL) (-115 184564 190637 190821 "BPADICRT" 191139 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-114 182914 184501 184546 "BPADIC" 184551 NIL BPADIC (NIL NIL) -8 NIL NIL) (-113 182614 182644 182757 "BOUNDZRO" 182878 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-112 178129 179220 180087 "BOP" 181767 T BOP (NIL) -8 NIL NIL) (-111 175750 176194 176714 "BOP1" 177642 NIL BOP1 (NIL T) -7 NIL NIL) (-110 174474 175160 175360 "BOOLEAN" 175570 T BOOLEAN (NIL) -8 NIL NIL) (-109 173841 174219 174271 "BMODULE" 174276 NIL BMODULE (NIL T T) -9 NIL 174340) (-108 169671 173639 173712 "BITS" 173788 T BITS (NIL) -8 NIL NIL) (-107 168768 169203 169355 "BINFILE" 169539 T BINFILE (NIL) -8 NIL NIL) (-106 168180 168302 168444 "BINDING" 168646 T BINDING (NIL) -8 NIL NIL) (-105 162079 167624 167789 "BINARY" 168035 T BINARY (NIL) -8 NIL NIL) (-104 159907 161335 161376 "BGAGG" 161636 NIL BGAGG (NIL T) -9 NIL 161773) (-103 159738 159770 159861 "BGAGG-" 159866 NIL BGAGG- (NIL T T) -8 NIL NIL) (-102 158836 159122 159327 "BFUNCT" 159553 T BFUNCT (NIL) -8 NIL NIL) (-101 157531 157709 157996 "BEZOUT" 158660 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-100 154048 156383 156713 "BBTREE" 157234 NIL BBTREE (NIL T) -8 NIL NIL) (-99 153786 153839 153865 "BASTYPE" 153982 T BASTYPE (NIL) -9 NIL NIL) (-98 153641 153670 153740 "BASTYPE-" 153745 NIL BASTYPE- (NIL T) -8 NIL NIL) (-97 153079 153155 153305 "BALFACT" 153552 NIL BALFACT (NIL T T) -7 NIL NIL) (-96 151966 152498 152683 "AUTOMOR" 152924 NIL AUTOMOR (NIL T) -8 NIL NIL) (-95 151692 151697 151723 "ATTREG" 151728 T ATTREG (NIL) -9 NIL NIL) (-94 149971 150389 150741 "ATTRBUT" 151358 T ATTRBUT (NIL) -8 NIL NIL) (-93 149507 149620 149646 "ATRIG" 149847 T ATRIG (NIL) -9 NIL NIL) (-92 149316 149357 149444 "ATRIG-" 149449 NIL ATRIG- (NIL T) -8 NIL NIL) (-91 149042 149185 149211 "ASTCAT" 149216 T ASTCAT (NIL) -9 NIL 149246) (-90 148839 148882 148974 "ASTCAT-" 148979 NIL ASTCAT- (NIL T) -8 NIL NIL) (-89 147036 148615 148703 "ASTACK" 148782 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145541 145838 146203 "ASSOCEQ" 146718 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144573 145200 145324 "ASP9" 145448 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144337 144521 144560 "ASP8" 144565 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143206 143942 144084 "ASP80" 144226 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142105 142841 142973 "ASP7" 143105 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141059 141782 141900 "ASP78" 142018 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140028 140739 140856 "ASP77" 140973 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 138940 139666 139797 "ASP74" 139928 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 137840 138575 138707 "ASP73" 138839 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 136795 137517 137635 "ASP6" 137753 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 135743 136472 136590 "ASP55" 136708 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 134693 135417 135536 "ASP50" 135655 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 133781 134394 134504 "ASP4" 134614 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 132869 133482 133592 "ASP49" 133702 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 131654 132408 132576 "ASP42" 132758 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130431 131187 131357 "ASP41" 131541 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129381 130108 130226 "ASP35" 130344 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129146 129329 129368 "ASP34" 129373 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 128883 128950 129026 "ASP33" 129101 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 127778 128518 128650 "ASP31" 128782 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127543 127726 127765 "ASP30" 127770 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127278 127347 127423 "ASP29" 127498 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127043 127226 127265 "ASP28" 127270 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 126808 126991 127030 "ASP27" 127035 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 125892 126506 126617 "ASP24" 126728 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 124808 125533 125663 "ASP20" 125793 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 123896 124509 124619 "ASP1" 124729 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 122840 123570 123689 "ASP19" 123808 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122577 122644 122720 "ASP12" 122795 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121429 122176 122320 "ASP10" 122464 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119328 121273 121364 "ARRAY2" 121369 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115144 118976 119090 "ARRAY1" 119245 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114176 114349 114570 "ARRAY12" 114967 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108536 110407 110482 "ARR2CAT" 113112 NIL ARR2CAT (NIL T T T) -9 NIL 113870) (-54 105970 106714 107668 "ARR2CAT-" 107673 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 104722 104874 105179 "APPRULE" 105806 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104375 104423 104541 "APPLYORE" 104668 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103349 103640 103835 "ANY" 104198 T ANY (NIL) -8 NIL NIL) (-50 102627 102750 102907 "ANY1" 103223 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100205 101077 101402 "ANTISYM" 102352 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 99720 99909 100006 "ANON" 100126 T ANON (NIL) -8 NIL NIL) (-47 93862 98265 98716 "AN" 99287 T AN (NIL) -8 NIL NIL) (-46 90260 91614 91664 "AMR" 92403 NIL AMR (NIL T T) -9 NIL 93002) (-45 89373 89594 89956 "AMR-" 89961 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 73923 89290 89351 "ALIST" 89356 NIL ALIST (NIL T T) -8 NIL NIL) (-43 70760 73517 73686 "ALGSC" 73841 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67316 67870 68477 "ALGPKG" 70200 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66593 66694 66878 "ALGMFACT" 67202 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62342 63023 63677 "ALGMANIP" 66117 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 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at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1080 (-208))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1300 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-525))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-998 *3 *4 *2)) (-4 *3 (-984)) (-4 *4 (-741)) + (-4 *2 (-795)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) + (-4 *4 (-795))))) (((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -1853 (-530)) (|:| -4162 (-597 *3)))) - (-5 *1 (-422 *3)) (-4 *3 (-1157 (-530)))))) 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(-4 *5 (-741)) + (-5 *2 + (-2 (|:| |mval| (-637 *4)) (|:| |invmval| (-637 *4)) + (|:| |genIdeal| (-482 *4 *5 *6 *7)))) + (-5 *1 (-482 *4 *5 *6 *7)) (-4 *7 (-890 *4 *5 *6))))) +(((*1 *1 *2) (-12 (-5 *1 (-964 *2)) (-4 *2 (-1135))))) (((*1 *2 *3) (-12 (-5 *3 (-1099)) (-4 *4 (-13 (-432) (-795) (-975 (-530)) (-593 (-530)))) @@ -8125,52 +7235,36 @@ (-4 *3 (-1172 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1164 *3 *2)) (-4 *3 (-984)) (-4 *2 (-1141 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1099)) - (-4 *4 (-13 (-289) (-795) (-140) (-975 (-530)) (-593 (-530)))) - (-5 *1 (-407 *4 *2)) (-4 *2 (-13 (-1121) (-29 *4))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-388 (-893 *5))) (-5 *4 (-1099)) (-4 *5 (-140)) - (-4 *5 (-13 (-432) (-975 (-530)) (-795) (-593 (-530)))) - (-5 *2 (-297 *5)) (-5 *1 (-550 *5))))) +(((*1 *2) + (-12 (-5 *2 (-110)) (-5 *1 (-422 *3)) (-4 *3 (-1157 (-530)))))) (((*1 *2 *3) - (-12 (-5 *3 (-570 *5)) (-4 *5 (-411 *4)) (-4 *4 (-975 (-530))) - (-4 *4 (-13 (-795) (-522))) (-5 *2 (-1095 *5)) (-5 *1 (-31 *4 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*3 - (-2 (|:| |lfn| (-597 (-297 (-208)))) (|:| -3677 (-597 (-208))))) - (-5 *2 (-973))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-923 *2)) (-4 *2 (-1121))))) + (-12 (-4 *4 (-522)) (-4 *5 (-741)) (-4 *6 (-795)) + (-4 *7 (-998 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-597 *7)) (|:| |badPols| (-597 *7)))) + (-5 *1 (-917 *4 *5 *6 *7)) (-5 *3 (-597 *7))))) (((*1 *2 *3) (-12 (-5 *3 (-1099)) (-4 *4 (-13 (-432) (-795) (-975 (-530)) (-593 (-530)))) @@ -8217,137 +7311,196 @@ ((*1 *2 *1) (-12 (-4 *1 (-1143 *3 *2)) (-4 *3 (-984)) (-4 *2 (-1172 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-547 *2)) (-4 *2 (-13 (-29 *4) (-1121))) - (-5 *1 (-545 *4 *2)) - (-4 *4 (-13 (-432) (-975 (-530)) (-795) (-593 (-530)))))) + (-12 (-5 *3 (-388 *5)) (-4 *5 (-1157 *4)) (-4 *4 (-522)) + (-4 *4 (-984)) (-4 *2 (-1172 *4)) (-5 *1 (-1175 *4 *5 *6 *2)) + (-4 *6 (-607 *5))))) +(((*1 *2 *3 *4 *3 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-530)) (-5 *4 (-637 (-159 (-208)))) (-5 *2 (-973)) + (-5 *1 (-705))))) +(((*1 *2 *3 *3 *3) + (-12 (-5 *3 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(-15 -1848 ((-1051 *3 (-570 $)) $)) - (-15 -1857 ((-1051 *3 (-570 $)) $)) - (-15 -2258 ($ (-1051 *3 (-570 $)))))))))) + (-12 (-4 *3 (-1157 (-388 (-530)))) (-5 *1 (-854 *3 *2)) + (-4 *2 (-1157 (-388 *3)))))) +(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-1148 *3)) (-4 *3 (-1135))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) + (-5 *1 (-704))))) +(((*1 *1 *1) (-12 (-4 *1 (-355 *2 *3)) (-4 *2 (-795)) (-4 *3 (-162)))) + ((*1 *1 *1) + (-12 (-5 *1 (-581 *2 *3 *4)) (-4 *2 (-795)) + (-4 *3 (-13 (-162) (-666 (-388 (-530))))) (-14 *4 (-862)))) + ((*1 *1 *1) (-12 (-5 *1 (-626 *2)) (-4 *2 (-795)))) + ((*1 *1 *1) (-12 (-5 *1 (-767 *2)) (-4 *2 (-795)))) + ((*1 *1 *1) (-12 (-4 *1 (-1196 *2 *3)) (-4 *2 (-795)) (-4 *3 (-984))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-530)) (-4 *1 (-55 *4 *3 *5)) (-4 *4 (-1135)) + (-4 *3 (-354 *4)) (-4 *5 (-354 *4))))) (((*1 *1 *1) (-12 (-5 *1 (-320 *2 *3 *4)) (-14 *2 (-597 (-1099))) (-14 *3 (-597 (-1099))) (-4 *4 (-368)))) @@ -8953,69 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((*1 *2 *1) (-12 (-5 *2 (-1099)) (-5 *1 (-1104)))) @@ -9069,8 +8549,8 @@ (-12 (-4 *4 (-13 (-795) - (-10 -8 (-15 -3173 ((-1099) $)) - (-15 -3994 ((-3 $ "failed") (-1099)))))) + (-10 -8 (-15 -3260 ((-1099) $)) + (-15 -4007 ((-3 $ "failed") (-1099)))))) (-4 *5 (-741)) (-4 *7 (-522)) (-5 *2 (-399 *3)) (-5 *1 (-436 *4 *5 *6 *7 *3)) (-4 *6 (-522)) (-4 *3 (-890 *7 *5 *4)))) @@ -9119,13 +8599,13 @@ (-12 (-4 *4 (-741)) (-4 *5 (-13 (-795) - (-10 -8 (-15 -3173 ((-1099) $)) - (-15 -3994 ((-3 $ "failed") (-1099)))))) + (-10 -8 (-15 -3260 ((-1099) $)) + (-15 -4007 ((-3 $ "failed") (-1099)))))) (-4 *6 (-289)) (-5 *2 (-399 *3)) (-5 *1 (-679 *4 *5 *6 *3)) (-4 *3 (-890 (-893 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-741)) - (-4 *5 (-13 (-795) (-10 -8 (-15 -3173 ((-1099) $))))) (-4 *6 (-522)) + (-4 *5 (-13 (-795) (-10 -8 (-15 -3260 ((-1099) $))))) (-4 *6 (-522)) (-5 *2 (-399 *3)) (-5 *1 (-681 *4 *5 *6 *3)) (-4 *3 (-890 (-388 (-893 *6)) *4 *5)))) ((*1 *2 *3) @@ -9161,73 +8641,48 @@ ((*1 *2 *1) (-12 (-5 *2 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+ (-3 (|:| |%series| *8) + (|:| |%problem| (-2 (|:| |func| (-1082)) (|:| |prob| (-1082)))))) + (-5 *1 (-403 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1082)) (-4 *9 (-923 *8)) + (-14 *10 (-1099))))) +(((*1 *2 *1) (-12 (-5 *2 (-597 (-1099))) (-5 *1 (-1103))))) (((*1 *2 *3) (-12 (-5 *3 (-51)) (-5 *1 (-50 *2)) (-4 *2 (-1135)))) ((*1 *1 *2) (-12 (-5 *2 (-893 (-360))) (-5 *1 (-320 *3 *4 *5)) @@ -9395,11 +8850,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) - (|:| -2902 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) + (|:| -1300 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))) (|:| |mdnia| (-2 (|:| |fn| (-297 (-208))) - (|:| -2902 (-597 (-1022 (-788 (-208))))) + (|:| -1300 (-597 (-1022 (-788 (-208))))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))))) (-5 *1 (-717)))) ((*1 *2 *1) @@ -9415,13 +8870,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-297 (-208))) (|:| -3677 (-597 (-208))) + (-2 (|:| |fn| (-297 (-208))) (|:| -3657 (-597 (-208))) (|:| |lb| (-597 (-788 (-208)))) (|:| |cf| (-597 (-297 (-208)))) (|:| |ub| (-597 (-788 (-208)))))) (|:| |lsa| (-2 (|:| |lfn| (-597 (-297 (-208)))) - (|:| -3677 (-597 (-208))))))) + (|:| -3657 (-597 (-208))))))) (-5 *1 (-786)))) ((*1 *2 *1) (-12 @@ -9440,26 +8895,26 @@ (-4 *4 (-741)) (-4 *5 (-795)) (-4 *1 (-916 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-975 *2)) (-4 *2 (-1135)))) ((*1 *1 *2) - (-1476 + (-1461 (-12 (-5 *2 (-893 *3)) - (-12 (-3694 (-4 *3 (-37 (-388 (-530))))) - (-3694 (-4 *3 (-37 (-530)))) (-4 *5 (-572 (-1099)))) + (-12 (-3676 (-4 *3 (-37 (-388 (-530))))) + (-3676 (-4 *3 (-37 (-530)))) (-4 *5 (-572 (-1099)))) (-4 *3 (-984)) (-4 *1 (-998 *3 *4 *5)) (-4 *4 (-741)) (-4 *5 (-795))) (-12 (-5 *2 (-893 *3)) - (-12 (-3694 (-4 *3 (-515))) (-3694 (-4 *3 (-37 (-388 (-530))))) + (-12 (-3676 (-4 *3 (-515))) (-3676 (-4 *3 (-37 (-388 (-530))))) (-4 *3 (-37 (-530))) (-4 *5 (-572 (-1099)))) (-4 *3 (-984)) (-4 *1 (-998 *3 *4 *5)) (-4 *4 (-741)) (-4 *5 (-795))) (-12 (-5 *2 (-893 *3)) - (-12 (-3694 (-4 *3 (-932 (-530)))) (-4 *3 (-37 (-388 (-530)))) + (-12 (-3676 (-4 *3 (-932 (-530)))) (-4 *3 (-37 (-388 (-530)))) (-4 *5 (-572 (-1099)))) (-4 *3 (-984)) (-4 *1 (-998 *3 *4 *5)) (-4 *4 (-741)) (-4 *5 (-795))))) ((*1 *1 *2) - (-1476 + (-1461 (-12 (-5 *2 (-893 (-530))) (-4 *1 (-998 *3 *4 *5)) - (-12 (-3694 (-4 *3 (-37 (-388 (-530))))) (-4 *3 (-37 (-530))) + (-12 (-3676 (-4 *3 (-37 (-388 (-530))))) (-4 *3 (-37 (-530))) (-4 *5 (-572 (-1099)))) (-4 *3 (-984)) (-4 *4 (-741)) (-4 *5 (-795))) (-12 (-5 *2 (-893 (-530))) (-4 *1 (-998 *3 *4 *5)) @@ -9469,19 +8924,23 @@ (-12 (-5 *2 (-893 (-388 (-530)))) (-4 *1 (-998 *3 *4 *5)) (-4 *3 (-37 (-388 (-530)))) (-4 *5 (-572 (-1099))) (-4 *3 (-984)) (-4 *4 (-741)) (-4 *5 (-795))))) -(((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-432)) (-4 *5 (-741)) (-4 *6 (-795)) - (-4 *7 (-998 *4 *5 *6)) (-5 *2 (-110)) - (-5 *1 (-928 *4 *5 *6 *7 *3)) (-4 *3 (-1003 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-432)) (-4 *5 (-741)) (-4 *6 (-795)) - (-4 *7 (-998 *4 *5 *6)) (-5 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+ (-5 *2 (-51)) (-5 *1 (-439 *8 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1080 (-2 (|:| |k| (-530)) (|:| |c| *3)))) + (-4 *3 (-984)) (-5 *1 (-555 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-984)) (-5 *1 (-556 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1080 (-2 (|:| |k| (-530)) (|:| |c| *3)))) + (-4 *3 (-984)) (-4 *1 (-1141 *3)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-719)) + (-5 *3 (-1080 (-2 (|:| |k| (-388 (-530))) (|:| |c| *4)))) + (-4 *4 (-984)) (-4 *1 (-1162 *4)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1080 *3)) (-4 *3 (-984)) (-4 *1 (-1172 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1080 (-2 (|:| |k| (-719)) (|:| |c| *3)))) + (-4 *3 (-984)) (-4 *1 (-1172 *3))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -10173,6 +9767,8 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-367 *2)) (-4 *2 (-1027)))) + ((*1 *1 *1 *1) (-12 (-5 *1 (-767 *2)) (-4 *2 (-795))))) (((*1 *2 *3) (-12 (-5 *3 (-1099)) (-4 *4 (-13 (-432) (-795) (-975 (-530)) (-593 (-530)))) @@ -10210,41 +9806,41 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-388 (-530))) (-4 *4 (-984)) (-4 *1 (-1164 *4 *3)) (-4 *3 (-1141 *4))))) -(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-530)) (-5 *3 (-862)) (-5 *1 (-647)))) - ((*1 *2 *2 *2 *3 *4) - (-12 (-5 *2 (-637 *5)) (-5 *3 (-96 *5)) (-5 *4 (-1 *5 *5)) - (-4 *5 (-344)) (-5 *1 (-918 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1099)) (-4 *4 (-432)) (-4 *4 (-795)) - (-5 *1 (-539 *4 *2)) (-4 *2 (-266)) (-4 *2 (-411 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1099)) - (-4 *5 (-13 (-522) (-795) (-975 (-530)) (-593 (-530)))) - (-5 *2 - (-2 (|:| |func| *3) (|:| |kers| (-597 (-570 *3))) - (|:| |vals| (-597 *3)))) - (-5 *1 (-259 *5 *3)) (-4 *3 (-13 (-27) (-1121) (-411 *5)))))) -(((*1 *2 *1 *1 *3) - (-12 (-5 *3 (-1 (-110) *5 *5)) (-4 *5 (-13 (-1027) (-33))) - (-5 *2 (-110)) (-5 *1 (-1064 *4 *5)) (-4 *4 (-13 (-1027) (-33)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 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+(((*1 *1 *1) (-12 (-5 *1 (-566 *2)) (-4 *2 (-1027)))) + ((*1 *1 *1) (-5 *1 (-586)))) +(((*1 *1 *2) (-12 (-5 *2 (-597 (-804))) (-5 *1 (-804))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-815)) (-5 *3 (-597 (-245))) (-5 *1 (-243))))) +(((*1 *2 *2) (-12 (-5 *2 (-530)) (-5 *1 (-867))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1082)) (-5 *1 (-112))))) +(((*1 *2 *2 *1) + (-12 (-5 *2 (-1203 *3 *4)) (-4 *1 (-355 *3 *4)) (-4 *3 (-795)) + (-4 *4 (-162)))) + ((*1 *1 *1 *1) (|partial| -12 (-5 *1 (-367 *2)) (-4 *2 (-1027)))) + ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-767 *2)) (-4 *2 (-795)))) + ((*1 *1 *1 *1) (|partial| -12 (-5 *1 (-767 *2)) (-4 *2 (-795)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1196 *2 *3)) (-4 *2 (-795)) (-4 *3 (-984)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-767 *3)) (-4 *1 (-1196 *3 *4)) (-4 *3 (-795)) + (-4 *4 (-984)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1196 *2 *3)) (-4 *2 (-795)) (-4 *3 (-984))))) +(((*1 *2 *3 *4 *3 *4 *3) + (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) + (-5 *1 (-705))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -10261,48 +9857,92 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) (-5 *1 (-258 *4 *3)) - (-4 *3 (-13 (-411 *4) (-941)))))) -(((*1 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) -(((*1 *2 *3) - (-12 (-5 *2 (-110)) (-5 *1 (-118 *3)) (-4 *3 (-1157 (-530)))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1099)) - (-4 *5 (-13 (-289) (-795) (-140) (-975 (-530)) (-593 (-530)))) - (-5 *2 (-547 *3)) (-5 *1 (-407 *5 *3)) - (-4 *3 (-13 (-1121) (-29 *5)))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-522)) (-5 *1 (-910 *3 *2)) (-4 *2 (-1157 *3)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) - (-4 *4 (-795)) (-4 *2 (-522)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1157 *2)) (-4 *2 (-984)) (-4 *2 (-522))))) -(((*1 *1 *2 *3 *1 *3) - (-12 (-5 *2 (-833 *4)) (-4 *4 (-1027)) (-5 *1 (-830 *4 *3)) - (-4 *3 (-1027))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-637 *4)) (-5 *3 (-862)) (|has| *4 (-6 (-4272 "*"))) - (-4 *4 (-984)) (-5 *1 (-966 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-597 (-637 *4))) (-5 *3 (-862)) - (|has| *4 (-6 (-4272 "*"))) (-4 *4 (-984)) (-5 *1 (-966 *4))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1 (-884 (-208)) (-884 (-208)))) (-5 *3 (-597 (-245))) - (-5 *1 (-243)))) + (|partial| -12 (-5 *3 (-1181 *4)) (-4 *4 (-593 (-530))) + (-5 *2 (-1181 (-388 (-530)))) (-5 *1 (-1206 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 (-804))) (-5 *1 (-804))))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-597 (-2 (|:| |totdeg| (-719)) (|:| -3109 *3)))) + (-5 *4 (-719)) (-4 *3 (-890 *5 *6 *7)) (-4 *5 (-432)) (-4 *6 (-741)) + (-4 *7 (-795)) (-5 *1 (-429 *5 *6 *7 *3))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-1186)) (-5 *1 (-1183))))) +(((*1 *1 *2 *1) (-12 (-4 *1 (-104 *2)) (-4 *2 (-1135)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-119 *2)) (-4 *2 (-795)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-124 *2)) (-4 *2 (-795)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-530)) (-4 *1 (-264 *3)) (-4 *3 (-1135)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-530)) (-4 *1 (-264 *2)) (-4 *2 (-1135)))) ((*1 *1 *2) - (-12 (-5 *2 (-1 (-884 (-208)) (-884 (-208)))) (-5 *1 (-245)))) + (-12 + (-5 *2 + (-2 + (|:| -3078 + (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) + (|:| -1300 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) + (|:| |relerr| (-208)))) + (|:| -1874 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1080 (-208))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1300 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))))) + (-5 *1 (-525)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-719)) (-4 *1 (-643 *2)) (-4 *2 (-1027)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -3078 + (-2 (|:| |xinit| (-208)) (|:| |xend| (-208)) + (|:| |fn| (-1181 (-297 (-208)))) (|:| |yinit| (-597 (-208))) + (|:| |intvals| (-597 (-208))) (|:| |g| (-297 (-208))) + (|:| |abserr| (-208)) (|:| |relerr| (-208)))) + (|:| -1874 + (-2 (|:| |stiffness| (-360)) (|:| |stability| (-360)) + (|:| |expense| (-360)) (|:| |accuracy| (-360)) + (|:| |intermediateResults| (-360)))))) + (-5 *1 (-751)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-597 (-460 *5 *6))) (-5 *3 (-460 *5 *6)) - (-14 *5 (-597 (-1099))) (-4 *6 (-432)) (-5 *2 (-1181 *6)) - (-5 *1 (-585 *5 *6))))) + (-12 (-5 *2 (-1186)) (-5 *1 (-1113 *3 *4)) (-4 *3 (-1027)) + (-4 *4 (-1027))))) +(((*1 *2 *1) (-12 (-4 *3 (-984)) (-5 *2 (-597 *1)) (-4 *1 (-1060 *3))))) +(((*1 *2 *2) (-12 (-5 *2 (-530)) (-5 *1 (-527))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1154 *5 *4)) (-4 *4 (-432)) (-4 *4 (-768)) + (-14 *5 (-1099)) (-5 *2 (-530)) (-5 *1 (-1041 *4 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-637 (-388 (-893 (-530))))) + (-5 *2 + (-597 + (-2 (|:| |radval| (-297 (-530))) (|:| |radmult| (-530)) + (|:| |radvect| (-597 (-637 (-297 (-530)))))))) + (-5 *1 (-969))))) +(((*1 *2 *2) + (|partial| -12 (-4 *3 (-1135)) (-5 *1 (-170 *3 *2)) + (-4 *2 (-624 *3))))) +(((*1 *1 *1) + (-12 (-4 *2 (-432)) (-4 *3 (-795)) (-4 *4 (-741)) + (-5 *1 (-927 *2 *3 *4 *5)) (-4 *5 (-890 *2 *4 *3))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -10319,50 +9959,81 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-522)) (-5 *2 (-719)) (-5 *1 (-42 *4 *3)) - (-4 *3 (-398 *4))))) -(((*1 *2 *2 *3) - (|partial| -12 - (-5 *3 (-597 (-2 (|:| |func| *2) (|:| |pole| (-110))))) - (-4 *2 (-13 (-411 *4) (-941))) (-4 *4 (-13 (-795) (-522))) - (-5 *1 (-258 *4 *2))))) -(((*1 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) -(((*1 *2 *1) (-12 (-4 *1 (-406 *3)) (-4 *3 (-1027)) (-5 *2 (-719))))) -(((*1 *1 *2) (-12 (-5 *2 (-597 *1)) (-4 *1 (-1060 *3)) (-4 *3 (-984)))) - ((*1 *2 *2 *1) - (|partial| -12 (-5 *2 (-388 *1)) (-4 *1 (-1157 *3)) (-4 *3 (-984)) - (-4 *3 (-522)))) - ((*1 *1 *1 *1) - (|partial| -12 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*1 *1 *2) + (-12 (-5 *2 (-884 *3)) (-4 *1 (-1060 *3)) (-4 *3 (-984)))) + ((*1 *2 *3 *3 *3 *3) + (-12 (-5 *2 (-884 (-208))) (-5 *1 (-1132)) (-5 *3 (-208))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -10379,47 +10050,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-522)) (-5 *2 (-719)) (-5 *1 (-42 *4 *3)) - (-4 *3 (-398 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-597 *6)) (-5 *4 (-597 (-1080 *7))) (-4 *6 (-795)) + (-4 *7 (-890 *5 (-502 *6) *6)) (-4 *5 (-984)) + (-5 *2 (-1 (-1080 *7) *7)) (-5 *1 (-1052 *5 *6 *7))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941)))))) +(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-94))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-951)) (-5 *2 (-804))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1095 *4)) (-4 *4 (-330)) + (-5 *2 (-1181 (-597 (-2 (|:| -3417 *4) (|:| -1986 (-1046)))))) + (-5 *1 (-327 *4))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1080 (-388 *3))) (-5 *1 (-163 *3)) (-4 *3 (-289))))) (((*1 *2 *3 *1) (|partial| -12 (-4 *1 (-35 *3 *4)) (-4 *3 (-1027)) (-4 *4 (-1027)) - (-5 *2 (-2 (|:| -2940 *3) (|:| -1806 *4)))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) -(((*1 *1 *1) (-12 (-4 *1 (-406 *2)) (-4 *2 (-1027)) (-4 *2 (-349))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-1157 *2)) (-4 *2 (-984)) (-4 *2 (-522))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1099)) (-5 *2 (-110)) (-5 *1 (-112)))) - ((*1 *2 *1 *3) (-12 (-4 *1 (-284)) (-5 *3 (-1099)) (-5 *2 (-110)))) - ((*1 *2 *1 *3) (-12 (-4 *1 (-284)) (-5 *3 (-112)) (-5 *2 (-110)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1099)) (-5 *2 (-110)) (-5 *1 (-570 *4)) (-4 *4 (-795)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-112)) (-5 *2 (-110)) (-5 *1 (-570 *4)) (-4 *4 (-795)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1027)) (-5 *2 (-110)) (-5 *1 (-828 *5 *3 *4)) - (-4 *3 (-827 *5)) (-4 *4 (-572 (-833 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-597 *6)) (-4 *6 (-827 *5)) (-4 *5 (-1027)) - (-5 *2 (-110)) (-5 *1 (-828 *5 *6 *4)) (-4 *4 (-572 (-833 *5)))))) -(((*1 *2 *2) (-12 (-5 *2 (-597 (-637 (-297 (-530))))) (-5 *1 (-969))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *3 (-597 (-460 *5 *6))) (-5 *4 (-806 *5)) - (-14 *5 (-597 (-1099))) (-5 *2 (-460 *5 *6)) (-5 *1 (-585 *5 *6)) - (-4 *6 (-432)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-597 (-460 *5 *6))) (-5 *4 (-806 *5)) - (-14 *5 (-597 (-1099))) (-5 *2 (-460 *5 *6)) (-5 *1 (-585 *5 *6)) - (-4 *6 (-432))))) + (-5 *2 (-2 (|:| -3078 *3) (|:| -1874 *4)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-643 *3)) (-4 *3 (-1027)) + (-5 *2 (-597 (-2 (|:| -1874 *3) (|:| -2632 (-719)))))))) +(((*1 *2 *3 *3 *4 *5) + (-12 (-5 *3 (-597 (-637 *6))) (-5 *4 (-110)) (-5 *5 (-530)) + (-5 *2 (-637 *6)) (-5 *1 (-967 *6)) (-4 *6 (-344)) (-4 *6 (-984)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-597 (-637 *4))) (-5 *2 (-637 *4)) (-5 *1 (-967 *4)) + (-4 *4 (-344)) (-4 *4 (-984)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *3 (-597 (-637 *5))) (-5 *4 (-530)) (-5 *2 (-637 *5)) + (-5 *1 (-967 *5)) (-4 *5 (-344)) (-4 *5 (-984))))) +(((*1 *1 *1 *1) (-4 *1 (-515)))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-4 *1 (-307 *2 *3)) (-4 *2 (-984)) (-4 *3 (-740))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -10436,12 +10099,16 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-522)) (-5 *2 (-719)) (-5 *1 (-42 *4 *3)) - (-4 *3 (-398 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941)))))) +(((*1 *2 *1 *1) + (-12 + (-5 *2 + (-2 (|:| -2204 (-730 *3)) (|:| |coef1| (-730 *3)) + (|:| |coef2| (-730 *3)))) + (-5 *1 (-730 *3)) (-4 *3 (-522)) (-4 *3 (-984)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-522)) (-4 *3 (-984)) (-4 *4 (-741)) (-4 *5 (-795)) + (-5 *2 (-2 (|:| -2204 *1) (|:| |coef1| *1) (|:| |coef2| *1))) + (-4 *1 (-998 *3 *4 *5))))) (((*1 *2 *1) (-12 (-4 *1 (-227 *2)) (-4 *2 (-1135)))) ((*1 *2 *1) (|partial| -12 (-4 *1 (-1129 *3 *4 *5 *2)) (-4 *3 (-522)) @@ -10449,32 +10116,21 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-719)) (-4 *1 (-1169 *3)) (-4 *3 (-1135)))) ((*1 *2 *1) (-12 (-4 *1 (-1169 *2)) (-4 *2 (-1135))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-522)) - (-5 *2 (-2 (|:| -1981 *4) (|:| -3624 *3) (|:| -3088 *3))) - (-5 *1 (-910 *4 *3)) (-4 *3 (-1157 *4)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-984)) (-4 *4 (-741)) (-4 *5 (-795)) - (-5 *2 (-2 (|:| -3624 *1) (|:| -3088 *1))) (-4 *1 (-998 *3 *4 *5)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-522)) (-4 *3 (-984)) - (-5 *2 (-2 (|:| -1981 *3) (|:| -3624 *1) (|:| -3088 *1))) - (-4 *1 (-1157 *3))))) +(((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-530)) (-5 *1 (-982))))) +(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-770))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-830 *4 *5)) (-5 *3 (-830 *4 *6)) (-4 *4 (-1027)) (-4 *5 (-1027)) (-4 *6 (-617 *5)) (-5 *1 (-826 *4 *5 *6))))) -(((*1 *2 *2) (-12 (-5 *2 (-637 (-297 (-530)))) (-5 *1 (-969))))) -(((*1 *2 *3) - (-12 (-5 *3 (-597 (-460 *4 *5))) (-14 *4 (-597 (-1099))) - (-4 *5 (-432)) (-5 *2 (-597 (-230 *4 *5))) (-5 *1 (-585 *4 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1135)) (-5 *1 (-308 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-597 *3)) (-4 *3 (-1135)) (-5 *1 (-493 *3 *4)) + (-14 *4 (-530))))) +(((*1 *2 *2 *2) (-12 (-5 *1 (-150 *2)) (-4 *2 (-515))))) +(((*1 *2 *3) (-12 (-5 *3 (-884 *2)) (-5 *1 (-922 *2)) (-4 *2 (-984))))) +(((*1 *2 *1) + (-12 (-4 *1 (-916 *3 *4 *5 *6)) (-4 *3 (-984)) (-4 *4 (-741)) + (-4 *5 (-795)) (-4 *6 (-998 *3 *4 *5)) (-5 *2 (-597 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-1080 *3)) (-5 *1 (-163 *3)) (-4 *3 (-289))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -10491,45 +10147,45 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3 *2 *4) - (-12 (-5 *3 (-112)) (-5 *4 (-719)) (-4 *5 (-432)) (-4 *5 (-795)) - (-4 *5 (-975 (-530))) (-4 *5 (-522)) (-5 *1 (-40 *5 *2)) - (-4 *2 (-411 *5)) - (-4 *2 - (-13 (-344) (-284) - (-10 -8 (-15 -1848 ((-1051 *5 (-570 $)) $)) - (-15 -1857 ((-1051 *5 (-570 $)) $)) - (-15 -2258 ($ (-1051 *5 (-570 $)))))))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941)))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-719)) (-4 *5 (-522)) + (-5 *2 + (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-910 *5 *3)) (-4 *3 (-1157 *5))))) (((*1 *2) (-12 (-5 *2 (-110)) (-5 *1 (-708))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) -(((*1 *2 *3 *4 *5 *6) - (-12 (-5 *6 (-862)) (-4 *5 (-289)) (-4 *3 (-1157 *5)) - (-5 *2 (-2 (|:| |plist| (-597 *3)) (|:| |modulo| *5))) - (-5 *1 (-440 *5 *3)) (-5 *4 (-597 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-344)) (-4 *4 (-522)) (-4 *5 (-1157 *4)) - (-5 *2 (-2 (|:| -3149 (-578 *4 *5)) (|:| -3138 (-388 *5)))) - (-5 *1 (-578 *4 *5)) (-5 *3 (-388 *5)))) - ((*1 *2 *1) - (-12 (-5 *2 (-597 (-1088 *3 *4))) (-5 *1 (-1088 *3 *4)) - (-14 *3 (-862)) (-4 *4 (-984)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-432)) (-4 *3 (-984)) - (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) - (-4 *1 (-1157 *3))))) (((*1 *2 *1) - (-12 (-4 *4 (-1027)) (-5 *2 (-830 *3 *4)) (-5 *1 (-826 *3 *4 *5)) - (-4 *3 (-1027)) (-4 *5 (-617 *4))))) + (-12 (|has| *1 (-6 -4269)) (-4 *1 (-468 *3)) (-4 *3 (-1135)) + (-5 *2 (-597 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-597 *3)) (-5 *1 (-686 *3)) (-4 *3 (-1027))))) +(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-770))))) +(((*1 *2 *3 *3 *4 *3 *3 *3 *3 *3 *3 *3 *5 *3 *6 *7) + (-12 (-5 *3 (-530)) (-5 *5 (-637 (-208))) + (-5 *6 (-3 (|:| |fn| (-369)) (|:| |fp| (-65 DOT)))) + (-5 *7 (-3 (|:| |fn| (-369)) (|:| |fp| (-66 IMAGE)))) (-5 *4 (-208)) + (-5 *2 (-973)) (-5 *1 (-704)))) + ((*1 *2 *3 *3 *4 *3 *3 *3 *3 *3 *3 *3 *5 *3 *6 *7 *8) + (-12 (-5 *3 (-530)) (-5 *5 (-637 (-208))) + (-5 *6 (-3 (|:| |fn| (-369)) (|:| |fp| (-65 DOT)))) + (-5 *7 (-3 (|:| |fn| (-369)) (|:| |fp| (-66 IMAGE)))) (-5 *8 (-369)) + (-5 *4 (-208)) (-5 *2 (-973)) (-5 *1 (-704))))) +(((*1 *2 *3 *4 *4 *5) + (|partial| -12 (-5 *4 (-570 *3)) (-5 *5 (-597 *3)) + (-4 *3 (-13 (-411 *6) (-27) (-1121))) + (-4 *6 (-13 (-432) (-975 (-530)) (-795) (-140) (-593 (-530)))) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-597 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-532 *6 *3 *7)) (-4 *7 (-1027))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-33)) (-5 *2 (-110))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-597 *5)) (-5 *4 (-530)) (-4 *5 (-793)) (-4 *5 (-344)) + (-5 *2 (-719)) (-5 *1 (-886 *5 *6)) (-4 *6 (-1157 *5))))) +(((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-13 (-344) (-140) (-975 (-530)))) + (-4 *5 (-1157 *4)) + (-5 *2 (-2 (|:| -2104 (-388 *5)) (|:| |coeff| (-388 *5)))) + (-5 *1 (-534 *4 *5)) (-5 *3 (-388 *5))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-804) (-804))) (-5 *1 (-112)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-804) (-597 (-804)))) (-5 *1 (-112)))) ((*1 *2 *1) @@ -10538,17 +10194,15 @@ (-12 (-5 *2 (-1186)) (-5 *1 (-198 *3)) (-4 *3 (-13 (-795) - (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 (*2 $)) - (-15 -1671 (*2 $))))))) + (-10 -8 (-15 -1902 ((-1082) $ (-1099))) (-15 -2388 (*2 $)) + (-15 -3595 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-375)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-530)) (-5 *2 (-1186)) (-5 *1 (-375)))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-480)))) ((*1 *2 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-1186)) (-5 *1 (-659)))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1116)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-530)) (-5 *2 (-1186)) (-5 *1 (-1116))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-637 (-388 (-893 (-530))))) - (-5 *2 (-637 (-297 (-530)))) (-5 *1 (-969))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-597 (-1082))) (-5 *1 (-375))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -10568,22 +10222,18 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *3) - (-12 (-14 *4 (-597 (-1099))) (-4 *5 (-432)) - (-5 *2 - (-2 (|:| |glbase| (-597 (-230 *4 *5))) (|:| |glval| (-597 (-530))))) - (-5 *1 (-585 *4 *5)) (-5 *3 (-597 (-230 *4 *5)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-388 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) + (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) + (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) (((*1 *1 *1) (-12 (-4 *1 (-235 *2 *3 *4 *5)) (-4 *2 (-984)) (-4 *3 (-795)) (-4 *4 (-248 *3)) (-4 *5 (-741))))) (((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -4270)) (-4 *1 (-144 *2)) (-4 *2 (-1135)) + (-12 (|has| *1 (-6 -4269)) (-4 *1 (-144 *2)) (-4 *2 (-1135)) (-4 *2 (-1027)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-110) *3)) (|has| *1 (-6 -4270)) (-4 *1 (-144 *3)) + (-12 (-5 *2 (-1 (-110) *3)) (|has| *1 (-6 -4269)) (-4 *1 (-144 *3)) (-4 *3 (-1135)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-110) *3)) (-4 *1 (-624 *3)) (-4 *3 (-1135)))) @@ -10595,27 +10245,25 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1064 *3 *4)) (-4 *3 (-13 (-1027) (-33))) (-4 *4 (-13 (-1027) (-33))) (-5 *1 (-1065 *3 *4))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1099)) (-5 *3 (-360)) (-5 *1 (-996))))) +(((*1 *2 *1) (-12 (-4 *1 (-284)) (-5 *2 (-597 (-112)))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-597 *5)) (-4 *5 (-1157 *3)) (-4 *3 (-289)) - (-5 *2 (-110)) (-5 *1 (-435 *3 *5))))) + (-12 (-5 *3 (-388 *6)) (-4 *5 (-1139)) (-4 *6 (-1157 *5)) + (-5 *2 (-2 (|:| -3194 (-719)) (|:| -2065 *3) (|:| |radicand| *6))) + (-5 *1 (-141 *5 *6 *7)) (-5 *4 (-719)) (-4 *7 (-1157 *3))))) +(((*1 *2) (-12 (-5 *2 (-862)) (-5 *1 (-1184)))) + ((*1 *2 *2) (-12 (-5 *2 (-862)) (-5 *1 (-1184))))) +(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-137))))) (((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1135)) (-4 *1 (-144 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-597 (-2 (|:| -3059 (-719)) (|:| -3721 *4) (|:| |num| *4)))) + (-5 *2 (-597 (-2 (|:| -3194 (-719)) (|:| -3705 *4) (|:| |num| *4)))) (-4 *4 (-1157 *3)) (-4 *3 (-13 (-344) (-140))) (-5 *1 (-380 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-5 *3 (-597 (-893 (-530)))) (-5 *4 (-110)) (-5 *1 (-418)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-5 *3 (-597 (-1099))) (-5 *4 (-110)) (-5 *1 (-418)))) ((*1 *2 *1) (-12 (-5 *2 (-1080 *3)) (-5 *1 (-560 *3)) (-4 *3 (-1135)))) @@ -10635,23 +10283,23 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-662 *2 *3 *4)) (-4 *2 (-795)) (-4 *3 (-1027)) (-14 *4 - (-1 (-110) (-2 (|:| -1910 *2) (|:| -3059 *3)) - (-2 (|:| -1910 *2) (|:| -3059 *3)))))) + (-1 (-110) (-2 (|:| -1986 *2) (|:| -3194 *3)) + (-2 (|:| -1986 *2) (|:| -3194 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *1 (-814 *2 *3)) (-4 *2 (-1135)) (-4 *3 (-1135)))) ((*1 *1 *2) - (-12 (-5 *2 (-597 (-2 (|:| -2940 (-1099)) (|:| -1806 *4)))) + (-12 (-5 *2 (-597 (-2 (|:| -3078 (-1099)) (|:| -1874 *4)))) (-4 *4 (-1027)) (-5 *1 (-830 *3 *4)) (-4 *3 (-1027)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-597 *5)) (-4 *5 (-13 (-1027) (-33))) (-5 *2 (-597 (-1064 *3 *5))) (-5 *1 (-1064 *3 *5)) (-4 *3 (-13 (-1027) (-33))))) ((*1 *2 *3) - (-12 (-5 *3 (-597 (-2 (|:| |val| *4) (|:| -2350 *5)))) + (-12 (-5 *3 (-597 (-2 (|:| |val| *4) (|:| -2473 *5)))) (-4 *4 (-13 (-1027) (-33))) (-4 *5 (-13 (-1027) (-33))) (-5 *2 (-597 (-1064 *4 *5))) (-5 *1 (-1064 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2350 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2473 *4))) (-4 *3 (-13 (-1027) (-33))) (-4 *4 (-13 (-1027) (-33))) (-5 *1 (-1064 *3 *4)))) ((*1 *1 *2 *3) @@ -10674,21 +10322,54 @@ (-4 *4 (-13 (-1027) (-33))) (-5 *1 (-1065 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1089 *2 *3)) (-4 *2 (-1027)) (-4 *3 (-1027))))) -(((*1 *2 *2 *2 *3 *3) - (-12 (-5 *3 (-719)) (-4 *4 (-984)) (-5 *1 (-1153 *4 *2)) - (-4 *2 (-1157 *4))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) (-5 *3 (-530))))) -(((*1 *2 *3) - (-12 (-5 *3 (-637 (-388 (-893 (-530))))) (-5 *2 (-597 (-297 (-530)))) - (-5 *1 (-969))))) -(((*1 *2 *3) - (-12 (-5 *3 (-597 (-460 *4 *5))) (-14 *4 (-597 (-1099))) - (-4 *5 (-432)) - (-5 *2 - (-2 (|:| |gblist| (-597 (-230 *4 *5))) - (|:| |gvlist| (-597 (-530))))) - (-5 *1 (-585 *4 *5))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-597 (-570 (-47)))) (-5 *1 (-47)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-570 (-47))) (-5 *1 (-47)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1095 (-47))) (-5 *3 (-597 (-570 (-47)))) (-5 *1 (-47)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1095 (-47))) (-5 *3 (-570 (-47))) (-5 *1 (-47)))) + ((*1 *2 *1) (-12 (-4 *1 (-156 *2)) (-4 *2 (-162)))) + ((*1 *2 *3) + (-12 (-4 *2 (-13 (-344) (-793))) (-5 *1 (-169 *2 *3)) + (-4 *3 (-1157 (-159 *2))))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-862)) (-4 *1 (-310 *3)) (-4 *3 (-344)) (-4 *3 (-349)))) + ((*1 *2 *1) (-12 (-4 *1 (-310 *2)) (-4 *2 (-344)))) + ((*1 *2 *1) + (-12 (-4 *1 (-351 *2 *3)) (-4 *3 (-1157 *2)) (-4 *2 (-162)))) + ((*1 *2 *1) + (-12 (-4 *4 (-1157 *2)) (-4 *2 (-932 *3)) (-5 *1 (-394 *3 *2 *4 *5)) + (-4 *3 (-289)) (-4 *5 (-13 (-390 *2 *4) (-975 *2))))) + ((*1 *2 *1) + (-12 (-4 *4 (-1157 *2)) (-4 *2 (-932 *3)) + (-5 *1 (-395 *3 *2 *4 *5 *6)) (-4 *3 (-289)) (-4 *5 (-390 *2 *4)) + (-14 *6 (-1181 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-862)) (-4 *5 (-984)) + (-4 *2 (-13 (-385) (-975 *5) (-344) (-1121) (-266))) + (-5 *1 (-423 *5 *3 *2)) (-4 *3 (-1157 *5)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-597 (-570 (-473)))) (-5 *1 (-473)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-570 (-473))) (-5 *1 (-473)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1095 (-473))) (-5 *3 (-597 (-570 (-473)))) + (-5 *1 (-473)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1095 (-473))) (-5 *3 (-570 (-473))) (-5 *1 (-473)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1181 *4)) (-5 *3 (-862)) (-4 *4 (-330)) + (-5 *1 (-500 *4)))) + ((*1 *2 *3) + (-12 (-4 *4 (-432)) (-4 *5 (-673 *4 *2)) (-4 *2 (-1157 *4)) + (-5 *1 (-723 *4 *2 *5 *3)) (-4 *3 (-1157 *5)))) + ((*1 *2 *1) (-12 (-4 *1 (-745 *2)) (-4 *2 (-162)))) + ((*1 *2 *1) (-12 (-4 *1 (-936 *2)) (-4 *2 (-162)))) + ((*1 *1 *1) (-4 *1 (-993)))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-719)) (-5 *1 (-548 *2)) (-4 *2 (-515)))) + ((*1 *2 *3) + (-12 (-5 *2 (-2 (|:| -1510 *3) (|:| -3194 (-719)))) (-5 *1 (-548 *3)) + (-4 *3 (-515))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-1098)) (-5 *1 (-311))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -10708,24 +10389,17 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941)))))) -(((*1 *1 *1) (-5 *1 (-208))) - ((*1 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1) (-4 *1 (-1063))) ((*1 *1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *5 (-1181 (-597 *3))) (-4 *4 (-289)) - (-5 *2 (-597 *3)) (-5 *1 (-435 *4 *3)) (-4 *3 (-1157 *4))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-530)) (-5 *1 (-399 *2)) (-4 *2 (-522))))) +(((*1 *2 *2) (|partial| -12 (-5 *1 (-548 *2)) (-4 *2 (-515))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-1181 *4)) (-5 *3 (-1046)) (-4 *4 (-330)) + (-5 *1 (-500 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1082)) (-5 *1 (-1117))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-432)) (-4 *4 (-522)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| -4129 *4))) (-5 *1 (-910 *4 *3)) + (-4 *3 (-1157 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-297 (-208))) (-5 *2 (-110)) (-5 *1 (-249))))) (((*1 *1 *2) (-12 (-4 *1 (-37 *2)) (-4 *2 (-162)))) ((*1 *1 *2) (-12 (-5 *2 (-1181 *3)) (-4 *3 (-344)) (-14 *6 (-1181 (-637 *3))) @@ -10733,69 +10407,69 @@ ((*1 *1 *2) (-12 (-5 *2 (-1051 (-530) (-570 (-47)))) (-5 *1 (-47)))) ((*1 *2 *3) (-12 (-5 *2 (-51)) (-5 *1 (-50 *3)) (-4 *3 (-1135)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268 'JINT 'X 'ELAM) (-2268) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377 'JINT 'X 'ELAM) (-2377) (-647)))) (-5 *1 (-59 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268) (-2268 'XC) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377) (-2377 'XC) (-647)))) (-5 *1 (-61 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-320 (-2268 'X) (-2268) (-647))) (-5 *1 (-62 *3)) + (-12 (-5 *2 (-320 (-2377 'X) (-2377) (-647))) (-5 *1 (-62 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-637 (-320 (-2268) (-2268 'X 'HESS) (-647)))) + (-12 (-5 *2 (-637 (-320 (-2377) (-2377 'X 'HESS) (-647)))) (-5 *1 (-63 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-320 (-2268) (-2268 'XC) (-647))) (-5 *1 (-64 *3)) + (-12 (-5 *2 (-320 (-2377) (-2377 'XC) (-647))) (-5 *1 (-64 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268 'X) (-2268 '-4114) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377 'X) (-2377 '-4126) (-647)))) (-5 *1 (-69 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268) (-2268 'X) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377) (-2377 'X) (-647)))) (-5 *1 (-72 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268 'X 'EPS) (-2268 '-4114) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377 'X 'EPS) (-2377 '-4126) (-647)))) (-5 *1 (-73 *3 *4 *5)) (-14 *3 (-1099)) (-14 *4 (-1099)) (-14 *5 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268 'EPS) (-2268 'YA 'YB) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377 'EPS) (-2377 'YA 'YB) (-647)))) (-5 *1 (-74 *3 *4 *5)) (-14 *3 (-1099)) (-14 *4 (-1099)) (-14 *5 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-320 (-2268) (-2268 'X) (-647))) (-5 *1 (-75 *3)) + (-12 (-5 *2 (-320 (-2377) (-2377 'X) (-647))) (-5 *1 (-75 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-320 (-2268) (-2268 'X) (-647))) (-5 *1 (-76 *3)) + (-12 (-5 *2 (-320 (-2377) (-2377 'X) (-647))) (-5 *1 (-76 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268) (-2268 'XC) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377) (-2377 'XC) (-647)))) (-5 *1 (-77 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268) (-2268 'X) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377) (-2377 'X) (-647)))) (-5 *1 (-78 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268) (-2268 'X) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377) (-2377 'X) (-647)))) (-5 *1 (-79 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268 'X '-4114) (-2268) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377 'X '-4126) (-2377) (-647)))) (-5 *1 (-80 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-637 (-320 (-2268 'X '-4114) (-2268) (-647)))) + (-12 (-5 *2 (-637 (-320 (-2377 'X '-4126) (-2377) (-647)))) (-5 *1 (-81 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-637 (-320 (-2268 'X) (-2268) (-647)))) (-5 *1 (-82 *3)) + (-12 (-5 *2 (-637 (-320 (-2377 'X) (-2377) (-647)))) (-5 *1 (-82 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268 'X) (-2268) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377 'X) (-2377) (-647)))) (-5 *1 (-83 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-1181 (-320 (-2268 'X) (-2268 '-4114) (-647)))) + (-12 (-5 *2 (-1181 (-320 (-2377 'X) (-2377 '-4126) (-647)))) (-5 *1 (-84 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-637 (-320 (-2268 'XL 'XR 'ELAM) (-2268) (-647)))) + (-12 (-5 *2 (-637 (-320 (-2377 'XL 'XR 'ELAM) (-2377) (-647)))) (-5 *1 (-85 *3)) (-14 *3 (-1099)))) ((*1 *1 *2) - (-12 (-5 *2 (-320 (-2268 'X) (-2268 '-4114) (-647))) (-5 *1 (-87 *3)) + (-12 (-5 *2 (-320 (-2377 'X) (-2377 '-4126) (-647))) (-5 *1 (-87 *3)) (-14 *3 (-1099)))) ((*1 *2 *1) (-12 (-5 *2 (-943 2)) (-5 *1 (-105)))) ((*1 *2 *1) (-12 (-5 *2 (-388 (-530))) (-5 *1 (-105)))) @@ -10819,8 +10493,8 @@ (-12 (-5 *2 (-597 *3)) (-4 *3 (-13 (-795) - (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 ((-1186) $)) - (-15 -1671 ((-1186) $))))) + (-10 -8 (-15 -1902 ((-1082) $ (-1099))) (-15 -2388 ((-1186) $)) + (-15 -3595 ((-1186) $))))) (-5 *1 (-198 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-943 10)) (-5 *1 (-201)))) ((*1 *2 *1) (-12 (-5 *2 (-388 (-530))) (-5 *1 (-201)))) @@ -10861,14 +10535,14 @@ ((*1 *1 *2) (-12 (-4 *1 (-355 *2 *3)) (-4 *2 (-795)) (-4 *3 (-162)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1897 (-597 (-311))))) (-4 *1 (-364)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-364)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-364)))) ((*1 *1 *2) (-12 (-5 *2 (-637 (-647))) (-4 *1 (-364)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1897 (-597 (-311))))) (-4 *1 (-365)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-365)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-365)))) @@ -10878,71 +10552,71 @@ ((*1 *1 *2) (-12 (-5 *2 (-804)) (-5 *1 (-375)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1897 (-597 (-311))))) (-4 *1 (-377)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-377)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-377)))) ((*1 *1 *2) (-12 (-5 *2 (-276 (-297 (-159 (-360))))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-276 (-297 (-360)))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-276 (-297 (-530)))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-297 (-159 (-360)))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-297 (-360))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-297 (-530))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-276 (-297 (-642)))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) 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(-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-297 (-649))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1897 (-597 (-311))))) (-5 *1 (-379 *3 *4 *5 *6)) (-14 *3 (-1099)) - (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-5 *1 (-379 *3 *4 *5 *6)) - (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *3 (-1099)) (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-5 *1 (-379 *3 *4 *5 *6)) (-14 *3 (-1099)) - (-14 *4 (-3 (|:| |fst| (-415)) (|:| -2875 "void"))) + (-14 *4 (-3 (|:| |fst| (-415)) (|:| -3020 "void"))) (-14 *5 (-597 (-1099))) (-14 *6 (-1103)))) ((*1 *1 *2) (-12 (-5 *2 (-312 *4)) (-4 *4 (-13 (-795) (-21))) @@ -10970,14 +10644,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-804)) (-5 *1 (-418)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1897 (-597 (-311))))) (-4 *1 (-420)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-420)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-420)))) ((*1 *1 *2) (-12 (-5 *2 (-1181 (-647))) (-4 *1 (-420)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1827 (-597 (-311))))) + (-5 *2 (-2 (|:| |localSymbols| (-1103)) (|:| -1897 (-597 (-311))))) (-4 *1 (-421)))) ((*1 *1 *2) (-12 (-5 *2 (-311)) (-4 *1 (-421)))) ((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-4 *1 (-421)))) @@ -11046,18 +10720,18 @@ ((*1 *1 *2) (-12 (-4 *3 (-984)) (-5 *1 (-661 *3 *2)) (-4 *2 (-1157 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -1910 *3) (|:| -3059 *4))) + (-12 (-5 *2 (-2 (|:| -1986 *3) (|:| -3194 *4))) (-5 *1 (-662 *3 *4 *5)) (-4 *3 (-795)) (-4 *4 (-1027)) (-14 *5 (-1 (-110) *2 *2)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -1910 *3) (|:| -3059 *4))) (-4 *3 (-795)) + (-12 (-5 *2 (-2 (|:| -1986 *3) (|:| -3194 *4))) (-4 *3 (-795)) (-4 *4 (-1027)) (-5 *1 (-662 *3 *4 *5)) (-14 *5 (-1 (-110) *2 *2)))) ((*1 *2 *1) (-12 (-4 *2 (-162)) (-5 *1 (-664 *2 *3 *4 *5 *6)) (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-597 (-2 (|:| -1981 *3) (|:| -3931 *4)))) (-4 *3 (-984)) + (-12 (-5 *2 (-597 (-2 (|:| -2065 *3) (|:| -3940 *4)))) (-4 *3 (-984)) (-4 *4 (-675)) (-5 *1 (-684 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-530)) (-4 *1 (-712)))) ((*1 *1 *2) @@ -11066,25 +10740,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) - (|:| -2902 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) + (|:| -1300 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))) (|:| |mdnia| (-2 (|:| |fn| (-297 (-208))) - (|:| -2902 (-597 (-1022 (-788 (-208))))) + (|:| -1300 (-597 (-1022 (-788 (-208))))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))))) (-5 *1 (-717)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-297 (-208))) - (|:| -2902 (-597 (-1022 (-788 (-208))))) (|:| |abserr| (-208)) + (|:| -1300 (-597 (-1022 (-788 (-208))))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))) (-5 *1 (-717)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) - (|:| -2902 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) + (|:| -1300 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) (|:| |relerr| (-208)))) (-5 *1 (-717)))) ((*1 *2 *1) (-12 (-5 *2 (-804)) (-5 *1 (-717)))) @@ -11110,23 +10784,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-297 (-208))) (|:| -3677 (-597 (-208))) + (-2 (|:| |fn| (-297 (-208))) (|:| -3657 (-597 (-208))) (|:| |lb| (-597 (-788 (-208)))) (|:| |cf| (-597 (-297 (-208)))) (|:| |ub| (-597 (-788 (-208)))))) (|:| |lsa| (-2 (|:| |lfn| (-597 (-297 (-208)))) - (|:| -3677 (-597 (-208))))))) + (|:| -3657 (-597 (-208))))))) (-5 *1 (-786)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-597 (-297 (-208)))) (|:| -3677 (-597 (-208))))) + (-2 (|:| |lfn| (-597 (-297 (-208)))) (|:| -3657 (-597 (-208))))) (-5 *1 (-786)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-297 (-208))) (|:| -3677 (-597 (-208))) + (-2 (|:| |fn| (-297 (-208))) (|:| -3657 (-597 (-208))) (|:| |lb| (-597 (-788 (-208)))) (|:| |cf| (-597 (-297 (-208)))) (|:| |ub| (-597 (-788 (-208)))))) (-5 *1 (-786)))) @@ -11285,12 +10959,13 @@ (-12 (-5 *2 (-615 *3 *4)) (-4 *3 (-795)) (-4 *4 (-162)) (-5 *1 (-1199 *3 *4)))) ((*1 *1 *2) (-12 (-5 *1 (-1202 *3 *2)) (-4 *3 (-984)) (-4 *2 (-791))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-795)) (-5 *1 (-228 *3))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-46 *2 *3)) (-4 *2 (-984)) (-4 *3 (-740)) (-4 *2 (-344)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-530)) (-5 *1 (-208)))) ((*1 *1 *1 *1) - (-1476 (-12 (-5 *1 (-276 *2)) (-4 *2 (-344)) (-4 *2 (-1135))) + (-1461 (-12 (-5 *1 (-276 *2)) (-4 *2 (-344)) (-4 *2 (-1135))) (-12 (-5 *1 (-276 *2)) (-4 *2 (-453)) (-4 *2 (-1135))))) ((*1 *1 *1 *1) (-4 *1 (-344))) ((*1 *1 *1 *2) (-12 (-5 *2 (-530)) (-5 *1 (-360)))) @@ -11338,8 +11013,6 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1202 *2 *3)) (-4 *2 (-344)) (-4 *2 (-984)) (-4 *3 (-791))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-984)) (-5 *1 (-1153 *3 *2)) (-4 *2 (-1157 *3))))) (((*1 *2 *3 *2 *3) (-12 (-5 *2 (-418)) (-5 *3 (-1099)) (-5 *1 (-1102)))) ((*1 *2 *3 *2) (-12 (-5 *2 (-418)) (-5 *3 (-1099)) (-5 *1 (-1102)))) @@ -11352,12 +11025,10 @@ (-12 (-5 *2 (-418)) (-5 *3 (-1099)) (-5 *1 (-1103)))) ((*1 *2 *3 *2 *1) (-12 (-5 *2 (-418)) (-5 *3 (-597 (-1099))) (-5 *1 (-1103))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) - (-5 *3 (-597 (-530))))) - ((*1 *2 *3) - (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) - (-5 *3 (-597 (-530)))))) +(((*1 *1 *1 *1) (-5 *1 (-804)))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-110)) (-5 *1 (-161)))) + ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1182)))) + ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1183))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -11377,29 +11048,30 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-110)) (-5 *1 (-161)))) - ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1182)))) - ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1183))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-637 (-388 (-893 (-530))))) - (-5 *2 (-597 (-637 (-297 (-530))))) (-5 *1 (-969)) - (-5 *3 (-297 (-530)))))) -(((*1 *1 *1) (-4 *1 (-583))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) -(((*1 *2 *3 *2) (-12 (-5 *2 (-208)) (-5 *3 (-719)) (-5 *1 (-209)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-159 (-208))) (-5 *3 (-719)) (-5 *1 (-209)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *3 (-719)) (-4 *4 (-289)) (-4 *6 (-1157 *4)) - (-5 *2 (-1181 (-597 *6))) (-5 *1 (-435 *4 *6)) (-5 *5 (-597 *6))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-522) (-795) (-975 (-530)))) + (-5 *2 (-159 (-297 *4))) (-5 *1 (-172 *4 *3)) + (-4 *3 (-13 (-27) (-1121) (-411 (-159 *4)))))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-432) (-795) (-975 (-530)) (-593 (-530)))) + (-5 *2 (-159 *3)) (-5 *1 (-1125 *4 *3)) + (-4 *3 (-13 (-27) (-1121) (-411 *4)))))) +(((*1 *2 *3 *2) + (-12 (-4 *2 (-13 (-344) (-793))) (-5 *1 (-169 *2 *3)) + (-4 *3 (-1157 (-159 *2))))) + ((*1 *2 *3) + (-12 (-4 *2 (-13 (-344) (-793))) (-5 *1 (-169 *2 *3)) + (-4 *3 (-1157 (-159 *2)))))) +(((*1 *2 *2) + (-12 (-5 *2 (-110)) (-5 *1 (-422 *3)) (-4 *3 (-1157 (-530)))))) +(((*1 *2 *1) (-12 (-4 *1 (-289)) (-5 *2 (-719))))) +(((*1 *2) (-12 (-5 *2 (-862)) (-5 *1 (-1184)))) + ((*1 *2 *2) (-12 (-5 *2 (-862)) (-5 *1 (-1184))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-637 *3)) (-4 *3 (-289)) (-5 *1 (-648 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-344)) (-5 *2 (-597 *3)) (-5 *1 (-886 *4 *3)) + (-4 *3 (-1157 *4))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-99)) (-5 *2 (-110)))) ((*1 *1 *1 *1) (-5 *1 (-804)))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) @@ -11408,8 +11080,8 @@ (-12 (-5 *1 (-198 *2)) (-4 *2 (-13 (-795) - (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 ((-1186) $)) - (-15 -1671 ((-1186) $))))))) + (-10 -8 (-15 -1902 ((-1082) $ (-1099))) (-15 -2388 ((-1186) $)) + (-15 -3595 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-276 *2)) (-4 *2 (-21)) (-4 *2 (-1135)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-276 *2)) (-4 *2 (-21)) (-4 *2 (-1135)))) ((*1 *1 *1 *1) @@ -11429,18 +11101,17 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-884 (-208))) (-5 *1 (-1132)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1179 *2)) (-4 *2 (-1135)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1179 *2)) (-4 *2 (-1135)) (-4 *2 (-21))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-984)) (-5 *1 (-1153 *3 *2)) (-4 *2 (-1157 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *3 (-597 (-530))) - (-5 *1 (-824))))) -(((*1 *2 *3) - (-12 (-5 *3 (-637 (-388 (-893 (-530))))) - (-5 *2 - (-597 - (-2 (|:| |radval| (-297 (-530))) (|:| |radmult| (-530)) - (|:| |radvect| (-597 (-637 (-297 (-530)))))))) - (-5 *1 (-969))))) +(((*1 *1) (-4 *1 (-23))) ((*1 *1) (-4 *1 (-33))) + ((*1 *1) + (-12 (-5 *1 (-132 *2 *3 *4)) (-14 *2 (-530)) (-14 *3 (-719)) + (-4 *4 (-162)))) + ((*1 *1) (-4 *1 (-675))) ((*1 *1) (-5 *1 (-1099)))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-1181 *5)) (-4 *5 (-740)) (-5 *2 (-110)) + (-5 *1 (-790 *4 *5)) (-14 *4 (-719))))) +(((*1 *2 *3 *4) + (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) + (-5 *1 (-654 *3 *4)) (-4 *3 (-1135)) (-4 *4 (-1135))))) (((*1 *1 *1) (-4 *1 (-93))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -11457,32 +11128,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-710)))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-110)) + (-4 *6 (-13 (-432) (-795) (-975 (-530)) (-593 (-530)))) + (-4 *3 (-13 (-27) (-1121) (-411 *6) (-10 -8 (-15 -2366 ($ *7))))) + (-4 *7 (-793)) + (-4 *8 + (-13 (-1159 *3 *7) (-344) (-1121) + (-10 -8 (-15 -3289 ($ $)) (-15 -1545 ($ $))))) + (-5 *2 + (-3 (|:| |%series| *8) + (|:| |%problem| (-2 (|:| |func| (-1082)) (|:| |prob| (-1082)))))) + (-5 *1 (-403 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1082)) (-4 *9 (-923 *8)) + (-14 *10 (-1099))))) +(((*1 *2 *3) + (-12 (-4 *4 (-330)) (-5 *2 (-399 (-1095 (-1095 *4)))) + (-5 *1 (-1134 *4)) (-5 *3 (-1095 (-1095 *4)))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *3 (-1 (-208) (-208) (-208))) + (-5 *4 (-3 (-1 (-208) (-208) (-208) (-208)) "undefined")) + (-5 *5 (-1022 (-208))) (-5 *6 (-597 (-245))) (-5 *2 (-1059 (-208))) + (-5 *1 (-645))))) +(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-770))))) +(((*1 *1) (-5 *1 (-418)))) (((*1 *2 *3 *4) - (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) - (-5 *1 (-654 *3 *4)) (-4 *3 (-1135)) (-4 *4 (-1135))))) -(((*1 *1 *1) (-4 *1 (-583))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) - (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) -(((*1 *1 *2 *1) (-12 (-5 *2 (-1098)) (-5 *1 (-311))))) -(((*1 *2 *2) (-12 (-5 *2 (-208)) (-5 *1 (-209)))) - ((*1 *2 *2) (-12 (-5 *2 (-159 (-208))) (-5 *1 (-209)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-412 *3 *2)) - (-4 *2 (-411 *3)))) - ((*1 *1 *1) (-4 *1 (-1063)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-597 *3)) (-4 *3 (-1157 *5)) (-4 *5 (-289)) - (-5 *2 (-719)) (-5 *1 (-435 *5 *3))))) + (-12 (-5 *3 (-769)) (-5 *4 (-51)) (-5 *2 (-1186)) (-5 *1 (-779))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-148))) ((*1 *1 *1 *1) (-12 (-5 *1 (-198 *2)) (-4 *2 (-13 (-795) - (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 ((-1186) $)) - (-15 -1671 ((-1186) $))))))) + (-10 -8 (-15 -1902 ((-1082) $ (-1099))) (-15 -2388 ((-1186) $)) + (-15 -3595 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-276 *2)) (-4 *2 (-25)) (-4 *2 (-1135)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-276 *2)) (-4 *2 (-25)) (-4 *2 (-1135)))) ((*1 *1 *2 *1) @@ -11505,14 +11183,28 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-984)) (-5 *1 (-1084 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-884 (-208))) (-5 *1 (-1132)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1179 *2)) (-4 *2 (-1135)) (-4 *2 (-25))))) -(((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-522)) - (-5 *2 (-2 (|:| -3624 *3) (|:| -3088 *3))) (-5 *1 (-1152 *4 *3)) - (-4 *3 (-1157 *4))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1080 (-597 (-530)))) (-5 *1 (-824)) - (-5 *3 (-597 (-530)))))) -(((*1 *1 *2) (-12 (-5 *1 (-964 *2)) (-4 *2 (-1135))))) +(((*1 *2 *3) + (-12 (-4 *4 (-354 *2)) (-4 *5 (-354 *2)) (-4 *2 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(-5 *3 (-112)) (-5 *2 (-110)) (-5 *1 (-283 *4)) (-4 *4 (-284)))) - ((*1 *2 *3) (-12 (-4 *1 (-284)) (-5 *3 (-112)) (-5 *2 (-110)))) - ((*1 *2 *3) - (-12 (-5 *3 (-112)) (-4 *5 (-795)) (-5 *2 (-110)) - (-5 *1 (-410 *4 *5)) (-4 *4 (-411 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-112)) (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) - (-5 *1 (-412 *4 *5)) (-4 *5 (-411 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-112)) (-4 *4 (-13 (-795) (-522))) (-5 *2 (-110)) - (-5 *1 (-584 *4 *5)) (-4 *5 (-13 (-411 *4) (-941) (-1121)))))) + (-12 (-5 *3 (-230 *4 *5)) (-14 *4 (-597 (-1099))) (-4 *5 (-984)) + (-5 *2 (-893 *5)) (-5 *1 (-885 *4 *5))))) (((*1 *1 *1) (-4 *1 (-93))) ((*1 *1 *1 *1) (-5 *1 (-208))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) @@ -11684,47 +11371,38 @@ ((*1 *2 *2) (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3))))) -(((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-5 *1 (-311))))) -(((*1 *2 *3) (-12 (-5 *3 (-804)) (-5 *2 (-1186)) (-5 *1 (-1062)))) - ((*1 *2 *3) - 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*2 *3 *4 *5 *3) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 (-1 (-3 (-2 (|:| -2104 *6) (|:| |coeff| *6)) "failed") *6)) + (-4 *6 (-344)) (-4 *7 (-1157 *6)) + (-5 *2 + (-3 (-2 (|:| |answer| (-388 *7)) (|:| |a0| *6)) + (-2 (|:| -2104 (-388 *7)) (|:| |coeff| (-388 *7))) "failed")) + (-5 *1 (-540 *6 *7)) (-5 *3 (-388 *7))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -11951,64 +11626,24 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3)))) ((*1 *1 *1) (-4 *1 (-1124)))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-110) *3)) (-4 *3 (-1135)) (-5 *1 (-560 *3)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-110) *3)) (-4 *3 (-1135)) (-5 *1 (-1080 *3))))) -(((*1 *2 *1) (-12 (|has| *1 (-6 -4270)) (-4 *1 (-33)) (-5 *2 (-719)))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |lfn| (-597 (-297 (-208)))) (|:| -3657 (-597 (-208))))) + (-5 *2 (-360)) (-5 *1 (-249)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1181 (-297 (-208)))) (-5 *2 (-360)) (-5 *1 (-287))))) +(((*1 *2 *1) (-12 (|has| *1 (-6 -4269)) (-4 *1 (-33)) (-5 *2 (-719)))) ((*1 *2 *1) (-12 (-4 *1 (-1030 *3 *4 *5 *6 *7)) (-4 *3 (-1027)) (-4 *4 (-1027)) (-4 *5 (-1027)) (-4 *6 (-1027)) (-4 *7 (-1027)) (-5 *2 (-530)))) ((*1 *2 *1) (-12 (-5 *2 (-719)) (-5 *1 (-1202 *3 *4)) (-4 *3 (-984)) (-4 *4 (-791))))) -(((*1 *2 *3) - (-12 - (-5 *2 - (-597 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530)))))) - (-5 *1 (-958 *3)) (-4 *3 (-1157 (-530))))) - ((*1 *2 *3 *4) - (-12 - (-5 *2 - (-597 