diff options
Diffstat (limited to 'src/share/algebra')
-rw-r--r-- | src/share/algebra/browse.daase | 1282 | ||||
-rw-r--r-- | src/share/algebra/category.daase | 1216 | ||||
-rw-r--r-- | src/share/algebra/compress.daase | 1323 | ||||
-rw-r--r-- | src/share/algebra/interp.daase | 8946 | ||||
-rw-r--r-- | src/share/algebra/operation.daase | 27603 |
5 files changed, 20186 insertions, 20184 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 33a5561f..8d60a197 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2283317 . 3451578536) +(2283643 . 3451919708) (-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."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . 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}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . 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}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4403 . T) (-4401 . T) (-4400 . T) ((-4408 "*") . T) (-4399 . T) (-4404 . T) (-4398 . T)) +((-4404 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4400 . T) (-4405 . T) (-4399 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -2313) +(-32 R -2312) ((|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 -1034) (QUOTE (-564))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4406))) +((|HasAttribute| |#1| (QUOTE -4407))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4406 . T) (-4407 . T)) +((-4407 . T) (-4408 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -2313 UP UPUP -3281) +(-40 -2312 UP UPUP -3665) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2750 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2750 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2750 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2750 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -2313) +((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2733 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2733 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2733 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2733 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -2312) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-307)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4403 |has| |#1| (-556)) (-4401 . T) (-4400 . T)) +((-4404 |has| |#1| (-556)) (-4402 . T) (-4401 . T)) ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) -((-4406 . T) (-4407 . T)) -((-2750 (-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|))))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|))))))) +((-4407 . T) (-4408 . T)) +((-2733 (-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|))))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4403 . T)) +((-4404 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2313) +(-54 |Base| R -2312) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -158,7 +158,7 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4406 . T) (-4407 . T)) +((-4407 . T) (-4408 . T)) NIL (-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-61 -2445) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +(-61 -2410) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2445) +(-62 -2410) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2445) +(-63 -2410) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2445) +(-64 -2410) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2445) +(-65 -2410) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -2445) +(-66 -2410) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -2445) +(-67 -2410) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2445) +(-68 -2410) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -2445) +(-69 -2410) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -2445) +(-70 -2410) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -2445) +(-71 -2410) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -2445) +(-72 -2410) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -2445) +(-73 -2410) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -2445) +(-74 -2410) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2445) +(-77 -2410) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2445) +(-78 -2410) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2445) +(-79 -2410) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2445) +(-80 -2410) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2445) +(-81 -2410) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -2445) +(-82 -2410) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2445) +(-83 -2410) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2445) +(-84 -2410) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2445) +(-85 -2410) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2445) +(-86 -2410) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2445) +(-87 -2410) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2445) +(-88 -2410) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2445) +(-89 -2410) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-363)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4406 . T)) +((-4407 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,{}b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4406 . T) ((-4408 "*") . T) (-4407 . T) (-4403 . T) (-4401 . T) (-4400 . T) (-4399 . T) (-4404 . T) (-4398 . T) (-4397 . T) (-4396 . T) (-4395 . T) (-4394 . T) (-4402 . T) (-4405 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4393 . T)) +((-4407 . T) ((-4409 "*") . T) (-4408 . T) (-4404 . T) (-4402 . T) (-4401 . T) (-4400 . T) (-4405 . T) (-4399 . T) (-4398 . T) (-4397 . T) (-4396 . T) (-4395 . T) (-4403 . T) (-4406 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4394 . T)) NIL (-99 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,{}n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f,{} g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4403 . T)) +((-4404 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4408 "*")))) +((|HasAttribute| |#1| (QUOTE (-4409 "*")))) (-105) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4406 . T)) +((-4407 . T)) NIL (-106 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,23 +358,23 @@ NIL NIL (-107 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4407 . T)) +((-4408 . T)) NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2750 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2733 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-858))))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -388,22 +388,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op,{} p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,{}p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|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|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-115 -2313 UP) +(-115 -2312 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL (-116 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2750 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2733 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4407))) +((|HasAttribute| |#1| (QUOTE -4408))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -414,15 +414,15 @@ NIL NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,20 +430,20 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4406 . T) (-4407 . T)) +((-4407 . T) (-4408 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2750 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2733 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -466,13 +466,13 @@ NIL NIL (-134) ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4408 "*") . T)) +(((-4409 "*") . T)) NIL -(-135 |minix| -3490 S T$) +(-135 |minix| -3445 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -3490 R) +(-136 |minix| -3445 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -494,8 +494,8 @@ NIL NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4406 . T) (-4396 . T) (-4407 . T)) -((-2750 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4407 . T) (-4397 . T) (-4408 . T)) +((-2733 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\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 @@ -510,7 +510,7 @@ NIL NIL (-145) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4403 . T)) +((-4404 . T)) NIL (-146 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,{}r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -518,9 +518,9 @@ NIL NIL (-147) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4403 . T)) +((-4404 . T)) NIL -(-148 -2313 UP UPUP) +(-148 -2312 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) NIL NIL @@ -531,14 +531,14 @@ NIL (-150 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasAttribute| |#1| (QUOTE -4406))) +((|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasAttribute| |#1| (QUOTE -4407))) (-151 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-152 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4401 . T) (-4400 . T) (-4403 . T)) +((-4402 . T) (-4401 . T) (-4404 . T)) NIL (-153) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,{}xMin,{}xMax,{}yMin,{}yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -560,7 +560,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-158 R -2313) +(-158 R -2312) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -591,10 +591,10 @@ NIL (-165 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4402)) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-846)))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-846)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4399 -2750 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4402 |has| |#1| (-6 -4402)) (-4405 |has| |#1| (-6 -4405)) (-3624 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 -2733 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3593 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -606,8 +606,8 @@ NIL NIL (-169 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}."))) -((-4399 -2750 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4402 |has| |#1| (-6 -4402)) (-4405 |has| |#1| (-6 -4405)) (-3624 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . 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(QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-824)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-846)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1194)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2750 (-12 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(QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4402)) (|HasAttribute| |#1| (QUOTE -4405)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) +((-4400 -2733 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3593 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-824)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-846)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1194)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4403)) (|HasAttribute| |#1| (QUOTE -4406)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) (-170 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 @@ -618,7 +618,7 @@ NIL NIL (-172) ((|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."))) -(((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-173) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -626,7 +626,7 @@ NIL NIL (-174 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4408 "*") . T) (-4399 . T) (-4404 . T) (-4398 . T) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") . T) (-4400 . T) (-4405 . T) (-4399 . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-175) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2313) +(-188 R -2312) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-215 -2313 UP UPUP R) +(-215 -2312 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 -(-216 -2313 FP) +(-216 -2312 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 (-217) ((|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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2750 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2733 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-218) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -2313) +(-219 R -2312) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -818,19 +818,19 @@ NIL NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-223 |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}."))) -((-4403 . T)) +((-4404 . T)) NIL -(-224 R -2313) +(-224 R -2312) ((|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 (-225) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3613 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3583 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-226) ((|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)}.}"))) @@ -838,15 +838,15 @@ NIL NIL (-227 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}"))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-228 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 (-229 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."))) -((-4407 . T)) +((-4408 . T)) NIL (-230 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}."))) @@ -854,7 +854,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (-231 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}."))) -((-4403 . T)) +((-4404 . T)) NIL (-232 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -862,36 +862,36 @@ NIL NIL (-233) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4403 . T)) +((-4404 . T)) NIL (-234 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4406))) +((|HasAttribute| |#1| (QUOTE -4407))) (-235 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}."))) -((-4407 . T)) +((-4408 . T)) NIL (-236) ((|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 -(-237 S -3490 R) +(-237 S -3445 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 (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4403)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -3490 R) +((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4404)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1094)))) +(-238 -3445 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"))) -((-4400 |has| |#2| (-1045)) (-4401 |has| |#2| (-1045)) (-4403 |has| |#2| (-6 -4403)) ((-4408 "*") |has| |#2| (-172)) (-4406 . T)) +((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) NIL -(-239 -3490 A B) +(-239 -3445 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.")) 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(LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2733 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-241) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -902,7 +902,7 @@ NIL NIL (-243) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4399 . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-244 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -910,16 +910,16 @@ NIL NIL (-245 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-246 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (-2733 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2733 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-248) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) NIL @@ -930,23 +930,23 @@ NIL NIL (-250 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4403 -2750 (-2368 (|has| |#4| (-1045)) (|has| |#4| (-233))) (-2368 (|has| |#4| (-1045)) (|has| |#4| (-896 (-1170)))) (|has| |#4| (-6 -4403)) (-2368 (|has| |#4| (-1045)) (|has| |#4| (-637 (-564))))) (-4400 |has| |#4| (-1045)) (-4401 |has| |#4| (-1045)) ((-4408 "*") |has| |#4| (-172)) (-4406 . 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-252 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-233)))) (-253 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."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL (-254 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}."))) -((-4406 . T) (-4407 . T)) +((-4407 . T) (-4408 . T)) NIL (-255) ((|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."))) @@ -986,8 +986,8 @@ NIL NIL (-264 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"))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-265 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 @@ -1032,11 +1032,11 @@ 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 -(-276 R -2313) +(-276 R -2312) ((|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 -(-277 R -2313) +(-277 R -2312) ((|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 @@ -1058,7 +1058,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094)))) (-282 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}."))) -((-4407 . T)) +((-4408 . T)) NIL (-283 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}."))) @@ -1079,18 +1079,18 @@ NIL (-287 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 -4407))) +((|HasAttribute| |#1| (QUOTE -4408))) (-288 |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 -(-289 S R |Mod| -1608 -4317 |exactQuo|) +(-289 S R |Mod| -3482 -2443 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-290) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4399 . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-291) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Identifier|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}.")) (|setProperty!| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `nothing.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1106,21 +1106,21 @@ NIL NIL (-294 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4403 -2750 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4400 |has| |#1| (-1045)) (-4401 |has| |#1| (-1045))) -((|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722)))) (|HasCategory| |#1| (QUOTE (-473))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2750 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-302))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-2750 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722)))) (-2750 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-172)))) +((-4404 -2733 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-1045)) (-4402 |has| |#1| (-1045))) +((|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722)))) (|HasCategory| |#1| (QUOTE (-473))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-302))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-2733 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722)))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-172)))) (-295 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-296) ((|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 -(-297 -2313 S) +(-297 -2312 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 -(-298 E -2313) +(-298 E -2312) ((|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 @@ -1158,7 +1158,7 @@ NIL NIL (-307) ((|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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-308 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1168,7 +1168,7 @@ 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 -(-310 -2313) +(-310 -2312) ((|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 @@ -1182,8 +1182,8 @@ NIL NIL (-313 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))}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2750 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2750 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2733 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2733 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) (-314 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 @@ -1194,9 +1194,9 @@ NIL NIL (-316 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."))) -((-4403 -2750 (-2368 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2750 (-2368 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4398 |has| |#1| (-556))) -((-2750 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-556))) (-2750 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2750 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2750 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2750 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2750 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) -(-317 R -2313) +((-4404 -2733 (-2364 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2733 (-2364 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) +((-2733 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2733 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2733 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2733 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2733 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) +(-317 R -2312) ((|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 @@ -1206,8 +1206,8 @@ NIL NIL (-319 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."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2983) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-320 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 @@ -1218,7 +1218,7 @@ NIL NIL (-322 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."))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) ((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-788)))) (-323 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1234,19 +1234,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172)))) (-326 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-327 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."))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -2313) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -2312) ((|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 (-368)))) -(-329 -2313) +(-329 -2312) ((|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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-330) ((|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."))) @@ -1264,15 +1264,15 @@ 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 -(-334 S -2313 UP UPUP R) +(-334 S -2312 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 -(-335 -2313 UP UPUP R) +(-335 -2312 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 -(-336 -2313 UP UPUP R) +(-336 -2312 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 @@ -1286,32 +1286,32 @@ NIL NIL (-339 |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.}"))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-379)))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) (-340 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 -(-341 S -2313 UP UPUP) +(-341 S -2312 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 (-368))) (|HasCategory| |#2| (QUOTE (-363)))) -(-342 -2313 UP UPUP) +(-342 -2312 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."))) -((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-343 |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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-344 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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-345 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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-346 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 @@ -1326,33 +1326,33 @@ NIL NIL (-349) ((|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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-350 R UP -2313) +(-350 R UP -2312) ((|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 (-351 |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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-352 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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-353 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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-354 |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}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-355 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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -2313 GF) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -2312 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 @@ -1360,21 +1360,21 @@ 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 -(-358 -2313 FP FPP) +(-358 -2312 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 (-359 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}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 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 (-361 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4403 . T)) +((-4404 . T)) NIL (-362 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1382,7 +1382,7 @@ NIL NIL (-363) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-364 |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."))) @@ -1398,7 +1398,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-556)))) (-367 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4403 |has| |#1| (-556)) (-4401 . T) (-4400 . T)) +((-4404 |has| |#1| (-556)) (-4402 . T) (-4401 . T)) NIL (-368) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1410,7 +1410,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-363)))) (-370 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) NIL (-371 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1419,14 +1419,14 @@ NIL (-372 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4407)) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094)))) +((|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094)))) (-373 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4406 . T)) +((-4407 . T)) NIL (-374 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4401 . T) (-4400 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4402 . T) (-4401 . T)) NIL (-375 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."))) @@ -1438,7 +1438,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-377 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}"))) -((-4403 . T)) +((-4404 . T)) NIL (-378 |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}."))) @@ -1446,7 +1446,7 @@ NIL NIL (-379) ((|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}.")) (|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}."))) -((-4389 . T) (-4397 . T) (-3613 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4390 . T) (-4398 . T) (-3583 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-380 |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}."))) @@ -1454,11 +1454,11 @@ NIL NIL (-381 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}"))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-382 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}."))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) NIL (-383) ((|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}."))) @@ -1470,7 +1470,7 @@ NIL NIL (-385 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."))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-386 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1478,7 +1478,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-846)))) (-387) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-388) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1490,13 +1490,13 @@ NIL NIL (-390 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) NIL (-391) ((|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 -(-392 -2313 UP UPUP R) +(-392 -2312 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 @@ -1520,11 +1520,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-398 -2445 |returnType| -1370 |symbols|) +(-398 -2410 |returnType| -2742 |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 -(-399 -2313 UP) +(-399 -2312 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1538,15 +1538,15 @@ NIL NIL (-402) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-403 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4389)) (|HasAttribute| |#1| (QUOTE -4397))) +((|HasAttribute| |#1| (QUOTE -4390)) (|HasAttribute| |#1| (QUOTE -4398))) (-404) ((|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\"."))) -((-3613 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3583 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-405 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."))) @@ -1558,15 +1558,15 @@ NIL NIL (-407 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."))) -((-4393 -12 (|has| |#1| (-6 -4404)) (|has| |#1| (-452)) (|has| |#1| (-6 -4393))) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2750 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4393)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4394 -12 (|has| |#1| (-6 -4405)) (|has| |#1| (-452)) (|has| |#1| (-6 -4394))) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2733 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4394)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-408 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 (-409 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) NIL (-410 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -2313 UP A) +(-413 R -2312 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4403 . T)) +((-4404 . T)) NIL -(-414 R -2313 UP A |ibasis|) +(-414 R -2312 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1034) (|devaluate| |#2|)))) @@ -1598,12 +1598,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-417 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) -((-4403 |has| |#1| (-556)) (-4401 . T) (-4400 . T)) +((-4404 |has| |#1| (-556)) (-4402 . T) (-4401 . T)) NIL (-418 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."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) (-419 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 @@ -1630,17 +1630,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-368)))) (-425 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4406 . T) (-4396 . T) (-4407 . T)) +((-4407 . T) (-4397 . T) (-4408 . T)) NIL -(-426 R -2313) +(-426 R -2312) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-427 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4393 -12 (|has| |#1| (-6 -4393)) (|has| |#2| (-6 -4393))) (-4400 . T) (-4401 . T) (-4403 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4393)) (|HasAttribute| |#2| (QUOTE -4393)))) -(-428 R -2313) +((-4394 -12 (|has| |#1| (-6 -4394)) (|has| |#2| (-6 -4394))) (-4401 . T) (-4402 . T) (-4404 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4394)) (|HasAttribute| |#2| (QUOTE -4394)))) +(-428 R -2312) ((|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 @@ -1650,17 +1650,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (-430 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}."))) -((-4403 -2750 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4398 |has| |#1| (-556))) +((-4404 -2733 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) NIL -(-431 R -2313) +(-431 R -2312) ((|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 -(-432 R -2313) +(-432 R -2312) ((|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)))) -(-433 R -2313) +(-433 R -2312) ((|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 @@ -1668,7 +1668,7 @@ 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 -(-435 R -2313 UP) +(-435 R -2312 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 -1034) (QUOTE (-48))))) @@ -1700,7 +1700,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-443 R UP -2313) +(-443 R UP -2312) ((|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 @@ -1738,16 +1738,16 @@ NIL NIL (-452) ((|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}."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-453 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"))) -((-4403 |has| (-407 (-948 |#1|)) (-556)) (-4401 . T) (-4400 . T)) +((-4404 |has| (-407 (-948 |#1|)) (-556)) (-4402 . T) (-4401 . T)) ((|HasCategory| (-407 (-948 |#1|)) (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-407 (-948 |#1|)) (QUOTE (-556)))) (-454 |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"))) -(((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (-2733 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2733 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-455 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 @@ -1774,7 +1774,7 @@ NIL NIL (-461 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) NIL (-462 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1782,7 +1782,7 @@ NIL NIL (-463 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) (-464 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}."))) @@ -1812,7 +1812,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-471 |lv| -2313 R) +(-471 |lv| -2312 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1822,23 +1822,23 @@ NIL NIL (-473) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4403 . T)) +((-4404 . T)) NIL (-474 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2983) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-475 |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."))) -((-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094)))) +((-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094)))) (-476 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)}"))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) (-477) ((|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}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-478) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1846,29 +1846,29 @@ NIL NIL (-479 |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."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-480) ((|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 (-481 |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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(|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2733 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-483) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL NIL (-484 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}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-485 -2313 UP UPUP R) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +(-485 -2312 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 @@ -1878,12 +1878,12 @@ NIL NIL (-487) ((|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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2750 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2733 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-488 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 -4406)) (|HasAttribute| |#1| (QUOTE -4407)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) +((|HasAttribute| |#1| (QUOTE -4407)) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-489 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,33 +1904,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -2313 UP |AlExt| |AlPol|) +(-494 -2312 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-495) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-497 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."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-498 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 -(-499 R UP -2313) +(-499 R UP -2312) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-500 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-858))))) (-501 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)}."))) @@ -1944,7 +1944,7 @@ 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 -(-504 -2313 |Expon| |VarSet| |DPoly|) +(-504 -2312 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1170))))) @@ -1994,36 +1994,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-788)))) (-516 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-517) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-518 |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}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2750 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-2733 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) (-519 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}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-520 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."))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-521 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 -4407))) +((|HasAttribute| |#3| (QUOTE -4408))) (-522 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 -4407))) +((|HasAttribute| |#7| (QUOTE -4408))) (-523 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."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-524) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2056,7 +2056,7 @@ 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 -(-532 K -2313 |Par|) +(-532 K -2312 |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 @@ -2080,7 +2080,7 @@ 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 -(-538 K -2313 |Par|) +(-538 K -2312 |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 @@ -2110,7 +2110,7 @@ NIL NIL (-545) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\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."))) -((-4404 . T) (-4405 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-546) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2130,13 +2130,13 @@ NIL NIL (-550 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) -(-551 R -2313) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +(-551 R -2312) ((|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 -(-552 R0 -2313 UP UPUP R) +(-552 R0 -2312 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 @@ -2146,7 +2146,7 @@ NIL NIL (-554 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."))) -((-3613 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3583 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-555 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."))) @@ -2154,9 +2154,9 @@ NIL NIL (-556) ((|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."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-557 R -2313) +(-557 R -2312) ((|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 @@ -2168,7 +2168,7 @@ 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 -(-560 R -2313 L) +(-560 R -2312 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 -652) (|devaluate| |#2|)))) @@ -2176,31 +2176,31 @@ 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 -(-562 -2313 UP UPUP R) +(-562 -2312 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 -(-563 -2313 UP) +(-563 -2312 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 (-564) ((|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}."))) -((-4388 . T) (-4394 . T) (-4398 . T) (-4393 . T) (-4404 . T) (-4405 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4389 . T) (-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-565) ((|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 -(-566 R -2313 L) +(-566 R -2312 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 -652) (|devaluate| |#2|)))) -(-567 R -2313) +(-567 R -2312) ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -2313 UP) +(-568 -2312 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 @@ -2208,27 +2208,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-570 -2313) +(-570 -2312) ((|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 (-571 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."))) -((-3613 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3583 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-572) ((|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 -(-573 R -2313) +(-573 R -2312) ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -2313 UP) +(-574 -2312 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 -(-575 R -2313) +(-575 R -2312) ((|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 @@ -2250,27 +2250,27 @@ NIL NIL (-580 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-581 |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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) (-582) ((|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 -(-583 R -2313) +(-583 R -2312) ((|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 -(-584 E -2313) +(-584 E -2312) ((|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 -(-585 -2313) +(-585 -2312) ((|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}."))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) ((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-586 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"))) @@ -2298,19 +2298,19 @@ NIL NIL (-592 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2750 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2733 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-593 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 (-594 |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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) (-595 |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.}"))) -((-4401 |has| |#1| (-556)) (-4400 |has| |#1| (-556)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4403 . T)) +((-4402 |has| |#1| (-556)) (-4401 |has| |#1| (-556)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-556)))) (-596 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),{}..]}."))) @@ -2320,7 +2320,7 @@ 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 -(-598 R -2313 FG) +(-598 R -2312 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 @@ -2330,12 +2330,12 @@ NIL NIL (-600 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-601 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 -4407)) (|HasCategory| |#2| (QUOTE (-846))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#3| (QUOTE (-1094)))) +((|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-846))) (|HasAttribute| |#1| (QUOTE -4407)) (|HasCategory| |#3| (QUOTE (-1094)))) (-602 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2350,19 +2350,19 @@ NIL NIL (-605 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4403 -2750 (-2368 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) -((-2750 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4404 -2733 (-2364 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) +((-2733 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-606 |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."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-607 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 (-608 |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}."))) -((-4407 . T)) +((-4408 . T)) NIL (-609 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"))) @@ -2380,7 +2380,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -2313 UP) +(-613 -2312 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2402,19 +2402,19 @@ NIL NIL (-618 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."))) -((-4403 . T)) +((-4404 . T)) NIL (-619 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}."))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-844)))) -(-620 R -2313) +(-620 R -2312) ((|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 (-621 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"))) -((-4401 . T) (-4400 . T) ((-4408 "*") . T) (-4399 . T) (-4403 . T)) +((-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4400 . T) (-4404 . T)) ((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-622 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."))) @@ -2430,7 +2430,7 @@ NIL NIL (-625 |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}}."))) -((-4403 . T)) +((-4404 . T)) NIL (-626 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}}."))) @@ -2440,30 +2440,30 @@ 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 -(-628 R -2313) +(-628 R -2312) ((|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 -(-629 |lv| -2313) +(-629 |lv| -2312) ((|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 (-630) ((|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."))) -((-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3726) (QUOTE (-52))))))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (QUOTE (-1094)))) +((-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3683) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (QUOTE (-1094)))) (-631 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-632 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4401 . T) (-4400 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4402 . T) (-4401 . T)) NIL (-633 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4403 -2750 (-2368 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) -((-2750 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4404 -2733 (-2364 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) +((-2733 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-634 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 @@ -2475,10 +2475,10 @@ NIL (-636 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 -((-2356 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-2354 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-637 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}."))) -((-4403 . T)) +((-4404 . T)) NIL (-638 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}."))) @@ -2494,16 +2494,16 @@ NIL NIL (-641 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."))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-642 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL (-643 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-644 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2515,22 +2515,22 @@ NIL (-646 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 -4407))) +((|HasAttribute| |#1| (QUOTE -4408))) (-647 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-648 R -2313 L) +(-648 R -2312 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 (-649 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}}"))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-650 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-651 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2538,15 +2538,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-652 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}."))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-653 -2313 UP) +(-653 -2312 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)))) -(-654 A -1634) +(-654 A -1460) ((|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}}"))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-655 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."))) @@ -2562,7 +2562,7 @@ NIL NIL (-658 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}."))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) ((|HasCategory| |#1| (QUOTE (-787)))) (-659 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."))) @@ -2570,7 +2570,7 @@ NIL NIL (-660 |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) (-4401 . T) (-4400 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4402 . T) (-4401 . T)) ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-172)))) (-661 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}."))) @@ -2578,13 +2578,13 @@ NIL NIL (-662 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}."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL -(-663 -2313) +(-663 -2312) ((|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 -(-664 -2313 |Row| |Col| M) +(-664 -2312 |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 @@ -2594,8 +2594,8 @@ NIL NIL (-666 |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."))) -((-4403 . T) (-4406 . T) (-4400 . T) (-4401 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2750 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4404 . T) (-4407 . T) (-4401 . T) (-4402 . T)) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2733 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-667) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2615,7 +2615,7 @@ NIL (-671 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 -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-672) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2659,10 +2659,10 @@ NIL (-682 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 (-4408 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556)))) +((|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556)))) (-683 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"))) -((-4406 . T) (-4407 . T)) +((-4407 . T) (-4408 . T)) NIL (-684 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."))) @@ -2670,8 +2670,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556)))) (-685 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."))) -((-4406 . T) (-4407 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4407 . T) (-4408 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-686 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 @@ -2680,7 +2680,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-688 S -2313 FLAF FLAS) +(-688 S -2312 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 @@ -2690,11 +2690,11 @@ NIL NIL (-690) ((|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"))) -((-4399 . T) (-4404 |has| (-695) (-363)) (-4398 |has| (-695) (-363)) (-3624 . T) (-4405 |has| (-695) (-6 -4405)) (-4402 |has| (-695) (-6 -4402)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2750 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2750 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2750 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2750 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2750 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2750 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2750 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-846))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4405)) (|HasAttribute| (-695) (QUOTE -4402)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) +((-4400 . T) (-4405 |has| (-695) (-363)) (-4399 |has| (-695) (-363)) (-3593 . T) (-4406 |has| (-695) (-6 -4406)) (-4403 |has| (-695) (-6 -4403)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2733 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2733 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2733 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2733 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2733 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2733 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2733 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-846))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4406)) (|HasAttribute| (-695) (QUOTE -4403)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) (-691 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}."))) -((-4407 . T)) +((-4408 . T)) NIL (-692 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}."))) @@ -2704,13 +2704,13 @@ 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 -(-694 OV E -2313 PG) +(-694 OV E -2312 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 (-695) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3613 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3583 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-696 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."))) @@ -2718,7 +2718,7 @@ NIL NIL (-697) ((|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}"))) -((-4405 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4406 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-698 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"))) @@ -2736,7 +2736,7 @@ 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 -(-702 S -3950 I) +(-702 S -3922 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 @@ -2746,7 +2746,7 @@ NIL NIL (-704 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)}.}"))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) NIL (-705 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}."))) @@ -2756,25 +2756,25 @@ 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 -(-707 R |Mod| -1608 -4317 |exactQuo|) +(-707 R |Mod| -3482 -2443 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-708 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4402 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-709 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-710 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) (-4403 . T)) +((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-711 R |Mod| -1608 -4317 |exactQuo|) +(-711 R |Mod| -3482 -2443 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4403 . T)) +((-4404 . T)) NIL (-712 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2782,11 +2782,11 @@ NIL NIL (-713 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) NIL -(-714 -2313) +(-714 -2312) ((|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]]}."))) -((-4403 . T)) +((-4404 . T)) NIL (-715 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."))) @@ -2810,7 +2810,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368)))) (-720 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."))) -((-4399 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 |has| |#1| (-363)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-721 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) @@ -2820,7 +2820,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-723 -2313 UP) +(-723 -2312 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 @@ -2838,8 +2838,8 @@ NIL NIL (-727 |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."))) -(((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (-2733 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2733 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-728 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2854,15 +2854,15 @@ NIL NIL (-731 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) (-4403 . T)) +((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-846)))) (-732 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4396 . T) (-4407 . T)) +((-4397 . T) (-4408 . T)) NIL (-733 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}."))) -((-4406 . T) (-4396 . T) (-4407 . T)) +((-4407 . T) (-4397 . T) (-4408 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-734) ((|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."))) @@ -2874,7 +2874,7 @@ NIL NIL (-736 |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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4401 . T) (-4400 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL (-737 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"))) @@ -2890,7 +2890,7 @@ NIL NIL (-740 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}."))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) NIL (-741) ((|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}."))) @@ -2972,11 +2972,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-761 -2313) +(-761 -2312) ((|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 -(-762 P -2313) +(-762 P -2312) ((|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 @@ -2984,7 +2984,7 @@ NIL NIL NIL NIL -(-764 UP -2313) +(-764 UP -2312) ((|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 @@ -2998,9 +2998,9 @@ NIL NIL (-767) ((|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."))) -(((-4408 "*") . T)) +(((-4409 "*") . T)) NIL -(-768 R -2313) +(-768 R -2312) ((|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 @@ -3020,7 +3020,7 @@ 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 -(-773 -2313 |ExtF| |SUEx| |ExtP| |n|) +(-773 -2312 |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 @@ -3034,23 +3034,23 @@ NIL NIL (-776 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."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . 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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 (-778 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-780 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.}"))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-781 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}."))) @@ -3102,25 +3102,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-368)))) (-793 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) NIL -(-794 -2750 R OS S) +(-794 -2733 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-795 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2750 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) +((-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2733 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-796) ((|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 -(-797 R -2313 L) +(-797 R -2312 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 -(-798 R -2313) +(-798 R -2312) ((|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 @@ -3128,7 +3128,7 @@ 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 -(-800 R -2313) +(-800 R -2312) ((|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 @@ -3136,11 +3136,11 @@ 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 -(-802 -2313 UP UPUP R) +(-802 -2312 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 -(-803 -2313 UP L LQ) +(-803 -2312 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 @@ -3148,41 +3148,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-805 -2313 UP L LQ) +(-805 -2312 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 -(-806 -2313 UP) +(-806 -2312 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 -(-807 -2313 L UP A LO) +(-807 -2312 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 -(-808 -2313 UP) +(-808 -2312 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)))) -(-809 -2313 LO) +(-809 -2312 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-810 -2313 LODO) +(-810 -2312 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-811 -3490 S |f|) +(-811 -3445 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4400 |has| |#2| (-1045)) (-4401 |has| |#2| (-1045)) (-4403 |has| |#2| (-6 -4403)) ((-4408 "*") |has| |#2| (-172)) (-4406 . 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T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-813 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4408 "*") |has| |#2| (-363)) (-4399 |has| |#2| (-363)) (-4404 |has| |#2| (-363)) (-4398 |has| |#2| (-363)) (-4403 . T) (-4401 . T) (-4400 . T)) +(((-4409 "*") |has| |#2| (-363)) (-4400 |has| |#2| (-363)) (-4405 |has| |#2| (-363)) (-4399 |has| |#2| (-363)) (-4404 . T) (-4402 . T) (-4401 . T)) ((|HasCategory| |#2| (QUOTE (-363)))) (-814 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}))."))) @@ -3194,7 +3194,7 @@ NIL NIL (-816) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-817) ((|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}"))) @@ -3222,7 +3222,7 @@ NIL NIL (-823 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}."))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-233)))) (-824) ((|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."))) @@ -3234,7 +3234,7 @@ NIL NIL (-826 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4406 . T) (-4396 . T) (-4407 . T)) +((-4407 . T) (-4397 . T) (-4408 . T)) NIL (-827) ((|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."))) @@ -3246,8 +3246,8 @@ NIL NIL (-829 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."))) -((-4403 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-2750 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4404 |has| |#1| (-844))) +((|HasCategory| |#1| (QUOTE (-844))) (-2733 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2733 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-830 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL @@ -3258,7 +3258,7 @@ NIL NIL (-832 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) (-4403 . T)) +((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-833) ((|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)."))) @@ -3286,13 +3286,13 @@ NIL NIL (-839 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4403 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-2750 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4404 |has| |#1| (-844))) +((|HasCategory| |#1| (QUOTE (-844))) (-2733 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2733 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-840) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-841 -3490 S) +(-841 -3445 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3306,7 +3306,7 @@ NIL NIL (-844) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4403 . T)) +((-4404 . T)) NIL (-845 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3322,19 +3322,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172)))) (-848 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) NIL (-849 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 (-363))) (|HasCategory| |#1| (QUOTE (-556)))) -(-850 R |sigma| -2288) +(-850 R |sigma| -3707) ((|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."))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-851 |x| R |sigma| -2288) +(-851 |x| R |sigma| -3707) ((|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}."))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) (-852 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..)}."))) @@ -3378,7 +3378,7 @@ NIL NIL (-862 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) (-4403 . T)) +((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (-863 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3390,24 +3390,24 @@ NIL NIL (-865 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-866 |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)."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-867 |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)."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2750 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2733 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) (-868 |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)}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2750 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2733 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-869 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 (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-870) ((|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 @@ -3463,7 +3463,7 @@ NIL (-883 |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 (-2356 (|HasCategory| |#2| (QUOTE (-1045)))) (-2356 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2356 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) +((-12 (-2354 (|HasCategory| |#2| (QUOTE (-1045)))) (-2354 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2354 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-884 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 @@ -3472,7 +3472,7 @@ 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 -(-886 R -3950) +(-886 R -3922) ((|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 @@ -3496,7 +3496,7 @@ 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 -(-892 UP -2313) +(-892 UP -2312) ((|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 @@ -3514,19 +3514,19 @@ NIL NIL (-896 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}."))) -((-4403 . T)) +((-4404 . T)) NIL (-897 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-898 |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 (-899 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."))) -((-4403 . T)) +((-4404 . T)) NIL (-900 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3534,8 +3534,8 @@ NIL NIL (-901 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4403 . T)) -((-2750 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) +((-4404 . T)) +((-2733 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (-902 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 @@ -3550,13 +3550,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-145)))) (-905) ((|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}."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-906 |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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-907 R0 -2313 UP UPUP R) +(-907 R0 -2312 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 @@ -3570,7 +3570,7 @@ NIL NIL (-910 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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-911 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."))) @@ -3584,7 +3584,7 @@ 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 -(-914 -2313) +(-914 -2312) ((|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 @@ -3594,17 +3594,17 @@ NIL NIL (-916) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-917) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4408 "*") . T)) +(((-4409 "*") . T)) NIL -(-918 -2313 P) +(-918 -2312 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-919 |xx| -2313) +(-919 |xx| -2312) ((|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 @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-925 R -2313) +(-925 R -2312) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3640,7 +3640,7 @@ 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 -(-928 S R -2313) +(-928 S R -2312) ((|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 @@ -3660,11 +3660,11 @@ 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 -882) (|devaluate| |#1|)))) -(-933 R -2313 -3950) +(-933 R -2312 -3922) ((|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 -(-934 -3950) +(-934 -3922) ((|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 @@ -3686,8 +3686,8 @@ NIL NIL (-939 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-940 |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 @@ -3707,12 +3707,12 @@ NIL (-944 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 (-905))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-846)))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-846)))) (-945 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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL -(-946 E V R P -2313) +(-946 E V R P -2312) ((|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 @@ -3722,9 +3722,9 @@ NIL NIL (-948 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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-949 E V R P -2313) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-949 E V R P -2312) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3746,13 +3746,13 @@ NIL NIL (-954 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"))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-955) ((|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 -(-956 -2313) +(-956 -2312) ((|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 @@ -3766,12 +3766,12 @@ NIL NIL (-959 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}"))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4404))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4405))) (-960 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"))) -((-4403 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE 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(|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) +((-4404 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-961) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3786,7 +3786,7 @@ NIL NIL (-964 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4406 . T) (-4407 . T)) +((-4407 . T) (-4408 . T)) NIL (-965 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}}"))) @@ -3806,7 +3806,7 @@ NIL NIL (-969 |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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-970) ((|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}."))) @@ -3818,7 +3818,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-556)))) (-972 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."))) -((-4406 . T)) +((-4407 . T)) NIL (-973 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."))) @@ -3834,7 +3834,7 @@ NIL NIL (-976 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-977 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3852,7 +3852,7 @@ 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 -(-981 K R UP -2313) +(-981 K R UP -2312) ((|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 @@ -3882,7 +3882,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145)))) (-988 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}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-989 |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}."))) @@ -3894,7 +3894,7 @@ NIL NIL (-991 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."))) -((-4406 . T) (-4407 . T)) +((-4407 . T) (-4408 . T)) NIL (-992 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}."))) @@ -3902,7 +3902,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-290)))) (-993 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}."))) -((-4399 |has| |#1| (-290)) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-994 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}."))) @@ -3910,12 +3910,12 @@ NIL NIL (-995 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.}"))) -((-4399 |has| |#1| (-290)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) +((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) (-996 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}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-997 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3924,14 +3924,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-999 -2313 UP UPUP |radicnd| |n|) +(-999 -2312 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2750 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2750 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2750 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2750 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2733 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2733 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2733 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2733 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) (-1000 |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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2750 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2733 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-1001) ((|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 @@ -3951,7 +3951,7 @@ NIL (-1005 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 -4407)) (|HasCategory| |#2| (QUOTE (-1094)))) +((|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-1094)))) (-1006 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -3962,21 +3962,21 @@ NIL NIL (-1008) ((|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}}"))) -((-4399 . T) (-4404 . T) (-4398 . T) (-4401 . T) (-4400 . T) ((-4408 "*") . T) (-4403 . T)) +((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) NIL -(-1009 R -2313) +(-1009 R -2312) ((|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 -(-1010 R -2313) +(-1010 R -2312) ((|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 -(-1011 -2313 UP) +(-1011 -2312 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 -(-1012 -2313 UP) +(-1012 -2312 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 @@ -4010,9 +4010,9 @@ NIL NIL (-1020 |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"))) -((-4399 . T) (-4404 . T) (-4398 . T) (-4401 . T) (-4400 . T) ((-4408 "*") . T) (-4403 . T)) -((-2750 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) -(-1021 -2313 L) +((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) +((-2733 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) +(-1021 -2312 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 @@ -4022,12 +4022,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1094)))) (-1023 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."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) (-1024 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 (-4408 "*")))) +((|HasAttribute| |#1| (QUOTE (-4409 "*")))) (-1025 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 @@ -4048,14 +4048,14 @@ 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 -(-1030 -2313 |Expon| |VarSet| |FPol| |LFPol|) +(-1030 -2312 |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"))) -(((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1031) ((|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.}"))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3726) (QUOTE (-52))))))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3683) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1032) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4098,7 +4098,7 @@ NIL NIL (-1042 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}."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) ((-12 (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1094))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -776) (|devaluate| |#1|) (LIST (QUOTE -860) (|devaluate| |#2|)))))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-860 |#2|) (QUOTE (-368))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1043) ((|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"))) @@ -4110,9 +4110,9 @@ NIL NIL (-1045) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4403 . T)) +((-4404 . T)) NIL -(-1046 |xx| -2313) +(-1046 |xx| -2312) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4122,12 +4122,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-307))) (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (QUOTE (-556))) (|HasCategory| |#4| (QUOTE (-172)))) (-1048 |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"))) -((-4406 . T) (-4401 . T) (-4400 . T)) +((-4407 . T) (-4402 . T) (-4401 . T)) NIL (-1049 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4406 . T) (-4401 . T) (-4400 . T)) -((-2750 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4402 . T) (-4401 . T)) +((-2733 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) (-1050 |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 @@ -4146,7 +4146,7 @@ NIL NIL (-1054) ((|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."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1055 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4154,19 +4154,19 @@ NIL NIL (-1056) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4394 . T) (-4398 . T) (-4393 . T) (-4404 . T) (-4405 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1057) ((|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}"))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3726) (QUOTE (-52))))))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3683) (QUOTE (-52))))))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1058 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -988) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-1170))))) (-1059 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL (-1060) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -4190,7 +4190,7 @@ NIL NIL (-1065 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}."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-1066 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."))) @@ -4208,11 +4208,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1070 |Base| R -2313) +(-1070 |Base| R -2312) ((|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 -(-1071 |Base| R -2313) +(-1071 |Base| R -2312) ((|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 @@ -4226,8 +4226,8 @@ NIL NIL (-1074 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."))) -((-4399 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((-4400 |has| |#1| (-363)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1075 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 @@ -4254,8 +4254,8 @@ NIL NIL (-1081 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"))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1082 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 @@ -4298,14 +4298,14 @@ NIL NIL (-1092 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}."))) -((-4396 . T)) +((-4397 . T)) NIL (-1093 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}."))) +((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL (-1094) -((|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}."))) +((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL (-1095 |m| |n|) @@ -4314,8 +4314,8 @@ NIL NIL (-1096 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)}}"))) -((-4406 . T) (-4396 . T) (-4407 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4407 . T) (-4397 . T) (-4408 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1097 |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.")) (|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 @@ -4342,7 +4342,7 @@ NIL NIL (-1103 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.}"))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-1104) ((|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."))) @@ -4358,8 +4358,8 @@ NIL NIL (-1107 |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}."))) -((-4400 |has| |#3| (-1045)) (-4401 |has| |#3| (-1045)) (-4403 |has| |#3| (-6 -4403)) ((-4408 "*") |has| |#3| (-172)) (-4406 . 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(|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2733 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (|HasAttribute| |#3| (QUOTE -4404)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-1108 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4368,7 +4368,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1110 R -2313) +(-1110 R -2312) ((|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 @@ -4386,19 +4386,19 @@ NIL NIL (-1114) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4394 . T) (-4398 . T) (-4393 . T) (-4404 . T) (-4405 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1115 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4406 . T) (-4407 . T)) +((-4407 . T) (-4408 . T)) NIL (-1116 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-363))) (|HasAttribute| |#3| (QUOTE (-4408 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) +((|HasCategory| |#3| (QUOTE (-363))) (|HasAttribute| |#3| (QUOTE (-4409 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) (-1117 |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."))) -((-4406 . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4407 . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1118 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}."))) @@ -4406,17 +4406,17 @@ NIL NIL (-1119 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."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1120 |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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1121 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}"))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL -(-1122 UP -2313) +(-1122 UP -2312) ((|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 @@ -4470,19 +4470,19 @@ NIL NIL (-1135 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2750 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2733 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) (-1136 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) -((-4403 . T) (-4395 |has| |#2| (-6 (-4408 "*"))) (-4406 . T) (-4400 . T) (-4401 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2750 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4404 . T) (-4396 |has| |#2| (-6 (-4409 "*"))) (-4407 . T) (-4401 . T) (-4402 . T)) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2733 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1137 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1138) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-1139 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.}"))) @@ -4490,12 +4490,12 @@ NIL NIL (-1140 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."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) (-1141 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}."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1142 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 @@ -4506,8 +4506,8 @@ NIL NIL (-1144 |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."))) -((-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094)))) +((-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094)))) (-1145) ((|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 @@ -4530,20 +4530,20 @@ NIL NIL (-1150 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1151) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-1152) NIL -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1153 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#1|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#1|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1154 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 @@ -4574,9 +4574,9 @@ NIL NIL (-1161 |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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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2983) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1168 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2983) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1169) ((|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}.")) 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(|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4658,8 +4658,8 @@ NIL NIL (-1182 |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}"))) -((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-4407 . T) (-4408 . T)) +((-12 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3026) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3683) (|devaluate| |#2|)))))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2733 (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1183 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 @@ -4670,7 +4670,7 @@ NIL NIL (-1185 |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})}."))) -((-4407 . T)) +((-4408 . T)) NIL (-1186 |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."))) @@ -4710,8 +4710,8 @@ NIL NIL (-1195 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4407 . T) (-4406 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-4408 . T) (-4407 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1196 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4720,7 +4720,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1198 R -2313) +(-1198 R -2312) ((|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 @@ -4728,7 +4728,7 @@ 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 -(-1200 R -2313) +(-1200 R -2312) ((|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 -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) @@ -4738,12 +4738,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-368)))) (-1202 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-1203 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1204 |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 @@ -4756,7 +4756,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-1207 -2313) +(-1207 -2312) ((|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 @@ -4782,7 +4782,7 @@ NIL NIL (-1213) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1214) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4806,7 +4806,7 @@ NIL NIL (-1219 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1220 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) @@ -4814,16 +4814,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-1221 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1222 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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(LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1224 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4858,8 +4858,8 @@ NIL NIL (-1232 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4402 |has| |#2| (-363)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4403 |has| |#2| (-363)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2733 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2733 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2733 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2733 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1233 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 @@ -4870,15 +4870,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1145)))) (-1235 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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4402 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL (-1236 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 -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2350) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2326) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) (-1237 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1238 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4890,7 +4890,7 @@ NIL NIL (-1240 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1241 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) @@ -4898,24 +4898,24 @@ NIL NIL (-1242 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1243 |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)}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2983) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-1244 |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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2733 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2983) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1245 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))}."))) -(((-4408 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4399 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-2750 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) +(((-4409 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4400 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-2733 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) (-1246 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4407))) +((|HasAttribute| |#1| (QUOTE -4408))) (-1247 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4927,20 +4927,20 @@ NIL (-1249 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1871) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2983) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1250 |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."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1251 |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}."))) -(((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2733 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2326) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2733 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2983) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3702) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1252 |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 -(-1253 -2313 UP L UTS) +(-1253 -2312 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 (-556)))) @@ -4958,7 +4958,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1257 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) NIL (-1258 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4966,8 +4966,8 @@ NIL NIL (-1259 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4407 . T) (-4406 . T)) -((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4407 . T)) +((-2733 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2733 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2733 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1260) ((|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|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4994,13 +4994,13 @@ NIL NIL (-1266 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4401 . T) (-4400 . T)) +((-4402 . T) (-4401 . T)) NIL (-1267 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 -(-1268 K R UP -2313) +(-1268 K R UP -2312) ((|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 @@ -5014,56 +5014,56 @@ NIL NIL (-1271 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)"))) -((-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) (-4403 . T)) +((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (-1272 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}}."))) -((-4407 . T) (-4406 . T)) +((-4408 . T) (-4407 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) (-1273 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})"))) -((-4400 . T) (-4401 . T) (-4403 . T)) +((-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1274 |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."))) -((-4403 . T) (-4399 |has| |#2| (-6 -4399)) (-4401 . T) (-4400 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4399))) +((-4404 . T) (-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4400))) (-1275 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 (-1276 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4399 |has| |#2| (-6 -4399)) (-4401 . T) (-4400 . T) (-4403 . T)) +((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL -(-1277 S -2313) +(-1277 S -2312) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -2313) +(-1278 -2312) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL (-1279 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4399 |has| |#2| (-6 -4399)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasAttribute| |#2| (QUOTE -4399))) +((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasAttribute| |#2| (QUOTE -4400))) (-1280 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4399 |has| |#2| (-6 -4399)) (-4401 . T) (-4400 . T) (-4403 . T)) +((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) NIL (-1281 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4399 |has| |#1| (-6 -4399)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4399))) +((-4400 |has| |#1| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4400))) (-1282 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4403 . T) (-4404 |has| |#1| (-6 -4404)) (-4399 |has| |#1| (-6 -4399)) (-4401 . T) (-4400 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4403)) (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4399))) +((-4404 . T) (-4405 |has| |#1| (-6 -4405)) (-4400 |has| |#1| (-6 -4400)) (-4402 . T) (-4401 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4400))) (-1283 |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."))) -((-4399 |has| |#2| (-6 -4399)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4399))) +((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4400))) (-1284 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 @@ -5078,7 +5078,7 @@ NIL NIL (-1287 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) NIL NIL NIL @@ -5096,4 +5096,4 @@ NIL NIL NIL NIL -((-3 NIL 2283297 2283302 2283307 2283312) (-2 NIL 2283277 2283282 2283287 2283292) (-1 NIL 2283257 2283262 2283267 2283272) (0 NIL 2283237 2283242 2283247 2283252) (-1287 "ZMOD.spad" 2283046 2283059 2283175 2283232) (-1286 "ZLINDEP.spad" 2282090 2282101 2283036 2283041) (-1285 "ZDSOLVE.spad" 2271939 2271961 2282080 2282085) (-1284 "YSTREAM.spad" 2271432 2271443 2271929 2271934) (-1283 "XRPOLY.spad" 2270652 2270672 2271288 2271357) (-1282 "XPR.spad" 2268443 2268456 2270370 2270469) (-1281 "XPOLY.spad" 2267998 2268009 2268299 2268368) (-1280 "XPOLYC.spad" 2267315 2267331 2267924 2267993) (-1279 "XPBWPOLY.spad" 2265752 2265772 2267095 2267164) (-1278 "XF.spad" 2264213 2264228 2265654 2265747) (-1277 "XF.spad" 2262654 2262671 2264097 2264102) (-1276 "XFALG.spad" 2259678 2259694 2262580 2262649) (-1275 "XEXPPKG.spad" 2258929 2258955 2259668 2259673) (-1274 "XDPOLY.spad" 2258543 2258559 2258785 2258854) (-1273 "XALG.spad" 2258203 2258214 2258499 2258538) (-1272 "WUTSET.spad" 2254042 2254059 2257849 2257876) (-1271 "WP.spad" 2253241 2253285 2253900 2253967) (-1270 "WHILEAST.spad" 2253039 2253048 2253231 2253236) (-1269 "WHEREAST.spad" 2252710 2252719 2253029 2253034) (-1268 "WFFINTBS.spad" 2250273 2250295 2252700 2252705) (-1267 "WEIER.spad" 2248487 2248498 2250263 2250268) (-1266 "VSPACE.spad" 2248160 2248171 2248455 2248482) (-1265 "VSPACE.spad" 2247853 2247866 2248150 2248155) (-1264 "VOID.spad" 2247530 2247539 2247843 2247848) (-1263 "VIEW.spad" 2245152 2245161 2247520 2247525) (-1262 "VIEWDEF.spad" 2240349 2240358 2245142 2245147) (-1261 "VIEW3D.spad" 2224184 2224193 2240339 2240344) (-1260 "VIEW2D.spad" 2211921 2211930 2224174 2224179) (-1259 "VECTOR.spad" 2210596 2210607 2210847 2210874) (-1258 "VECTOR2.spad" 2209223 2209236 2210586 2210591) (-1257 "VECTCAT.spad" 2207123 2207134 2209191 2209218) (-1256 "VECTCAT.spad" 2204831 2204844 2206901 2206906) (-1255 "VARIABLE.spad" 2204611 2204626 2204821 2204826) (-1254 "UTYPE.spad" 2204255 2204264 2204601 2204606) (-1253 "UTSODETL.spad" 2203548 2203572 2204211 2204216) (-1252 "UTSODE.spad" 2201736 2201756 2203538 2203543) (-1251 "UTS.spad" 2196525 2196553 2200203 2200300) (-1250 "UTSCAT.spad" 2193976 2193992 2196423 2196520) (-1249 "UTSCAT.spad" 2191071 2191089 2193520 2193525) (-1248 "UTS2.spad" 2190664 2190699 2191061 2191066) (-1247 "URAGG.spad" 2185296 2185307 2190654 2190659) (-1246 "URAGG.spad" 2179892 2179905 2185252 2185257) (-1245 "UPXSSING.spad" 2177535 2177561 2178973 2179106) (-1244 "UPXS.spad" 2174683 2174711 2175667 2175816) (-1243 "UPXSCONS.spad" 2172440 2172460 2172815 2172964) (-1242 "UPXSCCA.spad" 2171005 2171025 2172286 2172435) (-1241 "UPXSCCA.spad" 2169712 2169734 2170995 2171000) (-1240 "UPXSCAT.spad" 2168293 2168309 2169558 2169707) (-1239 "UPXS2.spad" 2167834 2167887 2168283 2168288) (-1238 "UPSQFREE.spad" 2166246 2166260 2167824 2167829) (-1237 "UPSCAT.spad" 2163839 2163863 2166144 2166241) (-1236 "UPSCAT.spad" 2161138 2161164 2163445 2163450) (-1235 "UPOLYC.spad" 2156116 2156127 2160980 2161133) (-1234 "UPOLYC.spad" 2150986 2150999 2155852 2155857) (-1233 "UPOLYC2.spad" 2150455 2150474 2150976 2150981) (-1232 "UP.spad" 2147612 2147627 2148005 2148158) (-1231 "UPMP.spad" 2146502 2146515 2147602 2147607) (-1230 "UPDIVP.spad" 2146065 2146079 2146492 2146497) (-1229 "UPDECOMP.spad" 2144302 2144316 2146055 2146060) (-1228 "UPCDEN.spad" 2143509 2143525 2144292 2144297) (-1227 "UP2.spad" 2142871 2142892 2143499 2143504) (-1226 "UNISEG.spad" 2142224 2142235 2142790 2142795) (-1225 "UNISEG2.spad" 2141717 2141730 2142180 2142185) (-1224 "UNIFACT.spad" 2140818 2140830 2141707 2141712) (-1223 "ULS.spad" 2131370 2131398 2132463 2132892) (-1222 "ULSCONS.spad" 2123764 2123784 2124136 2124285) (-1221 "ULSCCAT.spad" 2121493 2121513 2123610 2123759) (-1220 "ULSCCAT.spad" 2119330 2119352 2121449 2121454) (-1219 "ULSCAT.spad" 2117546 2117562 2119176 2119325) (-1218 "ULS2.spad" 2117058 2117111 2117536 2117541) (-1217 "UINT8.spad" 2116935 2116944 2117048 2117053) (-1216 "UINT64.spad" 2116811 2116820 2116925 2116930) (-1215 "UINT32.spad" 2116687 2116696 2116801 2116806) (-1214 "UINT16.spad" 2116563 2116572 2116677 2116682) (-1213 "UFD.spad" 2115628 2115637 2116489 2116558) (-1212 "UFD.spad" 2114755 2114766 2115618 2115623) (-1211 "UDVO.spad" 2113602 2113611 2114745 2114750) (-1210 "UDPO.spad" 2111029 2111040 2113558 2113563) (-1209 "TYPE.spad" 2110961 2110970 2111019 2111024) (-1208 "TYPEAST.spad" 2110880 2110889 2110951 2110956) (-1207 "TWOFACT.spad" 2109530 2109545 2110870 2110875) (-1206 "TUPLE.spad" 2109014 2109025 2109429 2109434) (-1205 "TUBETOOL.spad" 2105851 2105860 2109004 2109009) (-1204 "TUBE.spad" 2104492 2104509 2105841 2105846) (-1203 "TS.spad" 2103081 2103097 2104057 2104154) (-1202 "TSETCAT.spad" 2090208 2090225 2103049 2103076) (-1201 "TSETCAT.spad" 2077321 2077340 2090164 2090169) (-1200 "TRMANIP.spad" 2071687 2071704 2077027 2077032) (-1199 "TRIMAT.spad" 2070646 2070671 2071677 2071682) (-1198 "TRIGMNIP.spad" 2069163 2069180 2070636 2070641) (-1197 "TRIGCAT.spad" 2068675 2068684 2069153 2069158) (-1196 "TRIGCAT.spad" 2068185 2068196 2068665 2068670) (-1195 "TREE.spad" 2066756 2066767 2067792 2067819) (-1194 "TRANFUN.spad" 2066587 2066596 2066746 2066751) (-1193 "TRANFUN.spad" 2066416 2066427 2066577 2066582) (-1192 "TOPSP.spad" 2066090 2066099 2066406 2066411) (-1191 "TOOLSIGN.spad" 2065753 2065764 2066080 2066085) (-1190 "TEXTFILE.spad" 2064310 2064319 2065743 2065748) (-1189 "TEX.spad" 2061442 2061451 2064300 2064305) (-1188 "TEX1.spad" 2060998 2061009 2061432 2061437) (-1187 "TEMUTL.spad" 2060553 2060562 2060988 2060993) (-1186 "TBCMPPK.spad" 2058646 2058669 2060543 2060548) (-1185 "TBAGG.spad" 2057682 2057705 2058626 2058641) (-1184 "TBAGG.spad" 2056726 2056751 2057672 2057677) (-1183 "TANEXP.spad" 2056102 2056113 2056716 2056721) (-1182 "TABLE.spad" 2054513 2054536 2054783 2054810) (-1181 "TABLEAU.spad" 2053994 2054005 2054503 2054508) (-1180 "TABLBUMP.spad" 2050777 2050788 2053984 2053989) (-1179 "SYSTEM.spad" 2050005 2050014 2050767 2050772) (-1178 "SYSSOLP.spad" 2047478 2047489 2049995 2050000) (-1177 "SYSNNI.spad" 2046658 2046669 2047468 2047473) (-1176 "SYSINT.spad" 2046062 2046073 2046648 2046653) (-1175 "SYNTAX.spad" 2042256 2042265 2046052 2046057) (-1174 "SYMTAB.spad" 2040312 2040321 2042246 2042251) (-1173 "SYMS.spad" 2036297 2036306 2040302 2040307) (-1172 "SYMPOLY.spad" 2035304 2035315 2035386 2035513) (-1171 "SYMFUNC.spad" 2034779 2034790 2035294 2035299) (-1170 "SYMBOL.spad" 2032206 2032215 2034769 2034774) (-1169 "SWITCH.spad" 2028963 2028972 2032196 2032201) (-1168 "SUTS.spad" 2025862 2025890 2027430 2027527) (-1167 "SUPXS.spad" 2022997 2023025 2023994 2024143) (-1166 "SUP.spad" 2019766 2019777 2020547 2020700) (-1165 "SUPFRACF.spad" 2018871 2018889 2019756 2019761) (-1164 "SUP2.spad" 2018261 2018274 2018861 2018866) (-1163 "SUMRF.spad" 2017227 2017238 2018251 2018256) (-1162 "SUMFS.spad" 2016860 2016877 2017217 2017222) (-1161 "SULS.spad" 2007399 2007427 2008505 2008934) (-1160 "SUCHTAST.spad" 2007168 2007177 2007389 2007394) (-1159 "SUCH.spad" 2006848 2006863 2007158 2007163) (-1158 "SUBSPACE.spad" 1998855 1998870 2006838 2006843) (-1157 "SUBRESP.spad" 1998015 1998029 1998811 1998816) (-1156 "STTF.spad" 1994114 1994130 1998005 1998010) (-1155 "STTFNC.spad" 1990582 1990598 1994104 1994109) (-1154 "STTAYLOR.spad" 1982980 1982991 1990463 1990468) (-1153 "STRTBL.spad" 1981485 1981502 1981634 1981661) (-1152 "STRING.spad" 1980894 1980903 1980908 1980935) (-1151 "STRICAT.spad" 1980682 1980691 1980862 1980889) (-1150 "STREAM.spad" 1977540 1977551 1980207 1980222) (-1149 "STREAM3.spad" 1977085 1977100 1977530 1977535) (-1148 "STREAM2.spad" 1976153 1976166 1977075 1977080) (-1147 "STREAM1.spad" 1975857 1975868 1976143 1976148) (-1146 "STINPROD.spad" 1974763 1974779 1975847 1975852) (-1145 "STEP.spad" 1973964 1973973 1974753 1974758) (-1144 "STBL.spad" 1972490 1972518 1972657 1972672) (-1143 "STAGG.spad" 1971565 1971576 1972480 1972485) (-1142 "STAGG.spad" 1970638 1970651 1971555 1971560) (-1141 "STACK.spad" 1969989 1970000 1970245 1970272) (-1140 "SREGSET.spad" 1967693 1967710 1969635 1969662) (-1139 "SRDCMPK.spad" 1966238 1966258 1967683 1967688) (-1138 "SRAGG.spad" 1961335 1961344 1966206 1966233) (-1137 "SRAGG.spad" 1956452 1956463 1961325 1961330) (-1136 "SQMATRIX.spad" 1954068 1954086 1954984 1955071) (-1135 "SPLTREE.spad" 1948620 1948633 1953504 1953531) (-1134 "SPLNODE.spad" 1945208 1945221 1948610 1948615) (-1133 "SPFCAT.spad" 1943985 1943994 1945198 1945203) (-1132 "SPECOUT.spad" 1942535 1942544 1943975 1943980) (-1131 "SPADXPT.spad" 1934674 1934683 1942525 1942530) (-1130 "spad-parser.spad" 1934139 1934148 1934664 1934669) (-1129 "SPADAST.spad" 1933840 1933849 1934129 1934134) (-1128 "SPACEC.spad" 1917853 1917864 1933830 1933835) (-1127 "SPACE3.spad" 1917629 1917640 1917843 1917848) (-1126 "SORTPAK.spad" 1917174 1917187 1917585 1917590) (-1125 "SOLVETRA.spad" 1914931 1914942 1917164 1917169) (-1124 "SOLVESER.spad" 1913451 1913462 1914921 1914926) (-1123 "SOLVERAD.spad" 1909461 1909472 1913441 1913446) (-1122 "SOLVEFOR.spad" 1907881 1907899 1909451 1909456) (-1121 "SNTSCAT.spad" 1907481 1907498 1907849 1907876) (-1120 "SMTS.spad" 1905741 1905767 1907046 1907143) (-1119 "SMP.spad" 1903180 1903200 1903570 1903697) (-1118 "SMITH.spad" 1902023 1902048 1903170 1903175) (-1117 "SMATCAT.spad" 1900133 1900163 1901967 1902018) (-1116 "SMATCAT.spad" 1898175 1898207 1900011 1900016) (-1115 "SKAGG.spad" 1897136 1897147 1898143 1898170) (-1114 "SINT.spad" 1895962 1895971 1897002 1897131) (-1113 "SIMPAN.spad" 1895690 1895699 1895952 1895957) (-1112 "SIG.spad" 1895018 1895027 1895680 1895685) (-1111 "SIGNRF.spad" 1894126 1894137 1895008 1895013) (-1110 "SIGNEF.spad" 1893395 1893412 1894116 1894121) (-1109 "SIGAST.spad" 1892776 1892785 1893385 1893390) (-1108 "SHP.spad" 1890694 1890709 1892732 1892737) (-1107 "SHDP.spad" 1880405 1880432 1880914 1881045) (-1106 "SGROUP.spad" 1880013 1880022 1880395 1880400) (-1105 "SGROUP.spad" 1879619 1879630 1880003 1880008) (-1104 "SGCF.spad" 1872500 1872509 1879609 1879614) (-1103 "SFRTCAT.spad" 1871428 1871445 1872468 1872495) (-1102 "SFRGCD.spad" 1870491 1870511 1871418 1871423) (-1101 "SFQCMPK.spad" 1865128 1865148 1870481 1870486) (-1100 "SFORT.spad" 1864563 1864577 1865118 1865123) (-1099 "SEXOF.spad" 1864406 1864446 1864553 1864558) (-1098 "SEX.spad" 1864298 1864307 1864396 1864401) (-1097 "SEXCAT.spad" 1861849 1861889 1864288 1864293) (-1096 "SET.spad" 1860149 1860160 1861270 1861309) (-1095 "SETMN.spad" 1858583 1858600 1860139 1860144) (-1094 "SETCAT.spad" 1858068 1858077 1858573 1858578) (-1093 "SETCAT.spad" 1857551 1857562 1858058 1858063) (-1092 "SETAGG.spad" 1854072 1854083 1857531 1857546) (-1091 "SETAGG.spad" 1850601 1850614 1854062 1854067) (-1090 "SEQAST.spad" 1850304 1850313 1850591 1850596) (-1089 "SEGXCAT.spad" 1849426 1849439 1850294 1850299) (-1088 "SEG.spad" 1849239 1849250 1849345 1849350) (-1087 "SEGCAT.spad" 1848146 1848157 1849229 1849234) (-1086 "SEGBIND.spad" 1847218 1847229 1848101 1848106) (-1085 "SEGBIND2.spad" 1846914 1846927 1847208 1847213) (-1084 "SEGAST.spad" 1846628 1846637 1846904 1846909) (-1083 "SEG2.spad" 1846053 1846066 1846584 1846589) (-1082 "SDVAR.spad" 1845329 1845340 1846043 1846048) (-1081 "SDPOL.spad" 1842719 1842730 1843010 1843137) (-1080 "SCPKG.spad" 1840798 1840809 1842709 1842714) (-1079 "SCOPE.spad" 1839947 1839956 1840788 1840793) (-1078 "SCACHE.spad" 1838629 1838640 1839937 1839942) (-1077 "SASTCAT.spad" 1838538 1838547 1838619 1838624) (-1076 "SAOS.spad" 1838410 1838419 1838528 1838533) (-1075 "SAERFFC.spad" 1838123 1838143 1838400 1838405) (-1074 "SAE.spad" 1836298 1836314 1836909 1837044) (-1073 "SAEFACT.spad" 1835999 1836019 1836288 1836293) (-1072 "RURPK.spad" 1833640 1833656 1835989 1835994) (-1071 "RULESET.spad" 1833081 1833105 1833630 1833635) (-1070 "RULE.spad" 1831285 1831309 1833071 1833076) (-1069 "RULECOLD.spad" 1831137 1831150 1831275 1831280) (-1068 "RTVALUE.spad" 1830870 1830879 1831127 1831132) (-1067 "RSTRCAST.spad" 1830587 1830596 1830860 1830865) (-1066 "RSETGCD.spad" 1826965 1826985 1830577 1830582) (-1065 "RSETCAT.spad" 1816749 1816766 1826933 1826960) (-1064 "RSETCAT.spad" 1806553 1806572 1816739 1816744) (-1063 "RSDCMPK.spad" 1805005 1805025 1806543 1806548) (-1062 "RRCC.spad" 1803389 1803419 1804995 1805000) (-1061 "RRCC.spad" 1801771 1801803 1803379 1803384) (-1060 "RPTAST.spad" 1801473 1801482 1801761 1801766) (-1059 "RPOLCAT.spad" 1780833 1780848 1801341 1801468) (-1058 "RPOLCAT.spad" 1759907 1759924 1780417 1780422) (-1057 "ROUTINE.spad" 1755770 1755779 1758554 1758581) (-1056 "ROMAN.spad" 1755098 1755107 1755636 1755765) (-1055 "ROIRC.spad" 1754178 1754210 1755088 1755093) (-1054 "RNS.spad" 1753081 1753090 1754080 1754173) (-1053 "RNS.spad" 1752070 1752081 1753071 1753076) (-1052 "RNG.spad" 1751805 1751814 1752060 1752065) (-1051 "RMODULE.spad" 1751443 1751454 1751795 1751800) (-1050 "RMCAT2.spad" 1750851 1750908 1751433 1751438) (-1049 "RMATRIX.spad" 1749675 1749694 1750018 1750057) (-1048 "RMATCAT.spad" 1745208 1745239 1749631 1749670) (-1047 "RMATCAT.spad" 1740631 1740664 1745056 1745061) (-1046 "RINTERP.spad" 1740519 1740539 1740621 1740626) (-1045 "RING.spad" 1739989 1739998 1740499 1740514) (-1044 "RING.spad" 1739467 1739478 1739979 1739984) (-1043 "RIDIST.spad" 1738851 1738860 1739457 1739462) (-1042 "RGCHAIN.spad" 1737430 1737446 1738336 1738363) (-1041 "RGBCSPC.spad" 1737211 1737223 1737420 1737425) (-1040 "RGBCMDL.spad" 1736741 1736753 1737201 1737206) (-1039 "RF.spad" 1734355 1734366 1736731 1736736) (-1038 "RFFACTOR.spad" 1733817 1733828 1734345 1734350) (-1037 "RFFACT.spad" 1733552 1733564 1733807 1733812) (-1036 "RFDIST.spad" 1732540 1732549 1733542 1733547) (-1035 "RETSOL.spad" 1731957 1731970 1732530 1732535) (-1034 "RETRACT.spad" 1731385 1731396 1731947 1731952) (-1033 "RETRACT.spad" 1730811 1730824 1731375 1731380) (-1032 "RETAST.spad" 1730623 1730632 1730801 1730806) (-1031 "RESULT.spad" 1728683 1728692 1729270 1729297) (-1030 "RESRING.spad" 1728030 1728077 1728621 1728678) (-1029 "RESLATC.spad" 1727354 1727365 1728020 1728025) (-1028 "REPSQ.spad" 1727083 1727094 1727344 1727349) (-1027 "REP.spad" 1724635 1724644 1727073 1727078) (-1026 "REPDB.spad" 1724340 1724351 1724625 1724630) (-1025 "REP2.spad" 1713912 1713923 1724182 1724187) (-1024 "REP1.spad" 1707902 1707913 1713862 1713867) (-1023 "REGSET.spad" 1705699 1705716 1707548 1707575) (-1022 "REF.spad" 1705028 1705039 1705654 1705659) (-1021 "REDORDER.spad" 1704204 1704221 1705018 1705023) (-1020 "RECLOS.spad" 1702987 1703007 1703691 1703784) (-1019 "REALSOLV.spad" 1702119 1702128 1702977 1702982) (-1018 "REAL.spad" 1701991 1702000 1702109 1702114) (-1017 "REAL0Q.spad" 1699273 1699288 1701981 1701986) (-1016 "REAL0.spad" 1696101 1696116 1699263 1699268) (-1015 "RDUCEAST.spad" 1695822 1695831 1696091 1696096) (-1014 "RDIV.spad" 1695473 1695498 1695812 1695817) (-1013 "RDIST.spad" 1695036 1695047 1695463 1695468) (-1012 "RDETRS.spad" 1693832 1693850 1695026 1695031) (-1011 "RDETR.spad" 1691939 1691957 1693822 1693827) (-1010 "RDEEFS.spad" 1691012 1691029 1691929 1691934) (-1009 "RDEEF.spad" 1690008 1690025 1691002 1691007) (-1008 "RCFIELD.spad" 1687194 1687203 1689910 1690003) (-1007 "RCFIELD.spad" 1684466 1684477 1687184 1687189) (-1006 "RCAGG.spad" 1682378 1682389 1684456 1684461) (-1005 "RCAGG.spad" 1680217 1680230 1682297 1682302) (-1004 "RATRET.spad" 1679577 1679588 1680207 1680212) (-1003 "RATFACT.spad" 1679269 1679281 1679567 1679572) (-1002 "RANDSRC.spad" 1678588 1678597 1679259 1679264) (-1001 "RADUTIL.spad" 1678342 1678351 1678578 1678583) (-1000 "RADIX.spad" 1675243 1675257 1676809 1676902) (-999 "RADFF.spad" 1673657 1673693 1673775 1673931) (-998 "RADCAT.spad" 1673251 1673259 1673647 1673652) (-997 "RADCAT.spad" 1672843 1672853 1673241 1673246) (-996 "QUEUE.spad" 1672186 1672196 1672450 1672477) (-995 "QUAT.spad" 1670768 1670778 1671110 1671175) (-994 "QUATCT2.spad" 1670387 1670405 1670758 1670763) (-993 "QUATCAT.spad" 1668552 1668562 1670317 1670382) (-992 "QUATCAT.spad" 1666468 1666480 1668235 1668240) (-991 "QUAGG.spad" 1665294 1665304 1666436 1666463) (-990 "QQUTAST.spad" 1665063 1665071 1665284 1665289) (-989 "QFORM.spad" 1664526 1664540 1665053 1665058) (-988 "QFCAT.spad" 1663229 1663239 1664428 1664521) (-987 "QFCAT.spad" 1661523 1661535 1662724 1662729) (-986 "QFCAT2.spad" 1661214 1661230 1661513 1661518) (-985 "QEQUAT.spad" 1660771 1660779 1661204 1661209) (-984 "QCMPACK.spad" 1655518 1655537 1660761 1660766) (-983 "QALGSET.spad" 1651593 1651625 1655432 1655437) (-982 "QALGSET2.spad" 1649589 1649607 1651583 1651588) (-981 "PWFFINTB.spad" 1646899 1646920 1649579 1649584) (-980 "PUSHVAR.spad" 1646228 1646247 1646889 1646894) (-979 "PTRANFN.spad" 1642354 1642364 1646218 1646223) (-978 "PTPACK.spad" 1639442 1639452 1642344 1642349) (-977 "PTFUNC2.spad" 1639263 1639277 1639432 1639437) (-976 "PTCAT.spad" 1638512 1638522 1639231 1639258) (-975 "PSQFR.spad" 1637819 1637843 1638502 1638507) (-974 "PSEUDLIN.spad" 1636677 1636687 1637809 1637814) (-973 "PSETPK.spad" 1622110 1622126 1636555 1636560) (-972 "PSETCAT.spad" 1616030 1616053 1622090 1622105) (-971 "PSETCAT.spad" 1609924 1609949 1615986 1615991) (-970 "PSCURVE.spad" 1608907 1608915 1609914 1609919) (-969 "PSCAT.spad" 1607674 1607703 1608805 1608902) (-968 "PSCAT.spad" 1606531 1606562 1607664 1607669) (-967 "PRTITION.spad" 1605476 1605484 1606521 1606526) (-966 "PRTDAST.spad" 1605195 1605203 1605466 1605471) (-965 "PRS.spad" 1594757 1594774 1605151 1605156) (-964 "PRQAGG.spad" 1594188 1594198 1594725 1594752) (-963 "PROPLOG.spad" 1593591 1593599 1594178 1594183) (-962 "PROPFRML.spad" 1592399 1592410 1593581 1593586) (-961 "PROPERTY.spad" 1591885 1591893 1592389 1592394) (-960 "PRODUCT.spad" 1589565 1589577 1589851 1589906) (-959 "PR.spad" 1587951 1587963 1588656 1588783) (-958 "PRINT.spad" 1587703 1587711 1587941 1587946) (-957 "PRIMES.spad" 1585954 1585964 1587693 1587698) (-956 "PRIMELT.spad" 1583935 1583949 1585944 1585949) (-955 "PRIMCAT.spad" 1583558 1583566 1583925 1583930) (-954 "PRIMARR.spad" 1582563 1582573 1582741 1582768) (-953 "PRIMARR2.spad" 1581286 1581298 1582553 1582558) (-952 "PREASSOC.spad" 1580658 1580670 1581276 1581281) (-951 "PPCURVE.spad" 1579795 1579803 1580648 1580653) (-950 "PORTNUM.spad" 1579570 1579578 1579785 1579790) (-949 "POLYROOT.spad" 1578399 1578421 1579526 1579531) (-948 "POLY.spad" 1575696 1575706 1576213 1576340) (-947 "POLYLIFT.spad" 1574957 1574980 1575686 1575691) (-946 "POLYCATQ.spad" 1573059 1573081 1574947 1574952) (-945 "POLYCAT.spad" 1566465 1566486 1572927 1573054) (-944 "POLYCAT.spad" 1559173 1559196 1565637 1565642) (-943 "POLY2UP.spad" 1558621 1558635 1559163 1559168) (-942 "POLY2.spad" 1558216 1558228 1558611 1558616) (-941 "POLUTIL.spad" 1557157 1557186 1558172 1558177) (-940 "POLTOPOL.spad" 1555905 1555920 1557147 1557152) (-939 "POINT.spad" 1554744 1554754 1554831 1554858) (-938 "PNTHEORY.spad" 1551410 1551418 1554734 1554739) (-937 "PMTOOLS.spad" 1550167 1550181 1551400 1551405) (-936 "PMSYM.spad" 1549712 1549722 1550157 1550162) (-935 "PMQFCAT.spad" 1549299 1549313 1549702 1549707) (-934 "PMPRED.spad" 1548768 1548782 1549289 1549294) (-933 "PMPREDFS.spad" 1548212 1548234 1548758 1548763) (-932 "PMPLCAT.spad" 1547282 1547300 1548144 1548149) (-931 "PMLSAGG.spad" 1546863 1546877 1547272 1547277) (-930 "PMKERNEL.spad" 1546430 1546442 1546853 1546858) (-929 "PMINS.spad" 1546006 1546016 1546420 1546425) (-928 "PMFS.spad" 1545579 1545597 1545996 1546001) (-927 "PMDOWN.spad" 1544865 1544879 1545569 1545574) (-926 "PMASS.spad" 1543873 1543881 1544855 1544860) (-925 "PMASSFS.spad" 1542838 1542854 1543863 1543868) (-924 "PLOTTOOL.spad" 1542618 1542626 1542828 1542833) (-923 "PLOT.spad" 1537449 1537457 1542608 1542613) (-922 "PLOT3D.spad" 1533869 1533877 1537439 1537444) (-921 "PLOT1.spad" 1533010 1533020 1533859 1533864) (-920 "PLEQN.spad" 1520226 1520253 1533000 1533005) (-919 "PINTERP.spad" 1519842 1519861 1520216 1520221) (-918 "PINTERPA.spad" 1519624 1519640 1519832 1519837) (-917 "PI.spad" 1519231 1519239 1519598 1519619) (-916 "PID.spad" 1518187 1518195 1519157 1519226) (-915 "PICOERCE.spad" 1517844 1517854 1518177 1518182) (-914 "PGROEB.spad" 1516441 1516455 1517834 1517839) (-913 "PGE.spad" 1507694 1507702 1516431 1516436) (-912 "PGCD.spad" 1506576 1506593 1507684 1507689) (-911 "PFRPAC.spad" 1505719 1505729 1506566 1506571) (-910 "PFR.spad" 1502376 1502386 1505621 1505714) (-909 "PFOTOOLS.spad" 1501634 1501650 1502366 1502371) (-908 "PFOQ.spad" 1501004 1501022 1501624 1501629) (-907 "PFO.spad" 1500423 1500450 1500994 1500999) (-906 "PF.spad" 1499997 1500009 1500228 1500321) (-905 "PFECAT.spad" 1497663 1497671 1499923 1499992) (-904 "PFECAT.spad" 1495357 1495367 1497619 1497624) (-903 "PFBRU.spad" 1493227 1493239 1495347 1495352) (-902 "PFBR.spad" 1490765 1490788 1493217 1493222) (-901 "PERM.spad" 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1299191) (-788 "OAMON.spad" 1298577 1298585 1298706 1298711) (-787 "OAGROUP.spad" 1298439 1298447 1298567 1298572) (-786 "NUMTUBE.spad" 1298026 1298042 1298429 1298434) (-785 "NUMQUAD.spad" 1285888 1285896 1298016 1298021) (-784 "NUMODE.spad" 1277024 1277032 1285878 1285883) (-783 "NUMINT.spad" 1274582 1274590 1277014 1277019) (-782 "NUMFMT.spad" 1273422 1273430 1274572 1274577) (-781 "NUMERIC.spad" 1265494 1265504 1273227 1273232) (-780 "NTSCAT.spad" 1263996 1264012 1265462 1265489) (-779 "NTPOLFN.spad" 1263541 1263551 1263913 1263918) (-778 "NSUP.spad" 1256551 1256561 1261091 1261244) (-777 "NSUP2.spad" 1255943 1255955 1256541 1256546) (-776 "NSMP.spad" 1252138 1252157 1252446 1252573) (-775 "NREP.spad" 1250510 1250524 1252128 1252133) (-774 "NPCOEF.spad" 1249756 1249776 1250500 1250505) (-773 "NORMRETR.spad" 1249354 1249393 1249746 1249751) (-772 "NORMPK.spad" 1247256 1247275 1249344 1249349) (-771 "NORMMA.spad" 1246944 1246970 1247246 1247251) (-770 "NONE.spad" 1246685 1246693 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1018015 1021116 1021121) (-637 "LINEXP.spad" 1017435 1017445 1017983 1017998) (-636 "LINDEP.spad" 1016212 1016224 1017347 1017352) (-635 "LIMITRF.spad" 1014126 1014136 1016202 1016207) (-634 "LIMITPS.spad" 1013009 1013022 1014116 1014121) (-633 "LIE.spad" 1011023 1011035 1012299 1012444) (-632 "LIECAT.spad" 1010499 1010509 1010949 1011018) (-631 "LIECAT.spad" 1010003 1010015 1010455 1010460) (-630 "LIB.spad" 1008051 1008059 1008662 1008677) (-629 "LGROBP.spad" 1005404 1005423 1008041 1008046) (-628 "LF.spad" 1004323 1004339 1005394 1005399) (-627 "LFCAT.spad" 1003342 1003350 1004313 1004318) (-626 "LEXTRIPK.spad" 998845 998860 1003332 1003337) (-625 "LEXP.spad" 996848 996875 998825 998840) (-624 "LETAST.spad" 996547 996555 996838 996843) (-623 "LEADCDET.spad" 994931 994948 996537 996542) (-622 "LAZM3PK.spad" 993635 993657 994921 994926) (-621 "LAUPOL.spad" 992324 992337 993228 993297) (-620 "LAPLACE.spad" 991897 991913 992314 992319) (-619 "LA.spad" 991337 991351 991819 991858) (-618 "LALG.spad" 991113 991123 991317 991332) (-617 "LALG.spad" 990897 990909 991103 991108) (-616 "KVTFROM.spad" 990632 990642 990887 990892) (-615 "KTVLOGIC.spad" 990055 990063 990622 990627) (-614 "KRCFROM.spad" 989793 989803 990045 990050) (-613 "KOVACIC.spad" 988506 988523 989783 989788) (-612 "KONVERT.spad" 988228 988238 988496 988501) (-611 "KOERCE.spad" 987965 987975 988218 988223) (-610 "KERNEL.spad" 986500 986510 987749 987754) (-609 "KERNEL2.spad" 986203 986215 986490 986495) (-608 "KDAGG.spad" 985306 985328 986183 986198) (-607 "KDAGG.spad" 984417 984441 985296 985301) (-606 "KAFILE.spad" 983380 983396 983615 983642) (-605 "JORDAN.spad" 981207 981219 982670 982815) (-604 "JOINAST.spad" 980901 980909 981197 981202) (-603 "JAVACODE.spad" 980767 980775 980891 980896) (-602 "IXAGG.spad" 978890 978914 980757 980762) (-601 "IXAGG.spad" 976868 976894 978737 978742) (-600 "IVECTOR.spad" 975639 975654 975794 975821) (-599 "ITUPLE.spad" 974784 974794 975629 975634) (-598 "ITRIGMNP.spad" 973595 973614 974774 974779) (-597 "ITFUN3.spad" 973089 973103 973585 973590) (-596 "ITFUN2.spad" 972819 972831 973079 973084) (-595 "ITAYLOR.spad" 970611 970626 972655 972780) (-594 "ISUPS.spad" 963022 963037 969585 969682) (-593 "ISUMP.spad" 962519 962535 963012 963017) (-592 "ISTRING.spad" 961522 961535 961688 961715) (-591 "ISAST.spad" 961241 961249 961512 961517) (-590 "IRURPK.spad" 959954 959973 961231 961236) (-589 "IRSN.spad" 957914 957922 959944 959949) (-588 "IRRF2F.spad" 956389 956399 957870 957875) (-587 "IRREDFFX.spad" 955990 956001 956379 956384) (-586 "IROOT.spad" 954321 954331 955980 955985) (-585 "IR.spad" 952110 952124 954176 954203) (-584 "IR2.spad" 951130 951146 952100 952105) (-583 "IR2F.spad" 950330 950346 951120 951125) (-582 "IPRNTPK.spad" 950090 950098 950320 950325) (-581 "IPF.spad" 949655 949667 949895 949988) (-580 "IPADIC.spad" 949416 949442 949581 949650) (-579 "IP4ADDR.spad" 948973 948981 949406 949411) (-578 "IOMODE.spad" 948594 948602 948963 948968) (-577 "IOBFILE.spad" 947955 947963 948584 948589) (-576 "IOBCON.spad" 947820 947828 947945 947950) (-575 "INVLAPLA.spad" 947465 947481 947810 947815) (-574 "INTTR.spad" 940711 940728 947455 947460) (-573 "INTTOOLS.spad" 938422 938438 940285 940290) (-572 "INTSLPE.spad" 937728 937736 938412 938417) (-571 "INTRVL.spad" 937294 937304 937642 937723) (-570 "INTRF.spad" 935658 935672 937284 937289) (-569 "INTRET.spad" 935090 935100 935648 935653) (-568 "INTRAT.spad" 933765 933782 935080 935085) (-567 "INTPM.spad" 932128 932144 933408 933413) (-566 "INTPAF.spad" 929896 929914 932060 932065) (-565 "INTPACK.spad" 920206 920214 929886 929891) (-564 "INT.spad" 919567 919575 920060 920201) (-563 "INTHERTR.spad" 918833 918850 919557 919562) (-562 "INTHERAL.spad" 918499 918523 918823 918828) (-561 "INTHEORY.spad" 914912 914920 918489 918494) (-560 "INTG0.spad" 908375 908393 914844 914849) (-559 "INTFTBL.spad" 902404 902412 908365 908370) (-558 "INTFACT.spad" 901463 901473 902394 902399) (-557 "INTEF.spad" 899778 899794 901453 901458) (-556 "INTDOM.spad" 898393 898401 899704 899773) (-555 "INTDOM.spad" 897070 897080 898383 898388) (-554 "INTCAT.spad" 895323 895333 896984 897065) (-553 "INTBIT.spad" 894826 894834 895313 895318) (-552 "INTALG.spad" 894008 894035 894816 894821) (-551 "INTAF.spad" 893500 893516 893998 894003) (-550 "INTABL.spad" 892018 892049 892181 892208) (-549 "INT8.spad" 891898 891906 892008 892013) (-548 "INT64.spad" 891777 891785 891888 891893) (-547 "INT32.spad" 891656 891664 891767 891772) (-546 "INT16.spad" 891535 891543 891646 891651) (-545 "INS.spad" 889002 889010 891437 891530) (-544 "INS.spad" 886555 886565 888992 888997) (-543 "INPSIGN.spad" 885989 886002 886545 886550) (-542 "INPRODPF.spad" 885055 885074 885979 885984) (-541 "INPRODFF.spad" 884113 884137 885045 885050) (-540 "INNMFACT.spad" 883084 883101 884103 884108) (-539 "INMODGCD.spad" 882568 882598 883074 883079) (-538 "INFSP.spad" 880853 880875 882558 882563) (-537 "INFPROD0.spad" 879903 879922 880843 880848) (-536 "INFORM.spad" 877064 877072 879893 879898) (-535 "INFORM1.spad" 876689 876699 877054 877059) (-534 "INFINITY.spad" 876241 876249 876679 876684) (-533 "INETCLTS.spad" 876218 876226 876231 876236) (-532 "INEP.spad" 874750 874772 876208 876213) (-531 "INDE.spad" 874479 874496 874740 874745) (-530 "INCRMAPS.spad" 873900 873910 874469 874474) (-529 "INBFILE.spad" 872972 872980 873890 873895) (-528 "INBFF.spad" 868742 868753 872962 872967) (-527 "INBCON.spad" 867030 867038 868732 868737) (-526 "INBCON.spad" 865316 865326 867020 867025) (-525 "INAST.spad" 864977 864985 865306 865311) (-524 "IMPTAST.spad" 864685 864693 864967 864972) (-523 "IMATRIX.spad" 863630 863656 864142 864169) (-522 "IMATQF.spad" 862724 862768 863586 863591) (-521 "IMATLIN.spad" 861329 861353 862680 862685) (-520 "ILIST.spad" 859985 860000 860512 860539) (-519 "IIARRAY2.spad" 859373 859411 859592 859619) (-518 "IFF.spad" 858783 858799 859054 859147) (-517 "IFAST.spad" 858397 858405 858773 858778) (-516 "IFARRAY.spad" 855884 855899 857580 857607) (-515 "IFAMON.spad" 855746 855763 855840 855845) (-514 "IEVALAB.spad" 855135 855147 855736 855741) (-513 "IEVALAB.spad" 854522 854536 855125 855130) (-512 "IDPO.spad" 854320 854332 854512 854517) (-511 "IDPOAMS.spad" 854076 854088 854310 854315) (-510 "IDPOAM.spad" 853796 853808 854066 854071) (-509 "IDPC.spad" 852730 852742 853786 853791) (-508 "IDPAM.spad" 852475 852487 852720 852725) (-507 "IDPAG.spad" 852222 852234 852465 852470) (-506 "IDENT.spad" 851872 851880 852212 852217) (-505 "IDECOMP.spad" 849109 849127 851862 851867) (-504 "IDEAL.spad" 844032 844071 849044 849049) (-503 "ICDEN.spad" 843183 843199 844022 844027) (-502 "ICARD.spad" 842372 842380 843173 843178) (-501 "IBPTOOLS.spad" 840965 840982 842362 842367) (-500 "IBITS.spad" 840164 840177 840601 840628) (-499 "IBATOOL.spad" 837039 837058 840154 840159) (-498 "IBACHIN.spad" 835526 835541 837029 837034) (-497 "IARRAY2.spad" 834514 834540 835133 835160) (-496 "IARRAY1.spad" 833559 833574 833697 833724) (-495 "IAN.spad" 831772 831780 833375 833468) (-494 "IALGFACT.spad" 831373 831406 831762 831767) (-493 "HYPCAT.spad" 830797 830805 831363 831368) (-492 "HYPCAT.spad" 830219 830229 830787 830792) (-491 "HOSTNAME.spad" 830027 830035 830209 830214) (-490 "HOMOTOP.spad" 829770 829780 830017 830022) (-489 "HOAGG.spad" 827038 827048 829760 829765) (-488 "HOAGG.spad" 824081 824093 826805 826810) (-487 "HEXADEC.spad" 822183 822191 822548 822641) (-486 "HEUGCD.spad" 821198 821209 822173 822178) (-485 "HELLFDIV.spad" 820788 820812 821188 821193) (-484 "HEAP.spad" 820180 820190 820395 820422) (-483 "HEADAST.spad" 819711 819719 820170 820175) (-482 "HDP.spad" 809554 809570 809931 810062) (-481 "HDMP.spad" 806730 806745 807348 807475) (-480 "HB.spad" 804967 804975 806720 806725) (-479 "HASHTBL.spad" 803437 803468 803648 803675) (-478 "HASAST.spad" 803153 803161 803427 803432) (-477 "HACKPI.spad" 802636 802644 803055 803148) (-476 "GTSET.spad" 801575 801591 802282 802309) (-475 "GSTBL.spad" 800094 800129 800268 800283) (-474 "GSERIES.spad" 797261 797288 798226 798375) (-473 "GROUP.spad" 796530 796538 797241 797256) (-472 "GROUP.spad" 795807 795817 796520 796525) (-471 "GROEBSOL.spad" 794295 794316 795797 795802) (-470 "GRMOD.spad" 792866 792878 794285 794290) (-469 "GRMOD.spad" 791435 791449 792856 792861) (-468 "GRIMAGE.spad" 784040 784048 791425 791430) (-467 "GRDEF.spad" 782419 782427 784030 784035) (-466 "GRAY.spad" 780878 780886 782409 782414) (-465 "GRALG.spad" 779925 779937 780868 780873) (-464 "GRALG.spad" 778970 778984 779915 779920) (-463 "GPOLSET.spad" 778424 778447 778652 778679) (-462 "GOSPER.spad" 777689 777707 778414 778419) (-461 "GMODPOL.spad" 776827 776854 777657 777684) (-460 "GHENSEL.spad" 775896 775910 776817 776822) (-459 "GENUPS.spad" 771997 772010 775886 775891) (-458 "GENUFACT.spad" 771574 771584 771987 771992) (-457 "GENPGCD.spad" 771158 771175 771564 771569) (-456 "GENMFACT.spad" 770610 770629 771148 771153) (-455 "GENEEZ.spad" 768549 768562 770600 770605) (-454 "GDMP.spad" 765567 765584 766343 766470) (-453 "GCNAALG.spad" 759462 759489 765361 765428) (-452 "GCDDOM.spad" 758634 758642 759388 759457) (-451 "GCDDOM.spad" 757868 757878 758624 758629) (-450 "GB.spad" 755386 755424 757824 757829) (-449 "GBINTERN.spad" 751406 751444 755376 755381) (-448 "GBF.spad" 747163 747201 751396 751401) (-447 "GBEUCLID.spad" 745037 745075 747153 747158) (-446 "GAUSSFAC.spad" 744334 744342 745027 745032) (-445 "GALUTIL.spad" 742656 742666 744290 744295) (-444 "GALPOLYU.spad" 741102 741115 742646 742651) (-443 "GALFACTU.spad" 739267 739286 741092 741097) (-442 "GALFACT.spad" 729400 729411 739257 739262) (-441 "FVFUN.spad" 726423 726431 729390 729395) (-440 "FVC.spad" 725475 725483 726413 726418) (-439 "FUNDESC.spad" 725153 725161 725465 725470) (-438 "FUNCTION.spad" 725002 725014 725143 725148) (-437 "FT.spad" 723295 723303 724992 724997) (-436 "FTEM.spad" 722458 722466 723285 723290) (-435 "FSUPFACT.spad" 721358 721377 722394 722399) (-434 "FST.spad" 719444 719452 721348 721353) (-433 "FSRED.spad" 718922 718938 719434 719439) (-432 "FSPRMELT.spad" 717746 717762 718879 718884) (-431 "FSPECF.spad" 715823 715839 717736 717741) (-430 "FS.spad" 709885 709895 715598 715818) (-429 "FS.spad" 703725 703737 709440 709445) (-428 "FSINT.spad" 703383 703399 703715 703720) (-427 "FSERIES.spad" 702570 702582 703203 703302) (-426 "FSCINT.spad" 701883 701899 702560 702565) (-425 "FSAGG.spad" 701000 701010 701839 701878) (-424 "FSAGG.spad" 700079 700091 700920 700925) (-423 "FSAGG2.spad" 698778 698794 700069 700074) (-422 "FS2UPS.spad" 693261 693295 698768 698773) (-421 "FS2.spad" 692906 692922 693251 693256) (-420 "FS2EXPXP.spad" 692029 692052 692896 692901) (-419 "FRUTIL.spad" 690971 690981 692019 692024) (-418 "FR.spad" 684665 684675 689995 690064) (-417 "FRNAALG.spad" 679752 679762 684607 684660) (-416 "FRNAALG.spad" 674851 674863 679708 679713) (-415 "FRNAAF2.spad" 674305 674323 674841 674846) (-414 "FRMOD.spad" 673699 673729 674236 674241) (-413 "FRIDEAL.spad" 672894 672915 673679 673694) (-412 "FRIDEAL2.spad" 672496 672528 672884 672889) (-411 "FRETRCT.spad" 672007 672017 672486 672491) (-410 "FRETRCT.spad" 671384 671396 671865 671870) (-409 "FRAMALG.spad" 669712 669725 671340 671379) (-408 "FRAMALG.spad" 668072 668087 669702 669707) (-407 "FRAC.spad" 665171 665181 665574 665747) (-406 "FRAC2.spad" 664774 664786 665161 665166) (-405 "FR2.spad" 664108 664120 664764 664769) (-404 "FPS.spad" 660917 660925 663998 664103) (-403 "FPS.spad" 657754 657764 660837 660842) (-402 "FPC.spad" 656796 656804 657656 657749) (-401 "FPC.spad" 655924 655934 656786 656791) (-400 "FPATMAB.spad" 655686 655696 655914 655919) (-399 "FPARFRAC.spad" 654159 654176 655676 655681) (-398 "FORTRAN.spad" 652665 652708 654149 654154) (-397 "FORT.spad" 651594 651602 652655 652660) (-396 "FORTFN.spad" 648764 648772 651584 651589) (-395 "FORTCAT.spad" 648448 648456 648754 648759) (-394 "FORMULA.spad" 645912 645920 648438 648443) (-393 "FORMULA1.spad" 645391 645401 645902 645907) (-392 "FORDER.spad" 645082 645106 645381 645386) (-391 "FOP.spad" 644283 644291 645072 645077) (-390 "FNLA.spad" 643707 643729 644251 644278) (-389 "FNCAT.spad" 642294 642302 643697 643702) (-388 "FNAME.spad" 642186 642194 642284 642289) (-387 "FMTC.spad" 641984 641992 642112 642181) (-386 "FMONOID.spad" 639039 639049 641940 641945) (-385 "FM.spad" 638734 638746 638973 639000) (-384 "FMFUN.spad" 635764 635772 638724 638729) (-383 "FMC.spad" 634816 634824 635754 635759) (-382 "FMCAT.spad" 632470 632488 634784 634811) (-381 "FM1.spad" 631827 631839 632404 632431) (-380 "FLOATRP.spad" 629548 629562 631817 631822) (-379 "FLOAT.spad" 622836 622844 629414 629543) (-378 "FLOATCP.spad" 620253 620267 622826 622831) (-377 "FLINEXP.spad" 619965 619975 620233 620248) (-376 "FLINEXP.spad" 619631 619643 619901 619906) (-375 "FLASORT.spad" 618951 618963 619621 619626) (-374 "FLALG.spad" 616597 616616 618877 618946) (-373 "FLAGG.spad" 613615 613625 616577 616592) (-372 "FLAGG.spad" 610534 610546 613498 613503) (-371 "FLAGG2.spad" 609215 609231 610524 610529) (-370 "FINRALG.spad" 607244 607257 609171 609210) (-369 "FINRALG.spad" 605199 605214 607128 607133) (-368 "FINITE.spad" 604351 604359 605189 605194) (-367 "FINAALG.spad" 593332 593342 604293 604346) (-366 "FINAALG.spad" 582325 582337 593288 593293) (-365 "FILE.spad" 581908 581918 582315 582320) (-364 "FILECAT.spad" 580426 580443 581898 581903) (-363 "FIELD.spad" 579832 579840 580328 580421) (-362 "FIELD.spad" 579324 579334 579822 579827) (-361 "FGROUP.spad" 577933 577943 579304 579319) (-360 "FGLMICPK.spad" 576720 576735 577923 577928) (-359 "FFX.spad" 576095 576110 576436 576529) (-358 "FFSLPE.spad" 575584 575605 576085 576090) (-357 "FFPOLY.spad" 566836 566847 575574 575579) (-356 "FFPOLY2.spad" 565896 565913 566826 566831) (-355 "FFP.spad" 565293 565313 565612 565705) (-354 "FF.spad" 564741 564757 564974 565067) (-353 "FFNBX.spad" 563253 563273 564457 564550) (-352 "FFNBP.spad" 561766 561783 562969 563062) (-351 "FFNB.spad" 560231 560252 561447 561540) (-350 "FFINTBAS.spad" 557645 557664 560221 560226) (-349 "FFIELDC.spad" 555220 555228 557547 557640) (-348 "FFIELDC.spad" 552881 552891 555210 555215) (-347 "FFHOM.spad" 551629 551646 552871 552876) (-346 "FFF.spad" 549064 549075 551619 551624) (-345 "FFCGX.spad" 547911 547931 548780 548873) (-344 "FFCGP.spad" 546800 546820 547627 547720) (-343 "FFCG.spad" 545592 545613 546481 546574) (-342 "FFCAT.spad" 538619 538641 545431 545587) (-341 "FFCAT.spad" 531725 531749 538539 538544) (-340 "FFCAT2.spad" 531470 531510 531715 531720) (-339 "FEXPR.spad" 523179 523225 531226 531265) (-338 "FEVALAB.spad" 522885 522895 523169 523174) (-337 "FEVALAB.spad" 522376 522388 522662 522667) (-336 "FDIV.spad" 521818 521842 522366 522371) (-335 "FDIVCAT.spad" 519860 519884 521808 521813) (-334 "FDIVCAT.spad" 517900 517926 519850 519855) (-333 "FDIV2.spad" 517554 517594 517890 517895) (-332 "FCPAK1.spad" 516107 516115 517544 517549) (-331 "FCOMP.spad" 515486 515496 516097 516102) (-330 "FC.spad" 505401 505409 515476 515481) (-329 "FAXF.spad" 498336 498350 505303 505396) (-328 "FAXF.spad" 491323 491339 498292 498297) (-327 "FARRAY.spad" 489469 489479 490506 490533) (-326 "FAMR.spad" 487589 487601 489367 489464) (-325 "FAMR.spad" 485693 485707 487473 487478) (-324 "FAMONOID.spad" 485343 485353 485647 485652) (-323 "FAMONC.spad" 483565 483577 485333 485338) (-322 "FAGROUP.spad" 483171 483181 483461 483488) (-321 "FACUTIL.spad" 481367 481384 483161 483166) (-320 "FACTFUNC.spad" 480543 480553 481357 481362) (-319 "EXPUPXS.spad" 477376 477399 478675 478824) (-318 "EXPRTUBE.spad" 474604 474612 477366 477371) (-317 "EXPRODE.spad" 471476 471492 474594 474599) (-316 "EXPR.spad" 466751 466761 467465 467872) (-315 "EXPR2UPS.spad" 462843 462856 466741 466746) (-314 "EXPR2.spad" 462546 462558 462833 462838) (-313 "EXPEXPAN.spad" 459484 459509 460118 460211) (-312 "EXIT.spad" 459155 459163 459474 459479) (-311 "EXITAST.spad" 458891 458899 459145 459150) (-310 "EVALCYC.spad" 458349 458363 458881 458886) (-309 "EVALAB.spad" 457913 457923 458339 458344) (-308 "EVALAB.spad" 457475 457487 457903 457908) (-307 "EUCDOM.spad" 455017 455025 457401 457470) (-306 "EUCDOM.spad" 452621 452631 455007 455012) (-305 "ESTOOLS.spad" 444461 444469 452611 452616) (-304 "ESTOOLS2.spad" 444062 444076 444451 444456) (-303 "ESTOOLS1.spad" 443747 443758 444052 444057) (-302 "ES.spad" 436294 436302 443737 443742) (-301 "ES.spad" 428747 428757 436192 436197) (-300 "ESCONT.spad" 425520 425528 428737 428742) (-299 "ESCONT1.spad" 425269 425281 425510 425515) (-298 "ES2.spad" 424764 424780 425259 425264) (-297 "ES1.spad" 424330 424346 424754 424759) (-296 "ERROR.spad" 421651 421659 424320 424325) (-295 "EQTBL.spad" 420123 420145 420332 420359) (-294 "EQ.spad" 414997 415007 417796 417908) (-293 "EQ2.spad" 414713 414725 414987 414992) (-292 "EP.spad" 411027 411037 414703 414708) (-291 "ENV.spad" 409679 409687 411017 411022) (-290 "ENTIRER.spad" 409347 409355 409623 409674) (-289 "EMR.spad" 408548 408589 409273 409342) (-288 "ELTAGG.spad" 406788 406807 408538 408543) (-287 "ELTAGG.spad" 404992 405013 406744 406749) (-286 "ELTAB.spad" 404439 404457 404982 404987) (-285 "ELFUTS.spad" 403818 403837 404429 404434) (-284 "ELEMFUN.spad" 403507 403515 403808 403813) (-283 "ELEMFUN.spad" 403194 403204 403497 403502) (-282 "ELAGG.spad" 401137 401147 403174 403189) (-281 "ELAGG.spad" 399017 399029 401056 401061) (-280 "ELABEXPR.spad" 397940 397948 399007 399012) (-279 "EFUPXS.spad" 394716 394746 397896 397901) (-278 "EFULS.spad" 391552 391575 394672 394677) (-277 "EFSTRUC.spad" 389507 389523 391542 391547) (-276 "EF.spad" 384273 384289 389497 389502) (-275 "EAB.spad" 382549 382557 384263 384268) (-274 "E04UCFA.spad" 382085 382093 382539 382544) (-273 "E04NAFA.spad" 381662 381670 382075 382080) (-272 "E04MBFA.spad" 381242 381250 381652 381657) (-271 "E04JAFA.spad" 380778 380786 381232 381237) (-270 "E04GCFA.spad" 380314 380322 380768 380773) (-269 "E04FDFA.spad" 379850 379858 380304 380309) (-268 "E04DGFA.spad" 379386 379394 379840 379845) (-267 "E04AGNT.spad" 375228 375236 379376 379381) (-266 "DVARCAT.spad" 371913 371923 375218 375223) (-265 "DVARCAT.spad" 368596 368608 371903 371908) (-264 "DSMP.spad" 366027 366041 366332 366459) (-263 "DROPT.spad" 359972 359980 366017 366022) (-262 "DROPT1.spad" 359635 359645 359962 359967) (-261 "DROPT0.spad" 354462 354470 359625 359630) (-260 "DRAWPT.spad" 352617 352625 354452 354457) (-259 "DRAW.spad" 345217 345230 352607 352612) (-258 "DRAWHACK.spad" 344525 344535 345207 345212) (-257 "DRAWCX.spad" 341967 341975 344515 344520) (-256 "DRAWCURV.spad" 341504 341519 341957 341962) (-255 "DRAWCFUN.spad" 330676 330684 341494 341499) (-254 "DQAGG.spad" 328844 328854 330644 330671) (-253 "DPOLCAT.spad" 324185 324201 328712 328839) (-252 "DPOLCAT.spad" 319612 319630 324141 324146) (-251 "DPMO.spad" 311838 311854 311976 312277) (-250 "DPMM.spad" 304077 304095 304202 304503) (-249 "DOMCTOR.spad" 303969 303977 304067 304072) (-248 "DOMAIN.spad" 303100 303108 303959 303964) (-247 "DMP.spad" 300322 300337 300894 301021) (-246 "DLP.spad" 299670 299680 300312 300317) (-245 "DLIST.spad" 298249 298259 298853 298880) (-244 "DLAGG.spad" 296660 296670 298239 298244) (-243 "DIVRING.spad" 296202 296210 296604 296655) (-242 "DIVRING.spad" 295788 295798 296192 296197) (-241 "DISPLAY.spad" 293968 293976 295778 295783) (-240 "DIRPROD.spad" 283548 283564 284188 284319) (-239 "DIRPROD2.spad" 282356 282374 283538 283543) (-238 "DIRPCAT.spad" 281298 281314 282220 282351) (-237 "DIRPCAT.spad" 279969 279987 280893 280898) (-236 "DIOSP.spad" 278794 278802 279959 279964) (-235 "DIOPS.spad" 277778 277788 278774 278789) (-234 "DIOPS.spad" 276736 276748 277734 277739) (-233 "DIFRING.spad" 276028 276036 276716 276731) (-232 "DIFRING.spad" 275328 275338 276018 276023) (-231 "DIFEXT.spad" 274487 274497 275308 275323) (-230 "DIFEXT.spad" 273563 273575 274386 274391) (-229 "DIAGG.spad" 273193 273203 273543 273558) (-228 "DIAGG.spad" 272831 272843 273183 273188) (-227 "DHMATRIX.spad" 271135 271145 272288 272315) (-226 "DFSFUN.spad" 264543 264551 271125 271130) (-225 "DFLOAT.spad" 261264 261272 264433 264538) (-224 "DFINTTLS.spad" 259473 259489 261254 261259) (-223 "DERHAM.spad" 257383 257415 259453 259468) (-222 "DEQUEUE.spad" 256701 256711 256990 257017) (-221 "DEGRED.spad" 256316 256330 256691 256696) (-220 "DEFINTRF.spad" 253841 253851 256306 256311) (-219 "DEFINTEF.spad" 252337 252353 253831 253836) (-218 "DEFAST.spad" 251705 251713 252327 252332) (-217 "DECIMAL.spad" 249811 249819 250172 250265) (-216 "DDFACT.spad" 247610 247627 249801 249806) (-215 "DBLRESP.spad" 247208 247232 247600 247605) (-214 "DBASE.spad" 245862 245872 247198 247203) (-213 "DATAARY.spad" 245324 245337 245852 245857) (-212 "D03FAFA.spad" 245152 245160 245314 245319) (-211 "D03EEFA.spad" 244972 244980 245142 245147) (-210 "D03AGNT.spad" 244052 244060 244962 244967) (-209 "D02EJFA.spad" 243514 243522 244042 244047) (-208 "D02CJFA.spad" 242992 243000 243504 243509) (-207 "D02BHFA.spad" 242482 242490 242982 242987) (-206 "D02BBFA.spad" 241972 241980 242472 242477) (-205 "D02AGNT.spad" 236776 236784 241962 241967) (-204 "D01WGTS.spad" 235095 235103 236766 236771) (-203 "D01TRNS.spad" 235072 235080 235085 235090) (-202 "D01GBFA.spad" 234594 234602 235062 235067) (-201 "D01FCFA.spad" 234116 234124 234584 234589) (-200 "D01ASFA.spad" 233584 233592 234106 234111) (-199 "D01AQFA.spad" 233030 233038 233574 233579) (-198 "D01APFA.spad" 232454 232462 233020 233025) (-197 "D01ANFA.spad" 231948 231956 232444 232449) (-196 "D01AMFA.spad" 231458 231466 231938 231943) (-195 "D01ALFA.spad" 230998 231006 231448 231453) (-194 "D01AKFA.spad" 230524 230532 230988 230993) (-193 "D01AJFA.spad" 230047 230055 230514 230519) (-192 "D01AGNT.spad" 226106 226114 230037 230042) (-191 "CYCLOTOM.spad" 225612 225620 226096 226101) (-190 "CYCLES.spad" 222444 222452 225602 225607) (-189 "CVMP.spad" 221861 221871 222434 222439) (-188 "CTRIGMNP.spad" 220351 220367 221851 221856) (-187 "CTOR.spad" 220042 220050 220341 220346) (-186 "CTORKIND.spad" 219645 219653 220032 220037) (-185 "CTORCAT.spad" 218894 218902 219635 219640) (-184 "CTORCAT.spad" 218141 218151 218884 218889) (-183 "CTORCALL.spad" 217721 217729 218131 218136) (-182 "CSTTOOLS.spad" 216964 216977 217711 217716) (-181 "CRFP.spad" 210668 210681 216954 216959) (-180 "CRCEAST.spad" 210388 210396 210658 210663) (-179 "CRAPACK.spad" 209431 209441 210378 210383) (-178 "CPMATCH.spad" 208931 208946 209356 209361) (-177 "CPIMA.spad" 208636 208655 208921 208926) (-176 "COORDSYS.spad" 203529 203539 208626 208631) (-175 "CONTOUR.spad" 202936 202944 203519 203524) (-174 "CONTFRAC.spad" 198548 198558 202838 202931) (-173 "CONDUIT.spad" 198306 198314 198538 198543) (-172 "COMRING.spad" 197980 197988 198244 198301) (-171 "COMPPROP.spad" 197494 197502 197970 197975) (-170 "COMPLPAT.spad" 197261 197276 197484 197489) (-169 "COMPLEX.spad" 191285 191295 191529 191790) (-168 "COMPLEX2.spad" 190998 191010 191275 191280) (-167 "COMPFACT.spad" 190600 190614 190988 190993) (-166 "COMPCAT.spad" 188668 188678 190334 190595) (-165 "COMPCAT.spad" 186429 186441 188097 188102) (-164 "COMMUPC.spad" 186175 186193 186419 186424) (-163 "COMMONOP.spad" 185708 185716 186165 186170) (-162 "COMM.spad" 185517 185525 185698 185703) (-161 "COMMAAST.spad" 185280 185288 185507 185512) (-160 "COMBOPC.spad" 184185 184193 185270 185275) (-159 "COMBINAT.spad" 182930 182940 184175 184180) (-158 "COMBF.spad" 180298 180314 182920 182925) (-157 "COLOR.spad" 179135 179143 180288 180293) (-156 "COLONAST.spad" 178801 178809 179125 179130) (-155 "CMPLXRT.spad" 178510 178527 178791 178796) (-154 "CLLCTAST.spad" 178172 178180 178500 178505) (-153 "CLIP.spad" 174264 174272 178162 178167) (-152 "CLIF.spad" 172903 172919 174220 174259) (-151 "CLAGG.spad" 169388 169398 172893 172898) (-150 "CLAGG.spad" 165744 165756 169251 169256) (-149 "CINTSLPE.spad" 165069 165082 165734 165739) (-148 "CHVAR.spad" 163147 163169 165059 165064) (-147 "CHARZ.spad" 163062 163070 163127 163142) (-146 "CHARPOL.spad" 162570 162580 163052 163057) (-145 "CHARNZ.spad" 162323 162331 162550 162565) (-144 "CHAR.spad" 160191 160199 162313 162318) (-143 "CFCAT.spad" 159507 159515 160181 160186) (-142 "CDEN.spad" 158665 158679 159497 159502) (-141 "CCLASS.spad" 156814 156822 158076 158115) (-140 "CATEGORY.spad" 155904 155912 156804 156809) (-139 "CATCTOR.spad" 155795 155803 155894 155899) (-138 "CATAST.spad" 155413 155421 155785 155790) (-137 "CASEAST.spad" 155127 155135 155403 155408) (-136 "CARTEN.spad" 150230 150254 155117 155122) (-135 "CARTEN2.spad" 149616 149643 150220 150225) (-134 "CARD.spad" 146905 146913 149590 149611) (-133 "CAPSLAST.spad" 146679 146687 146895 146900) (-132 "CACHSET.spad" 146301 146309 146669 146674) (-131 "CABMON.spad" 145854 145862 146291 146296) (-130 "BYTEORD.spad" 145529 145537 145844 145849) (-129 "BYTE.spad" 144954 144962 145519 145524) (-128 "BYTEBUF.spad" 142811 142819 144123 144150) (-127 "BTREE.spad" 141880 141890 142418 142445) (-126 "BTOURN.spad" 140883 140893 141487 141514) (-125 "BTCAT.spad" 140271 140281 140851 140878) (-124 "BTCAT.spad" 139679 139691 140261 140266) (-123 "BTAGG.spad" 138801 138809 139647 139674) (-122 "BTAGG.spad" 137943 137953 138791 138796) (-121 "BSTREE.spad" 136678 136688 137550 137577) (-120 "BRILL.spad" 134873 134884 136668 136673) (-119 "BRAGG.spad" 133797 133807 134863 134868) (-118 "BRAGG.spad" 132685 132697 133753 133758) (-117 "BPADICRT.spad" 130666 130678 130921 131014) (-116 "BPADIC.spad" 130330 130342 130592 130661) (-115 "BOUNDZRO.spad" 129986 130003 130320 130325) (-114 "BOP.spad" 125004 125012 129976 129981) (-113 "BOP1.spad" 122390 122400 124960 124965) (-112 "BOOLEAN.spad" 121714 121722 122380 122385) (-111 "BMODULE.spad" 121426 121438 121682 121709) (-110 "BITS.spad" 120845 120853 121062 121089) (-109 "BINDING.spad" 120256 120264 120835 120840) (-108 "BINARY.spad" 118367 118375 118723 118816) (-107 "BGAGG.spad" 117564 117574 118347 118362) (-106 "BGAGG.spad" 116769 116781 117554 117559) (-105 "BFUNCT.spad" 116333 116341 116749 116764) (-104 "BEZOUT.spad" 115467 115494 116283 116288) (-103 "BBTREE.spad" 112286 112296 115074 115101) (-102 "BASTYPE.spad" 111958 111966 112276 112281) (-101 "BASTYPE.spad" 111628 111638 111948 111953) (-100 "BALFACT.spad" 111067 111080 111618 111623) (-99 "AUTOMOR.spad" 110514 110523 111047 111062) (-98 "ATTREG.spad" 107233 107240 110266 110509) (-97 "ATTRBUT.spad" 103256 103263 107213 107228) (-96 "ATTRAST.spad" 102973 102980 103246 103251) (-95 "ATRIG.spad" 102443 102450 102963 102968) (-94 "ATRIG.spad" 101911 101920 102433 102438) (-93 "ASTCAT.spad" 101815 101822 101901 101906) (-92 "ASTCAT.spad" 101717 101726 101805 101810) (-91 "ASTACK.spad" 101050 101059 101324 101351) (-90 "ASSOCEQ.spad" 99850 99861 101006 101011) (-89 "ASP9.spad" 98931 98944 99840 99845) (-88 "ASP8.spad" 97974 97987 98921 98926) (-87 "ASP80.spad" 97296 97309 97964 97969) (-86 "ASP7.spad" 96456 96469 97286 97291) (-85 "ASP78.spad" 95907 95920 96446 96451) (-84 "ASP77.spad" 95276 95289 95897 95902) (-83 "ASP74.spad" 94368 94381 95266 95271) (-82 "ASP73.spad" 93639 93652 94358 94363) (-81 "ASP6.spad" 92506 92519 93629 93634) (-80 "ASP55.spad" 91015 91028 92496 92501) (-79 "ASP50.spad" 88832 88845 91005 91010) (-78 "ASP4.spad" 88127 88140 88822 88827) (-77 "ASP49.spad" 87126 87139 88117 88122) (-76 "ASP42.spad" 85533 85572 87116 87121) (-75 "ASP41.spad" 84112 84151 85523 85528) (-74 "ASP35.spad" 83100 83113 84102 84107) (-73 "ASP34.spad" 82401 82414 83090 83095) (-72 "ASP33.spad" 81961 81974 82391 82396) (-71 "ASP31.spad" 81101 81114 81951 81956) (-70 "ASP30.spad" 79993 80006 81091 81096) (-69 "ASP29.spad" 79459 79472 79983 79988) (-68 "ASP28.spad" 70732 70745 79449 79454) (-67 "ASP27.spad" 69629 69642 70722 70727) (-66 "ASP24.spad" 68716 68729 69619 69624) (-65 "ASP20.spad" 68180 68193 68706 68711) (-64 "ASP1.spad" 67561 67574 68170 68175) (-63 "ASP19.spad" 62247 62260 67551 67556) (-62 "ASP12.spad" 61661 61674 62237 62242) (-61 "ASP10.spad" 60932 60945 61651 61656) (-60 "ARRAY2.spad" 60292 60301 60539 60566) (-59 "ARRAY1.spad" 59127 59136 59475 59502) (-58 "ARRAY12.spad" 57796 57807 59117 59122) (-57 "ARR2CAT.spad" 53458 53479 57764 57791) (-56 "ARR2CAT.spad" 49140 49163 53448 53453) (-55 "ARITY.spad" 48512 48519 49130 49135) (-54 "APPRULE.spad" 47756 47778 48502 48507) (-53 "APPLYORE.spad" 47371 47384 47746 47751) (-52 "ANY.spad" 45713 45720 47361 47366) (-51 "ANY1.spad" 44784 44793 45703 45708) (-50 "ANTISYM.spad" 43223 43239 44764 44779) (-49 "ANON.spad" 42916 42923 43213 43218) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2283623 2283628 2283633 2283638) (-2 NIL 2283603 2283608 2283613 2283618) (-1 NIL 2283583 2283588 2283593 2283598) (0 NIL 2283563 2283568 2283573 2283578) (-1287 "ZMOD.spad" 2283372 2283385 2283501 2283558) (-1286 "ZLINDEP.spad" 2282416 2282427 2283362 2283367) (-1285 "ZDSOLVE.spad" 2272265 2272287 2282406 2282411) (-1284 "YSTREAM.spad" 2271758 2271769 2272255 2272260) (-1283 "XRPOLY.spad" 2270978 2270998 2271614 2271683) (-1282 "XPR.spad" 2268769 2268782 2270696 2270795) (-1281 "XPOLY.spad" 2268324 2268335 2268625 2268694) (-1280 "XPOLYC.spad" 2267641 2267657 2268250 2268319) (-1279 "XPBWPOLY.spad" 2266078 2266098 2267421 2267490) (-1278 "XF.spad" 2264539 2264554 2265980 2266073) (-1277 "XF.spad" 2262980 2262997 2264423 2264428) (-1276 "XFALG.spad" 2260004 2260020 2262906 2262975) (-1275 "XEXPPKG.spad" 2259255 2259281 2259994 2259999) (-1274 "XDPOLY.spad" 2258869 2258885 2259111 2259180) (-1273 "XALG.spad" 2258529 2258540 2258825 2258864) (-1272 "WUTSET.spad" 2254368 2254385 2258175 2258202) (-1271 "WP.spad" 2253567 2253611 2254226 2254293) (-1270 "WHILEAST.spad" 2253365 2253374 2253557 2253562) (-1269 "WHEREAST.spad" 2253036 2253045 2253355 2253360) (-1268 "WFFINTBS.spad" 2250599 2250621 2253026 2253031) (-1267 "WEIER.spad" 2248813 2248824 2250589 2250594) (-1266 "VSPACE.spad" 2248486 2248497 2248781 2248808) (-1265 "VSPACE.spad" 2248179 2248192 2248476 2248481) (-1264 "VOID.spad" 2247856 2247865 2248169 2248174) (-1263 "VIEW.spad" 2245478 2245487 2247846 2247851) (-1262 "VIEWDEF.spad" 2240675 2240684 2245468 2245473) (-1261 "VIEW3D.spad" 2224510 2224519 2240665 2240670) (-1260 "VIEW2D.spad" 2212247 2212256 2224500 2224505) (-1259 "VECTOR.spad" 2210922 2210933 2211173 2211200) (-1258 "VECTOR2.spad" 2209549 2209562 2210912 2210917) (-1257 "VECTCAT.spad" 2207449 2207460 2209517 2209544) (-1256 "VECTCAT.spad" 2205157 2205170 2207227 2207232) (-1255 "VARIABLE.spad" 2204937 2204952 2205147 2205152) (-1254 "UTYPE.spad" 2204581 2204590 2204927 2204932) (-1253 "UTSODETL.spad" 2203874 2203898 2204537 2204542) (-1252 "UTSODE.spad" 2202062 2202082 2203864 2203869) (-1251 "UTS.spad" 2196851 2196879 2200529 2200626) (-1250 "UTSCAT.spad" 2194302 2194318 2196749 2196846) (-1249 "UTSCAT.spad" 2191397 2191415 2193846 2193851) (-1248 "UTS2.spad" 2190990 2191025 2191387 2191392) (-1247 "URAGG.spad" 2185622 2185633 2190980 2190985) (-1246 "URAGG.spad" 2180218 2180231 2185578 2185583) (-1245 "UPXSSING.spad" 2177861 2177887 2179299 2179432) (-1244 "UPXS.spad" 2175009 2175037 2175993 2176142) (-1243 "UPXSCONS.spad" 2172766 2172786 2173141 2173290) (-1242 "UPXSCCA.spad" 2171331 2171351 2172612 2172761) (-1241 "UPXSCCA.spad" 2170038 2170060 2171321 2171326) (-1240 "UPXSCAT.spad" 2168619 2168635 2169884 2170033) (-1239 "UPXS2.spad" 2168160 2168213 2168609 2168614) (-1238 "UPSQFREE.spad" 2166572 2166586 2168150 2168155) (-1237 "UPSCAT.spad" 2164165 2164189 2166470 2166567) (-1236 "UPSCAT.spad" 2161464 2161490 2163771 2163776) (-1235 "UPOLYC.spad" 2156442 2156453 2161306 2161459) (-1234 "UPOLYC.spad" 2151312 2151325 2156178 2156183) (-1233 "UPOLYC2.spad" 2150781 2150800 2151302 2151307) (-1232 "UP.spad" 2147938 2147953 2148331 2148484) (-1231 "UPMP.spad" 2146828 2146841 2147928 2147933) (-1230 "UPDIVP.spad" 2146391 2146405 2146818 2146823) (-1229 "UPDECOMP.spad" 2144628 2144642 2146381 2146386) (-1228 "UPCDEN.spad" 2143835 2143851 2144618 2144623) (-1227 "UP2.spad" 2143197 2143218 2143825 2143830) (-1226 "UNISEG.spad" 2142550 2142561 2143116 2143121) (-1225 "UNISEG2.spad" 2142043 2142056 2142506 2142511) (-1224 "UNIFACT.spad" 2141144 2141156 2142033 2142038) (-1223 "ULS.spad" 2131696 2131724 2132789 2133218) (-1222 "ULSCONS.spad" 2124090 2124110 2124462 2124611) (-1221 "ULSCCAT.spad" 2121819 2121839 2123936 2124085) (-1220 "ULSCCAT.spad" 2119656 2119678 2121775 2121780) (-1219 "ULSCAT.spad" 2117872 2117888 2119502 2119651) (-1218 "ULS2.spad" 2117384 2117437 2117862 2117867) (-1217 "UINT8.spad" 2117261 2117270 2117374 2117379) (-1216 "UINT64.spad" 2117137 2117146 2117251 2117256) (-1215 "UINT32.spad" 2117013 2117022 2117127 2117132) (-1214 "UINT16.spad" 2116889 2116898 2117003 2117008) (-1213 "UFD.spad" 2115954 2115963 2116815 2116884) (-1212 "UFD.spad" 2115081 2115092 2115944 2115949) (-1211 "UDVO.spad" 2113928 2113937 2115071 2115076) (-1210 "UDPO.spad" 2111355 2111366 2113884 2113889) (-1209 "TYPE.spad" 2111287 2111296 2111345 2111350) (-1208 "TYPEAST.spad" 2111206 2111215 2111277 2111282) (-1207 "TWOFACT.spad" 2109856 2109871 2111196 2111201) (-1206 "TUPLE.spad" 2109340 2109351 2109755 2109760) (-1205 "TUBETOOL.spad" 2106177 2106186 2109330 2109335) (-1204 "TUBE.spad" 2104818 2104835 2106167 2106172) (-1203 "TS.spad" 2103407 2103423 2104383 2104480) (-1202 "TSETCAT.spad" 2090534 2090551 2103375 2103402) (-1201 "TSETCAT.spad" 2077647 2077666 2090490 2090495) (-1200 "TRMANIP.spad" 2072013 2072030 2077353 2077358) (-1199 "TRIMAT.spad" 2070972 2070997 2072003 2072008) (-1198 "TRIGMNIP.spad" 2069489 2069506 2070962 2070967) (-1197 "TRIGCAT.spad" 2069001 2069010 2069479 2069484) (-1196 "TRIGCAT.spad" 2068511 2068522 2068991 2068996) (-1195 "TREE.spad" 2067082 2067093 2068118 2068145) (-1194 "TRANFUN.spad" 2066913 2066922 2067072 2067077) (-1193 "TRANFUN.spad" 2066742 2066753 2066903 2066908) (-1192 "TOPSP.spad" 2066416 2066425 2066732 2066737) (-1191 "TOOLSIGN.spad" 2066079 2066090 2066406 2066411) (-1190 "TEXTFILE.spad" 2064636 2064645 2066069 2066074) (-1189 "TEX.spad" 2061768 2061777 2064626 2064631) (-1188 "TEX1.spad" 2061324 2061335 2061758 2061763) (-1187 "TEMUTL.spad" 2060879 2060888 2061314 2061319) (-1186 "TBCMPPK.spad" 2058972 2058995 2060869 2060874) (-1185 "TBAGG.spad" 2058008 2058031 2058952 2058967) (-1184 "TBAGG.spad" 2057052 2057077 2057998 2058003) (-1183 "TANEXP.spad" 2056428 2056439 2057042 2057047) (-1182 "TABLE.spad" 2054839 2054862 2055109 2055136) (-1181 "TABLEAU.spad" 2054320 2054331 2054829 2054834) (-1180 "TABLBUMP.spad" 2051103 2051114 2054310 2054315) (-1179 "SYSTEM.spad" 2050331 2050340 2051093 2051098) (-1178 "SYSSOLP.spad" 2047804 2047815 2050321 2050326) (-1177 "SYSNNI.spad" 2046984 2046995 2047794 2047799) (-1176 "SYSINT.spad" 2046388 2046399 2046974 2046979) (-1175 "SYNTAX.spad" 2042582 2042591 2046378 2046383) (-1174 "SYMTAB.spad" 2040638 2040647 2042572 2042577) (-1173 "SYMS.spad" 2036623 2036632 2040628 2040633) (-1172 "SYMPOLY.spad" 2035630 2035641 2035712 2035839) (-1171 "SYMFUNC.spad" 2035105 2035116 2035620 2035625) (-1170 "SYMBOL.spad" 2032532 2032541 2035095 2035100) (-1169 "SWITCH.spad" 2029289 2029298 2032522 2032527) (-1168 "SUTS.spad" 2026188 2026216 2027756 2027853) (-1167 "SUPXS.spad" 2023323 2023351 2024320 2024469) (-1166 "SUP.spad" 2020092 2020103 2020873 2021026) (-1165 "SUPFRACF.spad" 2019197 2019215 2020082 2020087) (-1164 "SUP2.spad" 2018587 2018600 2019187 2019192) (-1163 "SUMRF.spad" 2017553 2017564 2018577 2018582) (-1162 "SUMFS.spad" 2017186 2017203 2017543 2017548) (-1161 "SULS.spad" 2007725 2007753 2008831 2009260) (-1160 "SUCHTAST.spad" 2007494 2007503 2007715 2007720) (-1159 "SUCH.spad" 2007174 2007189 2007484 2007489) (-1158 "SUBSPACE.spad" 1999181 1999196 2007164 2007169) (-1157 "SUBRESP.spad" 1998341 1998355 1999137 1999142) (-1156 "STTF.spad" 1994440 1994456 1998331 1998336) (-1155 "STTFNC.spad" 1990908 1990924 1994430 1994435) (-1154 "STTAYLOR.spad" 1983306 1983317 1990789 1990794) (-1153 "STRTBL.spad" 1981811 1981828 1981960 1981987) (-1152 "STRING.spad" 1981220 1981229 1981234 1981261) (-1151 "STRICAT.spad" 1981008 1981017 1981188 1981215) (-1150 "STREAM.spad" 1977866 1977877 1980533 1980548) (-1149 "STREAM3.spad" 1977411 1977426 1977856 1977861) (-1148 "STREAM2.spad" 1976479 1976492 1977401 1977406) (-1147 "STREAM1.spad" 1976183 1976194 1976469 1976474) (-1146 "STINPROD.spad" 1975089 1975105 1976173 1976178) (-1145 "STEP.spad" 1974290 1974299 1975079 1975084) (-1144 "STBL.spad" 1972816 1972844 1972983 1972998) (-1143 "STAGG.spad" 1971891 1971902 1972806 1972811) (-1142 "STAGG.spad" 1970964 1970977 1971881 1971886) (-1141 "STACK.spad" 1970315 1970326 1970571 1970598) (-1140 "SREGSET.spad" 1968019 1968036 1969961 1969988) (-1139 "SRDCMPK.spad" 1966564 1966584 1968009 1968014) (-1138 "SRAGG.spad" 1961661 1961670 1966532 1966559) (-1137 "SRAGG.spad" 1956778 1956789 1961651 1961656) (-1136 "SQMATRIX.spad" 1954394 1954412 1955310 1955397) (-1135 "SPLTREE.spad" 1948946 1948959 1953830 1953857) (-1134 "SPLNODE.spad" 1945534 1945547 1948936 1948941) (-1133 "SPFCAT.spad" 1944311 1944320 1945524 1945529) (-1132 "SPECOUT.spad" 1942861 1942870 1944301 1944306) (-1131 "SPADXPT.spad" 1935000 1935009 1942851 1942856) (-1130 "spad-parser.spad" 1934465 1934474 1934990 1934995) (-1129 "SPADAST.spad" 1934166 1934175 1934455 1934460) (-1128 "SPACEC.spad" 1918179 1918190 1934156 1934161) (-1127 "SPACE3.spad" 1917955 1917966 1918169 1918174) (-1126 "SORTPAK.spad" 1917500 1917513 1917911 1917916) (-1125 "SOLVETRA.spad" 1915257 1915268 1917490 1917495) (-1124 "SOLVESER.spad" 1913777 1913788 1915247 1915252) (-1123 "SOLVERAD.spad" 1909787 1909798 1913767 1913772) (-1122 "SOLVEFOR.spad" 1908207 1908225 1909777 1909782) (-1121 "SNTSCAT.spad" 1907807 1907824 1908175 1908202) (-1120 "SMTS.spad" 1906067 1906093 1907372 1907469) (-1119 "SMP.spad" 1903506 1903526 1903896 1904023) (-1118 "SMITH.spad" 1902349 1902374 1903496 1903501) (-1117 "SMATCAT.spad" 1900459 1900489 1902293 1902344) (-1116 "SMATCAT.spad" 1898501 1898533 1900337 1900342) (-1115 "SKAGG.spad" 1897462 1897473 1898469 1898496) (-1114 "SINT.spad" 1896288 1896297 1897328 1897457) (-1113 "SIMPAN.spad" 1896016 1896025 1896278 1896283) (-1112 "SIG.spad" 1895344 1895353 1896006 1896011) (-1111 "SIGNRF.spad" 1894452 1894463 1895334 1895339) (-1110 "SIGNEF.spad" 1893721 1893738 1894442 1894447) (-1109 "SIGAST.spad" 1893102 1893111 1893711 1893716) (-1108 "SHP.spad" 1891020 1891035 1893058 1893063) (-1107 "SHDP.spad" 1880731 1880758 1881240 1881371) (-1106 "SGROUP.spad" 1880339 1880348 1880721 1880726) (-1105 "SGROUP.spad" 1879945 1879956 1880329 1880334) (-1104 "SGCF.spad" 1872826 1872835 1879935 1879940) (-1103 "SFRTCAT.spad" 1871754 1871771 1872794 1872821) (-1102 "SFRGCD.spad" 1870817 1870837 1871744 1871749) (-1101 "SFQCMPK.spad" 1865454 1865474 1870807 1870812) (-1100 "SFORT.spad" 1864889 1864903 1865444 1865449) (-1099 "SEXOF.spad" 1864732 1864772 1864879 1864884) (-1098 "SEX.spad" 1864624 1864633 1864722 1864727) (-1097 "SEXCAT.spad" 1862175 1862215 1864614 1864619) (-1096 "SET.spad" 1860475 1860486 1861596 1861635) (-1095 "SETMN.spad" 1858909 1858926 1860465 1860470) (-1094 "SETCAT.spad" 1858231 1858240 1858899 1858904) (-1093 "SETCAT.spad" 1857551 1857562 1858221 1858226) (-1092 "SETAGG.spad" 1854072 1854083 1857531 1857546) (-1091 "SETAGG.spad" 1850601 1850614 1854062 1854067) (-1090 "SEQAST.spad" 1850304 1850313 1850591 1850596) (-1089 "SEGXCAT.spad" 1849426 1849439 1850294 1850299) (-1088 "SEG.spad" 1849239 1849250 1849345 1849350) (-1087 "SEGCAT.spad" 1848146 1848157 1849229 1849234) (-1086 "SEGBIND.spad" 1847218 1847229 1848101 1848106) (-1085 "SEGBIND2.spad" 1846914 1846927 1847208 1847213) (-1084 "SEGAST.spad" 1846628 1846637 1846904 1846909) (-1083 "SEG2.spad" 1846053 1846066 1846584 1846589) (-1082 "SDVAR.spad" 1845329 1845340 1846043 1846048) (-1081 "SDPOL.spad" 1842719 1842730 1843010 1843137) (-1080 "SCPKG.spad" 1840798 1840809 1842709 1842714) (-1079 "SCOPE.spad" 1839947 1839956 1840788 1840793) (-1078 "SCACHE.spad" 1838629 1838640 1839937 1839942) (-1077 "SASTCAT.spad" 1838538 1838547 1838619 1838624) (-1076 "SAOS.spad" 1838410 1838419 1838528 1838533) (-1075 "SAERFFC.spad" 1838123 1838143 1838400 1838405) (-1074 "SAE.spad" 1836298 1836314 1836909 1837044) (-1073 "SAEFACT.spad" 1835999 1836019 1836288 1836293) (-1072 "RURPK.spad" 1833640 1833656 1835989 1835994) (-1071 "RULESET.spad" 1833081 1833105 1833630 1833635) (-1070 "RULE.spad" 1831285 1831309 1833071 1833076) (-1069 "RULECOLD.spad" 1831137 1831150 1831275 1831280) (-1068 "RTVALUE.spad" 1830870 1830879 1831127 1831132) (-1067 "RSTRCAST.spad" 1830587 1830596 1830860 1830865) (-1066 "RSETGCD.spad" 1826965 1826985 1830577 1830582) (-1065 "RSETCAT.spad" 1816749 1816766 1826933 1826960) (-1064 "RSETCAT.spad" 1806553 1806572 1816739 1816744) (-1063 "RSDCMPK.spad" 1805005 1805025 1806543 1806548) (-1062 "RRCC.spad" 1803389 1803419 1804995 1805000) (-1061 "RRCC.spad" 1801771 1801803 1803379 1803384) (-1060 "RPTAST.spad" 1801473 1801482 1801761 1801766) (-1059 "RPOLCAT.spad" 1780833 1780848 1801341 1801468) (-1058 "RPOLCAT.spad" 1759907 1759924 1780417 1780422) (-1057 "ROUTINE.spad" 1755770 1755779 1758554 1758581) (-1056 "ROMAN.spad" 1755098 1755107 1755636 1755765) (-1055 "ROIRC.spad" 1754178 1754210 1755088 1755093) (-1054 "RNS.spad" 1753081 1753090 1754080 1754173) (-1053 "RNS.spad" 1752070 1752081 1753071 1753076) (-1052 "RNG.spad" 1751805 1751814 1752060 1752065) (-1051 "RMODULE.spad" 1751443 1751454 1751795 1751800) (-1050 "RMCAT2.spad" 1750851 1750908 1751433 1751438) (-1049 "RMATRIX.spad" 1749675 1749694 1750018 1750057) (-1048 "RMATCAT.spad" 1745208 1745239 1749631 1749670) (-1047 "RMATCAT.spad" 1740631 1740664 1745056 1745061) (-1046 "RINTERP.spad" 1740519 1740539 1740621 1740626) (-1045 "RING.spad" 1739989 1739998 1740499 1740514) (-1044 "RING.spad" 1739467 1739478 1739979 1739984) (-1043 "RIDIST.spad" 1738851 1738860 1739457 1739462) (-1042 "RGCHAIN.spad" 1737430 1737446 1738336 1738363) (-1041 "RGBCSPC.spad" 1737211 1737223 1737420 1737425) (-1040 "RGBCMDL.spad" 1736741 1736753 1737201 1737206) (-1039 "RF.spad" 1734355 1734366 1736731 1736736) (-1038 "RFFACTOR.spad" 1733817 1733828 1734345 1734350) (-1037 "RFFACT.spad" 1733552 1733564 1733807 1733812) (-1036 "RFDIST.spad" 1732540 1732549 1733542 1733547) (-1035 "RETSOL.spad" 1731957 1731970 1732530 1732535) (-1034 "RETRACT.spad" 1731385 1731396 1731947 1731952) (-1033 "RETRACT.spad" 1730811 1730824 1731375 1731380) (-1032 "RETAST.spad" 1730623 1730632 1730801 1730806) (-1031 "RESULT.spad" 1728683 1728692 1729270 1729297) (-1030 "RESRING.spad" 1728030 1728077 1728621 1728678) (-1029 "RESLATC.spad" 1727354 1727365 1728020 1728025) (-1028 "REPSQ.spad" 1727083 1727094 1727344 1727349) (-1027 "REP.spad" 1724635 1724644 1727073 1727078) (-1026 "REPDB.spad" 1724340 1724351 1724625 1724630) (-1025 "REP2.spad" 1713912 1713923 1724182 1724187) (-1024 "REP1.spad" 1707902 1707913 1713862 1713867) (-1023 "REGSET.spad" 1705699 1705716 1707548 1707575) (-1022 "REF.spad" 1705028 1705039 1705654 1705659) (-1021 "REDORDER.spad" 1704204 1704221 1705018 1705023) (-1020 "RECLOS.spad" 1702987 1703007 1703691 1703784) (-1019 "REALSOLV.spad" 1702119 1702128 1702977 1702982) (-1018 "REAL.spad" 1701991 1702000 1702109 1702114) (-1017 "REAL0Q.spad" 1699273 1699288 1701981 1701986) (-1016 "REAL0.spad" 1696101 1696116 1699263 1699268) (-1015 "RDUCEAST.spad" 1695822 1695831 1696091 1696096) (-1014 "RDIV.spad" 1695473 1695498 1695812 1695817) (-1013 "RDIST.spad" 1695036 1695047 1695463 1695468) (-1012 "RDETRS.spad" 1693832 1693850 1695026 1695031) (-1011 "RDETR.spad" 1691939 1691957 1693822 1693827) (-1010 "RDEEFS.spad" 1691012 1691029 1691929 1691934) (-1009 "RDEEF.spad" 1690008 1690025 1691002 1691007) (-1008 "RCFIELD.spad" 1687194 1687203 1689910 1690003) (-1007 "RCFIELD.spad" 1684466 1684477 1687184 1687189) (-1006 "RCAGG.spad" 1682378 1682389 1684456 1684461) (-1005 "RCAGG.spad" 1680217 1680230 1682297 1682302) (-1004 "RATRET.spad" 1679577 1679588 1680207 1680212) (-1003 "RATFACT.spad" 1679269 1679281 1679567 1679572) (-1002 "RANDSRC.spad" 1678588 1678597 1679259 1679264) (-1001 "RADUTIL.spad" 1678342 1678351 1678578 1678583) (-1000 "RADIX.spad" 1675243 1675257 1676809 1676902) (-999 "RADFF.spad" 1673657 1673693 1673775 1673931) (-998 "RADCAT.spad" 1673251 1673259 1673647 1673652) (-997 "RADCAT.spad" 1672843 1672853 1673241 1673246) (-996 "QUEUE.spad" 1672186 1672196 1672450 1672477) (-995 "QUAT.spad" 1670768 1670778 1671110 1671175) (-994 "QUATCT2.spad" 1670387 1670405 1670758 1670763) (-993 "QUATCAT.spad" 1668552 1668562 1670317 1670382) (-992 "QUATCAT.spad" 1666468 1666480 1668235 1668240) (-991 "QUAGG.spad" 1665294 1665304 1666436 1666463) (-990 "QQUTAST.spad" 1665063 1665071 1665284 1665289) (-989 "QFORM.spad" 1664526 1664540 1665053 1665058) (-988 "QFCAT.spad" 1663229 1663239 1664428 1664521) (-987 "QFCAT.spad" 1661523 1661535 1662724 1662729) (-986 "QFCAT2.spad" 1661214 1661230 1661513 1661518) (-985 "QEQUAT.spad" 1660771 1660779 1661204 1661209) (-984 "QCMPACK.spad" 1655518 1655537 1660761 1660766) (-983 "QALGSET.spad" 1651593 1651625 1655432 1655437) (-982 "QALGSET2.spad" 1649589 1649607 1651583 1651588) (-981 "PWFFINTB.spad" 1646899 1646920 1649579 1649584) (-980 "PUSHVAR.spad" 1646228 1646247 1646889 1646894) (-979 "PTRANFN.spad" 1642354 1642364 1646218 1646223) (-978 "PTPACK.spad" 1639442 1639452 1642344 1642349) (-977 "PTFUNC2.spad" 1639263 1639277 1639432 1639437) (-976 "PTCAT.spad" 1638512 1638522 1639231 1639258) (-975 "PSQFR.spad" 1637819 1637843 1638502 1638507) (-974 "PSEUDLIN.spad" 1636677 1636687 1637809 1637814) (-973 "PSETPK.spad" 1622110 1622126 1636555 1636560) (-972 "PSETCAT.spad" 1616030 1616053 1622090 1622105) (-971 "PSETCAT.spad" 1609924 1609949 1615986 1615991) (-970 "PSCURVE.spad" 1608907 1608915 1609914 1609919) (-969 "PSCAT.spad" 1607674 1607703 1608805 1608902) (-968 "PSCAT.spad" 1606531 1606562 1607664 1607669) (-967 "PRTITION.spad" 1605476 1605484 1606521 1606526) (-966 "PRTDAST.spad" 1605195 1605203 1605466 1605471) (-965 "PRS.spad" 1594757 1594774 1605151 1605156) (-964 "PRQAGG.spad" 1594188 1594198 1594725 1594752) (-963 "PROPLOG.spad" 1593591 1593599 1594178 1594183) (-962 "PROPFRML.spad" 1592399 1592410 1593581 1593586) (-961 "PROPERTY.spad" 1591885 1591893 1592389 1592394) (-960 "PRODUCT.spad" 1589565 1589577 1589851 1589906) (-959 "PR.spad" 1587951 1587963 1588656 1588783) (-958 "PRINT.spad" 1587703 1587711 1587941 1587946) (-957 "PRIMES.spad" 1585954 1585964 1587693 1587698) (-956 "PRIMELT.spad" 1583935 1583949 1585944 1585949) (-955 "PRIMCAT.spad" 1583558 1583566 1583925 1583930) (-954 "PRIMARR.spad" 1582563 1582573 1582741 1582768) (-953 "PRIMARR2.spad" 1581286 1581298 1582553 1582558) (-952 "PREASSOC.spad" 1580658 1580670 1581276 1581281) (-951 "PPCURVE.spad" 1579795 1579803 1580648 1580653) (-950 "PORTNUM.spad" 1579570 1579578 1579785 1579790) (-949 "POLYROOT.spad" 1578399 1578421 1579526 1579531) (-948 "POLY.spad" 1575696 1575706 1576213 1576340) (-947 "POLYLIFT.spad" 1574957 1574980 1575686 1575691) (-946 "POLYCATQ.spad" 1573059 1573081 1574947 1574952) (-945 "POLYCAT.spad" 1566465 1566486 1572927 1573054) (-944 "POLYCAT.spad" 1559173 1559196 1565637 1565642) (-943 "POLY2UP.spad" 1558621 1558635 1559163 1559168) (-942 "POLY2.spad" 1558216 1558228 1558611 1558616) (-941 "POLUTIL.spad" 1557157 1557186 1558172 1558177) (-940 "POLTOPOL.spad" 1555905 1555920 1557147 1557152) (-939 "POINT.spad" 1554744 1554754 1554831 1554858) (-938 "PNTHEORY.spad" 1551410 1551418 1554734 1554739) (-937 "PMTOOLS.spad" 1550167 1550181 1551400 1551405) (-936 "PMSYM.spad" 1549712 1549722 1550157 1550162) (-935 "PMQFCAT.spad" 1549299 1549313 1549702 1549707) (-934 "PMPRED.spad" 1548768 1548782 1549289 1549294) (-933 "PMPREDFS.spad" 1548212 1548234 1548758 1548763) (-932 "PMPLCAT.spad" 1547282 1547300 1548144 1548149) (-931 "PMLSAGG.spad" 1546863 1546877 1547272 1547277) (-930 "PMKERNEL.spad" 1546430 1546442 1546853 1546858) (-929 "PMINS.spad" 1546006 1546016 1546420 1546425) (-928 "PMFS.spad" 1545579 1545597 1545996 1546001) (-927 "PMDOWN.spad" 1544865 1544879 1545569 1545574) (-926 "PMASS.spad" 1543873 1543881 1544855 1544860) (-925 "PMASSFS.spad" 1542838 1542854 1543863 1543868) (-924 "PLOTTOOL.spad" 1542618 1542626 1542828 1542833) (-923 "PLOT.spad" 1537449 1537457 1542608 1542613) (-922 "PLOT3D.spad" 1533869 1533877 1537439 1537444) (-921 "PLOT1.spad" 1533010 1533020 1533859 1533864) (-920 "PLEQN.spad" 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1490595 1490610) (-900 "PERMGRP.spad" 1481182 1481192 1486436 1486441) (-899 "PERMCAT.spad" 1479734 1479744 1481162 1481177) (-898 "PERMAN.spad" 1478266 1478280 1479724 1479729) (-897 "PENDTREE.spad" 1477605 1477615 1477895 1477900) (-896 "PDRING.spad" 1476096 1476106 1477585 1477600) (-895 "PDRING.spad" 1474595 1474607 1476086 1476091) (-894 "PDEPROB.spad" 1473610 1473618 1474585 1474590) (-893 "PDEPACK.spad" 1467612 1467620 1473600 1473605) (-892 "PDECOMP.spad" 1467074 1467091 1467602 1467607) (-891 "PDECAT.spad" 1465428 1465436 1467064 1467069) (-890 "PCOMP.spad" 1465279 1465292 1465418 1465423) (-889 "PBWLB.spad" 1463861 1463878 1465269 1465274) (-888 "PATTERN.spad" 1458292 1458302 1463851 1463856) (-887 "PATTERN2.spad" 1458028 1458040 1458282 1458287) (-886 "PATTERN1.spad" 1456330 1456346 1458018 1458023) (-885 "PATRES.spad" 1453877 1453889 1456320 1456325) (-884 "PATRES2.spad" 1453539 1453553 1453867 1453872) (-883 "PATMATCH.spad" 1451696 1451727 1453247 1453252) (-882 "PATMAB.spad" 1451121 1451131 1451686 1451691) (-881 "PATLRES.spad" 1450205 1450219 1451111 1451116) (-880 "PATAB.spad" 1449969 1449979 1450195 1450200) (-879 "PARTPERM.spad" 1447331 1447339 1449959 1449964) (-878 "PARSURF.spad" 1446759 1446787 1447321 1447326) (-877 "PARSU2.spad" 1446554 1446570 1446749 1446754) (-876 "script-parser.spad" 1446074 1446082 1446544 1446549) (-875 "PARSCURV.spad" 1445502 1445530 1446064 1446069) (-874 "PARSC2.spad" 1445291 1445307 1445492 1445497) (-873 "PARPCURV.spad" 1444749 1444777 1445281 1445286) (-872 "PARPC2.spad" 1444538 1444554 1444739 1444744) (-871 "PAN2EXPR.spad" 1443950 1443958 1444528 1444533) (-870 "PALETTE.spad" 1442920 1442928 1443940 1443945) (-869 "PAIR.spad" 1441903 1441916 1442508 1442513) (-868 "PADICRC.spad" 1439233 1439251 1440408 1440501) (-867 "PADICRAT.spad" 1437248 1437260 1437469 1437562) (-866 "PADIC.spad" 1436943 1436955 1437174 1437243) (-865 "PADICCT.spad" 1435484 1435496 1436869 1436938) (-864 "PADEPAC.spad" 1434163 1434182 1435474 1435479) (-863 "PADE.spad" 1432903 1432919 1434153 1434158) (-862 "OWP.spad" 1432143 1432173 1432761 1432828) (-861 "OVERSET.spad" 1431716 1431724 1432133 1432138) (-860 "OVAR.spad" 1431497 1431520 1431706 1431711) (-859 "OUT.spad" 1430581 1430589 1431487 1431492) (-858 "OUTFORM.spad" 1419877 1419885 1430571 1430576) (-857 "OUTBFILE.spad" 1419295 1419303 1419867 1419872) (-856 "OUTBCON.spad" 1418293 1418301 1419285 1419290) (-855 "OUTBCON.spad" 1417289 1417299 1418283 1418288) (-854 "OSI.spad" 1416764 1416772 1417279 1417284) (-853 "OSGROUP.spad" 1416682 1416690 1416754 1416759) (-852 "ORTHPOL.spad" 1415143 1415153 1416599 1416604) (-851 "OREUP.spad" 1414596 1414624 1414823 1414862) (-850 "ORESUP.spad" 1413895 1413919 1414276 1414315) (-849 "OREPCTO.spad" 1411714 1411726 1413815 1413820) (-848 "OREPCAT.spad" 1405771 1405781 1411670 1411709) (-847 "OREPCAT.spad" 1399718 1399730 1405619 1405624) (-846 "ORDSET.spad" 1398884 1398892 1399708 1399713) (-845 "ORDSET.spad" 1398048 1398058 1398874 1398879) (-844 "ORDRING.spad" 1397438 1397446 1398028 1398043) (-843 "ORDRING.spad" 1396836 1396846 1397428 1397433) (-842 "ORDMON.spad" 1396691 1396699 1396826 1396831) (-841 "ORDFUNS.spad" 1395817 1395833 1396681 1396686) (-840 "ORDFIN.spad" 1395637 1395645 1395807 1395812) (-839 "ORDCOMP.spad" 1394102 1394112 1395184 1395213) (-838 "ORDCOMP2.spad" 1393387 1393399 1394092 1394097) (-837 "OPTPROB.spad" 1392025 1392033 1393377 1393382) (-836 "OPTPACK.spad" 1384410 1384418 1392015 1392020) (-835 "OPTCAT.spad" 1382085 1382093 1384400 1384405) (-834 "OPSIG.spad" 1381737 1381745 1382075 1382080) (-833 "OPQUERY.spad" 1381286 1381294 1381727 1381732) (-832 "OP.spad" 1381028 1381038 1381108 1381175) (-831 "OPERCAT.spad" 1380616 1380626 1381018 1381023) (-830 "OPERCAT.spad" 1380202 1380214 1380606 1380611) (-829 "ONECOMP.spad" 1378947 1378957 1379749 1379778) (-828 "ONECOMP2.spad" 1378365 1378377 1378937 1378942) (-827 "OMSERVER.spad" 1377367 1377375 1378355 1378360) (-826 "OMSAGG.spad" 1377155 1377165 1377323 1377362) (-825 "OMPKG.spad" 1375767 1375775 1377145 1377150) (-824 "OM.spad" 1374732 1374740 1375757 1375762) (-823 "OMLO.spad" 1374157 1374169 1374618 1374657) (-822 "OMEXPR.spad" 1373991 1374001 1374147 1374152) (-821 "OMERR.spad" 1373534 1373542 1373981 1373986) (-820 "OMERRK.spad" 1372568 1372576 1373524 1373529) (-819 "OMENC.spad" 1371912 1371920 1372558 1372563) (-818 "OMDEV.spad" 1366201 1366209 1371902 1371907) (-817 "OMCONN.spad" 1365610 1365618 1366191 1366196) (-816 "OINTDOM.spad" 1365373 1365381 1365536 1365605) (-815 "OFMONOID.spad" 1361560 1361570 1365363 1365368) (-814 "ODVAR.spad" 1360821 1360831 1361550 1361555) (-813 "ODR.spad" 1360465 1360491 1360633 1360782) (-812 "ODPOL.spad" 1357811 1357821 1358151 1358278) (-811 "ODP.spad" 1347658 1347678 1348031 1348162) (-810 "ODETOOLS.spad" 1346241 1346260 1347648 1347653) (-809 "ODESYS.spad" 1343891 1343908 1346231 1346236) (-808 "ODERTRIC.spad" 1339832 1339849 1343848 1343853) (-807 "ODERED.spad" 1339219 1339243 1339822 1339827) (-806 "ODERAT.spad" 1336770 1336787 1339209 1339214) (-805 "ODEPRRIC.spad" 1333661 1333683 1336760 1336765) (-804 "ODEPROB.spad" 1332918 1332926 1333651 1333656) (-803 "ODEPRIM.spad" 1330192 1330214 1332908 1332913) (-802 "ODEPAL.spad" 1329568 1329592 1330182 1330187) (-801 "ODEPACK.spad" 1316170 1316178 1329558 1329563) (-800 "ODEINT.spad" 1315601 1315617 1316160 1316165) (-799 "ODEIFTBL.spad" 1312996 1313004 1315591 1315596) (-798 "ODEEF.spad" 1308363 1308379 1312986 1312991) (-797 "ODECONST.spad" 1307882 1307900 1308353 1308358) (-796 "ODECAT.spad" 1306478 1306486 1307872 1307877) (-795 "OCT.spad" 1304616 1304626 1305332 1305371) (-794 "OCTCT2.spad" 1304260 1304281 1304606 1304611) (-793 "OC.spad" 1302034 1302044 1304216 1304255) (-792 "OC.spad" 1299533 1299545 1301717 1301722) (-791 "OCAMON.spad" 1299381 1299389 1299523 1299528) (-790 "OASGP.spad" 1299196 1299204 1299371 1299376) (-789 "OAMONS.spad" 1298716 1298724 1299186 1299191) (-788 "OAMON.spad" 1298577 1298585 1298706 1298711) (-787 "OAGROUP.spad" 1298439 1298447 1298567 1298572) (-786 "NUMTUBE.spad" 1298026 1298042 1298429 1298434) (-785 "NUMQUAD.spad" 1285888 1285896 1298016 1298021) (-784 "NUMODE.spad" 1277024 1277032 1285878 1285883) (-783 "NUMINT.spad" 1274582 1274590 1277014 1277019) (-782 "NUMFMT.spad" 1273422 1273430 1274572 1274577) (-781 "NUMERIC.spad" 1265494 1265504 1273227 1273232) (-780 "NTSCAT.spad" 1263996 1264012 1265462 1265489) (-779 "NTPOLFN.spad" 1263541 1263551 1263913 1263918) (-778 "NSUP.spad" 1256551 1256561 1261091 1261244) (-777 "NSUP2.spad" 1255943 1255955 1256541 1256546) (-776 "NSMP.spad" 1252138 1252157 1252446 1252573) (-775 "NREP.spad" 1250510 1250524 1252128 1252133) (-774 "NPCOEF.spad" 1249756 1249776 1250500 1250505) (-773 "NORMRETR.spad" 1249354 1249393 1249746 1249751) (-772 "NORMPK.spad" 1247256 1247275 1249344 1249349) (-771 "NORMMA.spad" 1246944 1246970 1247246 1247251) (-770 "NONE.spad" 1246685 1246693 1246934 1246939) (-769 "NONE1.spad" 1246361 1246371 1246675 1246680) (-768 "NODE1.spad" 1245830 1245846 1246351 1246356) (-767 "NNI.spad" 1244717 1244725 1245804 1245825) (-766 "NLINSOL.spad" 1243339 1243349 1244707 1244712) (-765 "NIPROB.spad" 1241880 1241888 1243329 1243334) (-764 "NFINTBAS.spad" 1239340 1239357 1241870 1241875) (-763 "NETCLT.spad" 1239314 1239325 1239330 1239335) (-762 "NCODIV.spad" 1237512 1237528 1239304 1239309) (-761 "NCNTFRAC.spad" 1237154 1237168 1237502 1237507) (-760 "NCEP.spad" 1235314 1235328 1237144 1237149) (-759 "NASRING.spad" 1234910 1234918 1235304 1235309) (-758 "NASRING.spad" 1234504 1234514 1234900 1234905) (-757 "NARNG.spad" 1233848 1233856 1234494 1234499) (-756 "NARNG.spad" 1233190 1233200 1233838 1233843) (-755 "NAGSP.spad" 1232263 1232271 1233180 1233185) (-754 "NAGS.spad" 1221788 1221796 1232253 1232258) (-753 "NAGF07.spad" 1220181 1220189 1221778 1221783) (-752 "NAGF04.spad" 1214413 1214421 1220171 1220176) (-751 "NAGF02.spad" 1208222 1208230 1214403 1214408) (-750 "NAGF01.spad" 1203825 1203833 1208212 1208217) (-749 "NAGE04.spad" 1197285 1197293 1203815 1203820) (-748 "NAGE02.spad" 1187627 1187635 1197275 1197280) (-747 "NAGE01.spad" 1183511 1183519 1187617 1187622) (-746 "NAGD03.spad" 1181431 1181439 1183501 1183506) (-745 "NAGD02.spad" 1173962 1173970 1181421 1181426) (-744 "NAGD01.spad" 1168075 1168083 1173952 1173957) (-743 "NAGC06.spad" 1163862 1163870 1168065 1168070) (-742 "NAGC05.spad" 1162331 1162339 1163852 1163857) (-741 "NAGC02.spad" 1161586 1161594 1162321 1162326) (-740 "NAALG.spad" 1161121 1161131 1161554 1161581) (-739 "NAALG.spad" 1160676 1160688 1161111 1161116) (-738 "MULTSQFR.spad" 1157634 1157651 1160666 1160671) (-737 "MULTFACT.spad" 1157017 1157034 1157624 1157629) (-736 "MTSCAT.spad" 1155051 1155072 1156915 1157012) (-735 "MTHING.spad" 1154708 1154718 1155041 1155046) (-734 "MSYSCMD.spad" 1154142 1154150 1154698 1154703) (-733 "MSET.spad" 1152084 1152094 1153848 1153887) (-732 "MSETAGG.spad" 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1113770) (-694 "MFINFACT.spad" 1111691 1111713 1112281 1112286) (-693 "MESH.spad" 1109423 1109431 1111681 1111686) (-692 "MDDFACT.spad" 1107616 1107626 1109413 1109418) (-691 "MDAGG.spad" 1106903 1106913 1107596 1107611) (-690 "MCMPLX.spad" 1102877 1102885 1103491 1103692) (-689 "MCDEN.spad" 1102085 1102097 1102867 1102872) (-688 "MCALCFN.spad" 1099187 1099213 1102075 1102080) (-687 "MAYBE.spad" 1098471 1098482 1099177 1099182) (-686 "MATSTOR.spad" 1095747 1095757 1098461 1098466) (-685 "MATRIX.spad" 1094451 1094461 1094935 1094962) (-684 "MATLIN.spad" 1091777 1091801 1094335 1094340) (-683 "MATCAT.spad" 1083362 1083384 1091745 1091772) (-682 "MATCAT.spad" 1074819 1074843 1083204 1083209) (-681 "MATCAT2.spad" 1074087 1074135 1074809 1074814) (-680 "MAPPKG3.spad" 1072986 1073000 1074077 1074082) (-679 "MAPPKG2.spad" 1072320 1072332 1072976 1072981) (-678 "MAPPKG1.spad" 1071138 1071148 1072310 1072315) (-677 "MAPPAST.spad" 1070451 1070459 1071128 1071133) (-676 "MAPHACK3.spad" 1070259 1070273 1070441 1070446) (-675 "MAPHACK2.spad" 1070024 1070036 1070249 1070254) (-674 "MAPHACK1.spad" 1069654 1069664 1070014 1070019) (-673 "MAGMA.spad" 1067444 1067461 1069644 1069649) (-672 "MACROAST.spad" 1067023 1067031 1067434 1067439) (-671 "M3D.spad" 1064719 1064729 1066401 1066406) (-670 "LZSTAGG.spad" 1061947 1061957 1064709 1064714) (-669 "LZSTAGG.spad" 1059173 1059185 1061937 1061942) (-668 "LWORD.spad" 1055878 1055895 1059163 1059168) (-667 "LSTAST.spad" 1055662 1055670 1055868 1055873) (-666 "LSQM.spad" 1053888 1053902 1054286 1054337) (-665 "LSPP.spad" 1053421 1053438 1053878 1053883) (-664 "LSMP.spad" 1052261 1052289 1053411 1053416) (-663 "LSMP1.spad" 1050065 1050079 1052251 1052256) (-662 "LSAGG.spad" 1049734 1049744 1050033 1050060) (-661 "LSAGG.spad" 1049423 1049435 1049724 1049729) (-660 "LPOLY.spad" 1048377 1048396 1049279 1049348) (-659 "LPEFRAC.spad" 1047634 1047644 1048367 1048372) (-658 "LO.spad" 1047035 1047049 1047568 1047595) (-657 "LOGIC.spad" 1046637 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169251 169256) (-149 "CINTSLPE.spad" 165069 165082 165734 165739) (-148 "CHVAR.spad" 163147 163169 165059 165064) (-147 "CHARZ.spad" 163062 163070 163127 163142) (-146 "CHARPOL.spad" 162570 162580 163052 163057) (-145 "CHARNZ.spad" 162323 162331 162550 162565) (-144 "CHAR.spad" 160191 160199 162313 162318) (-143 "CFCAT.spad" 159507 159515 160181 160186) (-142 "CDEN.spad" 158665 158679 159497 159502) (-141 "CCLASS.spad" 156814 156822 158076 158115) (-140 "CATEGORY.spad" 155904 155912 156804 156809) (-139 "CATCTOR.spad" 155795 155803 155894 155899) (-138 "CATAST.spad" 155413 155421 155785 155790) (-137 "CASEAST.spad" 155127 155135 155403 155408) (-136 "CARTEN.spad" 150230 150254 155117 155122) (-135 "CARTEN2.spad" 149616 149643 150220 150225) (-134 "CARD.spad" 146905 146913 149590 149611) (-133 "CAPSLAST.spad" 146679 146687 146895 146900) (-132 "CACHSET.spad" 146301 146309 146669 146674) (-131 "CABMON.spad" 145854 145862 146291 146296) (-130 "BYTEORD.spad" 145529 145537 145844 145849) 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68180 68193 68706 68711) (-64 "ASP1.spad" 67561 67574 68170 68175) (-63 "ASP19.spad" 62247 62260 67551 67556) (-62 "ASP12.spad" 61661 61674 62237 62242) (-61 "ASP10.spad" 60932 60945 61651 61656) (-60 "ARRAY2.spad" 60292 60301 60539 60566) (-59 "ARRAY1.spad" 59127 59136 59475 59502) (-58 "ARRAY12.spad" 57796 57807 59117 59122) (-57 "ARR2CAT.spad" 53458 53479 57764 57791) (-56 "ARR2CAT.spad" 49140 49163 53448 53453) (-55 "ARITY.spad" 48512 48519 49130 49135) (-54 "APPRULE.spad" 47756 47778 48502 48507) (-53 "APPLYORE.spad" 47371 47384 47746 47751) (-52 "ANY.spad" 45713 45720 47361 47366) (-51 "ANY1.spad" 44784 44793 45703 45708) (-50 "ANTISYM.spad" 43223 43239 44764 44779) (-49 "ANON.spad" 42916 42923 43213 43218) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 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"A1AGG.spad" 30 41 860 865))