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530)))))) - (-5 *1 (-958 *3)) (-4 *3 (-1157 (-530))) - (-5 *4 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530))))))) - ((*1 *2 *3 *4) - (-12 - (-5 *2 - (-597 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530)))))) - (-5 *1 (-958 *3)) (-4 *3 (-1157 (-530))) (-5 *4 (-388 (-530))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-388 (-530))) - (-5 *2 (-597 (-2 (|:| -3648 *5) (|:| -3657 *5)))) (-5 *1 (-958 *3)) - (-4 *3 (-1157 (-530))) (-5 *4 (-2 (|:| -3648 *5) (|:| -3657 *5))))) - ((*1 *2 *3) - (-12 - (-5 *2 - (-597 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530)))))) - (-5 *1 (-959 *3)) (-4 *3 (-1157 (-388 (-530)))))) - ((*1 *2 *3 *4) - (-12 - (-5 *2 - (-597 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530)))))) - (-5 *1 (-959 *3)) (-4 *3 (-1157 (-388 (-530)))) - (-5 *4 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530))))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-388 (-530))) - (-5 *2 (-597 (-2 (|:| -3648 *4) (|:| -3657 *4)))) (-5 *1 (-959 *3)) - (-4 *3 (-1157 *4)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-388 (-530))) - (-5 *2 (-597 (-2 (|:| -3648 *5) (|:| -3657 *5)))) (-5 *1 (-959 *3)) - (-4 *3 (-1157 *5)) (-5 *4 (-2 (|:| -3648 *5) (|:| -3657 *5)))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-597 (-893 *3))) (-4 *3 (-432)) - (-5 *1 (-341 *3 *4)) (-14 *4 (-597 (-1099))))) - ((*1 *2 *2) - (|partial| -12 (-5 *2 (-597 (-728 *3 (-806 *4)))) (-4 *3 (-432)) - (-14 *4 (-597 (-1099))) (-5 *1 (-582 *3 *4))))) -(((*1 *2 *2) (-12 (-5 *2 (-1046)) (-5 *1 (-311))))) -(((*1 *2 *1) (-12 (-4 *1 (-1060 *3)) (-4 *3 (-984)) (-5 *2 (-719))))) +(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-112))))) +(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-1082)) (-5 *3 (-771)) (-5 *1 (-770))))) +(((*1 *1 *1) + (|partial| -12 (-5 *1 (-276 *2)) (-4 *2 (-675)) (-4 *2 (-1135))))) (((*1 *1 *2) (-12 (-5 *2 (-597 (-597 *3))) (-4 *3 (-984)) (-4 *1 (-635 *3 *4 *5)) (-4 *4 (-354 *3)) (-4 *5 (-354 *3)))) @@ -12020,36 +11655,71 @@ (-12 (-5 *2 (-597 (-597 *5))) (-4 *5 (-984)) (-4 *1 (-987 *3 *4 *5 *6 *7)) (-4 *6 (-221 *4 *5)) (-4 *7 (-221 *3 *5))))) -(((*1 *2 *3 *4 *4 *5) - (-12 (-5 *3 (-1082)) (-5 *4 (-530)) (-5 *5 (-637 (-208))) - (-5 *2 (-973)) (-5 *1 (-706))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-597 *2)) (-4 *2 (-998 *4 *5 *6)) (-4 *4 (-522)) + (-4 *5 (-741)) (-4 *6 (-795)) (-5 *1 (-917 *4 *5 *6 *2))))) (((*1 *2 *1) - (-12 (-5 *2 (-388 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-522)) (-4 *4 (-932 *3)) (-5 *1 (-135 *3 *4 *2)) - (-4 *2 (-354 *4)))) - ((*1 *2 *3) - (-12 (-4 *4 (-522)) (-4 *5 (-932 *4)) (-4 *2 (-354 *4)) - (-5 *1 (-481 *4 *5 *2 *3)) (-4 *3 (-354 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-637 *5)) (-4 *5 (-932 *4)) (-4 *4 (-522)) - (-5 *2 (-637 *4)) (-5 *1 (-641 *4 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-522)) (-4 *4 (-932 *3)) (-5 *1 (-1150 *3 *4 *2)) - (-4 *2 (-1157 *4))))) -(((*1 *1 *2) (-12 (-5 *2 (-148)) (-5 *1 (-815))))) + (-12 + (-5 *2 + (-597 + (-2 + (|:| -3078 + (-2 (|:| |var| (-1099)) (|:| |fn| (-297 (-208))) + (|:| -1300 (-1022 (-788 (-208)))) (|:| |abserr| (-208)) + (|:| |relerr| (-208)))) + (|:| -1874 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1080 (-208))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1300 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-525)))) + ((*1 *2 *1) + (-12 (-4 *1 (-563 *3 *4)) (-4 *3 (-1027)) (-4 *4 (-1135)) + (-5 *2 (-597 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 (-311))) (-5 *1 (-311))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-631 *4 *3)) (-4 *4 (-1027)) + (-4 *3 (-1027))))) +(((*1 *2 *3) + (-12 (-4 *4 (-432)) + (-5 *2 + (-597 + (-2 (|:| |eigval| (-3 (-388 (-893 *4)) (-1089 (-1099) (-893 *4)))) + (|:| |eigmult| (-719)) + (|:| |eigvec| (-597 (-637 (-388 (-893 *4)))))))) + (-5 *1 (-274 *4)) (-5 *3 (-637 (-388 (-893 *4))))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-110) *3)) (-4 *3 (-1135)) (-5 *1 (-560 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-110) *3)) (-4 *3 (-1135)) (-5 *1 (-1080 *3))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-597 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530)))))) - (-5 *2 (-597 (-388 (-530)))) (-5 *1 (-958 *4)) - (-4 *4 (-1157 (-530)))))) +(((*1 *2 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-360)) (-5 *1 (-94)))) + ((*1 *2 *3 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-360)) (-5 *1 (-94))))) +(((*1 *2) + (-12 (-4 *4 (-1139)) (-4 *5 (-1157 *4)) (-4 *6 (-1157 (-388 *5))) + (-5 *2 (-719)) (-5 *1 (-322 *3 *4 *5 *6)) (-4 *3 (-323 *4 *5 *6)))) + ((*1 *2) + (-12 (-4 *1 (-323 *3 *4 *5)) (-4 *3 (-1139)) (-4 *4 (-1157 *3)) + (-4 *5 (-1157 (-388 *4))) (-5 *2 (-719)))) + ((*1 *2 *1) (-12 (-4 *1 (-1060 *3)) (-4 *3 (-984)) (-5 *2 (-719))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -12066,44 +11736,48 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3)))) ((*1 *1 *1) (-4 *1 (-1124)))) -(((*1 *2 *3) - (-12 (-5 *3 (-597 (-893 *4))) (-4 *4 (-432)) (-5 *2 (-110)) - (-5 *1 (-341 *4 *5)) (-14 *5 (-597 (-1099))))) - ((*1 *2 *3) - (-12 (-5 *3 (-597 (-728 *4 (-806 *5)))) (-4 *4 (-432)) - (-14 *5 (-597 (-1099))) (-5 *2 (-110)) (-5 *1 (-582 *4 *5))))) -(((*1 *1) (-12 (-4 *1 (-310 *2)) (-4 *2 (-349)) (-4 *2 (-344))))) -(((*1 *2 *1) (-12 (-4 *3 (-984)) (-5 *2 (-597 *1)) (-4 *1 (-1060 *3))))) -(((*1 *2 *3 *4 *4 *5 *4 *6 *4 *5) - (-12 (-5 *3 (-1082)) (-5 *5 (-637 (-208))) (-5 *6 (-637 (-530))) - (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-706))))) -(((*1 *2) - (-12 (-4 *4 (-162)) (-5 *2 (-1095 (-893 *4))) (-5 *1 (-397 *3 *4)) - (-4 *3 (-398 *4)))) - ((*1 *2) - (-12 (-4 *1 (-398 *3)) (-4 *3 (-162)) (-4 *3 (-344)) - (-5 *2 (-1095 (-893 *3))))) - ((*1 *2) - (-12 (-5 *2 (-1095 (-388 (-893 *3)))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) -(((*1 *2 *3) - (-12 (-4 *4 (-932 *2)) (-4 *2 (-522)) (-5 *1 (-135 *2 *4 *3)) - (-4 *3 (-354 *4)))) - ((*1 *2 *3) - (-12 (-4 *4 (-932 *2)) (-4 *2 (-522)) (-5 *1 (-481 *2 *4 *5 *3)) - (-4 *5 (-354 *2)) (-4 *3 (-354 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-637 *4)) (-4 *4 (-932 *2)) (-4 *2 (-522)) - (-5 *1 (-641 *2 *4)))) - ((*1 *2 *3) - (-12 (-4 *4 (-932 *2)) (-4 *2 (-522)) (-5 *1 (-1150 *2 *4 *3)) - (-4 *3 (-1157 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-388 (-893 *5))) (-5 *4 (-1099)) + (-4 *5 (-13 (-289) (-795) (-140))) (-5 *2 (-597 (-297 *5))) + (-5 *1 (-1055 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-597 (-388 (-893 *5)))) (-5 *4 (-597 (-1099))) + (-4 *5 (-13 (-289) (-795) (-140))) (-5 *2 (-597 (-597 (-297 *5)))) + (-5 *1 (-1055 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1157 *6)) + (-4 *6 (-13 (-27) (-411 *5))) + (-4 *5 (-13 (-795) (-522) (-975 (-530)))) (-4 *8 (-1157 (-388 *7))) + (-5 *2 (-547 *3)) (-5 *1 (-518 *5 *6 *7 *8 *3)) + (-4 *3 (-323 *6 *7 *8))))) +(((*1 *1 *1) + (-12 (-4 *2 (-140)) (-4 *2 (-289)) (-4 *2 (-432)) (-4 *3 (-795)) + (-4 *4 (-741)) (-5 *1 (-927 *2 *3 *4 *5)) (-4 *5 (-890 *2 *4 *3)))) + ((*1 *2 *3) (-12 (-5 *3 (-47)) (-5 *2 (-297 (-530))) (-5 *1 (-1045)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-432))) (-5 *1 (-1127 *3 *2)) + (-4 *2 (-13 (-411 *3) (-1121)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-522) (-795) (-975 (-530)) (-593 (-530)))) + (-5 *1 (-259 *3 *2)) (-4 *2 (-13 (-27) (-1121) (-411 *3))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1099)) + (-4 *4 (-13 (-522) (-795) (-975 (-530)) (-593 (-530)))) + (-5 *1 (-259 *4 *2)) (-4 *2 (-13 (-27) (-1121) (-411 *4)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-597 *8)) (-5 *4 (-597 *9)) (-4 *8 (-998 *5 *6 *7)) + (-4 *9 (-1003 *5 *6 *7 *8)) (-4 *5 (-432)) (-4 *6 (-741)) + (-4 *7 (-795)) (-5 *2 (-719)) (-5 *1 (-1001 *5 *6 *7 *8 *9)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-597 *8)) (-5 *4 (-597 *9)) (-4 *8 (-998 *5 *6 *7)) + (-4 *9 (-1036 *5 *6 *7 *8)) (-4 *5 (-432)) (-4 *6 (-741)) + (-4 *7 (-795)) (-5 *2 (-719)) (-5 *1 (-1069 *5 *6 *7 *8 *9))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-99)) (-5 *2 (-110)))) ((*1 *1 *2 *2) (-12 (-5 *1 (-276 *2)) (-4 *2 (-1135)))) ((*1 *2 *1 *1) (-12 (-5 *2 (-110)) (-5 *1 (-415)))) ((*1 *1 *1 *1) (-5 *1 (-804))) ((*1 *2 *1 *1) (-12 (-5 *2 (-110)) (-5 *1 (-964 *3)) (-4 *3 (-1135))))) +(((*1 *2 *3) (-12 (-5 *3 (-530)) (-5 *2 (-1186)) (-5 *1 (-945))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-862)) (-4 *6 (-13 (-522) (-795))) (-5 *2 (-597 (-297 *6))) (-5 *1 (-204 *5 *6)) (-5 *3 (-297 *6)) @@ -12130,10 +11804,7 @@ ((*1 *2 *1) (-12 (-5 *2 (-1194 *3 *4)) (-5 *1 (-1203 *3 *4)) (-4 *3 (-795)) (-4 *4 (-984))))) -(((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -3648 (-388 (-530))) (|:| -3657 (-388 (-530))))) - (-5 *2 (-388 (-530))) (-5 *1 (-958 *4)) (-4 *4 (-1157 (-530)))))) -(((*1 *1 *2) (-12 (-5 *2 (-148)) (-5 *1 (-815))))) +(((*1 *2 *3) (-12 (-5 *3 (-770)) (-5 *2 (-51)) (-5 *1 (-777))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -12153,54 +11824,55 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3)))) ((*1 *1 *1) (-4 *1 (-1124)))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941)))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1135)) (-4 *1 (-104 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-597 *4)) (-4 *4 (-795)) (-5 *2 (-597 (-615 *4 *5))) - (-5 *1 (-581 *4 *5 *6)) (-4 *5 (-13 (-162) (-666 (-388 (-530))))) - (-14 *6 (-862))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1095 *3)) (-4 *3 (-349)) (-4 *1 (-310 *3)) - (-4 *3 (-344))))) -(((*1 *2 *1) (-12 (-4 *3 (-984)) (-5 *2 (-597 *1)) (-4 *1 (-1060 *3))))) -(((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) - (-5 *1 (-706))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1095 (-388 (-893 *3)))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) -(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-137))))) -(((*1 *1 *1 *2 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(-4 *3 (-289)) (-5 *1 (-163 *3)))) + (-12 (-5 *2 (-2 (|:| |cd| (-1082)) (|:| -3907 (-1082)))) + (-5 *1 (-770))))) +(((*1 *2 *3) + (-12 (-4 *1 (-748)) + (-5 *3 + (-2 (|:| |xinit| (-208)) (|:| |xend| (-208)) + (|:| |fn| (-1181 (-297 (-208)))) (|:| |yinit| (-597 (-208))) + (|:| |intvals| (-597 (-208))) (|:| |g| (-297 (-208))) + (|:| |abserr| (-208)) (|:| |relerr| (-208)))) + (-5 *2 (-973))))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-597 *6)) (-4 *6 (-998 *3 *4 *5)) + (-4 *3 (-522)) (-4 *4 (-741)) (-4 *5 (-795)) + (-5 *1 (-1192 *3 *4 *5 *6)))) + ((*1 *1 *2 *3 *4) + (|partial| -12 (-5 *2 (-597 *8)) (-5 *3 (-1 (-110) *8 *8)) + (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-998 *5 *6 *7)) (-4 *5 (-522)) + (-4 *6 (-741)) (-4 *7 (-795)) (-5 *1 (-1192 *5 *6 *7 *8))))) +(((*1 *2 *2) (-12 (-5 *2 (-862)) (-5 *1 (-338 *3)) (-4 *3 (-330))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1099)) + (-4 *4 (-13 (-795) (-289) (-975 (-530)) (-593 (-530)) (-140))) + (-5 *2 (-1 *5 *5)) (-5 *1 (-752 *4 *5)) + (-4 *5 (-13 (-29 *4) (-1121) (-900)))))) +(((*1 *2 *2) (-12 (-5 *2 (-530)) (-5 *1 (-239))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-501 *3)) (-4 *3 (-13 (-675) (-25)))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-112)) (-5 *3 (-597 (-1 *4 (-597 *4)))) (-4 *4 (-1027)) + (-5 *1 (-111 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-112)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1027)) + (-5 *1 (-111 *4)))) ((*1 *2 *3) - (-12 (-5 *2 (-163 (-530))) (-5 *1 (-714 *3)) (-4 *3 (-385)))) - ((*1 *2 *1) - (-12 (-5 *2 (-163 (-388 (-530)))) (-5 *1 (-812 *3)) (-14 *3 (-530)))) - ((*1 *2 *1) - (-12 (-14 *3 (-530)) (-5 *2 (-163 (-388 (-530)))) - (-5 *1 (-813 *3 *4)) (-4 *4 (-810 *3))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1181 *6)) (-5 *4 (-1181 (-530))) (-5 *5 (-530)) - (-4 *6 (-1027)) (-5 *2 (-1 *6)) (-5 *1 (-956 *6))))) -(((*1 *2 *1) - (-12 (-5 *2 (-597 (-2 (|:| |k| (-622 *3)) (|:| |c| *4)))) - (-5 *1 (-581 *3 *4 *5)) (-4 *3 (-795)) - (-4 *4 (-13 (-162) (-666 (-388 (-530))))) (-14 *5 (-862))))) + (|partial| -12 (-5 *3 (-112)) (-5 *2 (-597 (-1 *4 (-597 *4)))) + (-5 *1 (-111 *4)) (-4 *4 (-1027))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -12221,42 +11893,41 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3)))) ((*1 *1 *1) (-4 *1 (-1124)))) -(((*1 *2 *3) - (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-501 *3)) (-4 *3 (-13 (-675) (-25)))))) +(((*1 *2 *1 *1) (-12 (-5 *2 (-110)) (-5 *1 (-473))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-1099)) (-5 *3 (-597 (-506))) (-5 *1 (-506))))) -(((*1 *2 *1) - (-12 (-4 *1 (-310 *3)) (-4 *3 (-344)) (-4 *3 (-349)) - (-5 *2 (-1095 *3))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-597 (-884 *4))) (-4 *1 (-1060 *4)) (-4 *4 (-984)) - (-5 *2 (-719))))) -(((*1 *2 *3 *3 *4 *4 *4 *4 *3 *3 *3 *3 *5 *3 *6) - (-12 (-5 *3 (-530)) (-5 *5 (-637 (-208))) - (-5 *6 (-3 (|:| |fn| (-369)) (|:| |fp| (-68 APROD)))) (-5 *4 (-208)) - (-5 *2 (-973)) (-5 *1 (-705))))) -(((*1 *2 *1) - (-12 (-5 *2 (-388 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) +(((*1 *2 *1) (-12 (-4 *1 (-348 *2)) (-4 *2 (-162))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) + (-4 *2 (-13 (-411 *3) (-941)))))) +(((*1 *2 *3) (-12 (-5 *3 (-360)) (-5 *2 (-208)) (-5 *1 (-1184)))) + ((*1 *2) (-12 (-5 *2 (-208)) (-5 *1 (-1184))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-289) (-140))) (-4 *5 (-13 (-795) (-572 (-1099)))) + (-4 *6 (-741)) (-5 *2 (-597 (-597 (-530)))) + (-5 *1 (-865 *4 *5 *6 *7)) (-5 *3 (-530)) (-4 *7 (-890 *4 *6 *5))))) +(((*1 *2 *2) + (-12 (-5 *2 (-597 (-597 *6))) (-4 *6 (-890 *3 *5 *4)) + (-4 *3 (-13 (-289) (-140))) (-4 *4 (-13 (-795) (-572 (-1099)))) + (-4 *5 (-741)) (-5 *1 (-865 *3 *4 *5 *6))))) (((*1 *1 *2 *2 *2) (-12 (-5 *1 (-210 *2)) (-4 *2 (-13 (-344) (-1121))))) ((*1 *2 *1 *3 *4 *4) (-12 (-5 *3 (-862)) (-5 *4 (-360)) (-5 *2 (-1186)) (-5 *1 (-1182)))) ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-360)) (-5 *2 (-1186)) (-5 *1 (-1183))))) -(((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-1148 *3)) (-4 *3 (-1135))))) -(((*1 *2 *2) (-12 (-5 *2 (-862)) (-5 *1 (-384 *3)) (-4 *3 (-385)))) - ((*1 *2) (-12 (-5 *2 (-862)) (-5 *1 (-384 *3)) (-4 *3 (-385)))) - ((*1 *2 *2) (-12 (-5 *2 (-862)) (|has| *1 (-6 -4261)) (-4 *1 (-385)))) - ((*1 *2) (-12 (-4 *1 (-385)) (-5 *2 (-862)))) - ((*1 *2 *1) (-12 (-4 *1 (-810 *3)) (-5 *2 (-1080 (-530)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-597 (-2 (|:| -3387 *4) (|:| -3073 (-530))))) - (-4 *4 (-1027)) (-5 *2 (-1 *4)) (-5 *1 (-956 *4))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-597 (-276 *4))) (-5 *1 (-581 *3 *4 *5)) (-4 *3 (-795)) - (-4 *4 (-13 (-162) (-666 (-388 (-530))))) (-14 *5 (-862))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-923 *2)) (-4 *2 (-1121))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *5) + (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) + (-5 *5 (-3 (|:| |fn| (-369)) (|:| |fp| (-61 LSFUN2)))) + (-5 *2 (-973)) (-5 *1 (-702))))) +(((*1 *2) + (-12 (-4 *3 (-741)) (-4 *4 (-795)) (-4 *2 (-850)) + (-5 *1 (-437 *3 *4 *2 *5)) (-4 *5 (-890 *2 *3 *4)))) + ((*1 *2) + (-12 (-4 *3 (-741)) (-4 *4 (-795)) (-4 *2 (-850)) + (-5 *1 (-847 *2 *3 *4 *5)) (-4 *5 (-890 *2 *3 *4)))) + ((*1 *2) (-12 (-4 *2 (-850)) (-5 *1 (-848 *2 *3)) (-4 *3 (-1157 *2))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-258 *3 *2)) (-4 *2 (-13 (-411 *3) (-941))))) @@ -12277,50 +11948,36 @@ (-12 (-5 *2 (-1080 *3)) (-4 *3 (-37 (-388 (-530)))) (-5 *1 (-1086 *3)))) ((*1 *1 *1) (-4 *1 (-1124)))) -(((*1 *2 *1 *1) - (|partial| -12 (-4 *1 (-310 *3)) (-4 *3 (-344)) (-4 *3 (-349)) - (-5 *2 (-1095 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-310 *3)) (-4 *3 (-344)) (-4 *3 (-349)) - (-5 *2 (-1095 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1157 *5)) (-4 *5 (-344)) + (-5 *2 (-2 (|:| -4182 (-399 *3)) (|:| |special| (-399 *3)))) + (-5 *1 (-676 *5 *3))))) (((*1 *1) (-5 *1 (-110)))) -(((*1 *2 *1) (-12 (-4 *1 (-1060 *3)) (-4 *3 (-984)) (-5 *2 (-110))))) -(((*1 *2 *3 *4 *3 *4 *5 *3 *4 *3 *3 *3 *3) - (-12 (-5 *4 (-637 (-208))) (-5 *5 (-637 (-530))) (-5 *3 (-530)) - (-5 *2 (-973)) (-5 *1 (-705))))) -(((*1 *2 *1) - (-12 (-5 *2 (-388 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-741)) (-4 *5 (-795)) (-4 *6 (-289)) + (-5 *2 (-597 (-719))) (-5 *1 (-726 *3 *4 *5 *6 *7)) + (-4 *3 (-1157 *6)) (-4 *7 (-890 *6 *4 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) (-5 *2 (-973)) (-5 *1 (-707))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-862)) (-5 *4 (-1082)) (-5 *2 (-1186)) (-5 *1 (-1182))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1099)) (-5 *4 (-893 (-530))) (-5 *2 (-311)) + (-5 *1 (-313))))) +(((*1 *2) + (-12 (-4 *3 (-432)) (-4 *4 (-741)) (-4 *5 (-795)) + (-4 *6 (-998 *3 *4 *5)) (-5 *2 (-1186)) + (-5 *1 (-928 *3 *4 *5 *6 *7)) (-4 *7 (-1003 *3 *4 *5 *6)))) + ((*1 *2) + (-12 (-4 *3 (-432)) (-4 *4 (-741)) (-4 *5 (-795)) + (-4 *6 (-998 *3 *4 *5)) (-5 *2 (-1186)) + (-5 *1 (-1034 *3 *4 *5 *6 *7)) (-4 *7 (-1003 *3 *4 *5 *6))))) (((*1 *2 *1) (-12 (-5 *2 (-597 (-906))) (-5 *1 (-106)))) ((*1 *2 *1) (-12 (-5 *2 (-44 (-1082) (-722))) (-5 *1 (-112))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-110)) - (-5 *2 - (-2 (|:| |contp| (-530)) - (|:| -4162 (-597 (-2 (|:| |irr| *3) (|:| -3001 (-530))))))) - (-5 *1 (-422 *3)) (-4 *3 (-1157 (-530))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-110)) - (-5 *2 - (-2 (|:| |contp| (-530)) - (|:| -4162 (-597 (-2 (|:| |irr| *3) (|:| -3001 (-530))))))) - (-5 *1 (-1146 *3)) (-4 *3 (-1157 (-530)))))) +(((*1 *2) (-12 (-5 *2 (-530)) (-5 *1 (-867))))) (((*1 *2 *1) - (-12 (-4 *3 (-162)) (-4 *2 (-23)) (-5 *1 (-271 *3 *4 *2 *5 *6 *7)) - (-4 *4 (-1157 *3)) (-14 *5 (-1 *4 *4 *2)) - (-14 *6 (-1 (-3 *2 "failed") *2 *2)) - (-14 *7 (-1 (-3 *4 "failed") *4 *4 *2)))) - ((*1 *2 *1) - (-12 (-4 *2 (-23)) (-5 *1 (-660 *3 *2 *4 *5 *6)) (-4 *3 (-162)) - (-14 *4 (-1 *3 *3 *2)) (-14 *5 (-1 (-3 *2 "failed") *2 *2)) - (-14 *6 (-1 (-3 *3 "failed") *3 *3 *2)))) - ((*1 *2) (-12 (-4 *2 (-1157 *3)) (-5 *1 (-661 *3 *2)) (-4 *3 (-984)))) - ((*1 *2 *1) - (-12 (-4 *2 (-23)) (-5 *1 (-664 *3 *2 *4 *5 *6)) (-4 *3 (-162)) - (-14 *4 (-1 *3 *3 *2)) (-14 *5 (-1 (-3 *2 "failed") *2 *2)) - (-14 *6 (-1 (-3 *3 "failed") *3 *3 *2)))) - ((*1 *2) (-12 (-4 *1 (-810 *3)) (-5 *2 (-530))))) + (-12 (-4 *1 (-348 *3)) (-4 *3 (-162)) (-4 *3 (-522)) + (-5 *2 (-1095 *3))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-719)) (-5 *2 (-1181 (-597 (-530)))) (-5 *1 (-459)))) ((*1 *1 *2 *3) @@ -12328,25 +11985,19 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1135)) (-5 *1 (-1080 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1135)) (-5 *1 (-1080 *3))))) -(((*1 *2 *3 *3 *3) - (|partial| -12 (-4 *4 (-13 (-344) (-140) (-975 (-530)))) - (-4 *5 (-1157 *4)) (-5 *2 (-597 (-388 *5))) (-5 *1 (-955 *4 *5)) - (-5 *3 (-388 *5))))) +(((*1 *1) (-5 *1 (-148)))) (((*1 *1 *1) (-4 *1 (-583))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-795) (-522))) (-5 *1 (-584 *3 *2)) (-4 *2 (-13 (-411 *3) (-941) (-1121)))))) -(((*1 *2 *3 *4 *5 *6 *7 *6) - (|partial| -12 - (-5 *5 - (-2 (|:| |contp| *3) - (|:| -4162 (-597 (-2 (|:| |irr| *10) (|:| -3001 (-530))))))) - (-5 *6 (-597 *3)) (-5 *7 (-597 *8)) (-4 *8 (-795)) (-4 *3 (-289)) - (-4 *10 (-890 *3 *9 *8)) (-4 *9 (-741)) - (-5 *2 - (-2 (|:| |polfac| (-597 *10)) (|:| |correct| *3) - (|:| |corrfact| (-597 (-1095 *3))))) - (-5 *1 (-580 *8 *9 *3 *10)) (-5 *4 (-597 (-1095 *3)))))) +(((*1 *1 *2 *3 *4) + (-12 (-14 *5 (-597 (-1099))) (-4 *2 (-162)) + (-4 *4 (-221 (-2267 *5) (-719))) + (-14 *6 + (-1 (-110) (-2 (|:| -1986 *3) (|:| -3194 *4)) + (-2 (|:| -1986 *3) (|:| -3194 *4)))) + (-5 *1 (-441 *5 *2 *3 *4 *6 *7)) (-4 *3 (-795)) + (-4 *7 (-890 *2 *4 (-806 *5)))))) (((*1 *1 *2) (-12 (-5 *2 (-597 *1)) (-4 *1 (-432)))) ((*1 *1 *1 *1) (-4 *1 (-432))) ((*1 *2 *3) @@ -12375,24 +12026,16 @@ ((*1 *2 *2 *1) (-12 (-4 *1 (-998 *2 *3 *4)) (-4 *2 (-984)) (-4 *3 (-741)) (-4 *4 (-795)) (-4 *2 (-432))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-307 *3 *4)) (-4 *3 (-984)) - (-4 *4 (-740))))) -(((*1 *1 *2 *2) (-12 (-5 *1 (-818 *2)) (-4 *2 (-1135)))) - ((*1 *1 *2 *2 *2) (-12 (-5 *1 (-820 *2)) (-4 *2 (-1135)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1060 *3)) (-4 *3 (-984)) (-5 *2 (-597 (-884 *3))))) - ((*1 *1 *2) - (-12 (-5 *2 (-597 (-884 *3))) (-4 *3 (-984)) (-4 *1 (-1060 *3)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-597 (-597 *3))) (-4 *1 (-1060 *3)) (-4 *3 (-984)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-597 (-884 *3))) (-4 *1 (-1060 *3)) (-4 *3 (-984))))) -(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) - (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *5 (-110)) - (-5 *6 (-208)) (-5 *7 (-3 (|:| |fn| (-369)) (|:| |fp| (-66 APROD)))) - (-5 *8 (-3 (|:| |fn| (-369)) (|:| |fp| (-71 MSOLVE)))) - (-5 *2 (-973)) (-5 *1 (-705))))) +(((*1 *1) (-5 *1 (-1182)))) +(((*1 *1 *1) + (-12 (-4 *2 (-289)) (-4 *3 (-932 *2)) (-4 *4 (-1157 *3)) + (-5 *1 (-394 *2 *3 *4 *5)) (-4 *5 (-13 (-390 *3 *4) (-975 *3)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *5 *5 *5)) (-4 *5 (-1172 *4)) + (-4 *4 (-37 (-388 (-530)))) + (-5 *2 (-1 (-1080 *4) (-1080 *4) (-1080 *4))) (-5 *1 (-1174 *4 *5))))) +(((*1 *2 *3 *3 *3) + (-12 (-5 *3 (-597 (-530))) (-5 *2 (-637 (-530))) (-5 *1 (-1037))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-432)) (-4 *4 (-795)) (-4 *5 (-741)) (-5 *2 (-110)) (-5 *1 (-927 *3 *4 *5 *6)) @@ -12400,54 +12043,28 @@ ((*1 *2 *1) (-12 (-5 *2 (-110)) (-5 *1 (-1064 *3 *4)) (-4 *3 (-13 (-1027) (-33))) (-4 *4 (-13 (-1027) (-33)))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-388 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-923 *2)) (-4 *2 (-1121))))) (((*1 *2 *3) (-12 (-5 *3 (-597 (-51))) (-5 *2 (-1186)) (-5 *1 (-805))))) +(((*1 *2) + (-12 + (-5 *2 (-2 (|:| -3884 (-597 (-1099))) (|:| -2594 (-597 (-1099))))) + (-5 *1 (-1137))))) +(((*1 *2 *1) (-12 (-4 *1 (-624 *2)) (-4 *2 (-1135))))) (((*1 *2 *3) - (-12 (-4 *4 (-330)) (-5 *2 (-399 *3)) (-5 *1 (-200 *4 *3)) - (-4 *3 (-1157 *4)))) - ((*1 *2 *3) - (-12 (-5 *2 (-399 *3)) (-5 *1 (-422 *3)) (-4 *3 (-1157 (-530))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-719)) (-5 *2 (-399 *3)) (-5 *1 (-422 *3)) - (-4 *3 (-1157 (-530))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-597 (-719))) (-5 *2 (-399 *3)) (-5 *1 (-422 *3)) - (-4 *3 (-1157 (-530))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-597 (-719))) (-5 *5 (-719)) (-5 *2 (-399 *3)) - (-5 *1 (-422 *3)) (-4 *3 (-1157 (-530))))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-719)) (-5 *2 (-399 *3)) (-5 *1 (-422 *3)) - (-4 *3 (-1157 (-530))))) - ((*1 *2 *3) - (-12 (-5 *2 (-399 *3)) (-5 *1 (-946 *3)) - (-4 *3 (-1157 (-388 (-530)))))) - ((*1 *2 *3) - (-12 (-5 *2 (-399 *3)) (-5 *1 (-1146 *3)) (-4 *3 (-1157 (-530)))))) -(((*1 *2 *1) (-12 (-4 *1 (-810 *3)) (-5 *2 (-530))))) -(((*1 *2 *3 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1157 *5)) - (-4 *5 (-13 (-344) (-140) (-975 (-530)))) - (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-388 *6)) (|:| |h| *6) - (|:| |c1| (-388 *6)) (|:| |c2| (-388 *6)) (|:| -4031 *6))) - (-5 *1 (-955 *5 *6)) (-5 *3 (-388 *6))))) -(((*1 *2 *3 *4 *5) - (-12 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(-1139)) (-4 *4 (-1157 *3)) + (-4 *5 (-1157 (-388 *4))) (-5 *2 (-110))))) +(((*1 *2) (-12 (-5 *2 (-110)) (-5 *1 (-1136 *3)) (-4 *3 (-1027))))) +(((*1 *1) (-5 *1 (-148)))) (((*1 *2 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-1186)) (-5 *1 (-805)))) ((*1 *2 *3) (-12 (-5 *3 (-804)) (-5 *2 (-1186)) (-5 *1 (-805)))) ((*1 *2 *3 *4) @@ -12455,78 +12072,81 @@ ((*1 *2 *3 *1) (-12 (-5 *3 (-530)) (-5 *2 (-1186)) (-5 *1 (-1080 *4)) (-4 *4 (-1027)) (-4 *4 (-1135))))) -(((*1 *2) - (-12 (-5 *2 (-388 (-893 *3))) (-5 *1 (-433 *3 *4 *5 *6)) - (-4 *3 (-522)) (-4 *3 (-162)) (-14 *4 (-862)) - (-14 *5 (-597 (-1099))) (-14 *6 (-1181 (-637 *3)))))) -(((*1 *1) (-5 *1 (-134)))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-884 *3) (-884 *3))) (-5 *1 (-165 *3)) + (-4 *3 (-13 (-344) (-1121) (-941)))))) (((*1 *2 *1) - (-12 (-4 *1 (-1143 *3 *2)) (-4 *3 (-984)) (-4 *2 (-1172 *3))))) -(((*1 *1 *1) (-4 *1 (-810 *2)))) -(((*1 *2 *3 *3 *3 *4 *5) - (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1157 *6)) - (-4 *6 (-13 (-344) (-140) (-975 *4))) (-5 *4 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*1 (-1054 *3 *2)) (-4 *3 (-1157 *2))))) +(((*1 *2 *3 *2) (-12 (-5 *3 (-719)) (-5 *1 (-801 *2)) (-4 *2 (-162)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1095 (-530))) (-5 *1 (-883)) (-5 *3 (-530))))) +(((*1 *2 *3) (-12 (-5 *3 (-208)) (-5 *2 (-1082)) (-5 *1 (-176)))) + ((*1 *2 *3) (-12 (-5 *3 (-208)) (-5 *2 (-1082)) (-5 *1 (-282)))) + ((*1 *2 *3) (-12 (-5 *3 (-208)) (-5 *2 (-1082)) (-5 *1 (-287))))) +(((*1 *2) + (-12 (-4 *4 (-162)) (-5 *2 (-110)) (-5 *1 (-347 *3 *4)) + (-4 *3 (-348 *4)))) + ((*1 *2) (-12 (-4 *1 (-348 *3)) (-4 *3 (-162)) (-5 *2 (-110))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-289)) (-5 *1 (-435 *3 *2)) (-4 *2 (-1157 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *3 (-289)) (-5 *1 (-440 *3 *2)) (-4 *2 (-1157 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *3 (-289)) (-14 *4 *3) (-14 *5 (-1 *3 *3 (-719))) + (-5 *1 (-509 *3 *2 *4 *5)) (-4 *2 (-1157 *3))))) (((*1 *2 *1) - (-12 (-5 *2 (-597 (-530))) (-5 *1 (-943 *3)) (-14 *3 (-530))))) -(((*1 *1 *1 *1 *2) - (|partial| -12 (-5 *2 (-110)) (-5 *1 (-555 *3)) (-4 *3 (-984))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |stiffness| (-360)) (|:| |stability| (-360)) - (|:| |expense| (-360)) (|:| |accuracy| (-360)) - (|:| |intermediateResults| (-360)))) - (-5 *2 (-973)) (-5 *1 (-287))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *5 *5)) - (-4 *5 (-13 (-344) (-10 -8 (-15 ** ($ $ (-388 (-530))))))) - (-5 *2 - (-2 (|:| |solns| (-597 *5)) - (|:| |maps| (-597 (-2 (|:| |arg| *5) (|:| |res| *5)))))) - (-5 *1 (-1054 *3 *5)) (-4 *3 (-1157 *5))))) + (-12 (-4 *1 (-1129 *3 *4 *5 *6)) (-4 *3 (-522)) (-4 *4 (-741)) + (-4 *5 (-795)) (-4 *6 (-998 *3 *4 *5)) + (-5 *2 (-2 (|:| -2361 (-597 *6)) (|:| -2551 (-597 *6))))))) (((*1 *2 *1) (-12 (-5 *2 (-1051 (-530) (-570 (-47)))) (-5 *1 (-47)))) ((*1 *2 *1) (-12 (-4 *3 (-289)) (-4 *4 (-932 *3)) (-4 *5 (-1157 *4)) @@ -13804,102 +13742,67 @@ (-12 (-4 *3 (-162)) (-4 *2 (-666 *3)) (-5 *1 (-613 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-675) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-932 *2)) (-4 *2 (-522))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) - (-12 (-5 *3 (-1082)) (-5 *4 (-530)) (-5 *5 (-637 (-208))) - (-5 *2 (-973)) (-5 *1 (-703))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-597 *2)) (-4 *2 (-890 *4 *5 *6)) (-4 *4 (-432)) - (-4 *5 (-741)) (-4 *6 (-795)) (-5 *1 (-429 *4 *5 *6 *2))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-597 *7)) (-4 *7 (-998 *4 *5 *6)) (-4 *4 (-432)) - (-4 *5 (-741)) (-4 *6 (-795)) (-5 *2 (-110)) - (-5 *1 (-928 *4 *5 *6 *7 *8)) (-4 *8 (-1003 *4 *5 *6 *7)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-998 *3 *4 *5)) (-4 *3 (-984)) (-4 *4 (-741)) - (-4 *5 (-795)) (-5 *2 (-110)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-597 *7)) (-4 *7 (-998 *4 *5 *6)) (-4 *4 (-432)) - (-4 *5 (-741)) (-4 *6 (-795)) (-5 *2 (-110)) - (-5 *1 (-1034 *4 *5 *6 *7 *8)) (-4 *8 (-1003 *4 *5 *6 *7)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1129 *3 *4 *5 *6)) (-4 *3 (-522)) (-4 *4 (-741)) - (-4 *5 (-795)) (-4 *6 (-998 *3 *4 *5)) (-5 *2 (-110))))) -(((*1 *1 *1) (-5 *1 (-804)))) -(((*1 *2 *1) - (-12 (-5 *2 (-597 (-530))) (-5 *1 (-943 *3)) (-14 *3 (-530))))) -(((*1 *1 *1) (-12 (-5 *1 (-555 *2)) (-4 *2 (-984))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1080 (-208))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2902 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *2 (-973)) (-5 *1 (-287))))) -(((*1 *2 *3 *2) - (|partial| -12 (-5 *2 (-1181 *4)) (-5 *3 (-637 *4)) (-4 *4 (-344)) - (-5 *1 (-618 *4)))) - ((*1 *2 *3 *2) - (|partial| -12 (-4 *4 (-344)) - (-4 *5 (-13 (-354 *4) (-10 -7 (-6 -4271)))) - (-4 *2 (-13 (-354 *4) (-10 -7 (-6 -4271)))) - (-5 *1 (-619 *4 *5 *2 *3)) (-4 *3 (-635 *4 *5 *2)))) - ((*1 *2 *3 *2 *4 *5) - (|partial| -12 (-5 *4 (-597 *2)) (-5 *5 (-1 *2 *2)) (-4 *2 (-344)) - (-5 *1 (-762 *2 *3)) (-4 *3 (-607 *2)))) + (-12 (-4 *4 (-741)) + (-4 *5 (-13 (-795) (-10 -8 (-15 -3260 ((-1099) $))))) (-4 *6 (-522)) + (-5 *2 (-2 (|:| -3418 (-893 *6)) (|:| -1726 (-893 *6)))) + (-5 *1 (-681 *4 *5 *6 *3)) (-4 *3 (-890 (-388 (-893 *6)) *4 *5))))) +(((*1 *2 *2) + (-12 (-5 *2 (-884 *3)) (-4 *3 (-13 (-344) (-1121) (-941))) + (-5 *1 (-165 *3))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1082)) (-5 *2 (-1186)) (-5 *1 (-1183))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-208)) (-5 *4 (-530)) + (-5 *5 (-3 (|:| |fn| (-369)) (|:| |fp| (-62 G)))) (-5 *2 (-973)) + (-5 *1 (-697))))) +(((*1 *2 *3 *4 *4 *5 *3 *3) + (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *5 (-208)) + (-5 *2 (-973)) (-5 *1 (-701))))) +(((*1 *2 *3) + (-12 (-4 *4 (-522)) (-4 *5 (-932 *4)) + (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4))) (-5 *1 (-135 *4 *5 *3)) + (-4 *3 (-354 *5)))) ((*1 *2 *3) - (-12 (-4 *2 (-13 (-344) (-10 -8 (-15 ** ($ $ (-388 (-530))))))) - (-5 *1 (-1054 *3 *2)) (-4 *3 (-1157 *2))))) -(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) - (-12 (-5 *3 (-1082)) (-5 *4 (-530)) (-5 *5 (-637 (-208))) - (-5 *2 (-973)) (-5 *1 (-703))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-597 *2)) (-4 *2 (-890 *4 *5 *6)) (-4 *4 (-432)) - (-4 *5 (-741)) (-4 *6 (-795)) (-5 *1 (-429 *4 *5 *6 *2))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-1 (-110) *9)) (-5 *5 (-1 (-110) *9 *9)) - (-4 *9 (-998 *6 *7 *8)) (-4 *6 (-522)) (-4 *7 (-741)) - (-4 *8 (-795)) (-5 *2 (-2 (|:| |bas| *1) (|:| -1596 (-597 *9)))) - (-5 *3 (-597 *9)) (-4 *1 (-1129 *6 *7 *8 *9)))) + (-12 (-4 *4 (-522)) (-4 *5 (-932 *4)) + (-5 *2 (-2 (|:| |num| *6) (|:| |den| *4))) + (-5 *1 (-481 *4 *5 *6 *3)) (-4 *6 (-354 *4)) (-4 *3 (-354 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-637 *5)) (-4 *5 (-932 *4)) (-4 *4 (-522)) + (-5 *2 (-2 (|:| |num| (-637 *4)) (|:| |den| *4))) + (-5 *1 (-641 *4 *5)))) ((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-1 (-110) *8 *8)) (-4 *8 (-998 *5 *6 *7)) - (-4 *5 (-522)) (-4 *6 (-741)) (-4 *7 (-795)) - (-5 *2 (-2 (|:| |bas| *1) (|:| -1596 (-597 *8)))) - (-5 *3 (-597 *8)) (-4 *1 (-1129 *5 *6 *7 *8))))) -(((*1 *1 *1 *1) (-5 *1 (-804)))) -(((*1 *1 *2) - (-12 (-5 *2 (-597 (-530))) (-5 *1 (-943 *3)) (-14 *3 (-530))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-555 *2)) (-4 *2 (-984))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| -1523 (-360)) (|:| -3901 (-1082)) - (|:| |explanations| (-597 (-1082))))) - (-5 *2 (-973)) (-5 *1 (-287)))) + (-12 (-4 *5 (-13 (-344) (-140) (-975 (-388 (-530))))) + (-4 *6 (-1157 *5)) + (-5 *2 (-2 (|:| -2776 *7) (|:| |rh| (-597 (-388 *6))))) + (-5 *1 (-755 *5 *6 *7 *3)) (-5 *4 (-597 (-388 *6))) + (-4 *7 (-607 *6)) (-4 *3 (-607 (-388 *6))))) ((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| -1523 (-360)) (|:| -3901 (-1082)) - (|:| |explanations| (-597 (-1082))) (|:| |extra| (-973)))) - (-5 *2 (-973)) (-5 *1 (-287))))) + (-12 (-4 *4 (-522)) (-4 *5 (-932 *4)) + (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4))) (-5 *1 (-1150 *4 *5 *3)) + (-4 *3 (-1157 *5))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-719)) (-4 *1 (-355 *3 *4)) (-4 *3 (-795)) + (-4 *4 (-162)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-719)) (-4 *1 (-1200 *3 *4)) (-4 *3 (-795)) + (-4 *4 (-984))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-597 (-230 *4 *5))) (-5 *2 (-230 *4 *5)) + (-14 *4 (-597 (-1099))) (-4 *5 (-432)) (-5 *1 (-585 *4 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1027)) (-5 *1 (-205 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1135)) (-4 *1 (-236 *3)))) + ((*1 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1135))))) +(((*1 *2 *3 *2 *2) + (-12 (-5 *2 (-597 (-460 *4 *5))) (-5 *3 (-806 *4)) + (-14 *4 (-597 (-1099))) (-4 *5 (-432)) (-5 *1 (-585 *4 *5))))) +(((*1 *1 *1) (-12 (-4 *1 (-934 *2)) (-4 *2 (-1135))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-730 *2)) (-4 *2 (-984))))) +(((*1 *2 *1) (-12 (-4 *1 (-349)) (-5 *2 (-862)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1181 *4)) (-4 *4 (-330)) (-5 *2 (-862)) + (-5 *1 (-500 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-597 *3)) (-4 *3 (-1027)) (-5 *1 (-846 *3))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1157 *2)) (-4 *2 (-984)) (-4 *2 (-522))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-530)) (-4 *1 (-55 *2 *4 *5)) (-4 *2 (-1135)) (-4 *4 (-354 *2)) (-4 *5 (-354 *2)))) @@ -13934,14 +13837,14 @@ (-12 (-5 *3 (-1099)) (-5 *2 (-228 (-1082))) (-5 *1 (-198 *4)) (-4 *4 (-13 (-795) - (-10 -8 (-15 -1832 ((-1082) $ *3)) (-15 -2278 ((-1186) $)) - (-15 -1671 ((-1186) $))))))) + (-10 -8 (-15 -1902 ((-1082) $ *3)) (-15 -2388 ((-1186) $)) + (-15 -3595 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-929)) (-5 *1 (-198 *3)) (-4 *3 (-13 (-795) - (-10 -8 (-15 -1832 ((-1082) $ (-1099))) (-15 -2278 ((-1186) $)) - (-15 -1671 ((-1186) $))))))) + (-10 -8 (-15 -1902 ((-1082) $ (-1099))) (-15 -2388 ((-1186) $)) + (-15 -3595 ((-1186) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-719)) (-5 *1 (-228 *4)) (-4 *4 (-795)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-228 *3)) (-4 *3 (-795)))) @@ -14028,28 +13931,24 @@ ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1169 *2)) (-4 *2 (-1135))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-597 *6)) (-5 *4 (-597 (-1080 *7))) (-4 *6 (-795)) - (-4 *7 (-890 *5 (-502 *6) *6)) (-4 *5 (-984)) - (-5 *2 (-1 (-1080 *7) *7)) (-5 *1 (-1052 *5 *6 *7))))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-530)) (-5 *4 (-637 (-208))) (-5 *2 (-973)) - (-5 *1 (-703))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-289) (-140))) (-4 *5 (-741)) (-4 *6 (-795)) - (-4 *7 (-890 *4 *5 *6)) (-5 *2 (-597 (-597 *7))) - (-5 *1 (-428 *4 *5 *6 *7)) (-5 *3 (-597 *7)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-110)) (-4 *5 (-13 (-289) (-140))) (-4 *6 (-741)) - (-4 *7 (-795)) (-4 *8 (-890 *5 *6 *7)) (-5 *2 (-597 (-597 *8))) - (-5 *1 (-428 *5 *6 *7 *8)) (-5 *3 (-597 *8)))) - ((*1 *2 *3) - (-12 (-4 *4 (-13 (-289) (-140))) (-4 *5 (-741)) (-4 *6 (-795)) - (-4 *7 (-890 *4 *5 *6)) (-5 *2 (-597 (-597 *7))) - (-5 *1 (-428 *4 *5 *6 *7)) (-5 *3 (-597 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-110)) (-4 *5 (-13 (-289) (-140))) (-4 *6 (-741)) - (-4 *7 (-795)) (-4 *8 (-890 *5 *6 *7)) (-5 *2 (-597 (-597 *8))) - (-5 *1 (-428 *5 *6 *7 *8)) (-5 *3 (-597 *8))))) + (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1157 *5)) (-4 *5 (-344)) + (-5 *2 (-2 (|:| |answer| *3) (|:| |polypart| *3))) + (-5 *1 (-540 *5 *3))))) +(((*1 *1 *2 *3) + (-12 (-5 *3 (-1099)) (-5 *1 (-547 *2)) (-4 *2 (-975 *3)) + (-4 *2 (-344)))) + ((*1 *1 *2 *2) (-12 (-5 *1 (-547 *2)) (-4 *2 (-344)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1099)) (-4 *4 (-13 (-795) (-522))) (-5 *1 (-584 *4 *2)) + (-4 *2 (-13 (-411 *4) (-941) (-1121))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1020 *2)) (-4 *2 (-13 (-411 *4) (-941) (-1121))) + (-4 *4 (-13 (-795) (-522))) (-5 *1 (-584 *4 *2)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-900)) (-5 *2 (-1099)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1020 *1)) (-4 *1 (-900))))) +(((*1 *1 *2 *3) + (-12 (-5 *1 (-408 *3 *2)) (-4 *3 (-13 (-162) (-37 (-388 (-530))))) + (-4 *2 (-13 (-795) (-21)))))) (((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1013 *3)) (-4 *3 (-129))))) (((*1 *2 *1) (-12 @@ -14059,7 +13958,7 @@ (-2 (|:| |var| (-1099)) (|:| |arrayIndex| (-597 (-893 (-530)))) (|:| |rand| - (-2 (|:| |ints2Floats?| (-110)) (|:| -3954 (-804)))))) + (-2 (|:| |ints2Floats?| (-110)) (|:| -3964 (-804)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1099)) (|:| |rand| (-804)) (|:| |ints2Floats?| (-110)))) @@ -14067,126 +13966,114 @@ (-2 (|:| |switch| (-1098)) (|:| |thenClause| (-311)) (|:| |elseClause| (-311)))) (|:| |returnBranch| - (-2 (|:| -1262 (-110)) - (|:| -3387 - (-2 (|:| |ints2Floats?| (-110)) (|:| -3954 (-804)))))) + (-2 (|:| -3250 (-110)) + (|:| -3417 + (-2 (|:| |ints2Floats?| (-110)) (|:| -3964 (-804)))))) (|:| |blockBranch| (-597 (-311))) (|:| |commentBranch| (-597 (-1082))) (|:| |callBranch| (-1082)) (|:| |forBranch| - (-2 (|:| -2902 (-1020 (-893 (-530)))) - (|:| |span| (-893 (-530))) (|:| -3912 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\ No newline at end of file |