\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 94d2b1ed..be17bbae 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(162119 . 3451578541) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) #0#) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) -((((-564)) . T) (($) -2750 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) +(162119 . 3451919713) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +((((-564)) . 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T)) (|has| |#1| (-556)) (|has| |#1| (-556)) @@ -256,21 +256,21 @@ (((|#2|) . T) (($) . T) (((-407 (-564))) . T)) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) -((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) (($) . 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T)) ((((-407 $) (-407 $)) |has| |#2| (-556)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-905)) ((((-1152) (-52)) . T)) ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((((-536)) . T) (((-225)) . T) (((-379)) . T) (((-888 (-379))) . T)) ((((-858)) . T)) -(-2750 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2733 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) (((|#1|) |has| |#1| (-172))) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-858)) . T)) @@ -297,15 +297,15 @@ (((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) (|has| |#1| (-1094)) (((|#1|) . 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T)) (((|#1| (-967)) . T)) (((#0=(-866 |#1|) $) |has| #0# (-286 #0# #0#))) @@ -314,7 +314,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1145)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -326,27 +326,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) -((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-814 (-1170))) . T) (($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . T)) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-814 (-1170))) . T) (($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . 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T)) -((($) -2750 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-858)) . T)) ((((-858)) . T)) (|has| (-1244 |#2| |#3| |#4|) (-147)) @@ -357,16 +357,16 @@ ((((-858)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2750 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2733 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) (((|#1|) . T)) ((((-564) |#1|) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) (((|#1|) . 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T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) @@ -475,10 +475,10 @@ ((((-564) |#4|) . T)) ((((-564) |#3|) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-407 (-564))) . T) (((-564)) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -489,7 +489,7 @@ ((((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . 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T)) ((((-858)) . T)) ((((-858)) . T)) @@ -732,22 +732,22 @@ (|has| |#1| (-1094)) (((|#2|) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564))))) -(((|#4|) -2750 (|has| |#4| (-172)) (|has| |#4| (-363)))) -(((|#3|) -2750 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(((|#4|) -2733 (|has| |#4| (-172)) (|has| |#4| (-363)))) +(((|#3|) -2733 (|has| |#3| (-172)) (|has| |#3| (-363)))) ((((-858)) . T)) (((|#1|) . T)) -(-2750 (|has| |#2| (-452)) (|has| |#2| (-905))) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-905))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2733 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((($ $) . T) ((#0=(-1170) $) |has| |#1| (-233)) ((#0# |#1|) |has| |#1| (-233)) ((#1=(-814 (-1170)) |#1|) . T) ((#1# $) . T)) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-905))) ((((-564) |#2|) . T)) ((((-858)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((($) -2750 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((|#3|) -2750 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045)))) +((($) -2733 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((|#3|) -2733 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045)))) ((((-564) |#1|) . T)) (|has| (-407 |#2|) (-147)) (|has| (-407 |#2|) (-145)) @@ -760,15 +760,15 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-858)) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-388) (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-388) (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#2| (-1145)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) @@ -786,7 +786,7 @@ ((((-388) (-1152)) . T)) (|has| |#1| (-556)) ((((-564) |#1|) . T)) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) . T)) @@ -802,7 +802,7 @@ ((((-641 |#1|)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#2|) |has| |#2| (-309 |#2|))) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -812,7 +812,7 @@ (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (|has| |#2| (-368)) -(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -826,8 +826,8 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((($) . T) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((($) . T) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($ $) . T)) ((((-858)) . T)) ((($ $) . T)) @@ -837,12 +837,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-407 (-564))) . T) (((-564)) . T)) ((((-564) (-144)) . T)) ((((-144)) . T)) (((|#1|) . T)) -(-2750 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2733 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-112)) . T)) @@ -851,26 +851,26 @@ ((((-858)) . T)) ((((-1175)) . T)) (|has| |#1| (-816)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#1| (-846)) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-556)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (|has| |#1| (-905)) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-858)) . T)) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-556))) ((((-858)) . T)) ((((-858)) . T)) ((((-858)) . T)) (((|#1| (-1259 |#1|) (-1259 |#1|)) . T)) ((((-564) (-144)) . T)) ((($) . T)) -(-2750 (|has| |#4| (-172)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2750 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2733 (|has| |#4| (-172)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2733 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-1175)) . T) (((-858)) . T)) ((((-1175)) . T)) ((((-858)) . T)) @@ -878,14 +878,14 @@ (((|#1| (-967)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) -(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2733 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2733 (|has| |#2| (-789)) (|has| |#2| (-844))) (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2750 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) (((|#1|) . T)) (|has| |#2| (-789)) -(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2733 (|has| |#2| (-789)) (|has| |#2| (-844))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#2| (-844)) @@ -901,8 +901,8 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-407 (-564))) . T) (($) . T)) -((($) |has| |#1| (-556)) ((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-564)) . T)) -((($) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +((($) |has| |#1| (-556)) ((|#1|) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-564)) . T)) +((($) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-824)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) (|has| |#1| (-1094)) @@ -912,29 +912,29 @@ (((|#4|) |has| |#4| (-1094))) (((|#3|) |has| |#3| (-1094))) (|has| |#3| (-368)) -((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +((((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) ((((-858)) . T)) ((((-858)) . T)) (((|#2|) . T)) (((|#1| |#2|) . 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T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-172)) (|has| |#1| (-556))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-144)) . T)) (((|#1|) . T)) -((($) -2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((|#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045)))) +((($) -2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((|#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045)))) ((((-144)) . T)) ((((-144)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#) ((|#2|) . T) (((-564)) . T)) (((|#1| |#2| |#3|) . T)) -(-2750 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2733 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) (|has| $ (-147)) (|has| $ (-147)) ((((-1175)) . T)) @@ -942,14 +942,14 @@ ((((-858)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) ((((-1170)) . T)) (|has| |#1| (-556)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) @@ -960,7 +960,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-844)) -(((|#2| (-240 (-2062 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-240 (-2069 |#1|) (-767)) (-860 |#1|)) . T)) (|has| |#3| (-844)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -975,20 +975,20 @@ (|has| |#1| (-145)) ((((-407 (-564))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2750 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2733 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1136 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1045))) -(((|#2|) . T) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) -(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) -(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) +(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +(-2733 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2733 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-695)) . T)) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-556)) (((|#1|) . T)) (((|#1|) . T)) @@ -1012,11 +1012,11 @@ (((|#1| (-407 (-564))) . T)) (((|#3|) . T) (((-610 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#1|) . 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T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) |has| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (-309 (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))))) ((((-858)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1036,10 +1036,10 @@ ((($ $) . T) ((#0=(-860 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-309 |#1|))) @@ -1127,11 +1127,11 @@ (|has| |#1| (-368)) ((((-1170) $) |has| |#1| (-514 (-1170) $)) (($ $) |has| |#1| (-309 $)) ((|#1| |#1|) |has| |#1| (-309 |#1|)) (((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) ((((-1170)) |has| |#1| (-896 (-1170)))) -(-2750 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) +(-2733 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-388) |#1|) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-1094)) (((|#2|) . T) (((-858)) . T)) ((((-858)) . T)) @@ -1139,8 +1139,8 @@ ((((-906 |#1|)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1149,16 +1149,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (((|#1| |#1|) . T)) (((#0=(-866 |#1|)) |has| #0# (-309 #0#))) -((((-564)) . T) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) +((((-564)) . T) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) (((|#1| |#2|) . T)) -(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) -(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2733 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2733 (|has| |#2| (-789)) (|has| |#2| (-844))) (((|#1|) . T)) (-12 (|has| |#1| (-789)) (|has| |#2| (-789))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789))) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (|has| |#1| (-1194)) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -1169,8 +1169,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (|has| |#1| (-363)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) . T) ((#0=(-407 (-564)) #0#) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -1185,14 +1185,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) -((($) . T) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) +((($) . T) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-556))) ((($) . T)) -(((#0=(-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) #0#) |has| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))))) +(((#0=(-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) #0#) |has| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))))) (|has| |#2| (-846)) ((($) . T)) (((|#2|) |has| |#2| (-1094))) -((((-858)) -2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +((((-858)) -2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) (|has| |#1| (-846)) (|has| |#1| (-846)) ((((-1152) (-52)) . T)) @@ -1201,10 +1201,10 @@ ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((($) . T) (((-564)) . T)) ((((-564) (-144)) . T)) -((((-564) (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T) ((|#1| |#2|) . T)) ((((-407 (-564))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-858)) . T)) ((((-906 |#1|)) . T)) (|has| |#1| (-363)) @@ -1231,21 +1231,21 @@ ((((-858)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-564) (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-172))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) -((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-564)) . 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T)) @@ -1253,39 +1253,39 @@ (|has| |#1| (-556)) ((((-1152) |#1|) . T)) (|has| |#1| (-1145)) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-954 |#1|)) . T)) -(((#0=(-407 (-564)) #0#) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) +(((#0=(-407 (-564)) #0#) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-564))) (((-564)) |has| |#1| (-1034 (-564))) (((-1170)) |has| |#1| (-1034 (-1170))) ((|#1|) . T)) ((((-564) |#2|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . 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T)) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) #0#) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-858)) -2750 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) +((((-858)) -2733 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) ((((-564) |#2|) . T)) -(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(((|#2| |#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) +(-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(((|#2| |#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) (((|#2|) . T) (((-564)) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T) ((|#2|) . T)) ((((-858)) . T)) ((((-858)) . T)) ((((-1152) (-1170) (-564) (-225) (-858)) . T)) @@ -1320,8 +1320,8 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -(((|#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +(((|#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-407 |#2|)) . T)) ((((-889 |#1|)) . T) ((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) @@ -1333,11 +1333,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1374,7 +1374,7 @@ ((((-995 |#1|)) . T) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-407 (-564))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1166 |#1|)) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1382,9 +1382,9 @@ (|has| |#1| (-846)) (((|#2|) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) ((((-564) |#2|) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#2|) . T)) ((((-564) |#3|) . T)) (((|#2|) . T)) @@ -1397,7 +1397,7 @@ (|has| |#1| (-1094)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) #0#) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#2|) . T)) @@ -1432,19 +1432,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) #0#) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) -((($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +(((#0=(-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) #0#) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-846)) (((|#2| (-767) (-1076)) . T)) (((|#1| |#2|) . T)) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-787)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2750 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-2750 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-2733 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-2733 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1152) |#1|) . T)) @@ -1458,10 +1458,10 @@ (((|#3|) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) -(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#1|) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094))) (((-954 |#1|)) . T)) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094))) (((-954 |#1|)) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1475,8 +1475,8 @@ ((($) . T)) ((((-388) (-1152)) . T)) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-858)) -2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3058 (-1152)) (|:| -3726 #0#))) . T)) +((((-858)) -2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3026 (-1152)) (|:| -3683 #0#))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) @@ -1484,7 +1484,7 @@ (|has| |#2| (-145)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-2750 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2733 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) (|has| |#1| (-363)) ((((-858)) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -1495,8 +1495,8 @@ (|has| |#1| (-844)) ((((-858)) . T)) (((|#2|) . T)) -((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1505,7 +1505,7 @@ ((((-858)) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2062 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-482 (-2069 |#1|) (-767)) (-860 |#1|)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1170)) (-1170)) . T)) (((|#1|) . T)) @@ -1525,16 +1525,16 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) -((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-1170) (-52)) . T)) ((($ $) . T)) (((|#1| (-564)) . T)) ((((-906 |#1|)) . T)) -(((|#1|) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -2750 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) +(((|#1|) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -2733 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) (|has| |#1| (-846)) (|has| |#1| (-846)) @@ -1553,11 +1553,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) (|has| |#2| (-846)) (|has| |#1| (-846)) -(((|#3|) -2750 (|has| |#3| (-172)) (|has| |#3| (-363)))) -(-2750 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) +(((|#3|) -2733 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(-2733 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-564) |#2|) . T)) -(((|#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-363)))) (|has| |#1| (-349)) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) (((|#2|) . T) (((-564)) . T)) @@ -1566,7 +1566,7 @@ (|has| |#1| (-816)) (|has| |#1| (-816)) (((|#1|) . T)) -(-2750 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-844)) (|has| |#1| (-844)) (|has| |#1| (-844)) @@ -1575,13 +1575,13 @@ ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-1170)) |has| |#1| (-896 (-1170))) (((-1076)) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((#0=(-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) #0#) |has| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))))) +(((#0=(-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) #0#) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-1094)) ((((-858)) . T) (((-1175)) . T)) @@ -1600,11 +1600,11 @@ (((|#1| (-767) (-1076)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2750 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2733 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) (((|#2|) |has| |#2| (-172))) -(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -1627,32 +1627,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) ((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) |has| |#1| (-556))) -((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) +((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) ((((-668 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1661,7 +1661,7 @@ ((((-858)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) ((((-1175)) . T)) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T) (((-564)) . T)) (((|#3|) . T) (((-564)) . T) (((-610 $)) . T)) @@ -1669,12 +1669,12 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#2|) . T)) -(-2750 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) (|has| |#1| (-1194)) (|has| |#1| (-1194)) -(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (|has| |#1| (-1194)) (|has| |#1| (-1194)) (((|#3| |#3|) . T)) @@ -1687,16 +1687,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((((-1152) (-52)) . T)) (|has| |#1| (-1094)) -(-2750 (|has| |#2| (-816)) (|has| |#2| (-846))) +(-2733 (|has| |#2| (-816)) (|has| |#2| (-846))) (((|#1|) . T)) (((|#1|) |has| |#1| (-172)) (($) . T)) -((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($) . T)) ((((-1168 |#1| |#2| |#3|)) -12 (|has| (-1168 |#1| |#2| |#3|) (-309 (-1168 |#1| |#2| |#3|))) (|has| |#1| (-363)))) ((((-858)) . T)) ((((-564)) . T) (($) . T)) ((((-767)) . T)) -(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) ((($) . T) (((-564)) . T)) @@ -1704,30 +1704,30 @@ (|has| |#2| (-905)) (|has| |#1| (-363)) (((|#2|) |has| |#2| (-1094))) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-536)) . T) (((-407 (-1166 (-564)))) . T) (((-225)) . T) (((-379)) . T)) ((((-379)) . T) (((-225)) . T) (((-858)) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) (|has| |#1| (-905)) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-905))) ((($) . T) ((|#2|) . T)) -(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((((-858)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((($ $) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((($ $) . T)) ((((-564) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-564)) . T)) ((((-112)) . T)) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-38 (-407 (-564)))) (((|#1| (-564)) . T)) ((($) . T)) @@ -1749,7 +1749,7 @@ (((|#1| (-1223 |#1| |#2| |#3|)) . T)) (((|#1| (-767)) . T)) (((|#1|) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) ((((-1152) |#1|) . T)) @@ -1769,18 +1769,18 @@ (((|#1|) . T)) ((((-564)) . T)) ((((-858)) . T)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) (((|#3|) . T)) -(-2750 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2733 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) -2750 (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) -2733 (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-767)) . T)) -((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-309 |#1|))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-564)) |has| |#1| (-882 (-564))) (((-379)) |has| |#1| (-882 (-379)))) @@ -1788,7 +1788,7 @@ (|has| |#1| (-556)) (((|#1|) . T)) ((((-858)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1796,7 +1796,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1094))) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(((|#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -2733 (|has| |#2| (-172)) (|has| |#2| (-363)))) ((((-1244 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-816)) @@ -1806,8 +1806,8 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| (-564) (-1076)) . T)) -(-2750 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +(-2733 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-767) (-1076)) . T)) (|has| |#1| (-846)) @@ -1820,33 +1820,33 @@ (|has| |#1| (-1094)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-1094)) -((((-564)) -2750 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) +((((-564)) -2733 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((|#2|) |has| |#1| (-363))) -(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) -((((-685 (-339 (-2363) (-2363 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) +(-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +((((-685 (-339 (-2336) (-2336 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) ((((-858)) . T)) (|has| |#3| (-844)) ((((-858)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -(((|#1| |#1|) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1| |#1|) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#1|) . T)) ((((-564)) . T)) ((((-564)) . T)) -(((|#1|) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1|) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#2|) |has| |#2| (-363))) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) (|has| |#1| (-846)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) |has| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))))) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-905))) +((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) |has| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) ((((-858)) . T)) ((((-858)) . T)) @@ -1877,25 +1877,25 @@ (|has| |#1| (-145)) ((((-564)) . T) ((|#1|) . T) (($) . T) (((-407 (-564))) . T) (((-1170)) |has| |#1| (-1034 (-1170)))) (((|#1| |#2|) . T)) -((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2750 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2733 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) ((((-144)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (((|#1|) . T)) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-564)) . T)) ((((-858)) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| (-407 |#2|) (-233)) ((((-641 |#1|)) . T)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-1045))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1922,7 +1922,7 @@ (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-767) (-1076)) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-564)) -2750 (|has| (-407 (-564)) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) . T)) +(((|#1|) . T) (((-564)) -2733 (|has| (-407 (-564)) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) . T)) (((|#1| (-600 |#1| |#3|) (-600 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1943,25 +1943,25 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-844)) ((((-564)) . T) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-1034 (-407 (-564))))) -((((-112)) |has| |#1| (-1094)) (((-858)) -2750 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) +((((-112)) |has| |#1| (-1094)) (((-858)) -2733 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) . T)) ((((-858)) . T)) ((((-564) |#1|) . T)) ((((-858)) . T)) ((((-695)) . T) (((-407 (-564))) . T) (((-564)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|))))) ((((-379)) . T)) ((((-695)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1|) |has| |#1| (-172))) ((((-407 (-948 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-846)) @@ -1972,14 +1972,14 @@ (((|#3|) |has| |#3| (-1045))) ((((-1170)) |has| |#2| (-896 (-1170)))) ((((-858)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-363)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) (|has| |#1| (-38 (-407 (-564)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2000,11 +2000,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-846)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) |has| (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)) (-309 (-2 (|:| -3026 |#1|) (|:| -3683 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2022,11 +2022,11 @@ ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#1| (-1018))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-858)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((($ $) . T) (((-610 $) $) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) ((($) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T)) -((($) -2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) +((($) -2733 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-363)) @@ -2037,11 +2037,11 @@ ((((-379)) . T)) (((|#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) ((((-858)) . T)) -(-2750 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-2733 (|has| |#2| (-452)) (|has| |#2| (-905))) (((|#1|) . T)) (|has| |#1| (-846)) (|has| |#1| (-846)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-767)) . T)) @@ -2052,13 +2052,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((((-564)) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564)))) (($) . T)) ((((-564)) . T)) (|has| |#1| (-363)) -(-2750 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-2750 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-2733 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-2733 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-363)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2073,23 +2073,23 @@ (((|#2|) . T)) (|has| |#1| (-1094)) (((|#1| |#2|) . T)) -((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-564)))))) +((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-564)))))) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) (((|#3|) |has| |#3| (-172))) -(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) ((((-858)) . T)) ((((-564)) . T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T)) ((((-948 |#1|)) . T) (((-858)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -2750 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) -((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -2733 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) +((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) ((((-948 |#1|)) . T)) ((($) . T)) ((((-564) |#1|) . T)) ((((-1170)) |has| (-407 |#2|) (-896 (-1170)))) -(((|#1|) . T) (($) -2750 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) +(((|#1|) . T) (($) -2733 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) ((((-536)) |has| |#2| (-612 (-536)))) ((((-685 |#2|)) . T) (((-858)) . T)) (((|#1|) . T)) @@ -2097,8 +2097,8 @@ (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) ((((-866 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2750 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2733 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2733 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) ((((-858)) . T)) (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) @@ -2114,17 +2114,17 @@ ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-1213))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-1213))) ((($) . T)) ((((-407 (-564))) |has| #0=(-407 |#2|) (-1034 (-407 (-564)))) (((-564)) |has| #0# (-1034 (-564))) ((#0#) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| (-767)) . T)) (|has| |#1| (-846)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-564)) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) |has| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))))) +((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-844)) (|has| |#1| (-38 (-407 (-564)))) @@ -2148,29 +2148,29 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) ((((-858)) . T)) -(((|#2|) . T) (((-564)) . T) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +(((|#2|) . T) (((-564)) . T) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) (((|#1| |#2|) . T)) ((((-144)) . T)) ((((-776 |#1| (-860 |#2|))) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (|has| |#1| (-1194)) ((((-858)) . T)) (((|#1|) . T)) -(-2750 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) +(-2733 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) (((|#2|) . T)) -((($ $) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($ $) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) ((((-906 |#1|)) . T)) ((($) . T)) ((((-407 (-948 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((($) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-858)) . T) (((-641 |#4|)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) |has| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (-309 (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) |has| (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|)) (-309 (-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))))) (|has| |#1| (-1094)) (|has| |#1| (-363)) (|has| |#1| (-846)) @@ -2179,16 +2179,16 @@ (((|#1|) . T)) ((((-668 |#1|)) . T)) ((($) . T) (((-407 (-564))) . T)) -((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-2750 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-2750 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-2733 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-2733 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) (|has| |#1| (-844)) (((|#1| |#2|) . T)) @@ -2212,9 +2212,9 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -2733 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) (((|#2|) |has| |#2| (-363))) (((|#2|) . T)) @@ -2236,13 +2236,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-2750 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) +(-2733 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) (|has| |#1| (-556)) (((|#2|) . T)) ((((-564)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#1|) . T)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2251,14 +2251,14 @@ ((($) . T)) (((|#1|) . T)) ((((-858)) . T)) -(((|#2|) |has| |#2| (-6 (-4408 "*")))) +(((|#2|) |has| |#2| (-6 (-4409 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#3|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-564)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-407 (-564))) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-564)) -2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))) (|has| |#1| (-1045))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -2750 (|has| |#1| (-556)) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-564)) -2733 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))) (|has| |#1| (-1045))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -2733 (|has| |#1| (-556)) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) ((((-407 (-564))) |has| |#2| (-1034 (-407 (-564)))) (((-564)) |has| |#2| (-1034 (-564))) ((|#2|) . T) (((-860 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-407 (-564))) . T)) ((((-1119 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) @@ -2271,12 +2271,12 @@ (((|#1| |#2|) . T)) ((((-1170) |#1|) . T)) (((|#4|) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1170) (-52)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) ((((-858)) . T)) -(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((#0=(-1245 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-172)) ((#0=(-407 (-564)) #0#) |has| |#1| (-556)) (($ $) |has| |#1| (-556))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) @@ -2296,14 +2296,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2| |#3|) . T)) -(-2750 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2733 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1| (-531 |#2|)) . T)) (((|#1| (-767)) . T)) (((|#1| (-531 (-1082 (-1170)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-905)) -(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2733 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-858)) . T)) ((($ $) . T) ((#0=(-1244 |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) |has| #0# (-38 (-407 (-564))))) ((((-906 |#1|)) . T)) @@ -2312,14 +2312,14 @@ ((((-858)) . T)) ((($) . T)) ((($) . T)) -(-2750 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564))))) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(-2750 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2750 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2733 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) ((((-564)) |has| |#1| (-637 (-564))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-858)) . T)) @@ -2352,27 +2352,27 @@ (((|#1|) |has| |#1| (-172))) ((((-858)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) -(((|#2|) -2750 (|has| |#2| (-6 (-4408 "*"))) (|has| |#2| (-172)))) -(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(((|#2|) -2733 (|has| |#2| (-6 (-4409 "*"))) (|has| |#2| (-172)))) +(-2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#2| (-846)) (|has| |#2| (-905)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) ((((-858)) . T)) ((((-536)) . T) (((-564)) . T) (((-888 (-564))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#1| |#2|) . T)) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) -(-2750 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-2733 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (|has| |#1| (-844)) @@ -2388,7 +2388,7 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-187)) . T) (((-858)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2401,7 +2401,7 @@ ((((-858)) . T)) ((((-1152)) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) (|has| |#1| (-846)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2413,16 +2413,16 @@ (((|#2|) . T)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T) (((-610 $)) . T)) -(-2750 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2750 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2733 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2733 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-1170) (-52)) . T)) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-905)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (|has| |#1| (-905)) @@ -2439,12 +2439,12 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#1| (-816)) (((#0=(-906 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-844)) -((((-1195 |#1|)) . T) (((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-1195 |#1|)) . T) (((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) ((#1=(-564) #1#) . T) (($ $) . T)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-1045)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045)))) @@ -2455,11 +2455,11 @@ (((|#2|) . T)) ((((-858)) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T) (((-564)) . T)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3058 (-1170)) (|:| -3726 #0#))) . T)) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3026 (-1170)) (|:| -3683 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-858)) . T)) @@ -2467,15 +2467,15 @@ (((#0=(-1245 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) (((#0=(-1076) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-564)) #0#) . T) ((#1=(-695) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-858)) . T)) (|has| |#1| (-1094)) (((|#1|) . T)) -(((|#1|) -2750 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -2750 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2733 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2733 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T)) ((((-579)) . T)) @@ -2498,7 +2498,7 @@ (((|#1|) . T)) ((((-564)) . T)) (((|#2|) . T) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (($) . T) (((-564)) . T)) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2536,7 +2536,7 @@ (|has| |#2| (-1018)) ((($) . T)) (|has| |#1| (-905)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2544,9 +2544,9 @@ ((($) . T)) (|has| |#1| (-363)) ((((-906 |#1|)) . T)) -((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-2750 (|has| |#1| (-368)) (|has| |#1| (-846))) +(-2733 (|has| |#1| (-368)) (|has| |#1| (-846))) (((|#1|) . T)) ((((-767)) . T)) ((((-858)) . T)) @@ -2557,16 +2557,16 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-767) |#1|) . T)) -(((|#2| (-240 (-2062 |#1|) (-767))) . T)) +(((|#2| (-240 (-2069 |#1|) (-767))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-1152)) . T) (((-858)) . T)) -(((#0=(-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) #0#) |has| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))))) +(((#0=(-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) #0#) |has| (-2 (|:| -3026 (-1170)) (|:| -3683 (-52))) (-309 (-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))))) ((((-1152)) . T)) (|has| |#1| (-905)) (|has| |#2| (-363)) -(-2750 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) (((|#1|) . T)) @@ -2583,11 +2583,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2750 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-824))) ((((-858)) . T)) -((((-1170)) -2750 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))))) +((((-1170)) -2733 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))))) (|has| |#1| (-363)) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-896 (-1170))))) (|has| |#1| (-363)) @@ -2598,7 +2598,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2623,9 +2623,9 @@ ((((-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-379)))) (((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-564))))) (|has| |#1| (-363)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-556)) (((|#1|) . T)) @@ -2634,22 +2634,22 @@ ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) (((|#1|) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(-2750 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#2|) . T)) (((|#2|) . T)) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-1152) |#1|) . T)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2657,7 +2657,7 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2750 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) ((($) . T)) @@ -2685,7 +2685,7 @@ ((((-858)) . T)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2707,7 +2707,7 @@ ((((-564)) . T)) ((((-858)) . T)) ((((-564)) . T)) -(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2733 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2719,9 +2719,9 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -(-2750 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +(-2733 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) (|has| |#1| (-1145)) ((((-564) |#1|) . T)) (((|#1|) . T)) @@ -2741,8 +2741,8 @@ (((|#1|) . T)) (|has| |#1| (-556)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2751,7 +2751,7 @@ (|has| |#1| (-556)) (|has| |#1| (-1094)) ((((-776 |#1| (-860 |#2|))) |has| (-776 |#1| (-860 |#2|)) (-309 (-776 |#1| (-860 |#2|))))) -(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2763,13 +2763,13 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) ((((-858)) . 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T)) +((((-1166 |#1|)) . T) (((-564)) . T) (($) -2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +(-2733 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-1082 (-1170))) . T) (($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . T)) (((#0=(-581 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -2793,13 +2793,13 @@ ((((-581 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) ((($) . T) (((-407 (-564))) . T)) ((($) . T) (((-407 (-564))) . T)) -(((|#2|) |has| |#2| (-6 (-4408 "*")))) +(((|#2|) |has| |#2| (-6 (-4409 "*")))) (((|#1|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (((|#1|) . T)) ((((-858)) . T)) ((((-294 |#3|)) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2750 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2733 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) @@ -2807,21 +2807,21 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) -2750 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . 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T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#2| (-905)) (|has| |#1| (-905)) -((($) -2750 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-858)) . T)) (((|#1|) . T)) -((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3026 (-1152)) (|:| -3683 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2836,10 +2836,10 @@ (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((#0=(-407 (-564)) #0#) . T)) ((((-407 (-564))) . T)) -(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1|) . T)) (((|#1|) . T)) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-407 (-564))) . T) (((-564)) . T) (($) . T)) ((((-536)) . T)) ((((-858)) . T)) @@ -2856,12 +2856,12 @@ ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-1170)) |has| |#1| (-896 (-1170)))) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) -((($) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2750 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((($) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2733 (|has| |#1| (-172)) (|has| |#1| (-556)))) ((($) . T) (((-407 (-564))) . T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((|#2|) |has| |#2| (-1045)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2750 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2733 (|has| |#1| (-172)) (|has| |#1| (-556)))) (|has| |#1| (-556)) (((|#1|) |has| |#1| (-363))) ((((-564)) . T)) @@ -2880,8 +2880,8 @@ ((((-858)) . T)) (|has| |#2| (-816)) (|has| |#2| (-816)) -((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2733 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) ((((-564)) |has| |#1| (-882 (-564))) (((-379)) |has| |#1| (-882 (-379)))) @@ -2907,12 +2907,12 @@ (((|#2| (-767)) . T)) ((((-1170)) . T)) ((((-866 |#1|)) . T)) -(-2750 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045))) -(-2750 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2733 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2733 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T)) (((|#1|) . T)) -(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) -(-2750 (-12 (|has| |#1| (-789)) (|has| |#2| (-789))) (-12 (|has| |#1| (-846)) (|has| |#2| (-846)))) +(-2733 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2733 (-12 (|has| |#1| (-789)) (|has| |#2| (-789))) (-12 (|has| |#1| (-846)) (|has| |#2| (-846)))) ((((-866 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-368)) @@ -2938,7 +2938,7 @@ (((|#1|) . T)) ((((-858)) . T)) (|has| |#2| (-905)) -((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) +((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564))))) ((((-858)) . T)) ((((-858)) . T)) @@ -2979,12 +2979,12 @@ ((((-407 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2062 |#1|) (-767))) . T)) +(((|#2| (-482 (-2069 |#1|) (-767))) . T)) ((((-564) |#1|) . T)) ((((-1152)) . T) (((-858)) . T)) (((|#2| |#2|) . T)) (((|#1| (-531 (-1170))) . T)) -(-2750 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-564)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2994,9 +2994,9 @@ ((($) . T) (((-407 (-564))) . T)) ((($) . T)) ((($) . 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T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-349))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) ((((-564)) . T)) @@ -3256,17 +3256,17 @@ ((((-129)) . T)) ((((-858)) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) (|has| |#1| (-363)) -((($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1098)) . T)) ((((-858)) . T)) -((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) ((($) . T)) -((($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1251 |#1| |#2| |#3|)) . T) (((-1223 |#1| |#2| |#3|)) . T)) ((((-1170)) . T) (((-858)) . T)) (|has| |#2| (-905)) @@ -3276,7 +3276,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-172))) ((((-695)) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-1175)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1175)) . T)) @@ -3288,13 +3288,13 @@ ((((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1175)) . T)) ((((-1175)) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-172)) (|has| |#1| (-556))) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) (((|#1| (-767)) . T)) @@ -3309,16 +3309,16 @@ ((((-888 (-379))) . T) (((-888 (-564))) . T) (((-1170)) . T) (((-536)) . T)) (((|#1|) . T)) ((((-858)) . T)) -(-2750 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2750 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) +(-2733 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) ((((-564)) . T)) ((((-564)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2750 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2733 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045)))) -(-2750 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) +(-2733 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3344,7 +3344,7 @@ (((|#1| |#2|) . T)) ((((-564)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-564)) . T)) -(-2750 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2733 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) @@ -3356,7 +3356,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((($) . T) (((-407 (-564))) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) @@ -3367,14 +3367,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-564)) . T)) ((((-1175)) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2750 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2733 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#2|) . T)) -(-2750 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-2733 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-858)) -2750 (-12 (|has| |#1| (-611 (-858))) (|has| |#2| (-611 (-858)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) +((((-858)) -2733 (-12 (|has| |#1| (-611 (-858))) (|has| |#2| (-611 (-858)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) ((((-407 |#2|) |#3|) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -3386,19 +3386,19 @@ (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((#0=(-564) #0#) . T)) ((($) . T) (((-407 (-564))) . T)) -(-2750 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2750 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2733 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2733 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T) (((-1175)) . T)) (|has| |#4| (-789)) -(-2750 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2733 (|has| |#4| (-789)) (|has| |#4| (-844))) (|has| |#4| (-844)) (|has| |#3| (-789)) ((((-1175)) . T)) -(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2733 (|has| |#3| (-789)) (|has| |#3| (-844))) (|has| |#3| (-844)) ((((-564)) . T)) (((|#2|) . T)) -((((-1170)) -2750 (-12 (|has| (-1168 |#1| |#2| |#3|) (-896 (-1170))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))))) +((((-1170)) -2733 (-12 (|has| (-1168 |#1| |#2| |#3|) (-896 (-1170))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))))) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-896 (-1170))))) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-767) |#1|))) (|has| |#1| (-896 (-1170))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3413,11 +3413,11 @@ ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-1134 |#1| |#2|)) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) -((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) +((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1018)) -(((|#2|) . T) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) ((((-858)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#2| (-1018))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3433,15 +3433,15 @@ ((((-1168 |#1| |#2| |#3|)) . T)) ((((-1168 |#1| |#2| |#3|)) . T) (((-1161 |#1| |#2| |#3|)) . T)) ((((-858)) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-564) |#1|) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-363)) -(((|#3|) . T) ((|#2|) . T) (($) -2750 (|has| |#4| (-172)) (|has| |#4| (-844)) (|has| |#4| (-1045))) ((|#4|) -2750 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1045)))) -(((|#2|) . T) (($) -2750 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((|#3|) -2750 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045)))) +(((|#3|) . T) ((|#2|) . T) (($) -2733 (|has| |#4| (-172)) (|has| |#4| (-844)) (|has| |#4| (-1045))) ((|#4|) -2733 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1045)))) +(((|#2|) . T) (($) -2733 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((|#3|) -2733 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-363)) @@ -3456,7 +3456,7 @@ ((((-187)) . T) (((-858)) . T)) ((((-858)) . T)) (((|#1|) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-129)) . T) (((-858)) . T)) ((((-564) |#1|) . T)) ((((-129)) . T)) @@ -3465,13 +3465,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) -(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2733 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2733 (|has| |#1| (-846)) (|has| |#1| (-1094))) ((((-858)) . T)) ((((-858)) . T)) ((((-858)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) +((((-2 (|:| -3026 (-1170)) (|:| -3683 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3485,8 +3485,8 @@ ((((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) -(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2733 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2733 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((($) . T)) (((|#2| (-531 (-860 |#1|))) . T)) ((((-1175)) . T)) @@ -3501,13 +3501,13 @@ ((((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2733 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#2| (-767)) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3026 |#1|) (|:| -3683 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3516,14 +3516,14 @@ ((((-564)) . T) (($) . 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T) (((-564)) -2750 (|has| (-995 |#1|) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) -2750 (|has| (-995 |#1|) (-1034 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +((((-995 |#1|)) . T) ((|#1|) . T) (((-564)) -2733 (|has| (-995 |#1|) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) -2733 (|has| (-995 |#1|) (-1034 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -3535,10 +3535,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1134 |#1| |#2|) #0#) |has| (-1134 |#1| |#2|) (-309 (-1134 |#1| |#2|)))) (((|#1|) . 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142430) ((-454 . -290) 142361) ((-1031 . -309) 142212) ((-677 . -490) 142193) ((-571 . -722) T) ((-672 . -490) 142174) ((-677 . -611) 142124) ((-672 . -611) 142090) ((-658 . -611) 142072) ((-478 . -490) 142053) ((-478 . -611) 142019) ((-245 . -612) 141980) ((-245 . -490) 141957) ((-138 . -490) 141938) ((-137 . -490) 141919) ((-133 . -490) 141900) ((-245 . -611) 141792) ((-213 . -102) T) ((-138 . -611) 141758) ((-137 . -611) 141724) ((-133 . -611) 141690) ((-1141 . -34) T) ((-939 . -1209) T) ((-343 . -713) 141635) ((-666 . -25) T) ((-666 . -21) T) ((-1170 . -614) 141616) ((-474 . -1045) T) ((-633 . -417) 141581) ((-605 . -417) 141546) ((-1114 . -1145) T) ((-581 . -290) T) ((-518 . -290) T) ((-1244 . -307) 141525) ((-474 . -233) 141477) ((-474 . -243) 141456) ((-1223 . -307) 141435) ((-1223 . -1018) NIL) ((-1074 . -131) T) ((-868 . -791) 141414) ((-144 . -102) T) ((-40 . -1094) T) ((-868 . -788) 141393) ((-641 . -1006) 141377) ((-580 . -1052) T) ((-564 . -1052) T) ((-495 . -1052) T) 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137495) ((-954 . -34) T) ((-355 . -233) 137474) ((-355 . -243) T) ((-352 . -233) 137453) ((-352 . -243) T) ((-344 . -233) 137432) ((-344 . -243) T) ((-247 . -326) 137389) ((-264 . -326) 137361) ((-264 . -233) 137340) ((-1150 . -151) 137324) ((-251 . -896) 137256) ((-250 . -896) 137188) ((-1076 . -846) T) ((-414 . -1106) T) ((-1049 . -23) T) ((-906 . -1045) T) ((-322 . -644) 137170) ((-1020 . -844) T) ((-1203 . -998) 137136) ((-1167 . -916) 137115) ((-1161 . -916) 137094) ((-1161 . -816) NIL) ((-906 . -243) T) ((-813 . -363) 137073) ((-385 . -23) T) ((-127 . -1094) 137051) ((-121 . -1094) 137029) ((-906 . -233) T) ((-128 . -34) T) ((-379 . -644) 136994) ((-866 . -713) 136981) ((-1042 . -151) 136946) ((-40 . -172) T) ((-690 . -411) 136928) ((-708 . -309) 136915) ((-832 . -644) 136875) ((-823 . -644) 136849) ((-319 . -25) T) ((-319 . -21) T) ((-654 . -286) 136828) ((-580 . -1094) T) ((-564 . -1094) T) ((-495 . -1094) T) ((-245 . -288) 136805) ((-313 . -231) 136766) ((-1166 . -882) NIL) ((-55 . -1094) T) ((-1119 . -882) 136625) ((-129 . -846) T) ((-1166 . -1034) 136505) ((-1119 . -1034) 136388) ((-183 . -611) 136370) ((-850 . -1034) 136266) ((-778 . -286) 136193) ((-813 . -1106) T) ((-1030 . -722) T) ((-600 . -647) 136177) ((-1042 . -972) 136106) ((-995 . -102) T) ((-813 . -23) T) ((-708 . -1145) 136084) ((-690 . -1052) T) ((-600 . -373) 136068) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -722) T) ((-706 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 136050) ((-1166 . -377) 136034) ((-1119 . -377) 136018) ((-1020 . -411) 135980) ((-141 . -229) 135962) ((-379 . -790) T) ((-379 . -787) T) ((-866 . -172) T) ((-379 . -722) T) ((-707 . -611) 135944) ((-708 . -38) 135773) ((-1259 . -1257) 135757) ((-351 . -402) T) ((-1259 . -1094) 135707) ((-580 . -713) 135694) ((-564 . -713) 135681) ((-495 . -713) 135646) ((-316 . -627) 135625) ((-832 . -722) T) ((-823 . -722) T) 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-614) 134844) ((-487 . -556) T) ((-478 . -614) 134825) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -556) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -614) 134802) ((-138 . -614) 134783) ((-137 . -614) 134764) ((-133 . -614) 134745) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1052) T) ((-580 . -172) T) ((-564 . -172) T) ((-495 . -172) T) ((-654 . -611) 134727) ((-733 . -732) 134711) ((-336 . -611) 134693) ((-68 . -383) T) ((-68 . -395) T) ((-1096 . -107) 134677) ((-1056 . -882) 134659) ((-948 . -882) 134584) ((-649 . -1106) T) ((-621 . -713) 134571) ((-481 . -882) NIL) ((-1140 . -102) T) ((-1088 . -616) 134555) ((-1056 . -1034) 134537) ((-97 . -611) 134519) ((-477 . -147) T) ((-948 . -1034) 134399) ((-117 . -713) 134344) ((-649 . -23) T) ((-481 . -1034) 134220) ((-1081 . -612) NIL) ((-1081 . -611) 134202) ((-778 . -612) NIL) ((-778 . -611) 134163) ((-776 . -612) 133797) ((-776 . -611) 133711) ((-1107 . -637) 133617) ((-461 . -611) 133599) ((-454 . -611) 133581) ((-454 . -612) 133442) ((-1031 . -229) 133388) ((-868 . -905) 133367) ((-126 . -34) T) ((-813 . -131) T) ((-645 . -611) 133349) ((-578 . -102) T) ((-355 . -1278) 133333) ((-352 . -1278) 133317) ((-344 . -1278) 133301) ((-127 . -514) 133234) ((-121 . -514) 133167) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 133105) ((-222 . -102) 133083) ((-690 . -1094) T) ((-695 . -172) T) ((-868 . -644) 133035) ((-65 . -384) T) ((-275 . -611) 133017) ((-65 . -395) T) ((-948 . -377) 133001) ((-866 . -290) T) ((-50 . -611) 132983) ((-995 . -38) 132931) ((-581 . -611) 132913) ((-481 . -377) 132897) ((-581 . -612) 132879) ((-518 . -611) 132861) ((-906 . -1278) 132848) ((-867 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132814) ((-487 . -363) T) ((-355 . -368) 132793) ((-352 . -368) 132772) ((-344 . -368) 132751) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132735) ((-867 . -880) 132712) ((-867 . -882) NIL) ((-960 . -846) 132611) ((-811 . -846) 132562) ((-1216 . -102) T) ((-650 . -652) 132546) ((-1195 . -34) T) ((-171 . -611) 132528) ((-1107 . -21) 132438) ((-1107 . -25) 132289) ((-867 . -1034) 132266) ((-948 . -896) 132247) ((-1232 . -47) 132224) ((-906 . -368) T) ((-59 . -647) 132208) ((-516 . -647) 132192) ((-481 . -896) 132169) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 132153) ((-59 . -373) 132137) ((-621 . -172) T) ((-516 . -373) 132121) ((-496 . -373) 132105) ((-823 . -704) 132089) ((-1166 . -307) 132068) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 132006) ((-169 . -1209) T) ((-633 . -740) 131990) ((-605 . -740) 131974) ((-1271 . -131) T) ((-1244 . -916) 131953) ((-1223 . -916) 131932) ((-1223 . -816) NIL) ((-690 . -713) 131882) ((-1222 . -905) 131835) ((-1020 . -1094) T) ((-867 . -377) 131812) ((-867 . -338) 131789) ((-901 . -1106) T) ((-169 . -880) 131773) ((-169 . -882) 131698) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1034) 131594) ((-319 . -846) T) ((-1259 . -514) 131527) ((-1243 . -644) 131424) ((-1222 . -644) 131294) ((-868 . -790) 131273) ((-868 . -787) 131252) ((-868 . -722) T) ((-487 . -23) T) ((-223 . -611) 131234) ((-174 . -452) T) ((-222 . -309) 131172) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1283 . -1276) 131151) ((-580 . -290) T) ((-564 . -290) T) ((-673 . -1034) 131135) ((-495 . -290) T) ((-136 . -470) 131090) ((-48 . -1094) T) ((-708 . -231) 131074) ((-867 . -896) NIL) ((-1232 . -882) NIL) ((-885 . -102) T) ((-881 . -102) T) ((-388 . -1094) T) ((-169 . -377) 131058) ((-169 . -338) 131042) ((-1232 . -1034) 130922) ((-851 . -1034) 130818) ((-1136 . -102) T) ((-649 . -131) T) ((-117 . -514) 130726) ((-658 . -788) 130705) ((-658 . -791) 130684) ((-571 . -1034) 130666) ((-294 . -1266) 130636) ((-862 . -102) T) ((-959 . -556) 130615) ((-1203 . -1051) 130498) ((-482 . -637) 130404) ((-900 . -1094) T) ((-1020 . -713) 130341) ((-707 . -1051) 130306) ((-615 . -102) T) ((-600 . -34) T) ((-1141 . -1209) T) 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. -1045) T) ((-385 . -21) T) ((-385 . -25) T) ((-690 . -514) NIL) ((-1020 . -172) T) ((-707 . -243) T) ((-1056 . -545) T) ((-506 . -102) T) ((-502 . -102) T) ((-354 . -172) T) ((-343 . -611) 129021) ((-394 . -611) 129003) ((-474 . -722) T) ((-1114 . -844) T) ((-888 . -1034) 128971) ((-108 . -846) T) ((-654 . -1051) 128955) ((-487 . -131) T) ((-1245 . -1052) T) ((-217 . -131) T) ((-1150 . -102) 128933) ((-99 . -1094) T) ((-245 . -662) 128917) ((-245 . -647) 128901) ((-654 . -111) 128880) ((-585 . -614) 128864) ((-316 . -411) 128848) ((-245 . -373) 128832) ((-1153 . -235) 128779) ((-995 . -231) 128763) ((-74 . -1209) T) ((-48 . -172) T) ((-697 . -387) T) ((-697 . -143) T) ((-1282 . -102) T) ((-1189 . -614) 128745) ((-1081 . -1051) 128588) ((-264 . -905) 128567) ((-247 . -905) 128546) ((-778 . -1051) 128369) ((-776 . -1051) 128212) ((-606 . -1209) T) ((-1158 . -611) 128194) ((-1081 . -111) 128023) ((-1042 . -102) T) ((-475 . -1209) T) ((-461 . -1051) 127994) ((-454 . -1051) 127837) ((-660 . -644) 127821) ((-867 . -307) T) ((-778 . -111) 127630) ((-776 . -111) 127459) ((-355 . -644) 127411) ((-352 . -644) 127363) ((-344 . -644) 127315) ((-264 . -644) 127240) ((-247 . -644) 127165) ((-1152 . -846) T) ((-1082 . -1034) 127149) ((-461 . -111) 127110) ((-454 . -111) 126939) ((-1070 . -1034) 126916) ((-996 . -34) T) ((-962 . -611) 126898) ((-954 . -1209) T) ((-126 . -1006) 126882) ((-959 . -1106) T) ((-867 . -1018) NIL) ((-731 . -1106) T) ((-711 . -1106) T) ((-654 . -614) 126800) ((-1259 . -489) 126784) ((-1136 . -38) 126744) ((-959 . -23) T) ((-861 . -1094) T) ((-839 . -102) T) ((-813 . -21) T) ((-813 . -25) T) ((-731 . -23) T) ((-711 . -23) T) ((-110 . -657) T) ((-906 . -644) 126709) ((-581 . -1051) 126674) ((-518 . -1051) 126619) ((-227 . -57) 126577) ((-453 . -23) T) ((-407 . -102) T) ((-263 . -102) T) ((-690 . -290) T) ((-862 . -38) 126547) ((-581 . -111) 126503) ((-518 . -111) 126432) ((-1081 . -614) 126168) ((-418 . -1106) T) ((-316 . -1052) 126058) ((-313 . -1052) T) ((-128 . -1209) T) ((-778 . -614) 125806) ((-776 . -614) 125572) ((-654 . -1045) T) ((-1287 . -1094) T) ((-454 . -614) 125357) ((-169 . -307) 125288) ((-418 . -23) T) ((-40 . -611) 125270) ((-40 . -612) 125254) ((-108 . -988) 125236) ((-116 . -865) 125220) ((-645 . -614) 125204) ((-48 . -514) 125170) ((-1195 . -1006) 125154) ((-1175 . -611) 125121) ((-1182 . -34) T) ((-950 . -611) 125087) ((-917 . -611) 125069) ((-1107 . -846) 125020) ((-767 . -611) 125002) ((-668 . -611) 124984) ((-1150 . -309) 124922) ((-479 . -34) T) ((-1086 . -1209) T) ((-477 . -452) T) ((-1135 . -34) T) ((-1081 . -1045) T) ((-50 . -614) 124891) ((-778 . -1045) T) ((-776 . -1045) T) ((-643 . -235) 124875) ((-630 . -235) 124821) ((-581 . -614) 124771) ((-518 . -614) 124701) ((-1232 . -307) 124680) ((-1081 . -326) 124641) ((-454 . -1045) T) ((-1172 . -21) T) ((-1081 . -233) 124620) ((-778 . -326) 124597) ((-778 . -233) T) ((-776 . -326) 124569) ((-727 . -1213) 124548) ((-327 . -647) 124532) ((-1172 . -25) T) ((-59 . -34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124511) ((-327 . -373) 124495) ((-497 . -34) T) ((-496 . -34) T) ((-999 . -1145) NIL) ((-727 . -556) 124426) ((-633 . -102) T) ((-605 . -102) T) ((-355 . -722) T) ((-352 . -722) T) ((-344 . -722) T) ((-264 . -722) T) ((-247 . -722) T) ((-1042 . -309) 124334) ((-897 . -1094) 124312) ((-50 . -1045) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-1168 . -556) 124291) ((-1167 . -1213) 124270) ((-581 . -1045) T) ((-518 . -1045) T) ((-1161 . -1213) 124249) ((-361 . -1034) 124233) ((-322 . -1034) 124217) ((-1020 . -290) T) ((-379 . -882) 124199) ((-1167 . -556) 124150) ((-1161 . -556) 124101) ((-999 . -38) 124046) ((-795 . -1106) T) ((-906 . -722) T) ((-581 . -243) T) ((-581 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1120 . -556) 124025) ((-354 . -290) T) ((-643 . -691) 124009) ((-379 . -1034) 123969) ((-1114 . -1052) T) ((-103 . -125) 123953) ((-795 . -23) T) ((-1281 . -1276) 123929) ((-1259 . -286) 123906) ((-407 . -309) 123871) 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-611) 123303) ((-121 . -611) 123235) ((-1287 . -172) T) ((-1167 . -363) 123214) ((-1161 . -363) 123193) ((-316 . -1094) T) ((-418 . -131) T) ((-313 . -1094) T) ((-407 . -38) 123145) ((-1127 . -102) T) ((-1245 . -713) 123037) ((-650 . -1052) T) ((-1129 . -1254) T) ((-319 . -145) 123016) ((-319 . -147) 122995) ((-139 . -1094) T) ((-136 . -1094) T) ((-114 . -1094) T) ((-854 . -102) T) ((-580 . -611) 122977) ((-564 . -612) 122876) ((-564 . -611) 122858) ((-495 . -611) 122840) ((-495 . -612) 122785) ((-485 . -23) T) ((-482 . -846) 122736) ((-487 . -637) 122718) ((-961 . -611) 122700) ((-217 . -637) 122682) ((-225 . -404) T) ((-658 . -644) 122666) ((-55 . -611) 122648) ((-1166 . -916) 122627) ((-727 . -1106) T) ((-351 . -102) T) ((-1208 . -1077) T) ((-1114 . -840) T) ((-814 . -846) T) ((-727 . -23) T) ((-343 . -1051) 122572) ((-1152 . -1151) T) ((-1141 . -107) 122556) ((-1168 . -1106) T) ((-1167 . -1106) T) ((-515 . -1034) 122540) ((-1161 . -1106) T) ((-1120 . -1106) T) ((-343 . -111) 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-145) NIL) ((-1114 . -612) 109167) ((-438 . -611) 109149) ((-217 . -147) T) ((-217 . -145) NIL) ((-1114 . -611) 109131) ((-129 . -102) T) ((-52 . -102) T) ((-1223 . -637) 109083) ((-479 . -107) 109033) ((-989 . -23) T) ((-1283 . -38) 109003) ((-1166 . -1106) T) ((-1119 . -1106) T) ((-1056 . -1213) T) ((-311 . -102) T) ((-850 . -1106) T) ((-948 . -1213) 108982) ((-481 . -1213) 108961) ((-727 . -846) 108940) ((-1056 . -556) T) ((-948 . -556) 108871) ((-1166 . -23) T) ((-1119 . -23) T) ((-850 . -23) T) ((-481 . -556) 108802) ((-1136 . -713) 108734) ((-1140 . -514) 108667) ((-1031 . -612) NIL) ((-1031 . -611) 108649) ((-96 . -1077) T) ((-862 . -713) 108619) ((-1203 . -47) 108588) ((-251 . -131) T) ((-250 . -131) T) ((-1098 . -1094) T) ((-999 . -1094) T) ((-62 . -611) 108570) ((-1161 . -846) NIL) ((-1020 . -788) T) ((-1020 . -791) T) ((-1287 . -1051) 108557) ((-1287 . -111) 108542) ((-866 . -644) 108529) ((-1251 . -25) T) ((-1251 . -21) T) ((-1244 . -21) T) ((-1244 . -25) T) ((-1223 . -21) T) ((-1223 . -25) T) ((-1023 . -151) 108513) ((-868 . -816) 108492) ((-868 . -916) T) ((-708 . -286) 108419) ((-595 . -21) T) ((-595 . -25) T) ((-594 . -21) T) ((-40 . -722) T) ((-222 . -514) 108352) ((-594 . -25) T) ((-476 . -151) 108336) ((-463 . -151) 108320) ((-917 . -790) T) ((-917 . -722) T) ((-767 . -789) T) ((-767 . -790) T) ((-506 . -1094) T) ((-502 . -1094) T) ((-767 . -722) T) ((-225 . -363) T) ((-1150 . -1094) 108298) ((-867 . -1213) T) ((-650 . -611) 108280) ((-867 . -556) T) ((-690 . -368) NIL) ((-1287 . -614) 108262) ((-1282 . -1094) T) ((-359 . -1266) 108246) ((-666 . -102) T) ((-353 . -1266) 108230) ((-345 . -1266) 108214) ((-548 . -102) T) ((-520 . -846) 108193) ((-813 . -452) 108172) ((-1042 . -1094) T) ((-1042 . -1065) 108101) ((-1023 . -972) 108070) ((-815 . -1106) T) ((-999 . -713) 108015) ((-386 . -1106) T) ((-476 . -972) 107984) ((-463 . -972) 107953) ((-110 . -151) 107935) ((-73 . -611) 107917) ((-889 . -611) 107899) ((-1074 . -720) 107878) ((-1287 . -1045) T) 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105407) ((-1081 . -882) NIL) ((-867 . -1106) T) ((-117 . -905) NIL) ((-1281 . -1280) 105383) ((-1279 . -1280) 105362) ((-778 . -882) NIL) ((-776 . -882) 105221) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 105199) ((-1100 . -395) T) ((-621 . -644) 105186) ((-454 . -882) NIL) ((-671 . -102) 105164) ((-1081 . -1034) 104991) ((-867 . -23) T) ((-778 . -1034) 104850) ((-776 . -1034) 104707) ((-117 . -644) 104652) ((-454 . -1034) 104528) ((-316 . -614) 104092) ((-313 . -614) 103975) ((-645 . -1034) 103959) ((-625 . -102) T) ((-222 . -489) 103943) ((-1259 . -34) T) ((-136 . -614) 103927) ((-633 . -713) 103911) ((-605 . -713) 103895) ((-666 . -38) 103855) ((-319 . -102) T) ((-85 . -611) 103837) ((-50 . -1034) 103821) ((-1114 . -1051) 103808) ((-1081 . -377) 103792) ((-778 . -377) 103776) ((-695 . -722) T) ((-695 . -790) T) ((-695 . -787) T) ((-581 . -1034) 103763) ((-518 . -1034) 103740) ((-60 . -57) 103702) ((-324 . -131) T) ((-316 . -1045) 103592) ((-313 . -1045) T) ((-169 . -1106) T) 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-231) 99766) ((-581 . -307) T) ((-518 . -307) T) ((-294 . -514) 99715) ((-108 . -309) NIL) ((-72 . -395) T) ((-1107 . -102) 99505) ((-829 . -411) 99489) ((-1114 . -791) T) ((-1114 . -788) T) ((-697 . -1094) T) ((-578 . -611) 99471) ((-379 . -363) T) ((-169 . -493) 99449) ((-222 . -611) 99381) ((-134 . -1094) T) ((-116 . -1094) T) ((-48 . -722) T) ((-1042 . -489) 99346) ((-141 . -425) 99328) ((-141 . -368) T) ((-1023 . -102) T) ((-512 . -509) 99307) ((-708 . -614) 99063) ((-476 . -102) T) ((-463 . -102) T) ((-1030 . -1106) T) ((-1216 . -611) 99045) ((-1175 . -1034) 98981) ((-1168 . -35) 98947) ((-1168 . -95) 98913) ((-1168 . -1197) 98879) ((-1168 . -1194) 98845) ((-1152 . -309) NIL) ((-89 . -396) T) ((-89 . -395) T) ((-1074 . -1145) 98824) ((-1167 . -1194) 98790) ((-1167 . -1197) 98756) ((-1030 . -23) T) ((-1167 . -95) 98722) ((-571 . -493) T) ((-1167 . -35) 98688) ((-1161 . -1194) 98654) ((-1161 . -1197) 98620) ((-1161 . -95) 98586) ((-361 . -1106) T) ((-359 . -1145) 98565) ((-353 . -1145) 98544) ((-345 . -1145) 98523) ((-1161 . -35) 98489) ((-1120 . -35) 98455) ((-1120 . -95) 98421) ((-108 . -1145) T) ((-1120 . -1197) 98387) ((-829 . -1052) 98366) ((-643 . -309) 98304) ((-630 . -309) 98155) ((-1120 . -1194) 98121) ((-708 . -1045) T) ((-1056 . -637) 98103) ((-1074 . -38) 97971) ((-948 . -637) 97919) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1106) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97898) ((-708 . -326) 97875) ((-481 . -637) 97823) ((-40 . -1034) 97711) ((-708 . -233) T) ((-697 . -713) 97698) ((-339 . -1094) T) ((-174 . -1094) T) ((-331 . -846) T) ((-418 . -452) 97648) ((-379 . -23) T) ((-359 . -38) 97613) ((-353 . -38) 97578) ((-345 . -38) 97543) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1106) T) ((-108 . -38) 97493) ((-823 . -1106) T) ((-770 . -1094) T) ((-116 . -713) 97480) ((-668 . -1034) 97464) ((-610 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1150 . -286) 97441) ((-1107 . -309) 97379) ((-1096 . -235) 97363) ((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97340) ((-96 . -102) T) ((-649 . -848) 97324) ((-1129 . -1077) T) ((-1056 . -21) T) ((-1056 . -25) T) ((-811 . -231) 97293) ((-948 . -25) T) ((-948 . -21) T) ((-619 . -1052) T) ((-1114 . -368) T) ((-481 . -25) T) ((-481 . -21) T) ((-1023 . -309) 97231) ((-885 . -611) 97213) ((-881 . -611) 97195) ((-251 . -846) 97146) ((-250 . -846) 97097) ((-523 . -514) 97030) ((-867 . -637) 97007) ((-476 . -309) 96945) ((-463 . -309) 96883) ((-351 . -290) T) ((-1150 . -1247) 96867) ((-1136 . -611) 96829) ((-1136 . -612) 96790) ((-1134 . -102) T) ((-995 . -1051) 96686) ((-40 . -896) 96638) ((-1150 . -602) 96615) ((-1287 . -644) 96602) ((-862 . -490) 96579) ((-1057 . -151) 96525) ((-868 . -1213) T) ((-995 . -111) 96407) ((-339 . -713) 96391) ((-862 . -611) 96353) ((-174 . -713) 96285) ((-407 . -286) 96243) ((-868 . -556) T) ((-108 . -400) 96225) ((-84 . -384) T) ((-84 . -395) T) ((-697 . -172) T) ((-615 . -611) 96207) ((-99 . -722) T) ((-482 . -102) 95997) ((-99 . -473) T) ((-116 . -172) T) ((-1107 . -38) 95967) ((-169 . -637) 95915) ((-1049 . -102) T) ((-995 . -614) 95805) ((-867 . -25) T) ((-811 . -238) 95784) ((-867 . -21) T) ((-814 . -102) T) ((-414 . -102) T) ((-385 . -102) T) ((-110 . -309) NIL) ((-227 . -102) 95762) ((-127 . -1209) T) ((-121 . -1209) T) ((-1030 . -131) T) ((-666 . -367) 95746) ((-995 . -1045) T) ((-1232 . -637) 95694) ((-1098 . -611) 95676) ((-999 . -611) 95658) ((-515 . -23) T) ((-510 . -23) T) ((-343 . -307) T) ((-508 . -23) T) ((-322 . -131) T) ((-3 . -1094) T) ((-999 . -612) 95642) ((-995 . -243) 95621) ((-995 . -233) 95600) ((-1287 . -722) T) ((-1251 . -145) 95579) ((-829 . -1094) T) ((-1251 . -147) 95558) ((-1244 . -147) 95537) ((-1244 . -145) 95516) ((-1243 . -1213) 95495) ((-1223 . -145) 95402) ((-1223 . -147) 95309) ((-1222 . -1213) 95288) ((-379 . -131) T) ((-564 . -882) 95270) ((0 . -1094) T) ((-174 . -172) T) ((-169 . -21) T) ((-169 . -25) T) ((-49 . -1094) T) ((-1245 . -644) 95175) ((-1243 . -556) 95126) ((-710 . -1106) T) ((-1222 . -556) 95077) ((-564 . -1034) 95059) ((-594 . -147) 95038) ((-594 . -145) 95017) ((-495 . -1034) 94960) ((-1129 . -1131) T) ((-87 . -384) T) ((-87 . -395) T) ((-868 . -363) T) ((-832 . -131) T) ((-823 . -131) T) ((-710 . -23) T) ((-506 . -611) 94926) ((-502 . -611) 94908) ((-1283 . -1052) T) ((-379 . -1054) T) ((-1022 . -1094) 94886) ((-55 . -1034) 94868) ((-897 . -34) T) ((-482 . -309) 94806) ((-591 . -102) T) ((-1150 . -612) 94767) ((-1150 . -611) 94699) ((-1166 . -846) 94678) ((-45 . -102) T) ((-1119 . -846) 94657) ((-813 . -102) T) ((-1232 . -25) T) ((-1232 . -21) T) ((-851 . -25) T) ((-44 . -367) 94641) ((-851 . -21) T) ((-727 . -452) 94592) ((-1282 . -611) 94574) ((-1049 . -309) 94512) ((-667 . -1077) T) ((-604 . -1077) T) ((-390 . -1094) T) ((-571 . -25) T) ((-571 . -21) T) ((-180 . -1077) T) ((-161 . -1077) T) ((-156 . -1077) T) ((-154 . -1077) T) ((-619 . -1094) T) ((-695 . -882) 94494) ((-1259 . -1209) T) ((-227 . -309) 94432) ((-144 . -368) T) ((-1042 . -612) 94374) ((-1042 . -611) 94317) ((-313 . -905) NIL) ((-1217 . -840) T) ((-695 . -1034) 94262) ((-707 . -916) T) ((-474 . -1213) 94241) ((-1167 . -452) 94220) ((-1161 . -452) 94199) ((-330 . -102) T) ((-868 . -1106) T) ((-316 . -644) 94020) ((-313 . -644) 93949) ((-474 . -556) 93900) ((-339 . -514) 93866) ((-550 . -151) 93816) ((-40 . -307) T) ((-839 . -611) 93798) ((-697 . -290) T) ((-868 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93768) ((-512 . -102) T) ((-407 . -612) 93575) ((-407 . -611) 93557) ((-263 . -611) 93539) ((-116 . -290) T) ((-1245 . -722) T) ((-1243 . -363) 93518) ((-1222 . -363) 93497) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93479) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93463) ((-733 . -34) T) ((-482 . -38) 93433) ((-141 . -34) T) ((-117 . -880) 93410) ((-117 . -882) NIL) ((-621 . -1034) 93293) ((-641 . -846) 93272) ((-1271 . -102) T) ((-295 . -102) T) ((-708 . -368) 93251) 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-23) T) ((-714 . -1106) T) ((-710 . -131) T) ((-649 . -102) T) ((-477 . -713) 92004) ((-45 . -282) 91954) ((-105 . -1094) T) ((-68 . -611) 91936) ((-966 . -102) T) ((-860 . -102) T) ((-621 . -896) 91895) ((-1283 . -1094) T) ((-381 . -1094) T) ((-1208 . -1094) T) ((-1107 . -231) 91864) ((-82 . -1209) T) ((-1056 . -846) T) ((-948 . -846) 91843) ((-117 . -896) NIL) ((-778 . -916) 91822) ((-709 . -846) T) ((-531 . -1094) T) ((-500 . -1094) T) ((-355 . -1213) T) ((-352 . -1213) T) ((-344 . -1213) T) ((-264 . -1213) 91801) ((-247 . -1213) 91780) ((-533 . -856) T) ((-481 . -846) 91759) ((-1152 . -824) T) ((-1136 . -1051) 91743) ((-390 . -757) T) ((-690 . -1209) T) ((-687 . -1034) 91727) ((-355 . -556) T) ((-352 . -556) T) ((-344 . -556) T) ((-264 . -556) 91658) ((-247 . -556) 91589) ((-525 . -1077) T) ((-1136 . -111) 91568) ((-453 . -740) 91538) ((-862 . -1051) 91508) ((-813 . -38) 91450) ((-690 . -880) 91432) ((-690 . -882) 91414) ((-295 . -309) 91218) ((-906 . -1213) T) ((-666 . -411) 91202) ((-862 . -111) 91167) ((-690 . -1034) 91112) ((-1000 . -452) T) ((-906 . -556) T) ((-533 . -611) 91094) ((-581 . -916) T) ((-474 . -1106) T) ((-518 . -916) T) ((-1150 . -288) 91071) ((-910 . -452) T) ((-65 . -611) 91053) ((-630 . -229) 90999) ((-474 . -23) T) ((-1114 . -790) T) ((-868 . -131) T) ((-1114 . -787) T) ((-1274 . -1276) 90978) ((-1114 . -722) T) ((-650 . -644) 90952) ((-294 . -611) 90693) ((-1136 . -614) 90611) ((-1031 . -34) T) ((-811 . -844) 90590) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -713) 90560) ((-690 . -377) 90542) ((-690 . -338) 90524) ((-477 . -172) T) ((-381 . -713) 90494) ((-862 . -614) 90429) ((-867 . -846) NIL) ((-564 . -1018) T) ((-495 . -1018) T) ((-1127 . -611) 90411) ((-1107 . -238) 90390) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90372) ((-1136 . -1045) T) ((-1172 . -38) 90269) ((-854 . -611) 90251) ((-564 . -545) T) ((-666 . -1052) T) ((-727 . -945) 90204) ((-1136 . -233) 90183) ((-1076 . -1094) T) ((-1030 . -25) T) ((-1030 . -21) T) ((-999 . -1051) 90128) ((-901 . -102) T) ((-862 . -1045) T) ((-690 . -896) NIL) ((-355 . -329) 90112) ((-355 . -363) T) ((-352 . -329) 90096) ((-352 . -363) T) ((-344 . -329) 90080) ((-344 . -363) T) ((-487 . -102) T) ((-1271 . -38) 90050) ((-546 . -846) T) ((-523 . -683) 90000) ((-217 . -102) T) ((-1020 . -1034) 89880) ((-999 . -111) 89809) ((-1168 . -969) 89778) ((-1167 . -969) 89740) ((-520 . -151) 89724) ((-1074 . -370) 89703) ((-351 . -611) 89685) ((-322 . -21) T) ((-354 . -1034) 89662) ((-322 . -25) T) ((-1161 . -969) 89631) ((-1120 . -969) 89598) ((-76 . -611) 89580) ((-695 . -307) T) ((-169 . -846) 89559) ((-129 . -840) T) ((-906 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-906 . -329) 89546) ((-86 . -611) 89528) ((-695 . -1018) T) ((-673 . -846) T) ((-1243 . -131) T) ((-1222 . -131) T) ((-897 . -1006) 89512) ((-832 . -21) T) ((-48 . -1034) 89455) ((-832 . -25) T) ((-823 . -25) T) ((-823 . -21) T) ((-1281 . -1052) T) ((-549 . -102) T) ((-1279 . -1052) T) 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. -131) T) ((-217 . -309) NIL) ((-407 . -111) 88435) ((-811 . -1052) 88365) ((-733 . -1092) 88349) ((-1243 . -493) 88315) ((-1222 . -493) 88281) ((-548 . -840) T) ((-141 . -1092) 88263) ((-477 . -290) T) ((-1282 . -1045) T) ((-1214 . -102) T) ((-1057 . -102) T) ((-839 . -614) 88131) ((-500 . -514) NIL) ((-482 . -238) 88110) ((-407 . -614) 88008) ((-1166 . -145) 87987) ((-1166 . -147) 87966) ((-1119 . -147) 87945) ((-1119 . -145) 87924) ((-633 . -1051) 87908) ((-605 . -1051) 87892) ((-1168 . -1250) 87876) ((-666 . -1094) T) ((-666 . -1048) 87816) ((-1168 . -1237) 87793) ((-548 . -1094) T) ((-487 . -1145) T) ((-1167 . -1242) 87754) ((-1167 . -1237) 87724) ((-1167 . -1240) 87708) ((-217 . -1145) T) ((-343 . -916) T) ((-814 . -266) 87692) ((-633 . -111) 87671) ((-605 . -111) 87650) ((-1161 . -1221) 87611) ((-839 . -1045) 87590) ((-1161 . -1237) 87567) ((-515 . -25) T) ((-495 . -302) T) ((-511 . -23) T) ((-510 . -25) T) ((-508 . -25) T) ((-507 . -23) T) ((-1161 . -1219) 87551) ((-407 . 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83434) ((-225 . -35) T) ((-49 . -611) 83416) ((-477 . -1052) T) ((-487 . -231) 83398) ((-484 . -964) 83382) ((-482 . -844) 83361) ((-217 . -231) 83343) ((-81 . -441) T) ((-81 . -395) T) ((-1140 . -34) T) ((-811 . -172) 83322) ((-727 . -102) T) ((-1022 . -611) 83289) ((-500 . -286) 83264) ((-316 . -377) 83233) ((-313 . -377) 83194) ((-313 . -338) 83155) ((-1079 . -611) 83137) ((-812 . -945) 83084) ((-658 . -131) T) ((-1232 . -145) 83063) ((-1232 . -147) 83042) ((-1168 . -102) T) ((-1167 . -102) T) ((-1161 . -102) T) ((-1153 . -1094) T) ((-1120 . -102) T) ((-222 . -34) T) ((-289 . -713) 83029) ((-1153 . -608) 83005) ((-592 . -309) NIL) ((-484 . -1094) 82983) ((-390 . -611) 82965) ((-510 . -846) T) ((-1144 . -229) 82915) ((-1251 . -1250) 82899) ((-1251 . -1237) 82876) ((-1244 . -1242) 82837) ((-1244 . -1237) 82807) ((-1244 . -1240) 82791) ((-1223 . -1221) 82752) ((-1223 . -1237) 82729) ((-619 . -611) 82711) ((-1223 . -1219) 82695) ((-695 . -916) T) ((-1168 . -284) 82661) ((-1167 . -284) 82627) ((-1161 . -284) 82593) ((-1074 . -1094) T) ((-1055 . -1094) T) ((-48 . -302) T) ((-316 . -896) 82559) ((-313 . -896) NIL) ((-1055 . -1062) 82538) ((-1114 . -882) 82520) ((-795 . -38) 82504) ((-264 . -637) 82452) ((-247 . -637) 82400) ((-697 . -1051) 82387) ((-594 . -1237) 82364) ((-1120 . -284) 82330) ((-319 . -172) 82261) ((-359 . -1094) T) ((-353 . -1094) T) ((-345 . -1094) T) ((-500 . -19) 82243) ((-1114 . -1034) 82225) ((-1096 . -151) 82209) ((-108 . -1094) T) ((-116 . -1051) 82196) ((-707 . -363) T) ((-500 . -602) 82171) ((-697 . -111) 82156) ((-436 . -102) T) ((-45 . -1143) 82106) ((-116 . -111) 82091) ((-633 . -716) T) ((-605 . -716) T) ((-811 . -514) 82024) ((-1031 . -1209) T) ((-939 . -151) 82008) ((-1217 . -611) 81990) ((-1166 . -452) 81921) ((-1160 . -1094) T) ((-1152 . -1094) T) ((-525 . -102) T) ((-520 . -102) 81871) ((-1136 . -644) 81845) ((-1119 . -452) 81796) ((-1081 . -1213) 81775) ((-778 . -1213) 81754) ((-776 . -1213) 81733) ((-62 . -1209) T) ((-477 . -611) 81685) ((-477 . -612) 81607) ((-1081 . -556) 81538) ((-990 . -1094) T) ((-778 . -556) 81449) ((-776 . -556) 81380) ((-482 . -411) 81349) ((-621 . -916) 81328) ((-454 . -1213) 81307) ((-727 . -309) 81294) ((-697 . -614) 81266) ((-398 . -611) 81248) ((-671 . -514) 81181) ((-660 . -25) T) ((-660 . -21) T) ((-454 . -556) 81112) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -916) T) ((-117 . -816) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -614) 81094) ((-116 . -614) 81066) ((-1261 . -611) 81048) ((-1215 . -846) T) ((-1203 . -1106) T) ((-1203 . -23) T) ((-1161 . -309) 80933) ((-1120 . -309) 80920) ((-1074 . -713) 80788) ((-862 . -644) 80748) ((-939 . -976) 80732) ((-906 . -21) T) ((-289 . -172) T) ((-906 . -25) T) ((-311 . -93) T) ((-868 . -846) 80683) ((-707 . -1106) T) ((-707 . -23) T) ((-697 . -1045) T) ((-643 . -1094) 80661) ((-630 . -1094) T) ((-581 . -1213) T) ((-518 . -1213) T) ((-697 . -233) T) ((-630 . -608) 80636) ((-581 . -556) T) ((-518 . -556) T) ((-359 . -713) 80588) ((-339 . -1051) 80572) ((-353 . -713) 80524) ((-345 . -713) 80476) ((-174 . -1051) 80408) ((-174 . -111) 80319) ((-108 . -713) 80269) ((-339 . -111) 80248) ((-274 . -1094) T) ((-273 . -1094) T) ((-272 . -1094) T) ((-271 . -1094) T) ((-270 . -1094) T) ((-269 . -1094) T) ((-268 . -1094) T) ((-212 . -1094) T) ((-211 . -1094) T) ((-169 . -1197) 80226) ((-169 . -1194) 80204) ((-209 . -1094) T) ((-208 . -1094) T) ((-116 . -1045) T) ((-207 . -1094) T) ((-206 . -1094) T) ((-203 . -1094) T) ((-202 . -1094) T) ((-201 . -1094) T) ((-200 . -1094) T) ((-199 . -1094) T) ((-198 . -1094) T) ((-197 . -1094) T) ((-196 . -1094) T) ((-195 . -1094) T) ((-194 . -1094) T) ((-193 . -1094) T) ((-240 . -102) 79994) ((-169 . -35) 79972) ((-169 . -95) 79950) ((-650 . -1034) 79846) ((-482 . -1052) 79776) ((-1107 . -1094) 79566) ((-1136 . -34) T) ((-666 . -489) 79550) ((-73 . -1209) T) 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-290) 78142) ((-345 . -172) T) ((-174 . -243) T) ((-1222 . -846) 78041) ((-108 . -172) T) ((-868 . -988) 78025) ((-654 . -1106) T) ((-581 . -363) T) ((-581 . -329) 78012) ((-518 . -329) 77989) ((-518 . -363) T) ((-316 . -307) 77968) ((-313 . -307) T) ((-600 . -846) 77947) ((-1107 . -713) 77889) ((-520 . -282) 77873) ((-654 . -23) T) ((-418 . -231) 77857) ((-313 . -1018) NIL) ((-336 . -23) T) ((-103 . -1006) 77841) ((-45 . -36) 77820) ((-610 . -1094) T) ((-351 . -368) T) ((-524 . -102) T) ((-495 . -27) T) ((-240 . -309) 77758) ((-1081 . -1106) T) ((-1282 . -644) 77732) ((-778 . -1106) T) ((-776 . -1106) T) ((-454 . -1106) T) ((-1056 . -452) T) ((-948 . -452) 77683) ((-1109 . -1077) T) ((-110 . -1094) T) ((-1081 . -23) T) ((-813 . -1052) T) ((-778 . -23) T) ((-776 . -23) T) ((-481 . -452) 77634) ((-1153 . -514) 77417) ((-381 . -382) 77396) ((-1172 . -411) 77380) ((-461 . -23) T) ((-454 . -23) T) ((-96 . -1094) T) ((-484 . -514) 77313) ((-289 . -290) T) ((-1076 . -611) 77295) ((-1076 . 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. -151) 67858) ((-418 . -1052) T) ((-487 . -713) 67808) ((-482 . -489) 67792) ((-327 . -846) 67771) ((-339 . -644) 67745) ((-50 . -21) T) ((-50 . -25) T) ((-217 . -713) 67695) ((-169 . -720) 67666) ((-174 . -644) 67598) ((-581 . -21) T) ((-581 . -25) T) ((-518 . -25) T) ((-518 . -21) T) ((-475 . -151) 67548) ((-1074 . -611) 67530) ((-1055 . -611) 67512) ((-989 . -102) T) ((-858 . -102) T) ((-795 . -411) 67476) ((-40 . -131) T) ((-695 . -363) T) ((-697 . -722) T) ((-697 . -790) T) ((-697 . -787) T) ((-212 . -891) T) ((-580 . -1106) T) ((-564 . -1106) T) ((-495 . -1106) T) ((-359 . -611) 67458) ((-353 . -611) 67440) ((-345 . -611) 67422) ((-66 . -396) T) ((-66 . -395) T) ((-108 . -612) 67352) ((-108 . -611) 67294) ((-211 . -891) T) ((-954 . -151) 67278) ((-767 . -131) T) ((-666 . -614) 67196) ((-134 . -722) T) ((-116 . -722) T) ((-1243 . -35) 67162) ((-1049 . -489) 67146) ((-580 . -23) T) ((-564 . -23) T) ((-495 . -23) T) ((-1222 . -95) 67112) ((-1222 . -35) 67078) ((-1166 . -102) T) 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. -430) 64176) ((-591 . -93) T) ((-1023 . -612) 64137) ((-1020 . -1213) T) ((-225 . -102) T) ((-1023 . -611) 64099) ((-812 . -231) 64083) ((-811 . -614) 63813) ((-1020 . -556) T) ((-829 . -644) 63786) ((-354 . -1213) T) ((-476 . -611) 63748) ((-476 . -612) 63709) ((-463 . -612) 63670) ((-463 . -611) 63632) ((-407 . -880) 63616) ((-319 . -1051) 63451) ((-407 . -882) 63376) ((-839 . -1034) 63272) ((-487 . -514) NIL) ((-482 . -602) 63249) ((-354 . -556) T) ((-217 . -514) NIL) ((-868 . -452) T) ((-418 . -1094) T) ((-407 . -1034) 63113) ((-319 . -111) 62934) ((-690 . -363) T) ((-225 . -284) T) ((-1206 . -614) 62911) ((-48 . -1213) T) ((-811 . -1045) 62841) ((-580 . -131) T) ((-564 . -131) T) ((-495 . -131) T) ((-1166 . -1145) 62819) ((-48 . -556) T) ((-1153 . -288) 62795) ((-1056 . -102) T) ((-948 . -102) T) ((-316 . -27) 62774) ((-811 . -233) 62726) ((-249 . -831) 62708) ((-240 . -844) 62687) ((-187 . -831) 62669) ((-709 . -102) T) ((-295 . -489) 62606) ((-481 . -102) T) ((-727 . -1052) T) 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. -612) 23648) ((-939 . -611) 23560) ((-641 . -489) 23544) ((-45 . -1006) 23494) ((-615 . -963) T) ((-491 . -102) T) ((-331 . -611) 23476) ((-1107 . -1034) 23303) ((-592 . -647) 23285) ((-130 . -1094) T) ((-128 . -1094) T) ((-592 . -373) 23267) ((-343 . -1266) 23244) ((-439 . -611) 23226) ((-1023 . -1209) T) ((-867 . -290) T) ((-1232 . -514) 23173) ((-476 . -1209) T) ((-463 . -1209) T) ((-585 . -102) T) ((-1166 . -286) 23100) ((-621 . -452) 23079) ((-996 . -991) 23063) ((-1274 . -382) 23035) ((-517 . -1094) T) ((-117 . -452) T) ((-1189 . -102) T) ((-1086 . -1094) 23013) ((-1030 . -1094) T) ((-1109 . -93) T) ((-889 . -846) T) ((-351 . -1213) T) ((-1251 . -1051) 22896) ((-1107 . -377) 22865) ((-1244 . -1051) 22700) ((-1223 . -1051) 22490) ((-1251 . -111) 22359) ((-1244 . -111) 22180) ((-1223 . -111) 21949) ((-1203 . -309) 21936) ((-351 . -556) T) ((-365 . -611) 21918) ((-289 . -307) T) ((-595 . -1051) 21891) ((-594 . -1051) 21774) ((-361 . -1094) T) ((-322 . -1094) T) ((-251 . -611) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 8e4bbd99..c5a002bc 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3451578535) -(4409 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3451919707) +(4410 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -477,662 +477,663 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |makeFR| |acsch| |acsc| |axesColorDefault| - |OMgetInteger| |evaluateInverse| |setPrologue!| - |indicialEquationAtInfinity| |besselJ| |sinh| |saturate| - 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|generalizedContinuumHypothesisAssumed?| |kind| |checkPrecision| - |real?| |separate| |viewPosDefault| |binomThmExpt| |iidsum| |toScale| - |factorset| |compdegd| |roughEqualIdeals?| |discreteLog| |isMult| - |maxint| |op| |colorDef| |test| |explicitlyFinite?| - |exteriorDifferential| |perfectNthPower?| |halfExtendedResultant1| - |multiEuclideanTree| |rootOf| |splitConstant| |lazyEvaluate| - |rootPoly| |palgLODE| |lprop| |oddlambert| |interactiveEnv| - |createNormalPrimitivePoly| |supersub| |deepCopy| |cAcot| |showAll?| - |ef2edf| |drawToScale| |llprop| |returnType!| |UnVectorise| - |divideIfCan| |rombergo| |components| |optAttributes| |f04jgf| - |bipolar| |repeating| |primextendedint| |pattern| |pmintegrate| |blue| - |cLog| |eq| |readable?| |uniform01| |vectorise| UP2UTS |maxIndex| - |OMgetError| |numericalIntegration| |rootRadius| |rightUnit| - |explogs2trigs| |iter| |freeOf?| |rootDirectory| |prefix| - |createPrimitivePoly| |mapMatrixIfCan| |antiCommutator| |splitNodeOf!| - |conical| |conditionsForIdempotents| |eof?| |partialFraction| - |nonSingularModel| |orthonormalBasis| |reduction| |cCosh| |getMeasure| - |union| |expandPower| |clearTheIFTable| |internalIntegrate0| - |lieAdmissible?| |exponential| |leftOne| |airyAi| |primlimitedint| - |removeRoughlyRedundantFactorsInContents| |tubePoints| |s17dhf| - |scopes| |message| |approxSqrt| |outputFixed| |chainSubResultants| - |ipow| |plus!| |iiatanh| |permutationGroup| |zeroOf| |entry?| |diff| - |chvar| |fortranInteger| |selectPolynomials| |f07fef| |viewport2D| - |minGbasis| |besselY| |outputArgs| |readIfCan!| |psolve| |close| - |factorByRecursion| |packageCall| |multiplyCoefficients| - |doubleComplex?| |nullary| |decomposeFunc| |henselFact| |numerator| - |recip| |f02bjf| |prefixRagits| |exprToGenUPS| |f01qcf| |lazyPrem| - |typeLists| |reindex| |seriesSolve| |distribute| |empty| |node| - |cAtan| |display| |asimpson| |setTex!| |bumprow| |exp| |deepExpand| - |remainder| |twist| |f02agf| |adaptive| |algintegrate| |isOp| - |makeUnit| |adaptive3D?| |unrankImproperPartitions1| |powmod| - |OMunhandledSymbol| |cons| |rangePascalTriangle| - |standardBasisOfCyclicSubmodule| |cCoth| |f04atf| - |nextLatticePermutation| |setValue!| |f01ref| |triangular?| - |exportedOperators| |algebraicVariables| |completeSmith| |removeSinSq| - |integralRepresents| |polyRDE| |sn| |genericRightTrace| |outerProduct| - |divisorCascade| |surface| |pleskenSplit| |getProperty| - |removeConstantTerm| |hasSolution?| |branchIfCan| |getVariableOrder| - |mainCoefficients| |newLine| |polyred| |parent| |exists?| |OMputError| - |monicRightDivide| |quasiMonicPolynomials| |shiftRoots| |harmonic| - |input| |addMatchRestricted| |fortranComplex| |modifyPointData| - |sequences| UTS2UP |f02wef| |asinIfCan| |trailingCoefficient| |f04axf| - |library| |lazyResidueClass| |complete| |quadraticForm| - |roughUnitIdeal?| |red| |mapUnivariateIfCan| |atanhIfCan| - |drawComplexVectorField| |permutations| |iisqrt2| |subPolSet?| - |rightTraceMatrix| |trivialIdeal?| |character?| |updateStatus!| - |source| |fixedPoints| |solveRetract| |symmetricPower| |mapdiv| - |rootOfIrreduciblePoly| |swapColumns!| |maxPoints| |hasoln| |implies| - |airyBi| |ddFact| |mainVariable| |complexEigenvalues| |power| - |rootSplit| |highCommonTerms| |laurentRep| |imagE| |diagonalMatrix| - |second| |stoseInvertible?sqfreg| |quickSort| |pushFortranOutputStack| - |algebraicDecompose| |jacobiIdentity?| |simpsono| |iiasinh| |set| - |representationType| |swapRows!| |viewThetaDefault| |setMaxPoints3D| - |third| |stFuncN| |sPol| |s19aaf| |OMgetEndAttr| |baseRDE| |signature| - |parseString| |s15adf| |nextPrime| |nonQsign| |resetNew| |qualifier| - |flagFactor| |horizConcat| |alphanumeric| |multisect| |sum| - |permutation| |c06gqf| |redpps| |direction| |f01rdf| |rarrow| - |alternative?| |target| |popFortranOutputStack| |OMputEndAttr| - |relerror| |cAsinh| |clipWithRanges| |denomRicDE| - |useSingleFactorBound?| |crushedSet| |reduceLODE| - |removeSuperfluousQuasiComponents| |bezoutMatrix| |shade| - |changeMeasure| |printStats!| |stop| |rdregime| |leadingBasisTerm| - |expextendedint| |s01eaf| |initTable!| |mkcomm| |octon| - |factorGroebnerBasis| |inverseLaplace| |void| |tab1| |iiacsc| - |hasTopPredicate?| |changeVar| |wronskianMatrix| - |functionIsOscillatory| |groebnerIdeal| |removeCoshSq| - |var2StepsDefault| |systemCommand| |useEisensteinCriterion| |d01gbf| - |e01bff| |Gamma| |s17def| |xCoord| |lp| |identification| |isImplies| - |trueEqual| |unitNormal| |balancedFactorisation| |presuper| |round| - |sub| |enumerate| |makeViewport3D| |integerBound| |ravel| |compBound| - |copies| |chiSquare| |coerceL| |iCompose| |unitVector| |reopen!| - |setMinPoints3D| |imaginary| |reshape| |degreeSubResultant| - |cycleTail| |integrate| |normal| |rootPower| |partitions| |newReduc| - |RemainderList| |recoverAfterFail| |insertMatch| |coth2trigh| - |constantIfCan| |solveInField| |optimize| |rightAlternative?| - |filename| |zeroDimensional?| |leastMonomial| |branchPointAtInfinity?| - |showScalarValues| |diag| |rationalIfCan| |setfirst!| - |fortranLinkerArgs| |OMputAtp| |logical?| |eq?| |numFunEvals| - |setlast!| |colorFunction| |exQuo| |symbolIfCan| |exactQuotient| - |setright!| |integer?| |pole?| |parse| |kovacic| |difference| - |optional?| |members| |cycles| |goodPoint| |cond| |quotientByP| - |root?| |decimal| |internalLastSubResultant| |primintfldpoly| - |mightHaveRoots| |safetyMargin| |SturmHabichtMultiple| - |startPolynomial| |e02ddf| |leftMinimalPolynomial| |jordanAlgebra?| - |unitNormalize| |OMputString| |linearDependenceOverZ| |kroneckerDelta| - |dn| |iisinh| |true| |associator| |OMputInteger| |exprToXXP| - |scaleRoots| |complexSolve| |resize| |edf2ef| |startTable!| - |stirling1| |polCase| |clip| |bfEntry| |inputBinaryFile| - |rightRegularRepresentation| |approxNthRoot| |summation| - |removeRedundantFactorsInPols| |modularGcd| |yellow| - |reducedDiscriminant| |anfactor| |genericLeftNorm| |pointData| - |primeFactor| |lazyPseudoQuotient| |linearPart| |expt| - |reducedContinuedFraction| |musserTrials| |groebgen| |safeFloor| - |cSech| |hermite| |reorder| |element?| |basisOfMiddleNucleus| - |eigenvector| |linSolve| |isPower| |string?| |f02akf| |graphCurves| - |factors| |ListOfTerms| |augment| |leftRecip| |hostPlatform| - |writeUInt8!| |maxColIndex| |drawComplex| |setRealSteps| - |nextNormalPoly| |c06fpf| |OMReadError?| |separant| |contains?| - |d02cjf| |resultantEuclideannaif| |bitLength| |Lazard2| - |doubleResultant| |nextItem| |unprotectedRemoveRedundantFactors| - |ratDsolve| |OMUnknownSymbol?| |alphabetic?| |curry| |rationalPoint?| - |clipPointsDefault| |polygon?| |delete| |primPartElseUnitCanonical| - |explicitlyEmpty?| |index| |rationalApproximation| |hitherPlane| - |leastPower| |arg1| |putGraph| |mapDown!| |e02agf| |objectOf| - |roughSubIdeal?| |increase| |const| |false| |sts2stst| |comparison| - |arg2| |f01brf| |univariate?| |algebraicSort| |strongGenerators| - |inputOutputBinaryFile| |d01amf| |df2st| |cotIfCan| |range| - |startTableGcd!| |algebraicOf| |selectODEIVPRoutines| |pair| |randnum| - |asechIfCan| |repeating?| |fortranDoubleComplex| |binomial| |padecf| - |rur| |conditions| |pmComplexintegrate| |externalList| |realRoots| EQ - |s18aff| |contractSolve| |distFact| |torsion?| |badValues| |value| - |sinh2csch| |match| |setScreenResolution| |selectsecond| - |LazardQuotient2| |cyclotomicDecomposition| |sumOfDivisors| - |irreducible?| |listexp| |heapSort| |#| |distdfact| |commutator| - |removeRedundantFactors| |result| |monicCompleteDecompose| |lintgcd| - |stoseInvertibleSetsqfreg| |iicoth| |indicialEquation| |ParCondList| - |limitPlus| |mathieu11| |supDimElseRittWu?| |groebner| - |LowTriBddDenomInv| |tab| |outputMeasure| |multinomial| - |palginfieldint| |rationalPoints| |polyPart| |orbits| |minset| - |binarySearchTree| |OMconnInDevice| |roughBasicSet| |reset| - |closedCurve?| |iiacot| |stopTableInvSet!| |OMopenString| |minrank| - |principalIdeal| |resultantReduit| |tubePlot| |sechIfCan| |charClass| - |represents| |lazyPseudoDivide| |upperCase!| |dualSignature| |column| - |factorAndSplit| |att2Result| |fprindINFO| |d03faf| |printInfo| - |wholeRadix| |write| |drawStyle| |rootKerSimp| |rischNormalize| - |selectOptimizationRoutines| |extractPoint| |identitySquareMatrix| - |e02baf| |limitedIntegrate| |linearlyDependent?| |save| |csc2sin| - |halfExtendedResultant2| |dictionary| |UP2ifCan| |computePowers| - |subResultantGcd| |branchPoint?| |sturmVariationsOf| |monicModulo| - |negative?| |plotPolar| |halfExtendedSubResultantGcd1| |push| |imagI| - |lepol| |e02adf| |categoryFrame| |sqfrFactor| |prime| |log10| - |oddintegers| |irreducibleFactor| |quasiComponent| |byteBuffer| - |subResultantGcdEuclidean| |OMgetEndApp| |zero?| |iiasech| |copyInto!| - |s19acf| |recur| |bitand| |gensym| |iiGamma| |elements| |variable?| - |deref| |particularSolution| |tubePointsDefault| |splitDenominator| - |recolor| |cyclotomic| |roughBase?| |Lazard| |bitior| |simpson| - |OMserve| |elliptic?| |cExp| |setTopPredicate| |isTerm| |taylorIfCan| - |problemPoints| |generator| |setleaves!| |palgextint| |pToDmp| - |tanSum| |directSum| |leftExactQuotient| |replace| |noKaratsuba| - |critpOrder| |generalInfiniteProduct| |rightMinimalPolynomial| - |hdmpToDmp| |multiple?| |zeroSetSplitIntoTriangularSystems| - |zeroMatrix| |lazyIntegrate| |submod| |push!| |createNormalElement| - |OMencodingXML| |forLoop| |csubst| |brillhartIrreducible?| |number?| - |SturmHabichtCoefficients| |generalizedContinuumHypothesisAssumed| - |reducedSystem| |cyclicCopy| |physicalLength!| |factorSquareFree| - |shellSort| |logIfCan| |wreath| |tryFunctionalDecomposition| - |denominators| |level| |viewpoint| |iterationVar| - |resultantReduitEuclidean| |charpol| |c06gcf| |f04arf| |subSet| |inf| - |odd?| |nextsubResultant2| |divisor| |complexEigenvectors| - |componentUpperBound| |d01ajf| - |rewriteSetByReducingWithParticularGenerators| |multiplyExponents| - |outputFloating| |aromberg| |positiveRemainder| |bubbleSort!| - |setFormula!| |palgintegrate| |bindings| |anticoord| |asinhIfCan| - |lineColorDefault| |integers| |e02ahf| |complexNormalize| |coerceP| - |fracPart| |internalInfRittWu?| |c05adf| |generalizedEigenvector| - |qroot| |noLinearFactor?| |mainPrimitivePart| |search| |c06fqf| - |selectSumOfSquaresRoutines| |outputSpacing| |composite| |e02daf| - |makeSin| |antisymmetric?| |ranges| |s13aaf| |matrix| |mdeg| |numer| - |outputAsTex| |lazyGintegrate| |singularAtInfinity?| |frobenius| - |elliptic| |oneDimensionalArray| |writeBytes!| |expressIdealMember| - |algDsolve| |rational?| |denom| |iisin| |findCycle| - |factorSquareFreeByRecursion| |RittWuCompare| |discriminantEuclidean| - |getStream| |c06gsf| |companionBlocks| |d02gbf| |e01bgf| |adjoint| - |slex| |graphs| |viewDefaults| |leftNorm| |delta| |bezoutResultant| - |FormatArabic| |stoseLastSubResultant| Y |complexLimit| |rCoord| |pi| - |rightExactQuotient| |initializeGroupForWordProblem| |e04naf| - |toseInvertibleSet| |iExquo| |coefChoose| |rotatez| |inconsistent?| - |pow| |startTableInvSet!| |infinity| |categories| |setAdaptive| - |expandTrigProducts| |modifyPoint| |cosSinInfo| |expint| F - |numberOfHues| |operations| |sizePascalTriangle| |idealSimplify| - |setProperty!| |move| |arbitrary| |c06fuf| |c06eaf| |fractRagits| - |localUnquote| |leadingIndex| |eigenMatrix| |diagonal?| |computeInt| - |changeNameToObjf| |child| |largest| |validExponential| |coerceImages| - |float?| |backOldPos| |shift| ~= |decrease| |headReduce| - |numberOfMonomials| |lastSubResultantElseSplit| |kernel| |null| - |paraboloidal| |BasicMethod| |nary?| |clipSurface| |biRank| - |polarCoordinates| |coerce| |select!| |predicates| |edf2fi| |mindeg| - |draw| |not| |reify| |usingTable?| |ocf2ocdf| |tube| |complexRoots| - |badNum| |construct| |reseed| |nullity| |exp1| |leadingExponent| |and| - |upperCase?| |relationsIdeal| |getBadValues| |conjugate| |pop!| - |lambda| |setRow!| |rightRankPolynomial| |collectQuasiMonic| |bits| - |lastSubResultant| |or| |zeroDimPrimary?| |supRittWu?| |dAndcExp| - |currentSubProgram| |makeop| |var2Steps| |fixPredicate| |totalDegree| - |curveColor| |radicalRoots| |xor| |leftGcd| |extendIfCan| - |principalAncestors| |complexIntegrate| - |rewriteIdealWithQuasiMonicGenerators| |prinshINFO| - |genericRightTraceForm| |bat1| |position!| |determinant| |showSummary| - |case| |dflist| |square?| |innerint| |blankSeparate| |bracket| - |cyclePartition| |imports| |resetVariableOrder| |rootNormalize| - |inGroundField?| |Zero| |makeYoungTableau| |outlineRender| - |internalIntegrate| |zeroSetSplit| |numberOfFractionalTerms| |obj| - |find| |isobaric?| |lhs| |conjugates| |unknownEndian| |isConnected?| - |showAttributes| |One| |linkToFortran| |OMclose| |basisOfLeftNucleus| - |internalAugment| |semiLastSubResultantEuclidean| |unaryFunction| - |e02bcf| |pr2dmp| |rhs| |initials| |lastSubResultantEuclidean| |cache| - |measure2Result| |firstDenom| |currentCategoryFrame| |commutative?| - |name| |cycleRagits| |splitSquarefree| |f02ajf| |preprocess| - |meshPar2Var| |po| |iifact| |factorPolynomial| |pseudoDivide| - |stopMusserTrials| |body| |lighting| |checkRur| - |univariatePolynomials| |evenlambert| |messagePrint| |intensity| - |iicos| |distance| |eulerE| |atanIfCan| |extendedIntegrate| - |insertionSort!| |s17dcf| |delay| |build| |writeByte!| - |dimensionOfIrreducibleRepresentation| |allRootsOf| - |resultantEuclidean| |minRowIndex| |primitivePart| |cRationalPower| - |semiResultantReduitEuclidean| |closed?| |addmod| |even?| |split| - |makingStats?| |cAcsch| |diagonals| |radicalEigenvalues| |ODESolve| - |aQuadratic| |inHallBasis?| |logpart| |central?| |tableau| - |OMgetEndBVar| |cschIfCan| |mainSquareFreePart| |vedf2vef| |depth| - |showIntensityFunctions| |cfirst| |iicot| |associates?| |setLength!| - |factorOfDegree| |ramified?| |tanhIfCan| |userOrdered?| - |showTheRoutinesTable| |denomLODE| |leadingCoefficientRicDE| |vspace| - |sinhIfCan| |matrixGcd| |f01maf| |port| |getPickedPoints| |sh| - |internalSubPolSet?| |Nul| |iitan| |tubeRadiusDefault| - |intermediateResultsIF| |leftFactorIfCan| |quadraticNorm| - |OMconnectTCP| |superHeight| F2FG |monomialIntegrate| |getCurve| - |finiteBasis| |univariatePolynomial| |Ci| |extendedint| |t| - |extractIfCan| |ldf2vmf| |exquo| |squareTop| |error| - |stoseInternalLastSubResultant| |stoseInvertible?| |testDim| |crest| - |explimitedint| |btwFact| |wrregime| |lifting| |div| |primitive?| - |nthFactor| |infinityNorm| |declare| |c05nbf| |region| |assert| - |output| |lowerCase?| |readBytes!| |rightScalarTimes!| |quo| - |superscript| |explicitEntries?| |redPo| |mappingAst| - |sortConstraints| GF2FG |calcRanges| |connectTo| |quatern| - |checkForZero| |ScanFloatIgnoreSpacesIfCan| |SturmHabicht| |setrest!| - |omError| |dfRange| |selectAndPolynomials| |rem| |coHeight| |e04ycf| - |setButtonValue| |pointColorPalette| |OMgetEndError| |fractionPart| - |s17aff| |digit| |head| |more?| |f04qaf| |critT| - |ScanFloatIgnoreSpaces| |call| |bandedJacobian| |isOpen?| - |positiveSolve| |cyclicParents| |fullPartialFraction| |tracePowMod| - |squareMatrix| |mapUp!| |firstUncouplingMatrix| |f02bbf| |iiasin| - |invertible?| |viewWriteAvailable| |varselect| |coefficient| - |cycleSplit!| |currentScope| |connect| |primitiveElement| - |hyperelliptic| |rightLcm| |binding| |pack!| |binaryFunction| - |rightFactorCandidate| |next| |genericLeftMinimalPolynomial| - |exactQuotient!| |rotate| |c06ekf| |tanNa| |getMultiplicationTable| - |linears| |sparsityIF| |mkAnswer| |tan2cot| |eigenvalues| - |rightQuotient| |floor| |lazyVariations| |trapezoidal| |finite?| - |leftCharacteristicPolynomial| |d02kef| |maxdeg| |numberOfOperations| - LODO2FUN |rootSimp| |postfix| |singular?| |sumSquares| |phiCoord| - |rename| |li| |solid?| |acosIfCan| |predicate| |cyclicEntries| |hcrf| - |midpoint| |numberOfPrimitivePoly| |virtualDegree| |semicolonSeparate| - |lquo| |ratpart| |setStatus| |prem| |null?| |bitCoef| |e02gaf| - |mapGen| |rowEchelonLocal| |mainContent| |groebner?| |entries| - |makeResult| |reciprocalPolynomial| |appendPoint| |remove!| |qfactor| - |roman| BY |zeroVector| |perfectSquare?| |leftFactor| |randomR| - |viewport3D| |basisOfCenter| |setMinPoints| |imagj| |OMsend| - |critBonD| |tableForDiscreteLogarithm| |c02aff| |normalizeIfCan| - |intChoose| |numberOfNormalPoly| |decompose| |htrigs| |pseudoQuotient| - |startStats!| |subTriSet?| |rightFactorIfCan| |diophantineSystem| - |generalPosition| |sizeLess?| |mathieu23| |hexDigit?| |rspace| - |localIntegralBasis| |pomopo!| |lfextlimint| |constantLeft| |char| - |constantKernel| |nextIrreduciblePoly| |every?| |lfextendedint| - |point?| |dec| |changeThreshhold| |e02ajf| |insert!| |associative?| - |purelyAlgebraicLeadingMonomial?| |subResultantsChain| |selectfirst| - |interReduce| |removeZero| |parameters| |f01bsf| - |SturmHabichtSequence| |dimensionsOf| |plusInfinity| - |fractionFreeGauss!| |lo| |OMbindTCP| |OMputEndAtp| |bivariate?| - |rightZero| |completeHensel| |radicalSolve| |minusInfinity| - |padicallyExpand| |setOrder| |romberg| |halfExtendedSubResultantGcd2| - NOT |divisors| |d01apf| |quadratic?| |less?| |cardinality| - |binaryTree| |coordinate| |partition| |incr| |geometric| OR |option?| - |imagi| |singularitiesOf| |deepestInitial| |makeGraphImage| - |lowerCase| |graphStates| |showTypeInOutput| |hi| |makeSeries| AND - |degree| |just| |removeSquaresIfCan| |OMputObject| |float| - |thenBranch| |constantToUnaryFunction| |rk4f| |returns| |mapExpon| - |primintegrate| |rewriteSetWithReduction| |d02raf| |OMreadStr| - |infix?| |seed| |conditionP| |ceiling| |fillPascalTriangle| - |solveLinearlyOverQ| |getSyntaxFormsFromFile| - |linearlyDependentOverZ?| |mergeFactors| |generic?| |sylvesterMatrix| - |mask| |print| |type| |pToHdmp| |minColIndex| |divideExponents| - |listOfLists| |space| |getOperator| |ffactor| |flatten| - |zeroSquareMatrix| |torsionIfCan| |resolve| |realElementary| |lookup| - |eyeDistance| |zoom| |addPointLast| |condition| |antiAssociative?| - |readUInt16!| |LiePoly| |primitivePart!| |nilFactor| |ksec| - |singleFactorBound| |genericLeftTraceForm| |intcompBasis| |subNode?| - |setClipValue| |rischDEsys| |leastAffineMultiple| |pushdown| |hasHi| - |revert| |duplicates| |pdf2ef| |initiallyReduce| |OMsupportsSymbol?| - |iiacosh| |rank| |s14abf| |mainValue| |divergence| |OMsetEncoding| - |twoFactor| |scalarTypeOf| |myDegree| |cycleEntry| - |removeRoughlyRedundantFactorsInPol| |routines| |s17akf| |normalise| - |euclideanNormalForm| |e02def| |bernoulliB| |f04mcf| - |createGenericMatrix| |credPol| |someBasis| |fortranReal| |setelt!| - |satisfy?| |contours| GE |comment| |clearTheSymbolTable| - |shallowExpand| |factorFraction| |inR?| |radPoly| |invmultisect| * - |index?| |s18acf| |extractProperty| GT |failed?| |linearMatrix| - |algSplitSimple| |subst| |lSpaceBasis| |basisOfLeftNucloid| - |normInvertible?| |orbit| |generalSqFr| |abelianGroup| LE |tan2trig| - |iiacsch| |argument| |modularGcdPrimitive| |generalizedEigenvectors| - |redPol| |pushdterm| |argumentListOf| |showAllElements| LT |cartesian| - |queue| |transcendentalDecompose| |semiSubResultantGcdEuclidean2| - |unitCanonical| |d01bbf| |patternVariable| = |squareFreeLexTriangular| - |e01bhf| |eigenvectors| |sizeMultiplication| |setFieldInfo| |simplify| - |lists| |denominator| |coleman| |listLoops| |maximumExponent| |imagJ| - |deleteRoutine!| |isList| |constant?| |generalLambert| - |genericLeftTrace| |hex| < |powern| |stoseInvertibleSetreg| - |transpose| |identityMatrix| |leftDiscriminant| |is?| - |leftAlternative?| |exponents| |createZechTable| > |symbolTableOf| - |leftMult| |LyndonWordsList1| |symmetricRemainder| - |radicalOfLeftTraceForm| |cSinh| |euler| |objects| |iidprod| |pade| - |separateDegrees| <= |genericLeftDiscriminant| |s21bdf| - |wordInStrongGenerators| |getButtonValue| |findConstructor| |base| - |acschIfCan| |integralMatrixAtInfinity| |nextPrimitivePoly| - |multMonom| >= |normal?| |radix| |mapUnivariate| - |mainDefiningPolynomial| |addPoint| |lift| |structuralConstants| - |compile| |univariatePolynomialsGcds| |inverseIntegralMatrix| |lfunc| - |d01alf| |tubeRadius| |lagrange| |factorials| |retract| |accuracyIF| - |hclf| |solve| |reduce| |lambert| |sup| |laguerreL| |chebyshevT| - |stoseIntegralLastSubResultant| |ode1| |property| |opeval| |fmecg| - |thetaCoord| |setref| |bumptab1| |powerSum| |absolutelyIrreducible?| + - |scan| |leftRegularRepresentation| |putColorInfo| |cyclic| - |generalizedInverse| |invertIfCan| |deepestTail| |ip4Address| - |nonLinearPart| |critMTonD1| |e02bbf| - |graphImage| |getGoodPrime| - |sort| |genericRightMinimalPolynomial| |merge!| |outputForm| - |aQuartic| |parents| |useNagFunctions| |e01sff| |diagonal| / - |wholePart| |toseSquareFreePart| |datalist| |units| |contract| - |numberOfDivisors| |nil?| |frst| |newSubProgram| |leftRank| - |completeHermite| |arrayStack| |pastel| |setchildren!| - |exprHasWeightCosWXorSinWX| |whatInfinity| |fixedPoint| - |createPrimitiveNormalPoly| |bag| |sech2cosh| |associatedSystem| - |OMgetObject| |top| |primeFrobenius| |OMwrite| |bright| |collectUnder| - |makeFloatFunction| |stFunc2| |swap!| |totalLex| |idealiser| |prime?| - |random| |writable?| |dihedralGroup| |mirror| |iitanh| |prinb| |plus| - |elColumn2!| |closeComponent| |compound?| |bandedHessian| |clearCache| - |list| |triangSolve| |prod| |subresultantVector| - |completeEchelonBasis| |iiasec| |bringDown| |point| |key| |generic| - |function| |Vectorise| |f02aaf| |code| |car| |integralAtInfinity?| - |zeroDim?| |birth| |previous| |lowerPolynomial| |acscIfCan| |totolex| - |monic?| |any?| |scripted?| |cdr| |factorSFBRlcUnit| - |basisOfRightNucleus| |extendedEuclidean| |showArrayValues| - |getIdentifier| |readInt8!| |lowerCase!| |iiabs| |eval| - |setDifference| |byte| |insertTop!| |elementary| |nthFractionalTerm| - 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|partialNumerators| |getGraph| |iicsc| |raisePolynomial| |integer| - |lazy?| |subResultantChain| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - |commutative|)
\ No newline at end of file + |Record| |Union| |seriesSolve| |popFortranOutputStack| |lazyEvaluate| + |sinh| |makeYoungTableau| |reduce| |intermediateResultsIF| + |gcdPrimitive| |innerSolve| |restorePrecision| |generators| + |lazyVariations| |ncols| |oneDimensionalArray| |getMatch| |cosh| + |fortranCharacter| |outputAsFortran| |style| |inverseLaplace| |edf2ef| + |limitPlus| |read!| |UnVectorise| |tanh| |splitDenominator| + |subtractIfCan| |normalizedAssociate| |basisOfLeftAnnihilator| + |OMconnOutDevice| |exptMod| |toseSquareFreePart| |newLine| + |commutativeEquality| |fillPascalTriangle| |coth| |factorAndSplit| + |e01bhf| |partialFraction| |perfectSquare?| |cycleRagits| |c02aff| + |symbolTable| |toseInvertibleSet| |sign| |datalist| |gcdcofact| |sech| + |label| |selectfirst| |parametersOf| |tryFunctionalDecomposition| + |isExpt| |d01gaf| |diagonalMatrix| |reducedQPowers| |move| |copies| + |csch| |bat| |quasiRegular| |truncate| |component| |tail| + |zeroDimPrimary?| |entry?| |normal?| |symmetricRemainder| + |padicFraction| |asinh| |basisOfMiddleNucleus| |member?| |Is| + |areEquivalent?| |upperCase?| |squareFreePart| |se2rfi| + |recoverAfterFail| |outputList| |resultantEuclidean| |acosh| |rules| + |rarrow| |dihedralGroup| |twoFactor| |isPlus| + |integralBasisAtInfinity| |unvectorise| |innerSolve1| |isEquiv| + |multiplyExponents| |lifting1| |atanh| |head| |showRegion| |goodPoint| + |unknown| |d02bbf| |point| |purelyTranscendental?| |extractClosed| + |binaryFunction| |roughSubIdeal?| |satisfy?| |rootPoly| |previous| + |acoth| |karatsubaDivide| |outlineRender| |leader| + |nextPrimitiveNormalPoly| |plotPolar| |getGoodPrime| |mathieu11| + |createNormalPoly| |clearDenominator| |recolor| |asech| + |indiceSubResultant| |rewriteIdealWithRemainder| |leftFactorIfCan| + |constructor| |OMsupportsCD?| |contract| |boundOfCauchy| |trapezoidal| + |divideIfCan| |byte| |d03edf| |distribute| |acoshIfCan| + |fixedPointExquo| |series| |normalizeIfCan| |startTable!| |iExquo| + |fill!| |tubePoints| |option| |resetBadValues| |multiple| |att2Result| + |OMencodingBinary| |nonSingularModel| |reverse!| + |topFortranOutputStack| |zCoord| ** |infinite?| |polyred| |d01ajf| + |applyQuote| |removeSinhSq| |writeBytes!| |children| |denominators| + |concat!| |leftFactor| |stoseInvertible?sqfreg| + |radicalOfLeftTraceForm| |arbitrary| |eigenvectors| + |solveLinearlyOverQ| |tablePow| |int| |mapCoef| |gramschmidt| + |linearlyDependent?| |diff| |withPredicates| |c06ebf| + |transcendenceDegree| |critM| |interReduce| |scalarTypeOf| |polyRicDE| + |dmpToHdmp| |min| |genericRightMinimalPolynomial| |supRittWu?| + |complex?| |insertMatch| |OMgetApp| |eigenvector| |alternative?| + |complexExpand| |rational| |linearMatrix| |uncouplingMatrices| + |rightTrim| |removeCosSq| |rightFactorCandidate| |radix| |isMult| + |internalIntegrate| |aromberg| |mirror| |quotientByP| |pushNewContour| + |increase| |ignore?| |setelt!| |minPoints3D| |leftTrim| |tValues| + |iiatan| |squareFreePrim| |s19adf| |bumptab| |quadraticNorm| + |changeMeasure| |f02fjf| |compose| |moreAlgebraic?| |copyInto!| + |iipow| |clearTheSymbolTable| |more?| |bitTruth| |rightScalarTimes!| + |addPointLast| |mindeg| |rombergo| |finite?| |rk4f| |unary?| + |fprindINFO| |associator| |scale| |makeprod| |hasoln| |setClosed| + |cSinh| |unexpand| |kind| |besselK| |btwFact| |genericPosition| |max| + |empty| |orthonormalBasis| |create3Space| |universe| |cschIfCan| + |consnewpol| |incrementKthElement| |checkPrecision| |op| |trueEqual| + |subresultantSequence| |perfectSqrt| |applyRules| |torsion?| + |resultant| |parent| |coth2trigh| |test| |eulerE| |simpleBounds?| + |laplace| |composites| |viewpoint| |specialTrigs| |setProperties!| + |atom?| |genericLeftMinimalPolynomial| |c06fuf| |buildSyntax| + |selectAndPolynomials| |normal01| |chainSubResultants| |myDegree| + |csc2sin| |removeRoughlyRedundantFactorsInPols| |mainContent| |limit| + |characteristicPolynomial| |setLabelValue| |printStatement| + |nextIrreduciblePoly| |pattern| |positiveRemainder| |transcendent?| + |initiallyReduced?| |rootsOf| |heapSort| |light| + |indiceSubResultantEuclidean| |recip| |magnitude| |root?| |eq| + |algSplitSimple| |reify| |rowEchLocal| |setAdaptive| |mesh| |maxint| + |printInfo| |ranges| |principalIdeal| |shallowExpand| |iter| + |OMconnectTCP| |ramifiedAtInfinity?| |critB| |antiAssociative?| + |prefix| |rangePascalTriangle| |bit?| |union| |s19acf| FG2F |nodeOf?| + |OMcloseConn| |semiSubResultantGcdEuclidean1| |printStats!| + |character?| |s14baf| |elementary| |leftNorm| |cartesian| + |selectFiniteRoutines| |prepareSubResAlgo| |OMputString| |message| + |OMputInteger| |solid| |implies| |color| |refine| + |primPartElseUnitCanonical| |parts| |returns| |f07fdf| |qualifier| + |stosePrepareSubResAlgo| |freeOf?| |vark| |coordinates| |putColorInfo| + |viewPhiDefault| |getMultiplicationTable| |identityMatrix| + |semiResultantEuclideannaif| |reducedContinuedFraction| |square?| + |cSin| |wrregime| |superscript| |palglimint0| |meshFun2Var| |iomode| + |selectOrPolynomials| |neglist| |whileLoop| |internalZeroSetSplit| + |basisOfCommutingElements| |overset?| |resetAttributeButtons| + |distdfact| |badValues| |hexDigit| |separant| |unitNormal| |close| + |OMputEndObject| |collectUnder| |setnext!| |SturmHabichtCoefficients| + |computeCycleEntry| |groebner?| |imagk| |surface| + |coercePreimagesImages| |node| |readUInt32!| |powers| |coHeight| + |duplicates| |bubbleSort!| |exp| |stirling2| |readUInt16!| + |createThreeSpace| |cons| |infix| |birth| |nthCoef| |atanIfCan| + |display| |irreducibleFactors| |idealiserMatrix| |trigs2explogs| + |halfExtendedResultant2| |cyclic| |normalized?| |expandTrigProducts| + |coefficient| |row| |resultantReduit| |operator| |exactQuotient| + |factorFraction| |lSpaceBasis| |airyBi| |updateStatus!| + |explicitlyEmpty?| |before?| |nand| |colorDef| |every?| |f02bjf| + |powerAssociative?| |outerProduct| |points| + |rightCharacteristicPolynomial| |relationsIdeal| |basisOfRightNucloid| + |nthFractionalTerm| |recur| |factor1| |s13aaf| |exprToXXP| |matrixGcd| + |rdregime| |symmetricTensors| |usingTable?| |bezoutResultant| + |seriesToOutputForm| |lexico| |flagFactor| |printInfo!| |lifting| + |mainMonomial| |transform| |leftUnit| |integerIfCan| |linears| + |standardBasisOfCyclicSubmodule| |innerint| |mapExpon| |input| |queue| + |rootDirectory| |sinIfCan| |irreducibleRepresentation| |s13adf| + |rightPower| |OMputSymbol| |source| |infiniteProduct| |library| + |interpolate| |scanOneDimSubspaces| |sample| + |generalizedContinuumHypothesisAssumed| |makeEq| |d01akf| |e01baf| + |overbar| |pleskenSplit| |leftDiscriminant| |balancedFactorisation| + |symmetricGroup| |setOfMinN| |e02bef| |rewriteIdealWithHeadRemainder| + |dictionary| |commutator| |sinh2csch| |iiperm| |findBinding| |repSq| + |musserTrials| |KrullNumber| |pdf2ef| |setFormula!| |fortranLiteral| + |basisOfCentroid| |subscriptedVariables| |lowerPolynomial| + |modifyPoint| |extendedIntegrate| |tubePlot| |makeFloatFunction| + |endOfFile?| |OMgetAttr| |basisOfLeftNucloid| |third| |list?| + |LiePoly| |entries| |contains?| |s17dgf| |signature| |sayLength| + |setPoly| |set| |subNodeOf?| |setright!| |c06ecf| |ocf2ocdf| |s17dhf| + |viewDeltaXDefault| |fortranDouble| |ddFact| |target| + |wordInStrongGenerators| |lfextendedint| |dmpToP| |sum| |e04ycf| + |split!| |normalDenom| |inR?| |leadingBasisTerm| |makeCrit| + |fixedPoints| |setErrorBound| |cycleSplit!| |pushFortranOutputStack| + |gensym| |iisech| |overlap| |f01maf| |optpair| |iprint| |exprex| + |getBadValues| |rationalApproximation| |s17agf| |explicitlyFinite?| + |horizConcat| |check| |scaleRoots| |mapmult| |pr2dmp| |testModulus| + |generalizedInverse| |sparsityIF| |cCoth| |stop| |void| |isOr| + |createLowComplexityNormalBasis| |rightNorm| |primitive?| + |createPrimitivePoly| |OMgetString| |pdct| |cot2trig| |FormatArabic| + |green| |operators| |systemCommand| |blankSeparate| |prefixRagits| + |rightDiscriminant| |totalfract| |primextintfrac| |ricDsolve| + |OMgetEndBind| |lp| |goodnessOfFit| |simplifyLog| |ravel| + |primintegrate| |stiffnessAndStabilityOfODEIF| |f01qef| |HenselLift| + |reducedSystem| |numberOfComposites| |setScreenResolution| + |removeRedundantFactors| |getProperty| |mapBivariate| |reshape| + |presuper| |mdeg| |nativeModuleExtension| |OMputEndBind| |argscript| + |UP2ifCan| |quotient| |algint| |gcdcofactprim| |is?| |lexGroebner| + |normal| |leftRankPolynomial| |transcendentalDecompose| + |palgintegrate| |initiallyReduce| |child?| |makeResult| + |primitivePart!| |d02cjf| |cosSinInfo| |insertionSort!| |sechIfCan| + |cos2sec| |sort!| |divideIfCan!| |solveRetract| |mainVariable| + |acscIfCan| |dimensions| |increasePrecision| |groebgen| |optimize| + |point?| |parse| |c06gbf| |normInvertible?| |socf2socdf| + |complexElementary| |getButtonValue| |top!| |autoReduced?| + |karatsubaOnce| |stFunc2| |integer?| |expextendedint| |conjugate| + |tube| |currentScope| |integralBasis| |update| |cond| + |exteriorDifferential| |setButtonValue| |alphanumeric| + |getPickedPoints| |binaryTournament| |linearAssociatedExp| + |invertIfCan| |getProperties| |aspFilename| |true| |iiGamma| + |vertConcat| |triangularSystems| |selectPDERoutines| |f04atf| + |initials| |OMParseError?| |OMlistCDs| |stoseInvertible?| + |hitherPlane| |selectMultiDimensionalRoutines| |d02gaf| |bracket| + |mapMatrixIfCan| |gcdPolynomial| |basisOfNucleus| |edf2df| + |reduceBasisAtInfinity| |stoseLastSubResultant| |kroneckerDelta| + |fortranCompilerName| |exprToGenUPS| |gderiv| |OMsupportsSymbol?| + |removeZeroes| |sncndn| |monicCompleteDecompose| |mkAnswer| + |complexForm| |charClass| |box| |rewriteSetWithReduction| |double?| + |testDim| |atrapezoidal| |ellipticCylindrical| |complexEigenvalues| + |selectsecond| |parabolic| |leftAlternative?| |round| |outputAsTex| + |ode2| |cyclicCopy| |computePowers| |reciprocalPolynomial| |pop!| + |removeConstantTerm| |one?| |s17dcf| |assign| |sturmSequence| |linear| + |subHeight| |hdmpToP| |permutationRepresentation| |clikeUniv| + |beauzamyBound| |totolex| |mainVariables| + |semiSubResultantGcdEuclidean2| |leftLcm| |droot| |orbit| + |complexRoots| |coth2tanh| |expint| |resultantEuclideannaif| + |setAttributeButtonStep| |safeFloor| |changeThreshhold| |polynomial| + |pole?| |dominantTerm| |decreasePrecision| |abs| |findConstructor| + |untab| |delete| |swap!| |precision| |meatAxe| |index| |multisect| + |duplicates?| |s01eaf| |cyclicGroup| |chebyshevU| |dihedral| |connect| + |perfectNthPower?| |pointColorPalette| |cyclePartition| |sh| + |capacity| |lastSubResultantEuclidean| |lintgcd| |deepestTail| |arg1| + |nextColeman| |mkPrim| |cCsc| |solveLinearPolynomialEquation| + |minimumDegree| |leastPower| |writeInt8!| |numberOfChildren| + |complexLimit| |arg2| |basisOfRightAnnihilator| |super| |elements| + |coefficients| |pair| |skewSFunction| |argumentList!| + |numericalOptimization| |setMinPoints| |LyndonWordsList| |stFunc1| + |intPatternMatch| |knownInfBasis| |f01qcf| |antiCommutator| |radPoly| + |var1Steps| |operation| |LazardQuotient2| |power| |value| |conditions| + |tan2cot| |d02raf| |represents| |mulmod| |physicalLength!| + |prolateSpheroidal| |#| |setRow!| |exponents| |f2df| |redmat| |match| + |c05pbf| |lazyGintegrate| EQ |s18adf| |complexSolve| |f2st| + |appendPoint| |weakBiRank| |hasSolution?| |result| |tanQ| + |unitCanonical| |e02ajf| |iiacosh| |pushucoef| |ipow| + |minimalPolynomial| |numberOfHues| |bitLength| |univariatePolynomials| + |pair?| |symFunc| |kovacic| |nthFactor| |createPrimitiveElement| + |unparse| |monic?| |nlde| |hypergeometric0F1| |reset| |permutation| + |cSech| |low| |notelem| |primitiveElement| |acschIfCan| |d03eef| + |unit| |totalLex| |internalSubPolSet?| |s19abf| |leviCivitaSymbol| + |createMultiplicationTable| |rightDivide| |subCase?| |toScale| |write| + |imports| |OMgetEndError| |oddInfiniteProduct| |rightRecip| |hMonic| + |pmComplexintegrate| |ef2edf| |genericRightNorm| |byteBuffer| |save| + |vconcat| |addiag| |splitNodeOf!| |bindings| |zeroSquareMatrix| + |radicalEigenvector| |rCoord| |putGraph| |log10| |numFunEvals3D| |any| + |npcoef| |charthRoot| |palgextint| |prem| |eigenvalues| + |replaceKthElement| |bitand| |just| |OMgetEndAttr| + |selectSumOfSquaresRoutines| |factorSquareFree| |defineProperty| + |iroot| |d01anf| |createZechTable| |rightExtendedGcd| |bitior| + |mainCharacterization| |setImagSteps| |cosh2sech| |numeric| |s14abf| + |invmultisect| |drawComplexVectorField| |equiv| |raisePolynomial| + |interval| |Gamma| |modularGcdPrimitive| + |rewriteIdealWithQuasiMonicGenerators| |radical| |reduceByQuasiMonic| + |infinityNorm| |biRank| |f01qdf| |sec2cos| |prepareDecompose| + |makeViewport2D| |lfinfieldint| |extendedEuclidean| |OMgetFloat| + |e04jaf| |aQuadratic| |generator| |froot| |dec| |evenlambert| |bag| + |flexibleArray| |difference| |safeCeiling| + |noncommutativeJordanAlgebra?| |OMgetInteger| |ratDsolve| + |generalLambert| |approxSqrt| |fglmIfCan| |genericLeftNorm| + |scalarMatrix| |Nul| |imagK| |rotate!| |setref| |randomLC| |bringDown| + |addPoint2| |GospersMethod| |rspace| |curve?| |pToDmp| |externalList| + |firstUncouplingMatrix| |halfExtendedSubResultantGcd2| + |repeatUntilLoop| |factorset| |ScanFloatIgnoreSpacesIfCan| + |roughBasicSet| |iiacos| |anticoord| |cyclicEqual?| |shiftRight| + |maxColIndex| |completeSmith| |outputFloating| + |subResultantGcdEuclidean| |gethi| |readLine!| |maxIndex| |drawCurves| + |OMputEndApp| |torsionIfCan| |isAbsolutelyIrreducible?| + |stoseSquareFreePart| |search| |radicalSimplify| |doubleComplex?| + |baseRDE| |createNormalElement| |index?| |null?| |axes| |elseBranch| + |OMUnknownSymbol?| |removeSquaresIfCan| |edf2efi| |outputSpacing| + |integralLastSubResultant| |polarCoordinates| |matrix| |shiftLeft| + |symmetricPower| |numer| |makeUnit| |showArrayValues| + |viewZoomDefault| |prinshINFO| |create| |setClipValue| |getlo| + |reduceLODE| |inHallBasis?| |denom| |eisensteinIrreducible?| |e01bgf| + |s17def| |generalizedEigenvectors| |monicDivide| |minimize| + |figureUnits| |permutations| |Beta| |divisors| |generalTwoFactor| + |messagePrint| |derivative| |cAsech| |eq?| Y |factorial| |c05nbf| + |evaluateInverse| |pi| |makeSketch| |s14aaf| |continuedFraction| + |minPoly| |pointData| |readByte!| |operations| |parabolicCylindrical| + |internalDecompose| |monomRDEsys| |infinity| |genericLeftTrace| + |removeSinSq| |categories| |createMultiplicationMatrix| |bytes| + |sech2cosh| |userOrdered?| |acothIfCan| |cap| |bumptab1| |drawComplex| + |leadingTerm| |qinterval| |chineseRemainder| |shift| |closedCurve?| F + |length| |normFactors| ~= |trapezoidalo| |bfKeys| |tanSum| |generic| + |coefChoose| |listOfMonoms| |SturmHabicht| |localIntegralBasis| + |scripts| |prinpolINFO| |coerce| |equality| |systemSizeIF| + |realElementary| |kernel| |f02bbf| |latex| |compdegd| |parseString| + |lazyPseudoRemainder| |construct| |OMgetError| |alphabetic?| |draw| + |linearAssociatedOrder| |realRoots| |rquo| |null| + |invertibleElseSplit?| |nthExponent| |genericRightTraceForm| |nullary| + |OMencodingXML| |getIdentifier| |asinhIfCan| |bitCoef| |mapdiv| + |pushuconst| |not| |OMgetEndApp| |cothIfCan| |setvalue!| |measure| + |powerSum| |s18acf| |logpart| |moebius| |adaptive3D?| |and| + |setProperty| |root| |composite| |rischDEsys| |showSummary| |iisqrt2| + |removeSuperfluousQuasiComponents| |showFortranOutputStack| |cubic| + |d01apf| |or| |OMputObject| |iiacot| |redPol| |numFunEvals| |select!| + |closedCurve| |realEigenvectors| |isAnd| |adjoint| |xor| |xCoord| + |modularFactor| |OMgetBVar| |patternMatchTimes| |obj| |modTree| + |showAttributes| |screenResolution3D| |s15aef| |invertibleSet| + |integralRepresents| |case| |minPoints| |associatedSystem| |pomopo!| + |showTheRoutinesTable| |rotatez| |lhs| |region| |cache| |palgint0| + |minus!| |hex| |Zero| |name| |intensity| |primeFactor| |cross| + |pureLex| |rhs| |setRealSteps| |ParCond| |directSum| |setPrologue!| + |cTanh| |One| |body| |cCot| |shrinkable| |lazyIrreducibleFactors| + |numericalIntegration| |compactFraction| |lookup| |s18aff| |Vectorise| + |OMputVariable| |subspace| |s15adf| |setrest!| |forLoop| |cycleLength| + |janko2| |subQuasiComponent?| |iiasin| |readInt8!| |getZechTable| + |relativeApprox| |merge| |tanAn| |evenInfiniteProduct| + |rootOfIrreduciblePoly| |basis| |curry| |mainMonomials| |pointPlot| + |pushdterm| |bat1| |leastAffineMultiple| |central?| |lineColorDefault| + |quadratic?| |e02gaf| |maxPoints3D| |sort| |roughEqualIdeals?| + |probablyZeroDim?| |decomposeFunc| |setelt| |shufflein| + |removeSuperfluousCases| |Aleph| |OMputBind| |euclideanSize| + |unrankImproperPartitions1| |thenBranch| |createIrreduciblePoly| + |c06frf| |setlast!| |extractProperty| |subPolSet?| |dimension| |leaf?| + |ode| |port| |zero?| |e02daf| |OMreadFile| |denomLODE| |bezoutMatrix| + |absolutelyIrreducible?| |sorted?| |polyRDE| |slex| + |algebraicCoefficients?| |stopTableInvSet!| |clearTable!| |fintegrate| + |bezoutDiscriminant| |combineFeatureCompatibility| |reflect| + |predicates| |inconsistent?| |random| |t| |associatedEquations| + |exquo| |rotatex| |lazyPseudoQuotient| |headAst| |lowerCase?| |error| + |s17dlf| |eyeDistance| |listYoungTableaus| |powern| |identification| + |div| |lfextlimint| |OMgetObject| |rootRadius| |assert| |aCubic| + |swapColumns!| |indicialEquationAtInfinity| |nextNormalPoly| + |normDeriv2| |iicos| |quo| |alphanumeric?| |nextPrime| + |toseLastSubResultant| |declare| |output| |dot| |kmax| |linear?| + |rationalPoint?| |f02aaf| |screenResolution| |leftTrace| |omError| + |csubst| |nullSpace| |contractSolve| |tableau| |mergeDifference| + |lowerCase!| |makeVariable| |rem| |position!| |setsubMatrix!| + |pushdown| |palgint| |mapGen| |upperCase| |showTheFTable| + |invertible?| |fortranLogical| |splitLinear| |henselFact| |squareFree| + |sn| |failed?| |primes| |rationalFunction| |karatsuba| |qelt| + |discreteLog| |makeSin| |OMreceive| |colorFunction| |call| + |stiffnessAndStabilityFactor| |lazyPquo| |irreducible?| + |rightTraceMatrix| |qsetelt| |PollardSmallFactor| |iiasech| |leftZero| + |discriminant| |leadingCoefficientRicDE| |edf2fi| |shade| |powmod| + |wordInGenerators| |pow| |xRange| |UpTriBddDenomInv| |multiEuclidean| + |OMopenString| |OMputEndError| |readBytes!| |symmetricDifference| + |quote| |graphState| |graphs| |yRange| |constantToUnaryFunction| + |constantLeft| |argumentListOf| |listBranches| |next| |mainKernel| + |characteristicSet| |iiabs| |zoom| |maxRowIndex| |zRange| |makeMulti| + |linearPart| |univcase| |brillhartIrreducible?| |clipPointsDefault| + |pushup| |maxPoints| |scan| |map!| |stoseInvertibleSetreg| |isImplies| + |primeFrobenius| |nonQsign| |rightUnit| |qsetelt!| |bothWays| + |OMgetEndBVar| |integralAtInfinity?| |c06ekf| |integralMatrix| + |dfRange| |determinant| |setEmpty!| |distFact| |li| |getExplanations| + |c06fpf| |s20acf| |distance| |f04adf| |cot2tan| |iFTable| + |rowEchelonLocal| |laurentIfCan| |OMputFloat| |rroot| |d02ejf| + |delete!| |fortranCarriageReturn| |hasHi| |OMread| |smith| + |genericRightTrace| |viewWriteAvailable| |setColumn!| |numerator| + |exQuo| |leaves| |leftRegularRepresentation| |zeroDimPrime?| |ord| + |nthr| |generalizedContinuumHypothesisAssumed?| |minrank| + |antisymmetric?| |countable?| |identity| |listexp| |trivialIdeal?| BY + |acsch| |startTableInvSet!| |categoryFrame| |numberOfComponents| + |quasiRegular?| |vspace| |regularRepresentation| |arity| + |functionIsContinuousAtEndPoints| |OMunhandledSymbol| + |quotedOperators| |constantKernel| |OMencodingSGML| |acotIfCan| |char| + |insertTop!| |viewDefaults| |makeGraphImage| |dark| |showAllElements| + |explogs2trigs| |constantOperator| |cCos| |asechIfCan| |enterInCache| + |polygon?| |plusInfinity| |mapSolve| |OMwrite| |resetNew| |nullary?| + |imaginary| |leftQuotient| |transpose| |subscript| |minusInfinity| + |graeffe| |lo| |dflist| |expt| |number?| |clipBoolean| |even?| + |zeroDim?| |tanNa| |groebnerIdeal| |lyndon?| |complete| + |unrankImproperPartitions0| |varselect| |e02ddf| |sinhcosh| + |factorPolynomial| |incr| |subTriSet?| |changeWeightLevel| NOT + |revert| |float| |numberOfMonomials| |deepCopy| |divisorCascade| + |e04mbf| |OMReadError?| |squareFreePolynomial| |hi| |besselY| + |epilogue| OR |simplifyExp| |escape| |numberOfImproperPartitions| + |genus| |stripCommentsAndBlanks| |signatureAst| |bipolarCylindrical| + |printTypes| |arguments| |curveColor| AND |symbolIfCan| |cExp| + |bivariateSLPEBR| |leftOne| |type| |real?| |swapRows!| |c05adf| + |rightMult| |mask| |resolve| |chebyshevT| |fractRadix| |presub| + |prologue| |cAcsc| |sqfrFactor| |summation| |mathieu22| |flatten| + |sinhIfCan| |virtualDegree| |minColIndex| |expintfldpoly| + |positiveSolve| |nextsubResultant2| |d01aqf| |condition| + |sortConstraints| |inverse| |euclideanGroebner| |unravel| + |semiResultantEuclidean2| |addMatch| |mainVariable?| |Si| + |listConjugateBases| |rationalPoints| |pastel| |degreeSubResultant| + |repeating?| |remainder| |extractPoint| |f04mcf| |lowerCase| + |factorList| |complexNumericIfCan| |rootSimp| |showScalarValues| + |split| |deriv| |bivariate?| |RittWuCompare| |leftMinimalPolynomial| + |iisinh| |removeCoshSq| |outputArgs| |LiePolyIfCan| + |computeCycleLength| |indicialEquations| GE |e04fdf| + |extendedResultant| |quasiMonic?| |mvar| |s17aef| |expIfCan| + |generalizedEigenvector| |mesh?| |SFunction| |cfirst| |comment| GT + |cAcot| |quadraticForm| |linkToFortran| |maximumExponent| + |extractIfCan| |pseudoDivide| |complement| |rightFactorIfCan| + |partialNumerators| |LyndonBasis| LE |weight| |fTable| |solveLinear| + |rischDE| |associatorDependence| |signAround| |gbasis| |harmonic| + |slash| |viewThetaDefault| |blue| * LT |setTopPredicate| + |lastSubResultantElseSplit| |sumOfKthPowerDivisors| |ListOfTerms| + |inf| |airyAi| |changeBase| |bottom!| |generalSqFr| + |shanksDiscLogAlgorithm| |multiple?| |extractBottom!| |pointLists| + |center| |identitySquareMatrix| |triangSolve| |divisor| |pol| + |separate| |removeRedundantFactorsInPols| |radicalRoots| |diagonal?| + |loopPoints| |stoseIntegralLastSubResultant| |divideExponents| + |updatF| |cyclicParents| |e02def| |typeList| |e01daf| |getCode| + |setchildren!| |nilFactor| |lfunc| = |fortranDoubleComplex| + |cycleTail| |rightZero| |unitsColorDefault| |gcdprim| |prime| + |exponentialOrder| GF2FG |indices| |primPartElseUnitCanonical!| + |ScanRoman| |commonDenominator| |groebSolve| |unmakeSUP| + |createGenericMatrix| |stopTable!| |singRicDE| + |semiDiscriminantEuclidean| |iicot| |flexible?| < |f04asf| |fortran| + |makingStats?| |twist| |nextLatticePermutation| |jordanAlgebra?| + |graphStates| |antiCommutative?| |polyPart| |diag| |strongGenerators| + > |cAsin| |semicolonSeparate| |mapExponents| |hconcat| |ldf2vmf| + |var2StepsDefault| |numberOfCycles| |readIfCan!| |hostByteOrder| + |mpsode| <= |roughUnitIdeal?| |showAll?| |OMclose| + |discriminantEuclidean| |intersect| |stopMusserTrials| |compile| + |qroot| |diophantineSystem| |postfix| |getGraph| >= |paraboloidal| + |laplacian| |normalize| |isTerm| |property| |retract| |explimitedint| + |shuffle| |tryFunctionalDecomposition?| |insertBottom!| + |setMaxPoints3D| |integralDerivationMatrix| |cLog| + |selectNonFiniteRoutines| |diagonalProduct| |completeHensel| |imagJ| + |yCoordinates| |isNot| |qPot| |inRadical?| |abelianGroup| + |retractable?| |youngGroup| |e01sef| |rectangularMatrix| |e02baf| + |prod| |primlimitedint| |Hausdorff| |nthExpon| + |exprHasWeightCosWXorSinWX| |leftGcd| |addMatchRestricted| + |zeroSetSplitIntoTriangularSystems| + |augment| |listOfLists| |ode1| + |units| |weierstrass| |outputFixed| |credPol| |viewPosDefault| + |dioSolve| |modularGcd| |computeInt| |ksec| - |mainForm| |integrate| + |fullPartialFraction| |times!| |complexEigenvectors| |inrootof| + |setleft!| |calcRanges| |OMopenFile| |over| / |alternating| |binomial| + |s18aef| |setValue!| |belong?| |bright| |oddintegers| + |generalPosition| |pseudoRemainder| |polynomialZeros| |rationalIfCan| + |basisOfLeftNucleus| |cAcsch| |quoByVar| 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|initial| + |nsqfree| |yellow| |perfectNthRoot| |fortranComplex| |constantRight| + |setUnion| |monomials| |midpoints| |leftRecip| |f01ref| |someBasis| + |binomThmExpt| |script| |reducedForm| |connectTo| |clipParametric| + |doubleDisc| |digit?| |limitedint| |padecf| |diagonals| |apply| + |subresultantVector| |readLineIfCan!| |irreducibleFactor| |iiacoth| + |whatInfinity| |changeNameToObjf| |setfirst!| |fortranTypeOf| + |pointColorDefault| |mat| |internalAugment| |infieldIntegrate| + |moebiusMu| |factorByRecursion| |setLength!| |oblateSpheroidal| + |setProperties| |monom| |homogeneous?| |s21bbf| |size| + |monicDecomposeIfCan| |tubeRadius| |vector| |tex| |stopTableGcd!| + |block| |minset| |dn| |Frobenius| |rule| |problemPoints| |ratpart| + |adaptive| |fullDisplay| |differentiate| |sizeLess?| |makeSeries| + |cTan| |mainPrimitivePart| |d01amf| |uniform01| |nary?| |terms| + |c06gsf| |padicallyExpand| |checkRur| |iiacsch| |sPol| + |jordanAdmissible?| |extend| |common| |mapUnivariateIfCan| + 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|nothing| |rur| |squareMatrix| |nextItem| + |packageCall| |copy!| |quasiComponent| + |semiDegreeSubResultantEuclidean| |mathieu23| |substring?| |iterators| + |crest| |updatD| |coshIfCan| |eulerPhi| |jacobian| |submod| + |cyclicSubmodule| |c06fqf| |tanIfCan| |sqfree| |lagrange| + |lieAlgebra?| |setStatus| |algintegrate| |setOrder| |s19aaf| |degree| + |extractSplittingLeaf| |suffix?| |df2st| |vectorise| |ffactor| + |atanhIfCan| |exportedOperators| |monicLeftDivide| |e01bff| + |complexIntegrate| |argument| |intcompBasis| |multiset| + |stoseInternalLastSubResultant| |coerceS| |aLinear| |unaryFunction| + |companionBlocks| |matrixConcat3D| |quartic| |prefix?| |regime| + |csch2sinh| |possiblyNewVariety?| |newReduc| |clipSurface| |coord| + |tanh2trigh| |partition| |checkForZero| |s18def| |width| + |nthRootIfCan| |evaluate| |phiCoord| |minIndex| |choosemon| + |BumInSepFFE| |constant?| |tab1| |hexDigit?| |logGamma| + |createPrimitiveNormalPoly| |OMputAtp| |maxrow| |ODESolve| + |thetaCoord| |basisOfRightNucleus| |iiasec| |properties| + |splitSquarefree| |anfactor| |part?| |ramified?| |sequences| + |continue| |writeUInt8!| |unprotectedRemoveRedundantFactors| + |chiSquare1| |translate| |OMconnInDevice| |besselI| |d01asf| + |stoseInvertible?reg| |accuracyIF| |chiSquare| |mapUp!| |extract!| + |tree| |groebnerFactorize| |errorInfo| |moduloP| + |semiResultantEuclidean1| |largest| |elRow1!| |ruleset| UTS2UP + |romberg| |makeSUP| |infRittWu?| |polar| |infix?| + |multiplyCoefficients| |factorials| |cPower| |validExponential| + |minRowIndex| |cAcosh| |algebraicVariables| |OMputAttr| + |realEigenvalues| |depth| |stronglyReduce| UP2UTS |degreePartition| + |bsolve| |deleteProperty!| |isOp| |halfExtendedSubResultantGcd1| + |stirling1| |symmetricSquare| |differentialVariables| |optional| + |cycle| |cotIfCan| |palgLODE| |leftScalarTimes!| |suchThat| |d02gbf| + |e02bcf| |stoseInvertibleSet| |numberOfDivisors| |supDimElseRittWu?| + |push!| |polygon| |range| |extension| |sylvesterSequence| |high| + |enqueue!| |intChoose| |randomR| |rename| |subNode?| |e02zaf| + |cyclotomic| |geometric| |whitePoint| |poisson| |logical?| + |lazyPremWithDefault| |host| |rk4| |clearCache| |firstSubsetGray| + |hessian| |chvar| |iiacsc| |quickSort| |interpret| |stack| + |changeName| |cscIfCan| |critMonD1| |getSyntaxFormsFromFile| |e01bef| + |expressIdealMember| |inverseIntegralMatrixAtInfinity| |rightOne| + |dAndcExp| |solid?| |tanhIfCan| |iilog| |f02wef| |sizeMultiplication| + |removeZero| |f02ajf| |integers| |viewDeltaYDefault| |tower| + |linGenPos| |coerceL| |coerceImages| |generate| |OMputEndAttr| + |printCode| |exprHasLogarithmicWeights| |nextSublist| |heap| + |setEpilogue!| ~ |primitivePart| |shallowCopy| |iitanh| |zeroSetSplit| + SEGMENT |fi2df| |permanent| |directory| |groebner| |mapUnivariate| + |ScanArabic| |log| |incrementBy| |hclf| |interpretString| |dim| + |linSolve| |perspective| |conjug| |OMencodingUnknown| |merge!| |const| + |components| |schwerpunkt| |cup| |open| 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|antisymmetricTensors| |rationalPower| |asimpson| |middle| + |numberOfComputedEntries| |startPolynomial| |imagi| |f02adf| + |selectPolynomials| |firstNumer| |expandLog| |mergeFactors| |brace| + |cyclicEntries| |leftTraceMatrix| |SturmHabichtSequence| + |resultantReduitEuclidean| |primaryDecomp| |changeVar| |lyndon| + |makeop| |OMputError| |rotate| |lexTriangular| |legendreP| |destruct| + |cAsinh| |rational?| |removeRoughlyRedundantFactorsInPol| + |meshPar2Var| |f04mbf| |complexNormalize| |prindINFO| |elRow2!| + |fortranReal| |trailingCoefficient| |unitVector| |find| |expPot| + |internalLastSubResultant| |e02dff| |moduleSum| |f02axf| |f04jgf| + |fractRagits| |remove| |linearDependenceOverZ| + |factorsOfCyclicGroupSize| |backOldPos| |s17ajf| |simplify| + |expenseOfEvaluation| |inc| |rotatey| |characteristic| |aQuartic| + |minPol| |modulus| |semiResultantReduitEuclidean| |ReduceOrder| + |elColumn2!| |solveLinearPolynomialEquationByRecursion| F2FG |getRef| + |bfEntry| |tab| |addPoint| 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|bivariatePolynomials| |weighted| + |bipolar| |monicRightDivide| |reopen!| |e04dgf| |isobaric?| |tRange| + |primintfldpoly| |domain| |constDsolve| |leftRank| |outputMeasure| + |localUnquote| |critpOrder| |d01fcf| |f04axf| |taylor| |dequeue| + |fixedDivisor| |monomialIntegrate| |package| |po| |inputBinaryFile| + |traverse| |separateDegrees| |quadratic| |decrease| |iicsch| |show| + |closed?| |laurent| |denominator| |copy| |mathieu12| + |linearPolynomials| |explicitEntries?| |extendedSubResultantGcd| + |createRandomElement| |structuralConstants| |fortranLiteralLine| + |outputBinaryFile| |puiseux| |rootKerSimp| |f02akf| |var1StepsDefault| + |lambda| |mindegTerm| |c02agf| |laguerre| |zeroDimensional?| |trigs| + |createNormalPrimitivePoly| |trace| |sup| |PDESolve| |closeComponent| + |invmod| |printHeader| |fracPart| |pseudoQuotient| |partialQuotients| + |increment| |rootProduct| |jacobi| |inv| |setPredicates| + |bandedJacobian| |autoCoerce| |expandPower| |e02adf| |iiasinh| + |viewport2D| |numberOfOperations| |mainSquareFreePart| |morphism| + |ground?| |OMserve| |fractionFreeGauss!| |atoms| |c06gcf| |parents| + |setAdaptive3D| |cAcoth| |OMputEndBVar| |f01brf| |s21baf| + |sylvesterMatrix| |ground| |s21bcf| |denomRicDE| |realSolve| |s17akf| + |readInt32!| |e01sff| |fixPredicate| |localAbs| |headReduced?| + |OMmakeConn| |leadingMonomial| |randnum| |conjugates| |bumprow| + |OMgetBind| |parametric?| |deepestInitial| |extractIndex| |repeating| + |monicRightFactorIfCan| |position| |setMinPoints3D| |midpoint| + |leadingCoefficient| |setScreenResolution3D| |findCycle| + |mightHaveRoots| |functionIsOscillatory| |rightTrace| + |rightRegularRepresentation| |match?| |generalInfiniteProduct| + |pointSizeDefault| |addmod| |tanintegrate| |OMUnknownCD?| + |primitiveMonomials| |returnTypeOf| |hash| |getCurve| |iifact| + |multinomial| |completeHermite| |genericLeftDiscriminant| + |quasiMonicPolynomials| |rischNormalize| |f02xef| |lazyResidueClass| + |reductum| |count| |coleman| |extensionDegree| |say| |fibonacci| + |nextNormalPrimitivePoly| |traceMatrix| |leadingIndex| |d02bhf| + |node?| |ridHack1| |B1solve| |outputAsScript| + |removeRedundantFactorsInContents| |nor| |redPo| |OMgetSymbol| + |leastMonomial| |getOrder| |supersub| |headReduce| |ratPoly| + |compound?| |f04arf| |symbol?| |minGbasis| |startStats!| |cylindrical| + |errorKind| |brillhartTrials| |OMbindTCP| |laguerreL| |debug| + |graphCurves| |clearTheIFTable| |representationType| + |internalInfRittWu?| |vedf2vef| |univariatePolynomialsGcds| + |elliptic?| |useSingleFactorBound?| |printingInfo?| |factorsOfDegree| + D |normalise| |order| |triangulate| |univariateSolve| + |derivationCoordinates| |toseInvertible?| |numberOfPrimitivePoly| + |f04maf| |unknownEndian| |isOpen?| |OMgetVariable| |physicalLength| + |totalDegree| |diagonal| |primextendedint| |univariate?| |OMgetEndAtp| + |pToHdmp| |numericIfCan| |maxrank| |characteristicSerie| |bigEndian| + |plot| |infLex?| |rightMinimalPolynomial| |f02aef| |deepExpand| + |makeTerm| |safetyMargin| |setStatus!| |arrayStack| + |definingPolynomial| |hue| LODO2FUN |sub| |init| |e02akf| + |patternMatch| |finiteBasis| |cAcos| |complementaryBasis| + |approxNthRoot| |palgRDE| |topPredicate| |delay| + |factorSquareFreeByRecursion| |selectOptimizationRoutines| |rootBound| + |subResultantGcd| |palginfieldint| |mappingAst| |s21bdf| |trunc| + |newTypeLists| |OMputEndAtp| |lex| |keys| |double| |numberOfVariables| + |initTable!| |branchPointAtInfinity?| |shiftRoots| + |cyclotomicFactorization| |pile| |listLoops| |internalIntegrate0| + |measure2Result| |ip4Address| |prevPrime| |zero| |rowEch| |bernoulli| + |rightGcd| |bandedHessian| |crushedSet| |e04gcf| |iflist2Result| + |badNum| |stoseInvertibleSetsqfreg| |showIntensityFunctions| + |eigenMatrix| |halfExtendedResultant1| |isConnected?| |factors| + |print| |constant| |subSet| |weights| |e02bdf| |open?| |And| + |inverseIntegralMatrix| |semiIndiceSubResultantEuclidean| |variable?| + |euclideanNormalForm| |imagj| |mathieu24| |besselJ| |Or| |pmintegrate| + |factorSquareFreePolynomial| |bombieriNorm| |setprevious!| + |generateIrredPoly| |normalForm| |cyclotomicDecomposition| + |addBadValue| |finiteBound| |Not| |df2mf| |hdmpToDmp| |plenaryPower| + |has?| |dmp2rfi| |monomRDE| |swap| |rootSplit| |showTheIFTable| + |resultantnaif| |algebraicSort| |level| |OMreadStr| |lazyPseudoDivide| + |lazyPrem| |declare!| |SturmHabichtMultiple| |branchPoint?| + |rightRankPolynomial| |/\\| |OMgetAtp| |enumerate| + |singularAtInfinity?| |leadingSupport| |univariatePolynomial| |\\/| + |paren| |OMlistSymbols| |remove!| |integral?| |any?| |build| |cSec| + |predicate| |insert!| |constantOpIfCan| |less?| + |exprHasAlgebraicWeight| |plus!| |integralMatrixAtInfinity| |Lazard2| + |matrixDimensions| |makeFR| |c06gqf| |lieAdmissible?| |mkcomm| + |nonLinearPart| |hyperelliptic| |rdHack1| |id| |branchIfCan| + |sequence| |cAsec| |d01bbf| |iiexp| |iicoth| + |constantCoefficientRicDE| |close!| |module| |multiEuclideanTree| + |idealiser| |resetVariableOrder| |infieldint| |simplifyPower| + |firstDenom| |reseed| |getOperands| |sizePascalTriangle| |table| + |rubiksGroup| |LyndonCoordinates| |hermite| + |solveLinearPolynomialEquationByFractions| |drawToScale| |saturate| + |overlabel| |Ei| |minimumExponent| |insert| |new| |deref| + |curveColorPalette| |symmetric?| |conical| |segment| + |degreeSubResultantEuclidean| |OMsend| |definingEquations| |mapDown!| + |lflimitedint| |varList| |seed| |totalDifferential| |fractionPart| + |extractTop!| |pointColor| |highCommonTerms| |sumOfDivisors| |options| + |rightExactQuotient| |digits| |iteratedInitials| |setMaxPoints| + |upperCase!| |shellSort| |squareFreeFactors| |getDatabase| + |removeIrreducibleRedundantFactors| |iibinom| |f02abf| |associative?| + |makeViewport3D| |parameters| |frobenius| |littleEndian| + |sturmVariationsOf| |qfactor| |collectQuasiMonic| |rightQuotient| + |symbolTableOf| |writeByte!| |quoted?| |typeLists| |mainValue| + |cardinality| 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|createLowComplexityTable| |bits| |roman| |normalizedDivide| + |initializeGroupForWordProblem| |scopes| |integerBound| |dilog| + |s17aff| |purelyAlgebraicLeadingMonomial?| |logIfCan| |normalElement| + |rank| |permutationGroup| |front| |leftMult| |e02agf| + |alternatingGroup| |dimensionOfIrreducibleRepresentation| |sin| + |numberOfFactors| |sincos| |divergence| |monicModulo| |exp1| + |hasPredicate?| |floor| |showClipRegion| |reindex| |isQuotient| + |yCoord| |cos| |comp| |direction| |internal?| |binding| |binaryTree| + |makeObject| |polygamma| |product| |countRealRoots| |map| |tan| + |taylorRep| |elliptic| |internalSubQuasiComponent?| |members| + |OMputApp| |rightUnits| |e02bbf| |sdf2lst| |useSingleFactorBound| + |currentEnv| |splitConstant| |cot| |ref| |inGroundField?| |subst| + |e01saf| |sumOfSquares| |coef| |ParCondList| |debug3D| |s13acf| + |subResultantChain| |leftRemainder| |sec| |approximants| + |normalizeAtInfinity| |tubeRadiusDefault| |commutative?| + |tableForDiscreteLogarithm| 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T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -2750 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045))) ((-637 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2750 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2750 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2750 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2750 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2750 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-1034 (-564)) -12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) ((-1034 |#2|) |has| |#2| (-1094)) ((-1051 |#2|) -2750 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1106) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1094) -2750 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) -((-2981 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2965 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-4289 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2981 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2965 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4289 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1209) (-1209)) (T -239)) -((-4289 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2965 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-2981 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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48 (|has| |#2| (-722))) (($ |#2| $) 49 (|has| |#2| (-722))) (($ (-767) $) NIL (|has| |#2| (-131))) (($ (-917) $) NIL (|has| |#2| (-25)))) (-2062 (((-767) $) NIL (|has| $ (-6 -4406))))) +((-3597 (*1 *1 *2) (-12 (-5 *2 (-1259 *4)) (-4 *4 (-1209)) (-4 *1 (-238 *3 *4)))) (-3644 (*1 *1 *2) (-12 (-5 *2 (-917)) (-4 *1 (-238 *3 *4)) (-4 *4 (-1045)) (-4 *4 (-1209)))) (-2529 (*1 *2 *1 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1209)) (-4 *2 (-1045)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1209)) (-4 *2 (-722)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1209)) (-4 *2 (-722))))) +(-13 (-602 (-564) |t#2|) (-611 (-1259 |t#2|)) (-10 -8 (-6 -4407) (-15 -3597 ($ (-1259 |t#2|))) (IF (|has| |t#2| (-1094)) (-6 (-411 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1045)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-231 |t#2|)) (-6 (-377 |t#2|)) (-15 -3644 ($ (-917))) (-15 -2529 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-722)) (PROGN (-6 (-722)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-368)) |%noBranch|) (IF (|has| |t#2| (-172)) (PROGN (-6 (-38 |t#2|)) (-6 (-172))) |%noBranch|) (IF (|has| |t#2| (-6 -4404)) (-6 -4404) |%noBranch|) (IF (|has| |t#2| (-844)) (-6 (-844)) |%noBranch|) (IF (|has| |t#2| (-789)) (-6 (-789)) |%noBranch|) (IF (|has| |t#2| (-363)) (-6 (-1266 |t#2|)) |%noBranch|))) +(((-21) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-23) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2733 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2733 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -2733 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-614 |#2|) -2733 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-858)) -2733 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -2733 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045))) ((-637 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2733 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2733 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2733 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2733 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2733 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-1034 (-564)) -12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) ((-1034 |#2|) |has| |#2| (-1094)) ((-1051 |#2|) -2733 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1106) -2733 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1094) -2733 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -2750 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 |#2|) . T) ((-614 |#3|) . T) ((-614 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-611 (-858)) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -2733 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 |#2|) . T) ((-614 |#3|) . T) ((-614 $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-611 (-858)) . 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T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1045)) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) |has| |#1| (-556)) ((-473) |has| |#1| (-473)) ((-514 (-610 $) $) . T) ((-514 $ $) . T) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-556)) ((-644 |#1|) |has| |#1| (-172)) ((-644 $) -2750 (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1045))) ((-637 |#1|) |has| |#1| (-1045)) ((-713 #0#) |has| |#1| (-556)) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) |has| |#1| (-556)) ((-722) -2750 (|has| |#1| (-1106)) (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-846) . T) ((-896 (-1170)) |has| |#1| (-1045)) ((-882 (-379)) |has| |#1| (-882 (-379))) ((-882 (-564)) |has| |#1| (-882 (-564))) ((-880 |#1|) . 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|relerr| (-225))))))) (T -559)) -((-3726 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -2029 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-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| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2029 (-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 (-559)))) (-2666 (*1 *2 *1) (-12 (-5 *2 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T) ((-644 |#2|) |has| |#1| (-363)) ((-644 $) . T) ((-637 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((-637 |#2|) |has| |#1| (-363)) ((-713 #1#) -2733 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-713 |#1|) |has| |#1| (-172)) ((-713 |#2|) |has| |#1| (-363)) ((-713 $) -2733 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-722) . 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T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-713 #1#) |has| |#1| (-38 (-407 (-564)))) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-722) . T) ((-846) |has| |#1| (-846)) ((-896 #2#) . T) ((-896 (-1170)) |has| |#1| (-896 (-1170))) ((-882 (-379)) -12 (|has| (-1076) (-882 (-379))) (|has| |#1| (-882 (-379)))) ((-882 (-564)) -12 (|has| (-1076) (-882 (-564))) (|has| |#1| (-882 (-564)))) ((-945 |#1| #0# #2#) . T) ((-905) |has| |#1| (-905)) ((-916) |has| |#1| (-363)) ((-1034 (-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((-1034 (-564)) |has| |#1| (-1034 (-564))) ((-1034 #2#) . T) ((-1034 |#1|) . T) ((-1051 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1051 |#1|) . T) ((-1051 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1045) . T) ((-1052) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-905))) -((-3743 (((-641 (-1076)) $) 34)) (-3900 (($ $) 31)) (-3720 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-3866 (($ $) 14)) (-3876 ((|#2| $) 12)) (-2762 ((|#3| $) 10))) -(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -3743 ((-641 (-1076)) |#1|)) (-15 -3720 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -3720 (|#1| |#1| (-1076) |#3|)) (-15 -3900 (|#1| |#1|)) (-15 -3720 (|#1| |#2| |#3|)) (-15 -2762 (|#3| |#1|)) (-15 -3866 (|#1| |#1|)) (-15 -3876 (|#2| |#1|))) (-1237 |#2| |#3|) (-1045) (-788)) (T -1236)) -NIL -(-10 -8 (-15 -3743 ((-641 (-1076)) |#1|)) (-15 -3720 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -3720 (|#1| |#1| (-1076) |#3|)) (-15 -3900 (|#1| |#1|)) (-15 -3720 (|#1| |#2| |#3|)) (-15 -2762 (|#3| |#1|)) (-15 -3866 (|#1| |#1|)) (-15 -3876 (|#2| |#1|))) -((-2337 (((-112) $ $) 7)) (-2148 (((-112) $) 16)) (-3743 (((-641 (-1076)) $) 77)) (-3257 (((-1170) $) 106)) (-1850 (((-2 (|:| -3506 $) (|:| 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(-767) (-1076)) (-286 |t#1| |t#1|) (-286 $ $) (-233) (-231 |t#1|) (-10 -8 (-15 -3262 ((-1259 |t#1|) $ (-767))) (-15 -3337 ((-1166 |t#1|) $)) (-15 -2890 ($ (-1166 |t#1|))) (-15 -1382 ($ $ (-767))) (-15 -2866 ((-3 $ "failed") $ (-767))) (-15 -2269 ((-2 (|:| -1876 $) (|:| -2786 $)) $ $)) (-15 -1399 ((-2 (|:| -1876 $) (|:| -2786 $)) $ (-767))) (-15 -2223 ($ $ (-767))) (-15 -2252 ($ $ (-767))) (-15 -3001 ($ $ $)) (-15 -3142 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1145)) (-6 (-1145)) |%noBranch|) (IF (|has| |t#1| (-172)) (PROGN (-15 -2576 (|t#1| $)) (-15 -1545 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-556)) (PROGN (-6 (-286 (-407 $) (-407 $))) (-15 -4361 ((-407 $) (-407 $) (-407 $))) (-15 -3924 ((-767) $ $)) (-15 -3971 ($ $ $)) (-15 -2367 ((-3 $ "failed") $ $)) (-15 -2367 ((-3 (-407 $) "failed") (-407 $) $)) (-15 -3801 ($ $ $)) (-15 -2823 ((-2 (|:| -4290 |t#1|) (|:| -1876 $) (|:| -2786 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-452)) (-15 -2860 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-363)) (PROGN (-6 (-307)) (-6 -4403) (-15 -4361 (|t#1| (-407 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-407 (-564)))) (-15 -2983 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-767)) . T) ((-25) . T) ((-38 #1=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -2733 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 #2=(-1076)) . T) ((-614 |#1|) . T) ((-614 $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-611 (-858)) . T) ((-172) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| (-1076) (-612 (-536))) (|has| |#1| (-612 (-536)))) ((-612 (-888 (-379))) -12 (|has| (-1076) (-612 (-888 (-379)))) (|has| |#1| (-612 (-888 (-379))))) ((-612 (-888 (-564))) -12 (|has| (-1076) (-612 (-888 (-564)))) (|has| |#1| (-612 (-888 (-564))))) ((-231 |#1|) . T) ((-233) . T) ((-286 (-407 $) (-407 $)) |has| |#1| (-556)) ((-286 |#1| |#1|) . T) ((-286 $ $) . T) ((-290) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 $) . T) ((-326 |#1| #0#) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -2733 (|has| |#1| (-905)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-514 #2# |#1|) . T) ((-514 #2# $) . T) ((-514 $ $) . T) ((-556) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-644 #1#) |has| |#1| (-38 (-407 (-564)))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-713 #1#) |has| |#1| (-38 (-407 (-564)))) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-722) . T) ((-846) |has| |#1| (-846)) ((-896 #2#) . T) ((-896 (-1170)) |has| |#1| (-896 (-1170))) ((-882 (-379)) -12 (|has| (-1076) (-882 (-379))) (|has| |#1| (-882 (-379)))) ((-882 (-564)) -12 (|has| (-1076) (-882 (-564))) (|has| |#1| (-882 (-564)))) ((-945 |#1| #0# #2#) . T) ((-905) |has| |#1| (-905)) ((-916) |has| |#1| (-363)) ((-1034 (-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((-1034 (-564)) |has| |#1| (-1034 (-564))) ((-1034 #2#) . T) ((-1034 |#1|) . T) ((-1051 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1051 |#1|) . T) ((-1051 $) -2733 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1045) . T) ((-1052) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-905))) +((-3702 (((-641 (-1076)) $) 34)) (-3878 (($ $) 31)) (-3679 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-3840 (($ $) 14)) (-3853 ((|#2| $) 12)) (-3258 ((|#3| $) 10))) +(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -3702 ((-641 (-1076)) |#1|)) (-15 -3679 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -3679 (|#1| |#1| (-1076) |#3|)) (-15 -3878 (|#1| |#1|)) (-15 -3679 (|#1| |#2| |#3|)) (-15 -3258 (|#3| |#1|)) (-15 -3840 (|#1| |#1|)) (-15 -3853 (|#2| |#1|))) (-1237 |#2| |#3|) (-1045) (-788)) (T -1236)) +NIL +(-10 -8 (-15 -3702 ((-641 (-1076)) |#1|)) (-15 -3679 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -3679 (|#1| |#1| (-1076) |#3|)) (-15 -3878 (|#1| |#1|)) (-15 -3679 (|#1| |#2| |#3|)) (-15 -3258 (|#3| |#1|)) (-15 -3840 (|#1| |#1|)) (-15 -3853 (|#2| |#1|))) +((-2315 (((-112) $ $) 7)) (-2480 (((-112) $) 17)) (-3702 (((-641 (-1076)) $) 78)) (-3229 (((-1170) $) 107)) (-1656 (((-2 (|:| -2112 $) (|:| 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T) ((-23) . T) ((-47 |#1| #0=(-407 (-564))) . T) ((-25) . T) ((-38 #1=(-407 (-564))) -2733 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2733 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-35) |has| |#1| (-38 (-407 (-564)))) ((-95) |has| |#1| (-38 (-407 (-564)))) ((-102) . T) ((-111 #1# #1#) -2733 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2733 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -2733 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) |has| |#1| (-172)) ((-614 $) -2733 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-611 (-858)) . 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2876736 2876799 2876889 "TEMUTL" 2877020 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2874890 2875170 2875495 "TBCMPPK" 2876459 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2866778 2873050 2873106 "TBAGG" 2873506 NIL TBAGG (NIL T T) -9 NIL 2873717 NIL) (-1184 2861848 2863336 2865090 "TBAGG-" 2865095 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2861232 2861339 2861484 "TANEXP" 2861737 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2854733 2861089 2861182 "TABLE" 2861187 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2854145 2854244 2854382 "TABLEAU" 2854630 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2848753 2849973 2851221 "TABLBUMP" 2852931 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2847975 2848122 2848303 "SYSTEM" 2848594 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2844434 2845133 2845916 "SYSSOLP" 2847226 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2843468 2843946 2844065 "SYSNNI" 2844251 NIL SYSNNI (NIL NIL) -8 NIL NIL 2844336) (-1176 2842765 2843197 2843276 "SYSINT" 2843336 NIL SYSINT (NIL NIL) -8 NIL NIL 2843381) (-1175 2839124 2840043 2840753 "SYNTAX" 2842077 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2836282 2836884 2837516 "SYMTAB" 2838514 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2831531 2832433 2833416 "SYMS" 2835321 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2828793 2830989 2831219 "SYMPOLY" 2831336 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2828310 2828385 2828508 "SYMFUNC" 2828705 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2824356 2825622 2826435 "SYMBOL" 2827519 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2817895 2819584 2821304 "SWITCH" 2822658 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2811156 2816716 2817019 "SUTS" 2817650 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2803249 2810403 2810676 "SUPXS" 2810941 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2794764 2802867 2802993 "SUP" 2803158 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2793923 2794050 2794267 "SUPFRACF" 2794632 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2793544 2793603 2793716 "SUP2" 2793858 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2791957 2792231 2792594 "SUMRF" 2793243 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2791271 2791337 2791536 "SUMFS" 2791878 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2775265 2790448 2790699 "SULS" 2791078 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2774894 2775087 2775157 "SUCHTAST" 2775217 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2774216 2774419 2774559 "SUCH" 2774802 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2768110 2769122 2770081 "SUBSPACE" 2773304 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2767540 2767630 2767794 "SUBRESP" 2767998 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2760905 2762205 2763516 "STTF" 2766276 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2755078 2756198 2757345 "STTFNC" 2759805 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2746389 2748260 2750054 "STTAYLOR" 2753319 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2739633 2746253 2746336 "STRTBL" 2746341 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2735024 2739588 2739619 "STRING" 2739624 T STRING (NIL) -8 NIL NIL NIL) (-1151 2729912 2734397 2734427 "STRICAT" 2734486 T STRICAT (NIL) -9 NIL 2734548 NIL) (-1150 2722715 2727531 2728142 "STREAM" 2729336 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2722225 2722302 2722446 "STREAM3" 2722632 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2721207 2721390 2721625 "STREAM2" 2722038 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2720895 2720947 2721040 "STREAM1" 2721149 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2719911 2720092 2720323 "STINPROD" 2720711 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2719489 2719673 2719703 "STEP" 2719783 T STEP (NIL) -9 NIL 2719861 NIL) (-1144 2713032 2719388 2719465 "STBL" 2719470 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2708206 2712253 2712296 "STAGG" 2712449 NIL STAGG (NIL T) -9 NIL 2712538 NIL) (-1142 2705908 2706510 2707382 "STAGG-" 2707387 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2704103 2705678 2705770 "STACK" 2705851 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2696826 2702244 2702700 "SREGSET" 2703733 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2689251 2690620 2692133 "SRDCMPK" 2695432 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2682218 2686691 2686721 "SRAGG" 2688024 T SRAGG (NIL) -9 NIL 2688632 NIL) (-1137 2681235 2681490 2681869 "SRAGG-" 2681874 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2675722 2680182 2680603 "SQMATRIX" 2680861 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2669469 2672440 2673167 "SPLTREE" 2675067 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2665459 2666125 2666771 "SPLNODE" 2668895 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2664506 2664739 2664769 "SPFCAT" 2665213 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2663243 2663453 2663717 "SPECOUT" 2664264 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2654895 2656639 2656669 "SPADXPT" 2661061 T SPADXPT (NIL) -9 NIL 2663095 NIL) (-1130 2654656 2654696 2654765 "SPADPRSR" 2654848 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2652838 2654611 2654642 "SPADAST" 2654647 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2644809 2646556 2646599 "SPACEC" 2650972 NIL SPACEC (NIL T) -9 NIL 2652788 NIL) (-1127 2642966 2644741 2644790 "SPACE3" 2644795 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2641718 2641889 2642180 "SORTPAK" 2642771 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2639768 2640071 2640490 "SOLVETRA" 2641382 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2638779 2639001 2639275 "SOLVESER" 2639541 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2633990 2634880 2635882 "SOLVERAD" 2637831 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2629805 2630414 2631143 "SOLVEFOR" 2633357 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2624102 2629154 2629251 "SNTSCAT" 2629256 NIL SNTSCAT (NIL T T T T) -9 NIL 2629326 NIL) (-1120 2618235 2622425 2622816 "SMTS" 2623792 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2612675 2618123 2618200 "SMP" 2618205 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2610834 2611135 2611533 "SMITH" 2612372 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2603721 2607885 2607988 "SMATCAT" 2609339 NIL SMATCAT (NIL NIL T T T) -9 NIL 2609889 NIL) (-1116 2600661 2601484 2602662 "SMATCAT-" 2602667 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2598374 2599897 2599940 "SKAGG" 2600201 NIL SKAGG (NIL T) -9 NIL 2600336 NIL) (-1114 2594709 2597790 2597985 "SINT" 2598172 T SINT (NIL) -8 NIL NIL 2598345) (-1113 2594481 2594519 2594585 "SIMPAN" 2594665 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2593787 2594016 2594156 "SIG" 2594363 T SIG (NIL) -8 NIL NIL NIL) (-1111 2592625 2592846 2593121 "SIGNRF" 2593546 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2591430 2591581 2591872 "SIGNEF" 2592454 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2590763 2591013 2591137 "SIGAST" 2591328 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2588453 2588907 2589413 "SHP" 2590304 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2582353 2588354 2588430 "SHDP" 2588435 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2581952 2582118 2582148 "SGROUP" 2582241 T SGROUP (NIL) -9 NIL 2582303 NIL) (-1105 2581810 2581836 2581909 "SGROUP-" 2581914 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2578645 2579343 2580066 "SGCF" 2581109 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2573040 2578092 2578189 "SFRTCAT" 2578194 NIL SFRTCAT (NIL T T T T) -9 NIL 2578233 NIL) (-1102 2566461 2567479 2568615 "SFRGCD" 2572023 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2559588 2560660 2561846 "SFQCMPK" 2565394 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2559210 2559299 2559409 "SFORT" 2559529 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2558355 2559050 2559171 "SEXOF" 2559176 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2557489 2558236 2558304 "SEX" 2558309 T SEX (NIL) -8 NIL NIL NIL) (-1097 2553028 2553717 2553812 "SEXCAT" 2556749 NIL SEXCAT (NIL T T T T T) -9 NIL 2557327 NIL) (-1096 2550208 2552962 2553010 "SET" 2553015 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2548459 2548921 2549226 "SETMN" 2549949 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2548065 2548191 2548221 "SETCAT" 2548338 T SETCAT (NIL) -9 NIL 2548423 NIL) (-1093 2547845 2547897 2547996 "SETCAT-" 2548001 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2544232 2546306 2546349 "SETAGG" 2547219 NIL SETAGG (NIL T) -9 NIL 2547559 NIL) (-1091 2543690 2543806 2544043 "SETAGG-" 2544048 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2543160 2543386 2543487 "SEQAST" 2543611 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2542359 2542653 2542714 "SEGXCAT" 2543000 NIL SEGXCAT (NIL T T) -9 NIL 2543120 NIL) (-1088 2541413 2542025 2542207 "SEG" 2542212 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2540392 2540606 2540649 "SEGCAT" 2541171 NIL SEGCAT (NIL T) -9 NIL 2541392 NIL) (-1086 2539441 2539771 2539971 "SEGBIND" 2540227 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2539062 2539121 2539234 "SEGBIND2" 2539376 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2538662 2538863 2538940 "SEGAST" 2539007 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2537881 2538007 2538211 "SEG2" 2538506 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2537318 2537816 2537863 "SDVAR" 2537868 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2529600 2537088 2537218 "SDPOL" 2537223 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2528193 2528459 2528778 "SCPKG" 2529315 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2527357 2527529 2527721 "SCOPE" 2528023 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2526577 2526711 2526890 "SCACHE" 2527212 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2526249 2526409 2526439 "SASTCAT" 2526444 T SASTCAT (NIL) -9 NIL 2526457 NIL) (-1076 2525763 2526084 2526160 "SAOS" 2526195 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2525328 2525363 2525536 "SAERFFC" 2525722 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2519294 2525225 2525305 "SAE" 2525310 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2518887 2518922 2519081 "SAEFACT" 2519253 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2517208 2517522 2517923 "RURPK" 2518553 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2515844 2516123 2516435 "RULESET" 2517042 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2513031 2513534 2513999 "RULE" 2515525 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2512670 2512825 2512908 "RULECOLD" 2512983 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2512460 2512488 2512559 "RTVALUE" 2512621 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2511958 2512177 2512271 "RSTRCAST" 2512388 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2506806 2507601 2508521 "RSETGCD" 2511157 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2496063 2501115 2501212 "RSETCAT" 2505331 NIL RSETCAT (NIL T T T T) -9 NIL 2506428 NIL) (-1064 2493990 2494529 2495353 "RSETCAT-" 2495358 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2486375 2487752 2489272 "RSDCMPK" 2492589 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2484380 2484821 2484895 "RRCC" 2485981 NIL RRCC (NIL T T) -9 NIL 2486325 NIL) (-1061 2483731 2483905 2484184 "RRCC-" 2484189 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2483201 2483427 2483528 "RPTAST" 2483652 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2457199 2466794 2466861 "RPOLCAT" 2477525 NIL RPOLCAT (NIL T T T) -9 NIL 2480684 NIL) (-1058 2448697 2451037 2454159 "RPOLCAT-" 2454164 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2439744 2446908 2447390 "ROUTINE" 2448237 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2436569 2439370 2439510 "ROMAN" 2439626 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2434840 2435429 2435689 "ROIRC" 2436374 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2431225 2433476 2433506 "RNS" 2433810 T RNS (NIL) -9 NIL 2434083 NIL) (-1053 2429734 2430117 2430651 "RNS-" 2430726 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2429183 2429565 2429595 "RNG" 2429600 T RNG (NIL) -9 NIL 2429621 NIL) (-1051 2428575 2428937 2428980 "RMODULE" 2429042 NIL RMODULE (NIL T) -9 NIL 2429084 NIL) (-1050 2427411 2427505 2427841 "RMCAT2" 2428476 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2424288 2426757 2427054 "RMATRIX" 2427173 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2417230 2419464 2419579 "RMATCAT" 2422938 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2423920 NIL) (-1047 2416605 2416752 2417059 "RMATCAT-" 2417064 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2416172 2416247 2416375 "RINTERP" 2416524 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2415291 2415819 2415849 "RING" 2415905 T RING (NIL) -9 NIL 2415997 NIL) (-1044 2415083 2415127 2415224 "RING-" 2415229 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2413924 2414161 2414419 "RIDIST" 2414847 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2405240 2413392 2413598 "RGCHAIN" 2413772 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2404616 2404996 2405037 "RGBCSPC" 2405095 NIL RGBCSPC (NIL T) -9 NIL 2405147 NIL) (-1040 2403800 2404155 2404196 "RGBCMDL" 2404428 NIL RGBCMDL (NIL T) -9 NIL 2404542 NIL) (-1039 2400794 2401408 2402078 "RF" 2403164 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2400440 2400503 2400606 "RFFACTOR" 2400725 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2400165 2400200 2400297 "RFFACT" 2400399 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2398282 2398646 2399028 "RFDIST" 2399805 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2397735 2397827 2397990 "RETSOL" 2398184 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2397371 2397451 2397494 "RETRACT" 2397627 NIL RETRACT (NIL T) -9 NIL 2397714 NIL) (-1033 2397220 2397245 2397332 "RETRACT-" 2397337 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2396849 2397042 2397112 "RETAST" 2397172 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2389703 2396502 2396629 "RESULT" 2396744 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2388321 2388972 2389171 "RESRING" 2389606 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2387957 2388006 2388104 "RESLATC" 2388258 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2387662 2387697 2387804 "REPSQ" 2387916 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2385084 2385664 2386266 "REP" 2387082 T REP (NIL) -7 NIL NIL NIL) (-1026 2384781 2384816 2384927 "REPDB" 2385043 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2378681 2380070 2381293 "REP2" 2383593 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2375058 2375739 2376547 "REP1" 2377908 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2367781 2373199 2373655 "REGSET" 2374688 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2366594 2366929 2367179 "REF" 2367566 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2365971 2366074 2366241 "REDORDER" 2366478 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2361966 2365184 2365411 "RECLOS" 2365799 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2361018 2361199 2361414 "REALSOLV" 2361773 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2360864 2360905 2360935 "REAL" 2360940 T REAL (NIL) -9 NIL 2360975 NIL) (-1017 2357347 2358149 2359033 "REAL0Q" 2360029 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2352948 2353936 2354997 "REAL0" 2356328 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2352446 2352665 2352759 "RDUCEAST" 2352876 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2351851 2351923 2352130 "RDIV" 2352368 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2350919 2351093 2351306 "RDIST" 2351673 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2349516 2349803 2350175 "RDETRS" 2350627 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2347328 2347782 2348320 "RDETR" 2349058 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2345939 2346217 2346621 "RDEEFS" 2347044 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2344434 2344740 2345172 "RDEEF" 2345627 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2338687 2341570 2341600 "RCFIELD" 2342895 T RCFIELD (NIL) -9 NIL 2343625 NIL) (-1007 2336751 2337255 2337951 "RCFIELD-" 2338026 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2333067 2334852 2334895 "RCAGG" 2335979 NIL RCAGG (NIL T) -9 NIL 2336444 NIL) (-1005 2332695 2332789 2332952 "RCAGG-" 2332957 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2332030 2332142 2332307 "RATRET" 2332579 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2331583 2331650 2331771 "RATFACT" 2331958 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2330891 2331011 2331163 "RANDSRC" 2331453 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2330625 2330669 2330742 "RADUTIL" 2330840 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2323768 2329458 2329768 "RADIX" 2330349 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2315416 2323612 2323740 "RADFF" 2323745 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2315068 2315143 2315171 "RADCAT" 2315328 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2314853 2314901 2314998 "RADCAT-" 2315003 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2313004 2314628 2314717 "QUEUE" 2314797 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2309572 2312941 2312986 "QUAT" 2312991 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2309210 2309253 2309380 "QUATCT2" 2309523 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2302949 2306259 2306299 "QUATCAT" 2307079 NIL QUATCAT (NIL T) -9 NIL 2307845 NIL) (-992 2299093 2300130 2301517 "QUATCAT-" 2301611 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2296613 2298177 2298218 "QUAGG" 2298593 NIL QUAGG (NIL T) -9 NIL 2298768 NIL) (-990 2296245 2296438 2296506 "QQUTAST" 2296565 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2295170 2295643 2295815 "QFORM" 2296117 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2286374 2291587 2291627 "QFCAT" 2292285 NIL QFCAT (NIL T) -9 NIL 2293286 NIL) (-987 2281946 2283147 2284738 "QFCAT-" 2284832 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2281584 2281627 2281754 "QFCAT2" 2281897 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2281044 2281154 2281284 "QEQUAT" 2281474 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2274191 2275263 2276447 "QCMPACK" 2279977 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2271767 2272188 2272616 "QALGSET" 2273846 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2271012 2271186 2271418 "QALGSET2" 2271587 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2269702 2269926 2270243 "PWFFINTB" 2270785 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2267884 2268052 2268406 "PUSHVAR" 2269516 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2263802 2264856 2264897 "PTRANFN" 2266781 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2262204 2262495 2262817 "PTPACK" 2263513 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2261836 2261893 2262002 "PTFUNC2" 2262141 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2256363 2260708 2260749 "PTCAT" 2261045 NIL PTCAT (NIL T) -9 NIL 2261198 NIL) (-975 2256021 2256056 2256180 "PSQFR" 2256322 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2254616 2254914 2255248 "PSEUDLIN" 2255719 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2241379 2243750 2246074 "PSETPK" 2252376 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2234423 2237137 2237233 "PSETCAT" 2240254 NIL PSETCAT (NIL T T T T) -9 NIL 2241068 NIL) (-971 2232259 2232893 2233714 "PSETCAT-" 2233719 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2231608 2231773 2231801 "PSCURVE" 2232069 T PSCURVE (NIL) -9 NIL 2232236 NIL) (-969 2227956 2229446 2229511 "PSCAT" 2230355 NIL PSCAT (NIL T T T) -9 NIL 2230595 NIL) (-968 2227019 2227235 2227635 "PSCAT-" 2227640 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2225751 2226384 2226589 "PRTITION" 2226834 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2225253 2225472 2225564 "PRTDAST" 2225679 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2214343 2216557 2218745 "PRS" 2223115 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2212201 2213693 2213733 "PRQAGG" 2213916 NIL PRQAGG (NIL T) -9 NIL 2214018 NIL) (-963 2211587 2211816 2211844 "PROPLOG" 2212029 T PROPLOG (NIL) -9 NIL 2212151 NIL) (-962 2210095 2210538 2210795 "PROPFRML" 2211363 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2209564 2209671 2209799 "PROPERTY" 2209987 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2203649 2207730 2208550 "PRODUCT" 2208790 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2200954 2203107 2203341 "PR" 2203460 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2200750 2200782 2200841 "PRINT" 2200915 T PRINT (NIL) -7 NIL NIL NIL) (-957 2200090 2200207 2200359 "PRIMES" 2200630 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2198155 2198556 2199022 "PRIMELT" 2199669 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2197884 2197933 2197961 "PRIMCAT" 2198085 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2194047 2197822 2197867 "PRIMARR" 2197872 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2193054 2193232 2193460 "PRIMARR2" 2193865 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2192697 2192753 2192864 "PREASSOC" 2192992 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2192172 2192305 2192333 "PPCURVE" 2192538 T PPCURVE (NIL) -9 NIL 2192674 NIL) (-950 2191794 2191967 2192050 "PORTNUM" 2192109 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2189153 2189552 2190144 "POLYROOT" 2191375 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2183090 2188757 2188917 "POLY" 2189026 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2182473 2182531 2182765 "POLYLIFT" 2183026 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2178748 2179197 2179826 "POLYCATQ" 2182018 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2165557 2170923 2170988 "POLYCAT" 2174502 NIL POLYCAT (NIL T T T) -9 NIL 2176430 NIL) (-944 2159006 2160868 2163252 "POLYCAT-" 2163257 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2158593 2158661 2158781 "POLY2UP" 2158932 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2158225 2158282 2158391 "POLY2" 2158530 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2156910 2157149 2157425 "POLUTIL" 2157999 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2155265 2155542 2155873 "POLTOPOL" 2156632 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2150780 2155201 2155247 "POINT" 2155252 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2148967 2149324 2149699 "PNTHEORY" 2150425 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2147386 2147683 2148095 "PMTOOLS" 2148665 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2146979 2147057 2147174 "PMSYM" 2147302 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2146489 2146558 2146732 "PMQFCAT" 2146904 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2145844 2145954 2146110 "PMPRED" 2146366 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2145240 2145326 2145487 "PMPREDFS" 2145745 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2143883 2144091 2144476 "PMPLCAT" 2145002 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2143415 2143494 2143646 "PMLSAGG" 2143798 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2142890 2142966 2143147 "PMKERNEL" 2143333 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2142507 2142582 2142695 "PMINS" 2142809 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2141935 2142004 2142220 "PMFS" 2142432 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2141163 2141281 2141486 "PMDOWN" 2141812 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2140330 2140488 2140669 "PMASS" 2141002 T PMASS (NIL) -7 NIL NIL NIL) (-925 2139608 2139718 2139880 "PMASSFS" 2140217 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2139263 2139331 2139425 "PLOTTOOL" 2139534 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2133870 2135074 2136222 "PLOT" 2138135 T PLOT (NIL) -8 NIL NIL NIL) (-922 2129674 2130718 2131639 "PLOT3D" 2132969 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2128586 2128763 2128998 "PLOT1" 2129478 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2103975 2108652 2113503 "PLEQN" 2123852 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2103293 2103415 2103595 "PINTERP" 2103840 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2102986 2103033 2103136 "PINTERPA" 2103240 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2102234 2102755 2102842 "PI" 2102882 T PI (NIL) -8 NIL NIL 2102949) (-916 2100623 2101572 2101600 "PID" 2101782 T PID (NIL) -9 NIL 2101916 NIL) (-915 2100348 2100385 2100473 "PICOERCE" 2100580 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2099668 2099807 2099983 "PGROEB" 2100204 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2095255 2096069 2096974 "PGE" 2098783 T PGE (NIL) -7 NIL NIL NIL) (-912 2093378 2093625 2093991 "PGCD" 2094972 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2092716 2092819 2092980 "PFRPAC" 2093262 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2089384 2091264 2091617 "PFR" 2092395 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2087773 2088017 2088342 "PFOTOOLS" 2089131 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2086306 2086545 2086896 "PFOQ" 2087530 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2084779 2084991 2085354 "PFO" 2086090 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2081359 2084668 2084737 "PF" 2084742 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2078785 2080030 2080058 "PFECAT" 2080643 T PFECAT (NIL) -9 NIL 2081027 NIL) (-904 2078230 2078384 2078598 "PFECAT-" 2078603 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2076833 2077085 2077386 "PFBRU" 2077979 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2074698 2075051 2075483 "PFBR" 2076484 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2070607 2072074 2072750 "PERM" 2074055 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2065868 2066814 2067684 "PERMGRP" 2069770 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2064000 2064931 2064972 "PERMCAT" 2065418 NIL PERMCAT (NIL T) -9 NIL 2065723 NIL) (-898 2063653 2063694 2063818 "PERMAN" 2063953 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2061189 2063318 2063440 "PENDTREE" 2063564 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2059274 2060016 2060057 "PDRING" 2060714 NIL PDRING (NIL T) -9 NIL 2061000 NIL) (-895 2058377 2058595 2058957 "PDRING-" 2058962 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2055619 2056370 2057038 "PDEPROB" 2057729 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2053164 2053668 2054223 "PDEPACK" 2055084 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2052076 2052266 2052517 "PDECOMP" 2052963 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2049681 2050498 2050526 "PDECAT" 2051313 T PDECAT (NIL) -9 NIL 2052026 NIL) (-890 2049432 2049465 2049555 "PCOMP" 2049642 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2047637 2048233 2048530 "PBWLB" 2049161 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2040137 2041710 2043048 "PATTERN" 2046320 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2039769 2039826 2039935 "PATTERN2" 2040074 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2037526 2037914 2038371 "PATTERN1" 2039358 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2034921 2035475 2035956 "PATRES" 2037091 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2034485 2034552 2034684 "PATRES2" 2034848 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2032368 2032773 2033180 "PATMATCH" 2034152 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2031904 2032087 2032128 "PATMAB" 2032235 NIL PATMAB (NIL T) -9 NIL 2032318 NIL) (-881 2030449 2030758 2031016 "PATLRES" 2031709 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2029995 2030118 2030159 "PATAB" 2030164 NIL PATAB (NIL T) -9 NIL 2030336 NIL) (-879 2027476 2028008 2028581 "PARTPERM" 2029442 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2027097 2027160 2027262 "PARSURF" 2027407 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2026729 2026786 2026895 "PARSU2" 2027034 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2026493 2026533 2026600 "PARSER" 2026682 T PARSER (NIL) -7 NIL NIL NIL) (-875 2026114 2026177 2026279 "PARSCURV" 2026424 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2025746 2025803 2025912 "PARSC2" 2026051 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2025385 2025443 2025540 "PARPCURV" 2025682 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2025017 2025074 2025183 "PARPC2" 2025322 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2024537 2024623 2024742 "PAN2EXPR" 2024918 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2023341 2023658 2023886 "PALETTE" 2024329 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2021809 2022346 2022706 "PAIR" 2023027 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2015706 2021068 2021262 "PADICRC" 2021664 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2008962 2015052 2015236 "PADICRAT" 2015554 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2007304 2008899 2008944 "PADIC" 2008949 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2004506 2006044 2006084 "PADICCT" 2006665 NIL PADICCT (NIL NIL) -9 NIL 2006947 NIL) (-864 2003463 2003663 2003931 "PADEPAC" 2004293 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2002675 2002808 2003014 "PADE" 2003325 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2001089 2001883 2002163 "OWP" 2002479 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2000609 2000795 2000892 "OVERSET" 2001012 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1999682 2000214 2000386 "OVAR" 2000477 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1998946 1999067 1999228 "OUT" 1999541 T OUT (NIL) -7 NIL NIL NIL) (-858 1987844 1990055 1992255 "OUTFORM" 1996766 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1987180 1987441 1987568 "OUTBFILE" 1987737 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1986487 1986652 1986680 "OUTBCON" 1986998 T OUTBCON (NIL) -9 NIL 1987164 NIL) (-855 1986088 1986200 1986357 "OUTBCON-" 1986362 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1985495 1985817 1985906 "OSI" 1986019 T OSI (NIL) -8 NIL NIL NIL) (-853 1985051 1985363 1985391 "OSGROUP" 1985396 T OSGROUP (NIL) -9 NIL 1985418 NIL) (-852 1983796 1984023 1984308 "ORTHPOL" 1984798 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1981374 1983631 1983752 "OREUP" 1983757 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1978804 1981065 1981192 "ORESUP" 1981316 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1976332 1976832 1977393 "OREPCTO" 1978293 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1970148 1972323 1972364 "OREPCAT" 1974712 NIL OREPCAT (NIL T) -9 NIL 1975816 NIL) (-847 1967295 1968077 1969135 "OREPCAT-" 1969140 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1966472 1966744 1966772 "ORDSET" 1967081 T ORDSET (NIL) -9 NIL 1967245 NIL) (-845 1965991 1966113 1966306 "ORDSET-" 1966311 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1964617 1965382 1965410 "ORDRING" 1965612 T ORDRING (NIL) -9 NIL 1965737 NIL) (-843 1964262 1964356 1964500 "ORDRING-" 1964505 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1963668 1964105 1964133 "ORDMON" 1964138 T ORDMON (NIL) -9 NIL 1964159 NIL) (-841 1962830 1962977 1963172 "ORDFUNS" 1963517 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1962194 1962587 1962615 "ORDFIN" 1962680 T ORDFIN (NIL) -9 NIL 1962754 NIL) (-839 1958780 1960780 1961189 "ORDCOMP" 1961818 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1958046 1958173 1958359 "ORDCOMP2" 1958640 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954654 1955537 1956351 "OPTPROB" 1957252 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1951456 1952095 1952799 "OPTPACK" 1953970 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1949169 1949909 1949937 "OPTCAT" 1950756 T OPTCAT (NIL) -9 NIL 1951406 NIL) (-834 1948612 1948846 1948951 "OPSIG" 1949084 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1948380 1948419 1948485 "OPQUERY" 1948566 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1945538 1946691 1947195 "OP" 1947909 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1945073 1945244 1945285 "OPERCAT" 1945420 NIL OPERCAT (NIL T) -9 NIL 1945488 NIL) (-830 1944919 1944946 1945032 "OPERCAT-" 1945037 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1941758 1943716 1944085 "ONECOMP" 1944583 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1941063 1941178 1941352 "ONECOMP2" 1941630 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1940482 1940588 1940718 "OMSERVER" 1940953 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1937370 1939922 1939962 "OMSAGG" 1940023 NIL OMSAGG (NIL T) -9 NIL 1940087 NIL) (-825 1935993 1936256 1936538 "OMPKG" 1937108 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1935423 1935526 1935554 "OM" 1935853 T OM (NIL) -9 NIL NIL NIL) (-823 1933997 1934972 1935141 "OMLO" 1935304 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1932922 1933069 1933296 "OMEXPR" 1933823 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1932240 1932468 1932604 "OMERR" 1932806 T OMERR (NIL) -8 NIL NIL NIL) (-820 1931418 1931661 1931821 "OMERRK" 1932100 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1930896 1931095 1931203 "OMENC" 1931330 T OMENC (NIL) -8 NIL NIL NIL) (-818 1924791 1925976 1927147 "OMDEV" 1929745 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1923860 1924031 1924225 "OMCONN" 1924617 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1922473 1923423 1923451 "OINTDOM" 1923456 T OINTDOM (NIL) -9 NIL 1923477 NIL) (-815 1918279 1919463 1920179 "OFMONOID" 1921789 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1917717 1918216 1918261 "ODVAR" 1918266 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1915167 1917462 1917617 "ODR" 1917622 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1907503 1914943 1915069 "ODPOL" 1915074 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1901373 1907375 1907480 "ODP" 1907485 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1900139 1900354 1900629 "ODETOOLS" 1901147 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1897106 1897764 1898480 "ODESYS" 1899472 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1891988 1892896 1893921 "ODERTRIC" 1896181 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1891414 1891496 1891690 "ODERED" 1891900 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1888302 1888850 1889527 "ODERAT" 1890837 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1885259 1885726 1886323 "ODEPRRIC" 1887831 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1883229 1883798 1884284 "ODEPROB" 1884793 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1879749 1880234 1880881 "ODEPRIM" 1882708 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1878998 1879100 1879360 "ODEPAL" 1879641 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1875160 1875951 1876815 "ODEPACK" 1878154 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1874193 1874300 1874529 "ODEINT" 1875049 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1868294 1869719 1871166 "ODEIFTBL" 1872766 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1863629 1864415 1865374 "ODEEF" 1867453 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1862964 1863053 1863283 "ODECONST" 1863534 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1861115 1861750 1861778 "ODECAT" 1862383 T ODECAT (NIL) -9 NIL 1862914 NIL) (-795 1858014 1860827 1860946 "OCT" 1861028 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1857652 1857695 1857822 "OCTCT2" 1857965 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1852418 1854826 1854866 "OC" 1855963 NIL OC (NIL T) -9 NIL 1856821 NIL) (-792 1849645 1850393 1851383 "OC-" 1851477 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1849023 1849465 1849493 "OCAMON" 1849498 T OCAMON (NIL) -9 NIL 1849519 NIL) (-790 1848580 1848895 1848923 "OASGP" 1848928 T OASGP (NIL) -9 NIL 1848948 NIL) (-789 1847867 1848330 1848358 "OAMONS" 1848398 T OAMONS (NIL) -9 NIL 1848441 NIL) (-788 1847307 1847714 1847742 "OAMON" 1847747 T OAMON (NIL) -9 NIL 1847767 NIL) (-787 1846611 1847103 1847131 "OAGROUP" 1847136 T OAGROUP (NIL) -9 NIL 1847156 NIL) (-786 1846301 1846351 1846439 "NUMTUBE" 1846555 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1839874 1841392 1842928 "NUMQUAD" 1844785 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1835630 1836618 1837643 "NUMODE" 1838869 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1833011 1833865 1833893 "NUMINT" 1834816 T NUMINT (NIL) -9 NIL 1835580 NIL) (-782 1831959 1832156 1832374 "NUMFMT" 1832813 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1818318 1821263 1823795 "NUMERIC" 1829466 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1812715 1817767 1817862 "NTSCAT" 1817867 NIL NTSCAT (NIL T T T T) -9 NIL 1817906 NIL) (-779 1811909 1812074 1812267 "NTPOLFN" 1812554 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1799741 1808734 1809546 "NSUP" 1811130 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1799373 1799430 1799539 "NSUP2" 1799678 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1789356 1799147 1799280 "NSMP" 1799285 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1787788 1788089 1788446 "NREP" 1789044 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1786379 1786631 1786989 "NPCOEF" 1787531 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1785445 1785560 1785776 "NORMRETR" 1786260 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1783486 1783776 1784185 "NORMPK" 1785153 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1783171 1783199 1783323 "NORMMA" 1783452 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1782998 1783128 1783157 "NONE" 1783162 T NONE (NIL) -8 NIL NIL NIL) (-769 1782787 1782816 1782885 "NONE1" 1782962 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1782270 1782332 1782518 "NODE1" 1782719 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1780540 1781364 1781619 "NNI" 1781966 T NNI (NIL) -8 NIL NIL 1782201) (-766 1778960 1779273 1779637 "NLINSOL" 1780208 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1775228 1776196 1777095 "NIPROB" 1778081 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1773985 1774219 1774521 "NFINTBAS" 1774990 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1773159 1773635 1773676 "NETCLT" 1773848 NIL NETCLT (NIL T) -9 NIL 1773930 NIL) (-762 1771867 1772098 1772379 "NCODIV" 1772927 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1771629 1771666 1771741 "NCNTFRAC" 1771824 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1769809 1770173 1770593 "NCEP" 1771254 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1768706 1769453 1769481 "NASRING" 1769591 T NASRING (NIL) -9 NIL 1769671 NIL) (-758 1768501 1768545 1768639 "NASRING-" 1768644 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1767654 1768153 1768181 "NARNG" 1768298 T NARNG (NIL) -9 NIL 1768389 NIL) (-756 1767346 1767413 1767547 "NARNG-" 1767552 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1766225 1766432 1766667 "NAGSP" 1767131 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1757497 1759181 1760854 "NAGS" 1764572 T NAGS (NIL) -7 NIL NIL NIL) (-753 1756045 1756353 1756684 "NAGF07" 1757186 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1750583 1751874 1753181 "NAGF04" 1754758 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1743551 1745165 1746798 "NAGF02" 1748970 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1738775 1739875 1740992 "NAGF01" 1742454 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1732403 1733969 1735554 "NAGE04" 1737210 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1723572 1725693 1727823 "NAGE02" 1730293 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1719525 1720472 1721436 "NAGE01" 1722628 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1717320 1717854 1718412 "NAGD03" 1718987 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1709070 1710998 1712952 "NAGD02" 1715386 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1702881 1704306 1705746 "NAGD01" 1707650 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1699090 1699912 1700749 "NAGC06" 1702064 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1697555 1697887 1698243 "NAGC05" 1698754 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1696931 1697050 1697194 "NAGC02" 1697431 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1695991 1696548 1696588 "NAALG" 1696667 NIL NAALG (NIL T) -9 NIL 1696728 NIL) (-739 1695826 1695855 1695945 "NAALG-" 1695950 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1689776 1690884 1692071 "MULTSQFR" 1694722 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1689095 1689170 1689354 "MULTFACT" 1689688 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1682180 1686058 1686111 "MTSCAT" 1687181 NIL MTSCAT (NIL T T) -9 NIL 1687695 NIL) (-735 1681892 1681946 1682038 "MTHING" 1682120 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1681684 1681717 1681777 "MSYSCMD" 1681852 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1677793 1680439 1680759 "MSET" 1681397 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1674888 1677354 1677395 "MSETAGG" 1677400 NIL MSETAGG (NIL T) -9 NIL 1677434 NIL) (-731 1670756 1672267 1673012 "MRING" 1674188 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1670322 1670389 1670520 "MRF2" 1670683 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1669940 1669975 1670119 "MRATFAC" 1670281 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1667552 1667847 1668278 "MPRFF" 1669645 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1661604 1667406 1667503 "MPOLY" 1667508 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1661094 1661129 1661337 "MPCPF" 1661563 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1660608 1660651 1660835 "MPC3" 1661045 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1659803 1659884 1660105 "MPC2" 1660523 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1658104 1658441 1658831 "MONOTOOL" 1659463 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1657355 1657646 1657674 "MONOID" 1657893 T MONOID (NIL) -9 NIL 1658040 NIL) (-721 1656901 1657020 1657201 "MONOID-" 1657206 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1647752 1653668 1653727 "MONOGEN" 1654401 NIL MONOGEN (NIL T T) -9 NIL 1654857 NIL) (-719 1644970 1645705 1646705 "MONOGEN-" 1646824 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1643829 1644249 1644277 "MONADWU" 1644669 T MONADWU (NIL) -9 NIL 1644907 NIL) (-717 1643201 1643360 1643608 "MONADWU-" 1643613 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1642586 1642804 1642832 "MONAD" 1643039 T MONAD (NIL) -9 NIL 1643151 NIL) (-715 1642271 1642349 1642481 "MONAD-" 1642486 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1640587 1641184 1641463 "MOEBIUS" 1642024 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1639979 1640357 1640397 "MODULE" 1640402 NIL MODULE (NIL T) -9 NIL 1640428 NIL) (-712 1639547 1639643 1639833 "MODULE-" 1639838 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1637254 1637911 1638238 "MODRING" 1639371 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1634225 1635359 1635880 "MODOP" 1636783 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1632840 1633292 1633569 "MODMONOM" 1634088 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1622637 1631131 1631545 "MODMON" 1632477 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1619820 1621481 1621757 "MODFIELD" 1622512 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1618824 1619101 1619291 "MMLFORM" 1619650 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1618350 1618393 1618572 "MMAP" 1618775 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1616559 1617300 1617341 "MLO" 1617764 NIL MLO (NIL T) -9 NIL 1618006 NIL) (-703 1613925 1614441 1615043 "MLIFT" 1616040 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1613316 1613400 1613554 "MKUCFUNC" 1613836 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1612915 1612985 1613108 "MKRECORD" 1613239 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1611962 1612124 1612352 "MKFUNC" 1612726 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1611350 1611454 1611610 "MKFLCFN" 1611845 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1610627 1610729 1610914 "MKBCFUNC" 1611243 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1607361 1610181 1610317 "MINT" 1610511 T MINT (NIL) -8 NIL NIL NIL) (-696 1606173 1606416 1606693 "MHROWRED" 1607116 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1601580 1604708 1605113 "MFLOAT" 1605788 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600937 1601013 1601184 "MFINFACT" 1601492 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1597252 1598100 1598984 "MESH" 1600073 T MESH (NIL) -7 NIL NIL NIL) (-692 1595642 1595954 1596307 "MDDFACT" 1596939 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1592484 1594801 1594842 "MDAGG" 1595097 NIL MDAGG (NIL T) -9 NIL 1595240 NIL) (-690 1582254 1591777 1591984 "MCMPLX" 1592297 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1581395 1581541 1581741 "MCDEN" 1582103 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1579285 1579555 1579935 "MCALCFN" 1581125 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1578210 1578450 1578683 "MAYBE" 1579091 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575822 1576345 1576907 "MATSTOR" 1577681 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571827 1575194 1575442 "MATRIX" 1575607 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1567591 1568300 1569036 "MATLIN" 1571184 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557745 1560883 1560960 "MATCAT" 1565840 NIL MATCAT (NIL T T T) -9 NIL 1567257 NIL) (-682 1554101 1555122 1556478 "MATCAT-" 1556483 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552695 1552848 1553181 "MATCAT2" 1553936 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550807 1551131 1551515 "MAPPKG3" 1552370 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549788 1549961 1550183 "MAPPKG2" 1550631 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1548287 1548571 1548898 "MAPPKG1" 1549494 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1547393 1547693 1547870 "MAPPAST" 1548130 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1547004 1547062 1547185 "MAPHACK3" 1547329 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1546596 1546657 1546771 "MAPHACK2" 1546936 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1546033 1546137 1546279 "MAPHACK1" 1546487 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1544139 1544733 1545037 "MAGMA" 1545761 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1543645 1543863 1543954 "MACROAST" 1544068 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1540111 1541884 1542345 "M3D" 1543217 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1534265 1538480 1538521 "LZSTAGG" 1539303 NIL LZSTAGG (NIL T) -9 NIL 1539598 NIL) (-669 1530222 1531396 1532853 "LZSTAGG-" 1532858 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1527336 1528113 1528600 "LWORD" 1529767 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526939 1527140 1527215 "LSTAST" 1527281 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1520132 1526710 1526844 "LSQM" 1526849 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1519356 1519495 1519723 "LSPP" 1519987 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1517168 1517469 1517925 "LSMP" 1519045 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513947 1514621 1515351 "LSMP1" 1516470 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507872 1513114 1513155 "LSAGG" 1513217 NIL LSAGG (NIL T) -9 NIL 1513295 NIL) (-661 1504567 1505491 1506704 "LSAGG-" 1506709 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1502193 1503711 1503960 "LPOLY" 1504362 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501775 1501860 1501983 "LPEFRAC" 1502102 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1500122 1500869 1501122 "LO" 1501607 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499774 1499886 1499914 "LOGIC" 1500025 T LOGIC (NIL) -9 NIL 1500106 NIL) (-656 1499636 1499659 1499730 "LOGIC-" 1499735 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498829 1498969 1499162 "LODOOPS" 1499492 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1496279 1498745 1498811 "LODO" 1498816 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494817 1495052 1495405 "LODOF" 1496026 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1491165 1493570 1493611 "LODOCAT" 1494049 NIL LODOCAT (NIL T) -9 NIL 1494260 NIL) (-651 1490898 1490956 1491083 "LODOCAT-" 1491088 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1488245 1490739 1490857 "LODO2" 1490862 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485707 1488182 1488227 "LODO1" 1488232 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1484567 1484732 1485044 "LODEEF" 1485530 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479853 1482697 1482738 "LNAGG" 1483685 NIL LNAGG (NIL T) -9 NIL 1484129 NIL) (-646 1479000 1479214 1479556 "LNAGG-" 1479561 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1475163 1475925 1476564 "LMOPS" 1478415 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1474558 1474920 1474961 "LMODULE" 1475022 NIL LMODULE (NIL T) -9 NIL 1475064 NIL) (-643 1471804 1474203 1474326 "LMDICT" 1474468 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1471530 1471712 1471772 "LITERAL" 1471777 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464761 1470476 1470774 "LIST" 1471265 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1464286 1464360 1464499 "LIST3" 1464681 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1463293 1463471 1463699 "LIST2" 1464104 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1461427 1461739 1462138 "LIST2MAP" 1462940 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1460149 1460793 1460834 "LINEXP" 1461089 NIL LINEXP (NIL T) -9 NIL 1461238 NIL) (-636 1458796 1459056 1459353 "LINDEP" 1459901 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1455563 1456282 1457059 "LIMITRF" 1458051 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453838 1454134 1454550 "LIMITPS" 1455258 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1448293 1453349 1453577 "LIE" 1453659 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1447342 1447785 1447825 "LIECAT" 1447965 NIL LIECAT (NIL T) -9 NIL 1448116 NIL) (-631 1447183 1447210 1447298 "LIECAT-" 1447303 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439795 1446632 1446797 "LIB" 1447038 T LIB (NIL) -8 NIL NIL NIL) (-629 1435430 1436313 1437248 "LGROBP" 1438912 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1433296 1433570 1433932 "LF" 1435151 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1432136 1432828 1432856 "LFCAT" 1433063 T LFCAT (NIL) -9 NIL 1433202 NIL) (-626 1429038 1429668 1430356 "LEXTRIPK" 1431500 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425809 1426608 1427111 "LEXP" 1428618 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1425312 1425530 1425622 "LETAST" 1425737 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423710 1424023 1424424 "LEADCDET" 1424994 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422900 1422974 1423203 "LAZM3PK" 1423631 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417844 1420977 1421515 "LAUPOL" 1422412 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1417409 1417453 1417621 "LAPLACE" 1417794 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1415375 1416510 1416761 "LA" 1417242 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1414448 1415006 1415047 "LALG" 1415109 NIL LALG (NIL T) -9 NIL 1415168 NIL) (-617 1414162 1414221 1414357 "LALG-" 1414362 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413997 1414021 1414062 "KVTFROM" 1414124 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412797 1413214 1413443 "KTVLOGIC" 1413788 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1412632 1412656 1412697 "KRCFROM" 1412759 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1411536 1411723 1412022 "KOVACIC" 1412432 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1411371 1411395 1411436 "KONVERT" 1411498 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1411206 1411230 1411271 "KOERCE" 1411333 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408939 1409700 1410093 "KERNEL" 1410845 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1408441 1408522 1408652 "KERNEL2" 1408853 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1402292 1406980 1407034 "KDAGG" 1407411 NIL KDAGG (NIL T T) -9 NIL 1407617 NIL) (-607 1401821 1401945 1402150 "KDAGG-" 1402155 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394996 1401482 1401637 "KAFILE" 1401699 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1389451 1394507 1394735 "JORDAN" 1394817 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388857 1389100 1389221 "JOINAST" 1389350 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388703 1388762 1388817 "JAVACODE" 1388822 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1385002 1386908 1386962 "IXAGG" 1387891 NIL IXAGG (NIL T T) -9 NIL 1388350 NIL) (-601 1383921 1384227 1384646 "IXAGG-" 1384651 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1379501 1383843 1383902 "IVECTOR" 1383907 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1378267 1378504 1378770 "ITUPLE" 1379268 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376703 1376880 1377186 "ITRIGMNP" 1378089 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1375448 1375652 1375935 "ITFUN3" 1376479 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1375080 1375137 1375246 "ITFUN2" 1375385 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372909 1373942 1374241 "ITAYLOR" 1374814 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361881 1367046 1368209 "ISUPS" 1371779 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360985 1361125 1361361 "ISUMP" 1361728 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1356249 1360786 1360865 "ISTRING" 1360938 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355752 1355970 1356062 "ISAST" 1356177 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354962 1355043 1355259 "IRURPK" 1355666 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353898 1354099 1354339 "IRSN" 1354742 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351927 1352282 1352718 "IRRF2F" 1353536 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1351674 1351712 1351788 "IRREDFFX" 1351883 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1350289 1350548 1350847 "IROOT" 1351407 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346920 1347973 1348665 "IR" 1349629 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1344533 1345028 1345594 "IR2" 1346398 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1343605 1343718 1343939 "IR2F" 1344416 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1343396 1343430 1343490 "IPRNTPK" 1343565 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1340003 1343285 1343354 "IPF" 1343359 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1338357 1339928 1339985 "IPADIC" 1339990 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337696 1337917 1338047 "IP4ADDR" 1338247 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1337196 1337400 1337510 "IOMODE" 1337606 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1336269 1336793 1336920 "IOBFILE" 1337089 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335757 1336173 1336201 "IOBCON" 1336206 T IOBCON (NIL) -9 NIL 1336227 NIL) (-575 1335254 1335312 1335502 "INVLAPLA" 1335693 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324902 1327256 1329642 "INTTR" 1332918 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1321246 1321988 1322852 "INTTOOLS" 1324087 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320832 1320923 1321040 "INTSLPE" 1321149 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318813 1320755 1320814 "INTRVL" 1320819 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1316415 1316927 1317502 "INTRF" 1318298 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315826 1315923 1316065 "INTRET" 1316313 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313823 1314212 1314682 "INTRAT" 1315434 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1311051 1311634 1312260 "INTPM" 1313308 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307753 1308353 1309098 "INTPAF" 1310437 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302932 1303894 1304945 "INTPACK" 1306722 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299836 1302661 1302788 "INT" 1302825 T INT (NIL) -8 NIL NIL NIL) (-563 1299088 1299240 1299448 "INTHERTR" 1299678 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1298527 1298607 1298795 "INTHERAL" 1299002 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1296373 1296816 1297273 "INTHEORY" 1298090 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287681 1289302 1291081 "INTG0" 1294725 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1268254 1273044 1277854 "INTFTBL" 1282891 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1267503 1267641 1267814 "INTFACT" 1268113 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264888 1265334 1265898 "INTEF" 1267057 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1263347 1264060 1264088 "INTDOM" 1264389 T INTDOM (NIL) -9 NIL 1264596 NIL) (-555 1262716 1262890 1263132 "INTDOM-" 1263137 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1259203 1261100 1261154 "INTCAT" 1261953 NIL INTCAT (NIL T) -9 NIL 1262273 NIL) (-553 1258675 1258778 1258906 "INTBIT" 1259095 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1257346 1257500 1257814 "INTALG" 1258520 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256803 1256893 1257063 "INTAF" 1257250 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1250257 1256613 1256753 "INTABL" 1256758 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1249588 1250027 1250092 "INT8" 1250126 T INT8 (NIL) -8 NIL NIL 1250171) (-548 1248918 1249357 1249422 "INT64" 1249456 T INT64 (NIL) -8 NIL NIL 1249501) (-547 1248248 1248687 1248752 "INT32" 1248786 T INT32 (NIL) -8 NIL NIL 1248831) (-546 1247578 1248017 1248082 "INT16" 1248116 T INT16 (NIL) -8 NIL NIL 1248161) (-545 1242585 1245267 1245295 "INS" 1246229 T INS (NIL) -9 NIL 1246894 NIL) (-544 1239825 1240596 1241570 "INS-" 1241643 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1238600 1238827 1239125 "INPSIGN" 1239578 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237718 1237835 1238032 "INPRODPF" 1238480 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1236612 1236729 1236966 "INPRODFF" 1237598 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1235612 1235764 1236024 "INNMFACT" 1236448 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234809 1234906 1235094 "INMODGCD" 1235511 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1233317 1233562 1233886 "INFSP" 1234554 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1232501 1232618 1232801 "INFPROD0" 1233197 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1229383 1230566 1231081 "INFORM" 1231994 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228993 1229053 1229151 "INFORM1" 1229318 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1228516 1228605 1228719 "INFINITY" 1228899 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227692 1228236 1228337 "INETCLTS" 1228435 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1226308 1226558 1226879 "INEP" 1227440 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1225584 1226205 1226270 "INDE" 1226275 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1225148 1225216 1225333 "INCRMAPS" 1225511 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223966 1224417 1224623 "INBFILE" 1224962 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1219266 1220202 1221146 "INBFF" 1223054 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1218174 1218443 1218471 "INBCON" 1218984 T INBCON (NIL) -9 NIL 1219250 NIL) (-526 1217426 1217649 1217925 "INBCON-" 1217930 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216932 1217150 1217241 "INAST" 1217355 T INAST (NIL) -8 NIL NIL NIL) (-524 1216386 1216611 1216717 "IMPTAST" 1216846 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212880 1216230 1216334 "IMATRIX" 1216339 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1211592 1211715 1212030 "IMATQF" 1212736 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209812 1210039 1210376 "IMATLIN" 1211348 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1204438 1209736 1209794 "ILIST" 1209799 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1202391 1204298 1204411 "IIARRAY2" 1204416 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197816 1202302 1202366 "IFF" 1202371 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1197190 1197433 1197549 "IFAST" 1197720 T IFAST (NIL) -8 NIL NIL NIL) (-516 1192233 1196482 1196670 "IFARRAY" 1197047 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1191440 1192137 1192210 "IFAMON" 1192215 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1191024 1191089 1191143 "IEVALAB" 1191350 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190699 1190767 1190927 "IEVALAB-" 1190932 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1190357 1190613 1190676 "IDPO" 1190681 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1189634 1190246 1190321 "IDPOAMS" 1190326 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188968 1189523 1189598 "IDPOAM" 1189603 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1188053 1188303 1188356 "IDPC" 1188769 NIL IDPC (NIL T T) -9 NIL 1188918 NIL) (-508 1187549 1187945 1188018 "IDPAM" 1188023 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186952 1187441 1187514 "IDPAG" 1187519 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186624 1186788 1186863 "IDENT" 1186897 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182879 1183727 1184622 "IDECOMP" 1185781 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175743 1176802 1177849 "IDEAL" 1181915 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174907 1175019 1175218 "ICDEN" 1175627 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1174005 1174387 1174534 "ICARD" 1174780 T ICARD (NIL) -8 NIL NIL NIL) (-501 1172065 1172378 1172783 "IBPTOOLS" 1173682 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167699 1171685 1171798 "IBITS" 1171984 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1164422 1164998 1165693 "IBATOOL" 1167116 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1162201 1162663 1163196 "IBACHIN" 1163957 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1160078 1162047 1162150 "IARRAY2" 1162155 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1156232 1160004 1160061 "IARRAY1" 1160066 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1150216 1154644 1155125 "IAN" 1155771 T IAN (NIL) -8 NIL NIL NIL) (-494 1149727 1149784 1149957 "IALGFACT" 1150153 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1149255 1149368 1149396 "HYPCAT" 1149603 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148793 1148910 1149096 "HYPCAT-" 1149101 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1148415 1148588 1148671 "HOSTNAME" 1148730 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1148260 1148297 1148338 "HOMOTOP" 1148343 NIL HOMOTOP (NIL T) -9 NIL 1148376 NIL) (-489 1144939 1146270 1146311 "HOAGG" 1147292 NIL HOAGG (NIL T) -9 NIL 1147971 NIL) (-488 1143533 1143932 1144458 "HOAGG-" 1144463 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1137564 1143128 1143277 "HEXADEC" 1143404 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1136312 1136534 1136797 "HEUGCD" 1137341 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1135415 1136149 1136279 "HELLFDIV" 1136284 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133642 1135192 1135280 "HEAP" 1135359 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132932 1133194 1133328 "HEADAST" 1133528 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126846 1132847 1132909 "HDP" 1132914 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1120589 1126481 1126633 "HDMP" 1126747 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119913 1120053 1120217 "HB" 1120445 T HB (NIL) -7 NIL NIL NIL) (-479 1113410 1119759 1119863 "HASHTBL" 1119868 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112913 1113131 1113223 "HASAST" 1113338 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110718 1112535 1112717 "HACKPI" 1112751 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1106413 1110571 1110684 "GTSET" 1110689 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099939 1106291 1106389 "GSTBL" 1106394 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092244 1098970 1099235 "GSERIES" 1099730 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1091411 1091802 1091830 "GROUP" 1092033 T GROUP (NIL) -9 NIL 1092167 NIL) (-472 1090777 1090936 1091187 "GROUP-" 1091192 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089144 1089465 1089852 "GROEBSOL" 1090454 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088084 1088346 1088397 "GRMOD" 1088926 NIL GRMOD (NIL T T) -9 NIL 1089094 NIL) (-469 1087852 1087888 1088016 "GRMOD-" 1088021 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083169 1084206 1085206 "GRIMAGE" 1086872 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081635 1081896 1082220 "GRDEF" 1082865 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081079 1081195 1081336 "GRAY" 1081514 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080292 1080672 1080723 "GRALG" 1080876 NIL GRALG (NIL T T) -9 NIL 1080969 NIL) (-464 1079953 1080026 1080189 "GRALG-" 1080194 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076757 1079538 1079716 "GPOLSET" 1079860 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076111 1076168 1076426 "GOSPER" 1076694 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071870 1072549 1073075 "GMODPOL" 1075810 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070875 1071059 1071297 "GHENSEL" 1071682 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064926 1065769 1066796 "GENUPS" 1069959 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064623 1064674 1064763 "GENUFACT" 1064869 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064035 1064112 1064277 "GENPGCD" 1064541 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1063509 1063544 1063757 "GENMFACT" 1063994 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062075 1062332 1062639 "GENEEZ" 1063252 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055976 1061686 1061848 "GDMP" 1061998 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1045345 1049747 1050853 "GCNAALG" 1054959 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043764 1044600 1044628 "GCDDOM" 1044883 T GCDDOM (NIL) -9 NIL 1045040 NIL) (-451 1043234 1043361 1043576 "GCDDOM-" 1043581 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041906 1042091 1042395 "GB" 1043013 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1030522 1032852 1035244 "GBINTERN" 1039597 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1028359 1028651 1029072 "GBF" 1030197 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027140 1027305 1027572 "GBEUCLID" 1028175 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1026489 1026614 1026763 "GAUSSFAC" 1027011 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024856 1025158 1025472 "GALUTIL" 1026208 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023164 1023438 1023762 "GALPOLYU" 1024583 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1020529 1020819 1021226 "GALFACTU" 1022861 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1012335 1013834 1015442 "GALFACT" 1018961 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009723 1010381 1010409 "FVFUN" 1011565 T FVFUN (NIL) -9 NIL 1012285 NIL) (-440 1008989 1009171 1009199 "FVC" 1009490 T FVC (NIL) -9 NIL 1009673 NIL) (-439 1008659 1008814 1008882 "FUNDESC" 1008941 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1008301 1008456 1008537 "FUNCTION" 1008611 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006072 1006623 1007089 "FT" 1007855 T FT (NIL) -8 NIL NIL NIL) (-436 1004890 1005373 1005576 "FTEM" 1005889 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003146 1003435 1003839 "FSUPFACT" 1004581 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1001543 1001832 1002164 "FST" 1002834 T FST (NIL) -8 NIL NIL NIL) (-433 1000714 1000820 1001015 "FSRED" 1001425 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 999392 999648 1000002 "FSPRMELT" 1000429 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 996477 996915 997414 "FSPECF" 998955 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 978531 986980 987020 "FS" 990868 NIL FS (NIL T) -9 NIL 993157 NIL) (-429 967178 970171 974227 "FS-" 974524 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966692 966746 966923 "FSINT" 967119 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 965011 965685 965988 "FSERIES" 966471 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 964025 964141 964372 "FSCINT" 964891 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 960259 962969 963010 "FSAGG" 963380 NIL FSAGG (NIL T) -9 NIL 963639 NIL) (-424 958021 958622 959418 "FSAGG-" 959513 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 957063 957206 957433 "FSAGG2" 957874 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954717 954997 955551 "FS2UPS" 956781 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 954299 954342 954497 "FS2" 954668 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 953156 953327 953636 "FS2EXPXP" 954124 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 952582 952697 952849 "FRUTIL" 953036 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 944022 948077 949435 "FR" 951256 NIL FR (NIL T) -8 NIL NIL NIL) (-417 939097 941740 941780 "FRNAALG" 943176 NIL FRNAALG (NIL T) -9 NIL 943783 NIL) (-416 934770 935846 937121 "FRNAALG-" 937871 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 934408 934451 934578 "FRNAAF2" 934721 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932815 933262 933557 "FRMOD" 934220 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 930593 931198 931515 "FRIDEAL" 932606 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929788 929875 930164 "FRIDEAL2" 930500 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928921 929335 929376 "FRETRCT" 929381 NIL FRETRCT (NIL T) -9 NIL 929557 NIL) (-410 928033 928264 928615 "FRETRCT-" 928620 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 925237 926421 926480 "FRAMALG" 927362 NIL FRAMALG (NIL T T) -9 NIL 927654 NIL) (-408 923371 923826 924456 "FRAMALG-" 924679 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 917319 922846 923122 "FRAC" 923127 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916955 917012 917119 "FRAC2" 917256 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 916591 916648 916755 "FR2" 916892 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 911256 914116 914144 "FPS" 915263 T FPS (NIL) -9 NIL 915820 NIL) (-403 910705 910814 910978 "FPS-" 911124 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 908151 909794 909822 "FPC" 910047 T FPC (NIL) -9 NIL 910189 NIL) (-401 907944 907984 908081 "FPC-" 908086 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906822 907432 907473 "FPATMAB" 907478 NIL FPATMAB (NIL T) -9 NIL 907630 NIL) (-399 904522 904998 905424 "FPARFRAC" 906459 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899915 900414 901096 "FORTRAN" 903954 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897631 898131 898670 "FORT" 899396 T FORT (NIL) -7 NIL NIL NIL) (-396 895307 895869 895897 "FORTFN" 896957 T FORTFN (NIL) -9 NIL 897581 NIL) (-395 895071 895121 895149 "FORTCAT" 895208 T FORTCAT (NIL) -9 NIL 895270 NIL) (-394 893204 893687 894077 "FORMULA" 894701 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892992 893022 893091 "FORMULA1" 893168 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 892515 892567 892740 "FORDER" 892934 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891611 891775 891968 "FOP" 892342 T FOP (NIL) -7 NIL NIL NIL) (-390 890219 890891 891065 "FNLA" 891493 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888974 889363 889391 "FNCAT" 889851 T FNCAT (NIL) -9 NIL 890111 NIL) (-388 888540 888933 888961 "FNAME" 888966 T FNAME (NIL) -8 NIL NIL NIL) (-387 887195 888132 888160 "FMTC" 888165 T FMTC (NIL) -9 NIL 888201 NIL) (-386 883555 884718 885347 "FMONOID" 886599 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882774 883297 883446 "FM" 883451 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880198 880844 880872 "FMFUN" 882016 T FMFUN (NIL) -9 NIL 882724 NIL) (-383 879467 879648 879676 "FMC" 879966 T FMC (NIL) -9 NIL 880148 NIL) (-382 876661 877495 877549 "FMCAT" 878744 NIL FMCAT (NIL T T) -9 NIL 879239 NIL) (-381 875554 876427 876527 "FM1" 876606 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873328 873744 874238 "FLOATRP" 875105 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866929 871057 871678 "FLOAT" 872727 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864367 864867 865445 "FLOATCP" 866396 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863168 863980 864021 "FLINEXP" 864026 NIL FLINEXP (NIL T) -9 NIL 864119 NIL) (-376 862322 862557 862885 "FLINEXP-" 862890 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861398 861542 861766 "FLASORT" 862174 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858615 859457 859509 "FLALG" 860736 NIL FLALG (NIL T T) -9 NIL 861203 NIL) (-373 852399 856101 856142 "FLAGG" 857404 NIL FLAGG (NIL T) -9 NIL 858056 NIL) (-372 851125 851464 851954 "FLAGG-" 851959 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850167 850310 850537 "FLAGG2" 850978 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847134 848116 848175 "FINRALG" 849303 NIL FINRALG (NIL T T) -9 NIL 849811 NIL) (-369 846294 846523 846862 "FINRALG-" 846867 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845700 845913 845941 "FINITE" 846137 T FINITE (NIL) -9 NIL 846244 NIL) (-367 838158 840319 840359 "FINAALG" 844026 NIL FINAALG (NIL T) -9 NIL 845479 NIL) (-366 833490 834540 835684 "FINAALG-" 837063 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832885 833245 833348 "FILE" 833420 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831569 831881 831935 "FILECAT" 832619 NIL FILECAT (NIL T T) -9 NIL 832835 NIL) (-363 829429 830931 830959 "FIELD" 830999 T FIELD (NIL) -9 NIL 831079 NIL) (-362 828049 828434 828945 "FIELD-" 828950 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825926 826684 827031 "FGROUP" 827735 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825016 825180 825400 "FGLMICPK" 825758 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820875 824941 824998 "FFX" 825003 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820476 820537 820672 "FFSLPE" 820808 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816465 817248 818044 "FFPOLY" 819712 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815969 816005 816214 "FFPOLY2" 816423 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811839 815888 815951 "FFP" 815956 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807264 811750 811814 "FF" 811819 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802417 806607 806797 "FFNBX" 807118 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797373 801552 801810 "FFNBP" 802271 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792033 796657 796868 "FFNB" 797206 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790865 791063 791378 "FFINTBAS" 791830 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787085 789272 789300 "FFIELDC" 789920 T FFIELDC (NIL) -9 NIL 790296 NIL) (-348 785747 786118 786615 "FFIELDC-" 786620 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785316 785362 785486 "FFHOM" 785689 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783011 783498 784015 "FFF" 784831 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778656 782753 782854 "FFCGX" 782954 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774304 778388 778495 "FFCGP" 778599 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769514 774031 774139 "FFCG" 774240 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751339 760385 760471 "FFCAT" 765636 NIL FFCAT (NIL T T T) -9 NIL 767087 NIL) (-341 746537 747584 748898 "FFCAT-" 750128 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745948 745991 746226 "FFCAT2" 746488 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735145 738920 740140 "FEXPR" 744800 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734145 734580 734621 "FEVALAB" 734705 NIL FEVALAB (NIL T) -9 NIL 734966 NIL) (-337 733304 733514 733852 "FEVALAB-" 733857 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731897 732687 732890 "FDIV" 733203 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728963 729678 729793 "FDIVCAT" 731361 NIL FDIVCAT (NIL T T T T) -9 NIL 731798 NIL) (-334 728725 728752 728922 "FDIVCAT-" 728927 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727945 728032 728309 "FDIV2" 728632 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726631 726890 727179 "FCPAK1" 727676 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725757 726131 726272 "FCOMP" 726522 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709486 712907 716445 "FC" 722239 T FC (NIL) -8 NIL NIL NIL) (-329 702057 706050 706090 "FAXF" 707892 NIL FAXF (NIL T) -9 NIL 708584 NIL) (-328 699333 699991 700816 "FAXF-" 701281 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694433 698709 698885 "FARRAY" 699190 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689678 691718 691771 "FAMR" 692794 NIL FAMR (NIL T T) -9 NIL 693254 NIL) (-325 688568 688870 689305 "FAMR-" 689310 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687764 688490 688543 "FAMONOID" 688548 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685576 686260 686313 "FAMONC" 687254 NIL FAMONC (NIL T T) -9 NIL 687640 NIL) (-322 684268 685330 685467 "FAGROUP" 685472 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 682063 682382 682785 "FACUTIL" 683949 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681162 681347 681569 "FACTFUNC" 681873 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673559 680413 680625 "EXPUPXS" 681018 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 671042 671582 672168 "EXPRTUBE" 672993 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667236 667828 668565 "EXPRODE" 670381 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652602 665891 666319 "EXPR" 666840 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647009 647596 648409 "EXPR2UPS" 651900 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646645 646702 646809 "EXPR2" 646946 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638042 645777 646074 "EXPEXPAN" 646482 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637869 637999 638028 "EXIT" 638033 T EXIT (NIL) -8 NIL NIL NIL) (-311 637376 637593 637684 "EXITAST" 637798 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637003 637065 637178 "EVALCYC" 637308 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636544 636662 636703 "EVALAB" 636873 NIL EVALAB (NIL T) -9 NIL 636977 NIL) (-308 636025 636147 636368 "EVALAB-" 636373 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633485 634761 634789 "EUCDOM" 635344 T EUCDOM (NIL) -9 NIL 635694 NIL) (-306 631890 632332 632922 "EUCDOM-" 632927 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619428 622188 624938 "ESTOOLS" 629160 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619060 619117 619226 "ESTOOLS2" 619365 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618811 618853 618933 "ESTOOLS1" 619012 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612716 614444 614472 "ES" 617240 T ES (NIL) -9 NIL 618649 NIL) (-301 607663 608950 610767 "ES-" 610931 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604037 604798 605578 "ESCONT" 606903 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603782 603814 603896 "ESCONT1" 603999 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603457 603507 603607 "ES2" 603726 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603087 603145 603254 "ES1" 603393 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602303 602432 602608 "ERROR" 602931 T ERROR (NIL) -7 NIL NIL NIL) (-295 595806 602162 602253 "EQTBL" 602258 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588357 591120 592569 "EQ" 594390 NIL -2045 (NIL T) -8 NIL NIL NIL) (-293 587989 588046 588155 "EQ2" 588294 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583278 584327 585420 "EP" 586928 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581878 582169 582475 "ENV" 582992 T ENV (NIL) -8 NIL NIL NIL) (-290 581049 581577 581605 "ENTIRER" 581610 T ENTIRER (NIL) -9 NIL 581656 NIL) (-289 577543 579004 579374 "EMR" 580848 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576687 576872 576926 "ELTAGG" 577306 NIL ELTAGG (NIL T T) -9 NIL 577517 NIL) (-287 576406 576468 576609 "ELTAGG-" 576614 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576195 576224 576278 "ELTAB" 576362 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575321 575467 575666 "ELFUTS" 576046 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575063 575119 575147 "ELEMFUN" 575252 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574933 574954 575022 "ELEMFUN-" 575027 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569824 573033 573074 "ELAGG" 574014 NIL ELAGG (NIL T) -9 NIL 574477 NIL) (-281 568109 568543 569206 "ELAGG-" 569211 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566774 567052 567345 "ELABEXPR" 567836 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559638 561441 562268 "EFUPXS" 566050 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553088 554889 555699 "EFULS" 558914 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550510 550868 551347 "EFSTRUC" 552720 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 539581 541147 542707 "EF" 549025 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538682 539066 539215 "EAB" 539452 T EAB (NIL) -8 NIL NIL NIL) (-274 537891 538641 538669 "E04UCFA" 538674 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537100 537850 537878 "E04NAFA" 537883 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 536309 537059 537087 "E04MBFA" 537092 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 535518 536268 536296 "E04JAFA" 536301 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534729 535477 535505 "E04GCFA" 535510 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533940 534688 534716 "E04FDFA" 534721 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533149 533899 533927 "E04DGFA" 533932 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527322 528674 530038 "E04AGNT" 531805 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526028 526508 526548 "DVARCAT" 527023 NIL DVARCAT (NIL T) -9 NIL 527222 NIL) (-265 525232 525444 525758 "DVARCAT-" 525763 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518124 525031 525160 "DSMP" 525165 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512933 514069 515137 "DROPT" 517076 T DROPT (NIL) -8 NIL NIL NIL) (-262 512598 512657 512755 "DROPT1" 512868 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507713 508839 509976 "DROPT0" 511481 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506058 506383 506769 "DRAWPT" 507347 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500645 501568 502647 "DRAW" 505032 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 500278 500331 500449 "DRAWHACK" 500586 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499009 499278 499569 "DRAWCX" 500007 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 498524 498593 498744 "DRAWCURV" 498935 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488992 490954 493069 "DRAWCFUN" 496429 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485805 487687 487728 "DQAGG" 488357 NIL DQAGG (NIL T) -9 NIL 488630 NIL) (-253 474076 480783 480866 "DPOLCAT" 482718 NIL DPOLCAT (NIL T T T T) -9 NIL 483263 NIL) (-252 468912 470261 472219 "DPOLCAT-" 472224 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 462061 468773 468871 "DPMO" 468876 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 455113 461841 462008 "DPMM" 462013 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454745 455032 455080 "DOMCTOR" 455085 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454040 454267 454404 "DOMAIN" 454628 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447783 453675 453827 "DMP" 453941 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 447383 447439 447583 "DLP" 447721 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 441253 446710 446900 "DLIST" 447225 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 438097 440106 440147 "DLAGG" 440697 NIL DLAGG (NIL T) -9 NIL 440927 NIL) (-243 436902 437540 437568 "DIVRING" 437660 T DIVRING (NIL) -9 NIL 437743 NIL) (-242 436139 436329 436629 "DIVRING-" 436634 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 434241 434598 435004 "DISPLAY" 435753 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 428177 434155 434218 "DIRPROD" 434223 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 427025 427228 427493 "DIRPROD2" 427970 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 416282 422240 422293 "DIRPCAT" 422703 NIL DIRPCAT (NIL NIL T) -9 NIL 423543 NIL) (-237 413608 414250 415131 "DIRPCAT-" 415468 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412895 413055 413241 "DIOSP" 413442 T DIOSP (NIL) -7 NIL NIL NIL) (-235 409597 411807 411848 "DIOPS" 412282 NIL DIOPS (NIL T) -9 NIL 412511 NIL) (-234 409146 409260 409451 "DIOPS-" 409456 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408030 408632 408660 "DIFRING" 408847 T DIFRING (NIL) -9 NIL 408957 NIL) (-232 407676 407753 407905 "DIFRING-" 407910 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 405473 406719 406760 "DIFEXT" 407123 NIL DIFEXT (NIL T) -9 NIL 407417 NIL) (-230 403758 404186 404852 "DIFEXT-" 404857 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401080 403290 403331 "DIAGG" 403336 NIL DIAGG (NIL T) -9 NIL 403356 NIL) (-228 400464 400621 400873 "DIAGG-" 400878 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395929 399423 399700 "DHMATRIX" 400233 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 391541 392450 393460 "DFSFUN" 394939 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386646 390472 390784 "DFLOAT" 391249 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384874 385155 385551 "DFINTTLS" 386354 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381930 382895 383295 "DERHAM" 384540 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379779 381705 381794 "DEQUEUE" 381874 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378994 379127 379323 "DEGRED" 379641 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 375389 376134 376987 "DEFINTRF" 378222 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372916 373385 373984 "DEFINTEF" 374908 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 372293 372536 372651 "DEFAST" 372821 T DEFAST (NIL) -8 NIL NIL NIL) (-217 366324 371888 372037 "DECIMAL" 372164 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363834 364294 364800 "DDFACT" 365868 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 363430 363473 363624 "DBLRESP" 363785 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 361329 361663 362023 "DBASE" 363197 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 360598 360809 360955 "DATAARY" 361228 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359731 360557 360585 "D03FAFA" 360590 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358865 359690 359718 "D03EEFA" 359723 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356815 357281 357770 "D03AGNT" 358396 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356131 356774 356802 "D02EJFA" 356807 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 355447 356090 356118 "D02CJFA" 356123 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354763 355406 355434 "D02BHFA" 355439 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354079 354722 354750 "D02BBFA" 354755 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347276 348865 350471 "D02AGNT" 352493 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345044 345567 346113 "D01WGTS" 346750 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344138 345003 345031 "D01TRNS" 345036 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343233 344097 344125 "D01GBFA" 344130 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342328 343192 343220 "D01FCFA" 343225 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341423 342287 342315 "D01ASFA" 342320 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340518 341382 341410 "D01AQFA" 341415 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 339613 340477 340505 "D01APFA" 340510 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338708 339572 339600 "D01ANFA" 339605 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337803 338667 338695 "D01AMFA" 338700 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336898 337762 337790 "D01ALFA" 337795 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335993 336857 336885 "D01AKFA" 336890 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335088 335952 335980 "D01AJFA" 335985 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328383 329936 331497 "D01AGNT" 333547 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327720 327848 328000 "CYCLOTOM" 328251 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324455 325168 325895 "CYCLES" 327013 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323767 323901 324072 "CVMP" 324316 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321538 321796 322172 "CTRIGMNP" 323495 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321033 321332 321405 "CTOR" 321485 T CTOR (NIL) -8 NIL NIL NIL) (-186 320569 320764 320865 "CTORKIND" 320952 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319917 320176 320204 "CTORCAT" 320386 T CTORCAT (NIL) -9 NIL 320499 NIL) (-184 319515 319626 319785 "CTORCAT-" 319790 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319031 319218 319316 "CTORCALL" 319437 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318405 318504 318657 "CSTTOOLS" 318928 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314204 314861 315619 "CRFP" 317717 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313706 313925 314017 "CRCEAST" 314132 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312753 312938 313166 "CRAPACK" 313510 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312137 312238 312442 "CPMATCH" 312629 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311862 311890 311996 "CPIMA" 312103 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308226 308898 309616 "COORDSYS" 311197 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307638 307759 307901 "CONTOUR" 308104 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303556 305641 306133 "CONTFRAC" 307178 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303436 303457 303485 "CONDUIT" 303522 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302601 303129 303157 "COMRING" 303162 T COMRING (NIL) -9 NIL 303214 NIL) (-171 301682 301959 302143 "COMPPROP" 302437 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301343 301378 301506 "COMPLPAT" 301641 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291392 301152 301261 "COMPLEX" 301266 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291028 291085 291192 "COMPLEX2" 291329 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290746 290781 290879 "COMPFACT" 290987 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274900 285128 285168 "COMPCAT" 286172 NIL COMPCAT (NIL T) -9 NIL 287568 NIL) (-165 264411 267339 270966 "COMPCAT-" 271322 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264140 264168 264271 "COMMUPC" 264377 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263934 263968 264027 "COMMONOP" 264101 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263517 263685 263772 "COMM" 263867 T COMM (NIL) -8 NIL NIL NIL) (-161 263120 263321 263396 "COMMAAST" 263462 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262369 262563 262591 "COMBOPC" 262929 T COMBOPC (NIL) -9 NIL 263104 NIL) (-159 261265 261475 261717 "COMBINAT" 262159 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 257462 258036 258676 "COMBF" 260687 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256247 256578 256813 "COLOR" 257247 T COLOR (NIL) -8 NIL NIL NIL) (-156 255750 255968 256060 "COLONAST" 256175 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255390 255437 255562 "CMPLXRT" 255697 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254865 255090 255189 "CLLCTAST" 255311 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250365 251395 252475 "CLIP" 253805 T CLIP (NIL) -7 NIL NIL NIL) (-152 248738 249471 249710 "CLIF" 250192 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244960 246884 246925 "CLAGG" 247854 NIL CLAGG (NIL T) -9 NIL 248390 NIL) (-150 243382 243839 244422 "CLAGG-" 244427 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242926 243011 243151 "CINTSLPE" 243291 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240427 240898 241446 "CHVAR" 242454 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239662 240190 240218 "CHARZ" 240223 T CHARZ (NIL) -9 NIL 240238 NIL) (-146 239416 239456 239534 "CHARPOL" 239616 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238535 239096 239124 "CHARNZ" 239171 T CHARNZ (NIL) -9 NIL 239227 NIL) (-144 236524 237225 237560 "CHAR" 238220 T CHAR (NIL) -8 NIL NIL NIL) (-143 236250 236311 236339 "CFCAT" 236450 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235495 235606 235788 "CDEN" 236134 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231487 234648 234928 "CCLASS" 235235 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230794 230937 231100 "CATEGORY" 231344 T -10 (NIL) -8 NIL NIL NIL) (-139 230426 230713 230761 "CATCTOR" 230766 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229904 230129 230227 "CATAST" 230348 T CATAST (NIL) -8 NIL NIL NIL) (-137 229407 229625 229717 "CASEAST" 229832 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224443 225436 226189 "CARTEN" 228710 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 223551 223699 223920 "CARTEN2" 224290 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221893 222701 222958 "CARD" 223314 T CARD (NIL) -8 NIL NIL NIL) (-133 221496 221697 221772 "CAPSLAST" 221838 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220868 221196 221224 "CACHSET" 221356 T CACHSET (NIL) -9 NIL 221433 NIL) (-131 220364 220660 220688 "CABMON" 220738 T CABMON (NIL) -9 NIL 220794 NIL) (-130 219864 220068 220178 "BYTEORD" 220274 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218867 219398 219540 "BYTE" 219703 T BYTE (NIL) -8 NIL NIL 219825) (-128 214267 218372 218544 "BYTEBUF" 218715 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211824 213959 214066 "BTREE" 214193 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209321 211472 211594 "BTOURN" 211734 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206738 208791 208832 "BTCAT" 208900 NIL BTCAT (NIL T) -9 NIL 208977 NIL) (-124 206405 206485 206634 "BTCAT-" 206639 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201697 205548 205576 "BTAGG" 205798 T BTAGG (NIL) -9 NIL 205959 NIL) (-122 201187 201312 201518 "BTAGG-" 201523 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198230 200465 200680 "BSTREE" 201004 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197368 197494 197678 "BRILL" 198086 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194067 196094 196135 "BRAGG" 196784 NIL BRAGG (NIL T) -9 NIL 197042 NIL) (-118 192596 193002 193557 "BRAGG-" 193562 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185852 191942 192126 "BPADICRT" 192444 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184194 185789 185834 "BPADIC" 185839 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183892 183922 184036 "BOUNDZRO" 184158 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179011 180182 181125 "BOP" 182969 T BOP (NIL) -8 NIL NIL NIL) (-113 176632 177076 177596 "BOP1" 178524 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175334 176056 176249 "BOOLEAN" 176459 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174696 175074 175128 "BMODULE" 175133 NIL BMODULE (NIL T T) -9 NIL 175198 NIL) (-110 170524 174494 174567 "BITS" 174643 T BITS (NIL) -8 NIL NIL NIL) (-109 169945 170064 170204 "BINDING" 170404 T BINDING (NIL) -8 NIL NIL NIL) (-108 163979 169542 169690 "BINARY" 169817 T BINARY (NIL) -8 NIL NIL NIL) (-107 161806 163234 163275 "BGAGG" 163535 NIL BGAGG (NIL T) -9 NIL 163672 NIL) (-106 161637 161669 161760 "BGAGG-" 161765 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160735 161021 161226 "BFUNCT" 161452 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159425 159603 159891 "BEZOUT" 160559 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155942 158277 158607 "BBTREE" 159128 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155676 155729 155757 "BASTYPE" 155876 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155529 155557 155630 "BASTYPE-" 155635 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154963 155039 155191 "BALFACT" 155440 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153846 154378 154564 "AUTOMOR" 154808 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153572 153577 153603 "ATTREG" 153608 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151851 152269 152621 "ATTRBUT" 153238 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151486 151679 151745 "ATTRAST" 151803 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151022 151135 151161 "ATRIG" 151362 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150831 150872 150959 "ATRIG-" 150964 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150502 150662 150688 "ASTCAT" 150693 T ASTCAT (NIL) -9 NIL 150723 NIL) (-92 150229 150288 150407 "ASTCAT-" 150412 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148426 150005 150093 "ASTACK" 150172 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146931 147228 147593 "ASSOCEQ" 148108 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145963 146590 146714 "ASP9" 146838 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145726 145911 145950 "ASP8" 145955 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144594 145331 145473 "ASP80" 145615 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143492 144229 144361 "ASP7" 144493 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142446 143169 143287 "ASP78" 143405 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141415 142126 142243 "ASP77" 142360 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140327 141053 141184 "ASP74" 141315 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139227 139962 140094 "ASP73" 140226 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138331 139053 139153 "ASP6" 139158 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137275 138008 138126 "ASP55" 138244 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136224 136949 137068 "ASP50" 137187 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135312 135925 136035 "ASP4" 136145 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134400 135013 135123 "ASP49" 135233 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133184 133939 134107 "ASP42" 134289 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131960 132717 132887 "ASP41" 133071 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130910 131637 131755 "ASP35" 131873 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130675 130858 130897 "ASP34" 130902 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130412 130479 130555 "ASP33" 130630 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129305 130047 130179 "ASP31" 130311 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129070 129253 129292 "ASP30" 129297 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128805 128874 128950 "ASP29" 129025 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128570 128753 128792 "ASP28" 128797 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128335 128518 128557 "ASP27" 128562 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127419 128033 128144 "ASP24" 128255 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126495 127221 127333 "ASP20" 127338 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125583 126196 126306 "ASP1" 126416 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124525 125257 125376 "ASP19" 125495 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124262 124329 124405 "ASP12" 124480 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123114 123861 124005 "ASP10" 124149 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121013 122958 123049 "ARRAY2" 123054 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116826 120661 120775 "ARRAY1" 120930 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115858 116031 116252 "ARRAY12" 116649 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110217 112088 112163 "ARR2CAT" 114793 NIL ARR2CAT (NIL T T T) -9 NIL 115551 NIL) (-56 107651 108395 109349 "ARR2CAT-" 109354 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106995 107278 107403 "ARITY" 107544 T ARITY (NIL) -8 NIL NIL NIL) (-54 105743 105895 106201 "APPRULE" 106831 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105394 105442 105561 "APPLYORE" 105689 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104368 104659 104854 "ANY" 105217 T ANY (NIL) -8 NIL NIL NIL) (-51 103646 103769 103926 "ANY1" 104242 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101203 102083 102410 "ANTISYM" 103370 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100722 100910 101006 "ANON" 101125 T ANON (NIL) -8 NIL NIL NIL) (-48 94846 99261 99715 "AN" 100286 T AN (NIL) -8 NIL NIL NIL) (-47 91094 92456 92507 "AMR" 93255 NIL AMR (NIL T T) -9 NIL 93855 NIL) (-46 90206 90427 90790 "AMR-" 90795 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74756 90123 90184 "ALIST" 90189 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71585 74350 74519 "ALGSC" 74674 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68140 68695 69302 "ALGPKG" 71025 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67417 67518 67702 "ALGMFACT" 68026 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63841 64496 "ALGMANIP" 66940 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54552 62781 62931 "ALGFF" 63088 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52805 53379 53417 "ALGEBRA" 53422 NIL ALGEBRA (NIL T) -9 NIL 53463 NIL) (-37 52523 52582 52714 "ALGEBRA-" 52719 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34782 50525 50577 "ALAGG" 50713 NIL ALAGG (NIL T T) -9 NIL 50874 NIL) (-35 34318 34431 34457 "AHYP" 34658 T AHYP (NIL) -9 NIL NIL NIL) (-34 33249 33497 33523 "AGG" 34022 T AGG (NIL) -9 NIL 34301 NIL) (-33 32683 32845 33059 "AGG-" 33064 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30359 30782 31200 "AF" 32325 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29866 30084 30174 "ADDAST" 30287 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29134 29393 29549 "ACPLOT" 29728 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3216864 3216869 3216874 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3216849 3216854 3216859 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3216834 3216839 3216844 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3216819 3216824 3216829 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3215961 3216694 3216771 "ZMOD" 3216776 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3215071 3215235 3215444 "ZLINDEP" 3215793 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3204371 3206139 3208111 "ZDSOLVE" 3213201 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3203617 3203758 3203947 "YSTREAM" 3204217 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3201391 3202918 3203122 "XRPOLY" 3203460 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3197944 3199262 3199837 "XPR" 3200863 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3195665 3197275 3197479 "XPOLY" 3197775 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3193422 3194790 3194845 "XPOLYC" 3195133 NIL XPOLYC (NIL T T) -9 NIL 3195246 NIL) (-1279 3189798 3191939 3192327 "XPBWPOLY" 3193080 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3185674 3187961 3188003 "XF" 3188624 NIL XF (NIL T) -9 NIL 3189024 NIL) (-1277 3185295 3185383 3185552 "XF-" 3185557 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3180595 3181884 3181939 "XFALG" 3184111 NIL XFALG (NIL T T) -9 NIL 3184900 NIL) (-1275 3179728 3179832 3180037 "XEXPPKG" 3180487 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3177837 3179578 3179674 "XDPOLY" 3179679 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3176748 3177348 3177391 "XALG" 3177396 NIL XALG (NIL T) -9 NIL 3177507 NIL) (-1272 3170190 3174725 3175219 "WUTSET" 3176340 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3168446 3169242 3169565 "WP" 3170001 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3168048 3168268 3168338 "WHILEAST" 3168398 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3167520 3167765 3167859 "WHEREAST" 3167976 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3166406 3166604 3166899 "WFFINTBS" 3167317 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3164310 3164737 3165199 "WEIER" 3165978 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3163431 3163881 3163923 "VSPACE" 3164059 NIL VSPACE (NIL T) -9 NIL 3164133 NIL) (-1265 3163269 3163296 3163387 "VSPACE-" 3163392 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3163077 3163120 3163188 "VOID" 3163223 T VOID (NIL) -8 NIL NIL NIL) (-1263 3161213 3161572 3161978 "VIEW" 3162693 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3157637 3158276 3159013 "VIEWDEF" 3160498 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3146941 3149185 3151358 "VIEW3D" 3155486 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3139192 3140852 3142431 "VIEW2D" 3145384 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3134546 3138962 3139054 "VECTOR" 3139135 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3133123 3133382 3133700 "VECTOR2" 3134276 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3126602 3130907 3130950 "VECTCAT" 3131943 NIL VECTCAT (NIL T) -9 NIL 3132529 NIL) (-1256 3125616 3125870 3126260 "VECTCAT-" 3126265 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3125070 3125267 3125387 "VARIABLE" 3125531 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3125003 3125008 3125038 "UTYPE" 3125043 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3123833 3123987 3124249 "UTSODETL" 3124829 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3121273 3121733 3122257 "UTSODE" 3123374 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3113110 3118899 3119388 "UTS" 3120842 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3104318 3109677 3109720 "UTSCAT" 3110832 NIL UTSCAT (NIL T) -9 NIL 3111589 NIL) (-1249 3101666 3102388 3103377 "UTSCAT-" 3103382 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3101293 3101336 3101469 "UTS2" 3101617 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3095519 3098131 3098174 "URAGG" 3100244 NIL URAGG (NIL T) -9 NIL 3100967 NIL) (-1246 3092458 3093321 3094444 "URAGG-" 3094449 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3088147 3091072 3091544 "UPXSSING" 3092122 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3080213 3087394 3087667 "UPXS" 3087932 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3073286 3080117 3080189 "UPXSCONS" 3080194 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3063496 3070281 3070343 "UPXSCCA" 3070917 NIL UPXSCCA (NIL T T) -9 NIL 3071150 NIL) (-1241 3063134 3063219 3063393 "UPXSCCA-" 3063398 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3053197 3059755 3059798 "UPXSCAT" 3060446 NIL UPXSCAT (NIL T) -9 NIL 3061054 NIL) (-1239 3052627 3052706 3052885 "UPXS2" 3053112 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3051281 3051534 3051885 "UPSQFREE" 3052370 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3045034 3048083 3048138 "UPSCAT" 3049299 NIL UPSCAT (NIL T T) -9 NIL 3050073 NIL) (-1236 3044238 3044445 3044772 "UPSCAT-" 3044777 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3030053 3038086 3038129 "UPOLYC" 3040230 NIL UPOLYC (NIL T) -9 NIL 3041451 NIL) (-1234 3021381 3023807 3026954 "UPOLYC-" 3026959 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3021008 3021051 3021184 "UPOLYC2" 3021332 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 3012547 3020691 3020820 "UP" 3020927 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 3011886 3011993 3012157 "UPMP" 3012436 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 3011439 3011520 3011659 "UPDIVP" 3011799 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 3010007 3010256 3010572 "UPDECOMP" 3011188 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 3009242 3009354 3009539 "UPCDEN" 3009891 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 3008761 3008830 3008979 "UP2" 3009167 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 3007228 3007965 3008242 "UNISEG" 3008519 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 3006443 3006570 3006775 "UNISEG2" 3007071 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 3005503 3005683 3005909 "UNIFACT" 3006259 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2989435 3004680 3004931 "ULS" 3005310 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2977434 2989339 2989411 "ULSCONS" 2989416 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2960015 2971992 2972054 "ULSCCAT" 2972692 NIL ULSCCAT (NIL T T) -9 NIL 2972980 NIL) (-1220 2959065 2959310 2959698 "ULSCCAT-" 2959703 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2948905 2955377 2955420 "ULSCAT" 2956283 NIL ULSCAT (NIL T) -9 NIL 2957013 NIL) (-1218 2948335 2948414 2948593 "ULS2" 2948820 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2947425 2947935 2948042 "UINT8" 2948153 T UINT8 (NIL) -8 NIL NIL 2948238) (-1216 2946514 2947024 2947131 "UINT64" 2947242 T UINT64 (NIL) -8 NIL NIL 2947327) (-1215 2945603 2946113 2946220 "UINT32" 2946331 T UINT32 (NIL) -8 NIL NIL 2946416) (-1214 2944692 2945202 2945309 "UINT16" 2945420 T UINT16 (NIL) -8 NIL NIL 2945505) (-1213 2943061 2944018 2944048 "UFD" 2944260 T UFD (NIL) -9 NIL 2944374 NIL) (-1212 2942855 2942901 2942996 "UFD-" 2943001 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2941937 2942120 2942336 "UDVO" 2942661 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2939753 2940162 2940633 "UDPO" 2941501 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2939686 2939691 2939721 "TYPE" 2939726 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2939446 2939641 2939672 "TYPEAST" 2939677 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2938417 2938619 2938859 "TWOFACT" 2939240 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2937440 2937826 2938061 "TUPLE" 2938217 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2935131 2935650 2936189 "TUBETOOL" 2936923 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2933980 2934185 2934426 "TUBE" 2934924 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2928709 2932952 2933235 "TS" 2933732 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2917349 2921468 2921565 "TSETCAT" 2926834 NIL TSETCAT (NIL T T T T) -9 NIL 2928365 NIL) (-1201 2912081 2913681 2915572 "TSETCAT-" 2915577 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2906343 2907190 2908132 "TRMANIP" 2911217 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2905784 2905847 2906010 "TRIMAT" 2906275 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2903580 2903817 2904181 "TRIGMNIP" 2905533 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2903100 2903213 2903243 "TRIGCAT" 2903456 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2902769 2902848 2902989 "TRIGCAT-" 2902994 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2899614 2901627 2901908 "TREE" 2902523 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2898888 2899416 2899446 "TRANFUN" 2899481 T TRANFUN (NIL) -9 NIL 2899547 NIL) (-1193 2898167 2898358 2898638 "TRANFUN-" 2898643 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2897971 2898003 2898064 "TOPSP" 2898128 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2897319 2897434 2897588 "TOOLSIGN" 2897852 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2895953 2896496 2896735 "TEXTFILE" 2897102 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2893865 2894406 2894835 "TEX" 2895546 T TEX (NIL) -8 NIL NIL NIL) (-1188 2893646 2893677 2893749 "TEX1" 2893828 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2893294 2893357 2893447 "TEMUTL" 2893578 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2891448 2891728 2892053 "TBCMPPK" 2893017 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2883225 2889608 2889664 "TBAGG" 2890064 NIL TBAGG (NIL T T) -9 NIL 2890275 NIL) (-1184 2878295 2879783 2881537 "TBAGG-" 2881542 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2877679 2877786 2877931 "TANEXP" 2878184 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2871069 2877536 2877629 "TABLE" 2877634 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2870481 2870580 2870718 "TABLEAU" 2870966 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2865089 2866309 2867557 "TABLBUMP" 2869267 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2864311 2864458 2864639 "SYSTEM" 2864930 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2860770 2861469 2862252 "SYSSOLP" 2863562 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2859777 2860282 2860401 "SYSNNI" 2860587 NIL SYSNNI (NIL NIL) -8 NIL NIL 2860672) (-1176 2859047 2859506 2859585 "SYSINT" 2859645 NIL SYSINT (NIL NIL) -8 NIL NIL 2859690) (-1175 2855379 2856325 2857035 "SYNTAX" 2858359 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2852537 2853139 2853771 "SYMTAB" 2854769 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2847786 2848688 2849671 "SYMS" 2851576 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2845021 2847244 2847474 "SYMPOLY" 2847591 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2844538 2844613 2844736 "SYMFUNC" 2844933 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2840557 2841850 2842663 "SYMBOL" 2843747 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2834096 2835785 2837505 "SWITCH" 2838859 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2827330 2832917 2833220 "SUTS" 2833851 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2819396 2826577 2826850 "SUPXS" 2827115 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2810884 2819014 2819140 "SUP" 2819305 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2810043 2810170 2810387 "SUPFRACF" 2810752 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2809664 2809723 2809836 "SUP2" 2809978 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2808077 2808351 2808714 "SUMRF" 2809363 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2807391 2807457 2807656 "SUMFS" 2807998 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2791358 2806568 2806819 "SULS" 2807198 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2790960 2791180 2791250 "SUCHTAST" 2791310 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2790255 2790485 2790625 "SUCH" 2790868 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2784122 2785161 2786120 "SUBSPACE" 2789343 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2783552 2783642 2783806 "SUBRESP" 2784010 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2776917 2778217 2779528 "STTF" 2782288 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2771090 2772210 2773357 "STTFNC" 2775817 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2762401 2764272 2766066 "STTAYLOR" 2769331 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2755531 2762265 2762348 "STRTBL" 2762353 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2750895 2755486 2755517 "STRING" 2755522 T STRING (NIL) -8 NIL NIL NIL) (-1151 2745756 2750268 2750298 "STRICAT" 2750357 T STRICAT (NIL) -9 NIL 2750419 NIL) (-1150 2738511 2743375 2743986 "STREAM" 2745180 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2738021 2738098 2738242 "STREAM3" 2738428 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2737003 2737186 2737421 "STREAM2" 2737834 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2736691 2736743 2736836 "STREAM1" 2736945 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2735707 2735888 2736119 "STINPROD" 2736507 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2735261 2735469 2735499 "STEP" 2735579 T STEP (NIL) -9 NIL 2735657 NIL) (-1144 2728693 2735160 2735237 "STBL" 2735242 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2723819 2727914 2727957 "STAGG" 2728110 NIL STAGG (NIL T) -9 NIL 2728199 NIL) (-1142 2721521 2722123 2722995 "STAGG-" 2723000 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2719668 2721291 2721383 "STACK" 2721464 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2712364 2717809 2718265 "SREGSET" 2719298 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2704789 2706158 2707671 "SRDCMPK" 2710970 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2697706 2702229 2702259 "SRAGG" 2703562 T SRAGG (NIL) -9 NIL 2704170 NIL) (-1137 2696723 2696978 2697357 "SRAGG-" 2697362 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2691183 2695670 2696091 "SQMATRIX" 2696349 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2684869 2687901 2688628 "SPLTREE" 2690528 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2680832 2681525 2682171 "SPLNODE" 2684295 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2679879 2680112 2680142 "SPFCAT" 2680586 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2678616 2678826 2679090 "SPECOUT" 2679637 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2670242 2672012 2672042 "SPADXPT" 2676434 T SPADXPT (NIL) -9 NIL 2678468 NIL) (-1130 2670003 2670043 2670112 "SPADPRSR" 2670195 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2668158 2669958 2669989 "SPADAST" 2669994 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2660103 2661876 2661919 "SPACEC" 2666292 NIL SPACEC (NIL T) -9 NIL 2668108 NIL) (-1127 2658233 2660035 2660084 "SPACE3" 2660089 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2656985 2657156 2657447 "SORTPAK" 2658038 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2655035 2655338 2655757 "SOLVETRA" 2656649 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2654046 2654268 2654542 "SOLVESER" 2654808 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2649257 2650147 2651149 "SOLVERAD" 2653098 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2645072 2645681 2646410 "SOLVEFOR" 2648624 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2639342 2644421 2644518 "SNTSCAT" 2644523 NIL SNTSCAT (NIL T T T T) -9 NIL 2644593 NIL) (-1120 2633448 2637665 2638056 "SMTS" 2639032 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2627861 2633336 2633413 "SMP" 2633418 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2626020 2626321 2626719 "SMITH" 2627558 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2618880 2623071 2623174 "SMATCAT" 2624525 NIL SMATCAT (NIL NIL T T T) -9 NIL 2625075 NIL) (-1116 2615820 2616643 2617821 "SMATCAT-" 2617826 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2613486 2615056 2615099 "SKAGG" 2615360 NIL SKAGG (NIL T) -9 NIL 2615495 NIL) (-1114 2609794 2612902 2613097 "SINT" 2613284 T SINT (NIL) -8 NIL NIL 2613457) (-1113 2609566 2609604 2609670 "SIMPAN" 2609750 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2608845 2609101 2609241 "SIG" 2609448 T SIG (NIL) -8 NIL NIL NIL) (-1111 2607683 2607904 2608179 "SIGNRF" 2608604 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2606488 2606639 2606930 "SIGNEF" 2607512 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2605794 2606071 2606195 "SIGAST" 2606386 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2603484 2603938 2604444 "SHP" 2605335 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2597336 2603385 2603461 "SHDP" 2603466 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2596911 2597101 2597131 "SGROUP" 2597224 T SGROUP (NIL) -9 NIL 2597286 NIL) (-1105 2596769 2596795 2596868 "SGROUP-" 2596873 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2593604 2594302 2595025 "SGCF" 2596068 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2587972 2593051 2593148 "SFRTCAT" 2593153 NIL SFRTCAT (NIL T T T T) -9 NIL 2593192 NIL) (-1102 2581393 2582411 2583547 "SFRGCD" 2586955 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2574520 2575592 2576778 "SFQCMPK" 2580326 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2574142 2574231 2574341 "SFORT" 2574461 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2573260 2573982 2574103 "SEXOF" 2574108 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2572367 2573141 2573209 "SEX" 2573214 T SEX (NIL) -8 NIL NIL NIL) (-1097 2567880 2568595 2568690 "SEXCAT" 2571627 NIL SEXCAT (NIL T T T T T) -9 NIL 2572205 NIL) (-1096 2565033 2567814 2567862 "SET" 2567867 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2563257 2563746 2564051 "SETMN" 2564774 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2562753 2562905 2562935 "SETCAT" 2563111 T SETCAT (NIL) -9 NIL 2563221 NIL) (-1093 2562533 2562585 2562684 "SETCAT-" 2562689 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2558894 2560994 2561037 "SETAGG" 2561907 NIL SETAGG (NIL T) -9 NIL 2562247 NIL) (-1091 2558352 2558468 2558705 "SETAGG-" 2558710 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2557795 2558048 2558149 "SEQAST" 2558273 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2556994 2557288 2557349 "SEGXCAT" 2557635 NIL SEGXCAT (NIL T T) -9 NIL 2557755 NIL) (-1088 2556000 2556660 2556842 "SEG" 2556847 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2554979 2555193 2555236 "SEGCAT" 2555758 NIL SEGCAT (NIL T) -9 NIL 2555979 NIL) (-1086 2553980 2554358 2554558 "SEGBIND" 2554814 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2553601 2553660 2553773 "SEGBIND2" 2553915 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2553174 2553402 2553479 "SEGAST" 2553546 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2552393 2552519 2552723 "SEG2" 2553018 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2551803 2552328 2552375 "SDVAR" 2552380 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2544058 2551573 2551703 "SDPOL" 2551708 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2542651 2542917 2543236 "SCPKG" 2543773 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2541815 2541987 2542179 "SCOPE" 2542481 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2541035 2541169 2541348 "SCACHE" 2541670 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2540681 2540867 2540897 "SASTCAT" 2540902 T SASTCAT (NIL) -9 NIL 2540915 NIL) (-1076 2540168 2540516 2540592 "SAOS" 2540627 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2539733 2539768 2539941 "SAERFFC" 2540127 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2533672 2539630 2539710 "SAE" 2539715 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2533265 2533300 2533459 "SAEFACT" 2533631 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2531586 2531900 2532301 "RURPK" 2532931 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2530195 2530501 2530813 "RULESET" 2531420 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2527355 2527885 2528350 "RULE" 2529876 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2526967 2527149 2527232 "RULECOLD" 2527307 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2526757 2526785 2526856 "RTVALUE" 2526918 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2526228 2526474 2526568 "RSTRCAST" 2526685 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2521076 2521871 2522791 "RSETGCD" 2525427 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2510306 2515385 2515482 "RSETCAT" 2519601 NIL RSETCAT (NIL T T T T) -9 NIL 2520698 NIL) (-1064 2508233 2508772 2509596 "RSETCAT-" 2509601 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2500618 2501995 2503515 "RSDCMPK" 2506832 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2498597 2499064 2499138 "RRCC" 2500224 NIL RRCC (NIL T T) -9 NIL 2500568 NIL) (-1061 2497948 2498122 2498401 "RRCC-" 2498406 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2497391 2497644 2497745 "RPTAST" 2497869 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2471362 2480984 2481051 "RPOLCAT" 2491715 NIL RPOLCAT (NIL T T T) -9 NIL 2494874 NIL) (-1058 2462860 2465200 2468322 "RPOLCAT-" 2468327 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2453791 2461071 2461553 "ROUTINE" 2462400 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2450589 2453417 2453557 "ROMAN" 2453673 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2448833 2449449 2449709 "ROIRC" 2450394 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2445191 2447469 2447499 "RNS" 2447803 T RNS (NIL) -9 NIL 2448076 NIL) (-1053 2443700 2444083 2444617 "RNS-" 2444692 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2443123 2443531 2443561 "RNG" 2443566 T RNG (NIL) -9 NIL 2443587 NIL) (-1051 2442491 2442877 2442920 "RMODULE" 2442982 NIL RMODULE (NIL T) -9 NIL 2443024 NIL) (-1050 2441327 2441421 2441757 "RMCAT2" 2442392 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2438177 2440673 2440970 "RMATRIX" 2441089 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2431093 2433353 2433468 "RMATCAT" 2436827 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2437809 NIL) (-1047 2430468 2430615 2430922 "RMATCAT-" 2430927 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2430035 2430110 2430238 "RINTERP" 2430387 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2429128 2429682 2429712 "RING" 2429768 T RING (NIL) -9 NIL 2429860 NIL) (-1044 2428920 2428964 2429061 "RING-" 2429066 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2427761 2427998 2428256 "RIDIST" 2428684 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2419050 2427229 2427435 "RGCHAIN" 2427609 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2418400 2418806 2418847 "RGBCSPC" 2418905 NIL RGBCSPC (NIL T) -9 NIL 2418957 NIL) (-1040 2417558 2417939 2417980 "RGBCMDL" 2418212 NIL RGBCMDL (NIL T) -9 NIL 2418326 NIL) (-1039 2414552 2415166 2415836 "RF" 2416922 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2414198 2414261 2414364 "RFFACTOR" 2414483 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2413923 2413958 2414055 "RFFACT" 2414157 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2412040 2412404 2412786 "RFDIST" 2413563 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2411493 2411585 2411748 "RETSOL" 2411942 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2411129 2411209 2411252 "RETRACT" 2411385 NIL RETRACT (NIL T) -9 NIL 2411472 NIL) (-1033 2410978 2411003 2411090 "RETRACT-" 2411095 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2410580 2410800 2410870 "RETAST" 2410930 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2403318 2410233 2410360 "RESULT" 2410475 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2401909 2402587 2402786 "RESRING" 2403221 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2401545 2401594 2401692 "RESLATC" 2401846 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2401250 2401285 2401392 "REPSQ" 2401504 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2398672 2399252 2399854 "REP" 2400670 T REP (NIL) -7 NIL NIL NIL) (-1026 2398369 2398404 2398515 "REPDB" 2398631 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2392269 2393658 2394881 "REP2" 2397181 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2388646 2389327 2390135 "REP1" 2391496 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2381342 2386787 2387243 "REGSET" 2388276 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2380107 2380490 2380740 "REF" 2381127 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2379484 2379587 2379754 "REDORDER" 2379991 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2375452 2378697 2378924 "RECLOS" 2379312 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2374504 2374685 2374900 "REALSOLV" 2375259 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2374350 2374391 2374421 "REAL" 2374426 T REAL (NIL) -9 NIL 2374461 NIL) (-1017 2370833 2371635 2372519 "REAL0Q" 2373515 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2366434 2367422 2368483 "REAL0" 2369814 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2365905 2366151 2366245 "RDUCEAST" 2366362 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2365310 2365382 2365589 "RDIV" 2365827 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2364378 2364552 2364765 "RDIST" 2365132 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2362975 2363262 2363634 "RDETRS" 2364086 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2360787 2361241 2361779 "RDETR" 2362517 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2359398 2359676 2360080 "RDEEFS" 2360503 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2357893 2358199 2358631 "RDEEF" 2359086 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2352119 2355029 2355059 "RCFIELD" 2356354 T RCFIELD (NIL) -9 NIL 2357084 NIL) (-1007 2350183 2350687 2351383 "RCFIELD-" 2351458 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2346452 2348284 2348327 "RCAGG" 2349411 NIL RCAGG (NIL T) -9 NIL 2349876 NIL) (-1005 2346080 2346174 2346337 "RCAGG-" 2346342 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2345415 2345527 2345692 "RATRET" 2345964 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2344968 2345035 2345156 "RATFACT" 2345343 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2344276 2344396 2344548 "RANDSRC" 2344838 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2344010 2344054 2344127 "RADUTIL" 2344225 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2337126 2342843 2343153 "RADIX" 2343734 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2328747 2336970 2337098 "RADFF" 2337103 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2328399 2328474 2328502 "RADCAT" 2328659 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2328184 2328232 2328329 "RADCAT-" 2328334 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2326287 2327959 2328048 "QUEUE" 2328128 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2322828 2326224 2326269 "QUAT" 2326274 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2322466 2322509 2322636 "QUATCT2" 2322779 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2316178 2319515 2319555 "QUATCAT" 2320335 NIL QUATCAT (NIL T) -9 NIL 2321101 NIL) (-992 2312322 2313359 2314746 "QUATCAT-" 2314840 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2309795 2311406 2311447 "QUAGG" 2311822 NIL QUAGG (NIL T) -9 NIL 2311997 NIL) (-990 2309400 2309620 2309688 "QQUTAST" 2309747 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2308298 2308798 2308970 "QFORM" 2309272 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2299476 2304715 2304755 "QFCAT" 2305413 NIL QFCAT (NIL T) -9 NIL 2306414 NIL) (-987 2295048 2296249 2297840 "QFCAT-" 2297934 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2294686 2294729 2294856 "QFCAT2" 2294999 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2294146 2294256 2294386 "QEQUAT" 2294576 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2287293 2288365 2289549 "QCMPACK" 2293079 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2284842 2285290 2285718 "QALGSET" 2286948 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2284087 2284261 2284493 "QALGSET2" 2284662 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2282777 2283001 2283318 "PWFFINTB" 2283860 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2280959 2281127 2281481 "PUSHVAR" 2282591 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2276877 2277931 2277972 "PTRANFN" 2279856 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2275279 2275570 2275892 "PTPACK" 2276588 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2274911 2274968 2275077 "PTFUNC2" 2275216 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2269390 2273783 2273824 "PTCAT" 2274120 NIL PTCAT (NIL T) -9 NIL 2274273 NIL) (-975 2269048 2269083 2269207 "PSQFR" 2269349 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2267643 2267941 2268275 "PSEUDLIN" 2268746 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2254406 2256777 2259101 "PSETPK" 2265403 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2247424 2250164 2250260 "PSETCAT" 2253281 NIL PSETCAT (NIL T T T T) -9 NIL 2254095 NIL) (-971 2245260 2245894 2246715 "PSETCAT-" 2246720 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2244609 2244774 2244802 "PSCURVE" 2245070 T PSCURVE (NIL) -9 NIL 2245237 NIL) (-969 2240931 2242447 2242512 "PSCAT" 2243356 NIL PSCAT (NIL T T T) -9 NIL 2243596 NIL) (-968 2239994 2240210 2240610 "PSCAT-" 2240615 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2238699 2239359 2239564 "PRTITION" 2239809 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2238174 2238420 2238512 "PRTDAST" 2238627 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2227264 2229478 2231666 "PRS" 2236036 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2225075 2226614 2226654 "PRQAGG" 2226837 NIL PRQAGG (NIL T) -9 NIL 2226939 NIL) (-963 2224435 2224690 2224718 "PROPLOG" 2224903 T PROPLOG (NIL) -9 NIL 2225025 NIL) (-962 2222916 2223386 2223643 "PROPFRML" 2224211 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2222385 2222492 2222620 "PROPERTY" 2222808 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2216443 2220551 2221371 "PRODUCT" 2221611 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2213721 2215901 2216135 "PR" 2216254 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2213517 2213549 2213608 "PRINT" 2213682 T PRINT (NIL) -7 NIL NIL NIL) (-957 2212857 2212974 2213126 "PRIMES" 2213397 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2210922 2211323 2211789 "PRIMELT" 2212436 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2210651 2210700 2210728 "PRIMCAT" 2210852 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2206766 2210589 2210634 "PRIMARR" 2210639 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2205773 2205951 2206179 "PRIMARR2" 2206584 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2205416 2205472 2205583 "PREASSOC" 2205711 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2204891 2205024 2205052 "PPCURVE" 2205257 T PPCURVE (NIL) -9 NIL 2205393 NIL) (-950 2204486 2204686 2204769 "PORTNUM" 2204828 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2201845 2202244 2202836 "POLYROOT" 2204067 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2195755 2201449 2201609 "POLY" 2201718 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2195138 2195196 2195430 "POLYLIFT" 2195691 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2191413 2191862 2192491 "POLYCATQ" 2194683 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2178195 2183588 2183653 "POLYCAT" 2187167 NIL POLYCAT (NIL T T T) -9 NIL 2189095 NIL) (-944 2171644 2173506 2175890 "POLYCAT-" 2175895 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2171231 2171299 2171419 "POLY2UP" 2171570 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2170863 2170920 2171029 "POLY2" 2171168 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2169548 2169787 2170063 "POLUTIL" 2170637 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2167903 2168180 2168511 "POLTOPOL" 2169270 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2163370 2167839 2167885 "POINT" 2167890 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2161557 2161914 2162289 "PNTHEORY" 2163015 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2159976 2160273 2160685 "PMTOOLS" 2161255 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2159569 2159647 2159764 "PMSYM" 2159892 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2159079 2159148 2159322 "PMQFCAT" 2159494 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2158434 2158544 2158700 "PMPRED" 2158956 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2157830 2157916 2158077 "PMPREDFS" 2158335 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2156473 2156681 2157066 "PMPLCAT" 2157592 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2156005 2156084 2156236 "PMLSAGG" 2156388 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2155480 2155556 2155737 "PMKERNEL" 2155923 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2155097 2155172 2155285 "PMINS" 2155399 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2154525 2154594 2154810 "PMFS" 2155022 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2153753 2153871 2154076 "PMDOWN" 2154402 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2152920 2153078 2153259 "PMASS" 2153592 T PMASS (NIL) -7 NIL NIL NIL) (-925 2152198 2152308 2152470 "PMASSFS" 2152807 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2151853 2151921 2152015 "PLOTTOOL" 2152124 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2146460 2147664 2148812 "PLOT" 2150725 T PLOT (NIL) -8 NIL NIL NIL) (-922 2142264 2143308 2144229 "PLOT3D" 2145559 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2141176 2141353 2141588 "PLOT1" 2142068 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2116565 2121242 2126093 "PLEQN" 2136442 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2115883 2116005 2116185 "PINTERP" 2116430 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2115576 2115623 2115726 "PINTERPA" 2115830 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2114797 2115345 2115432 "PI" 2115472 T PI (NIL) -8 NIL NIL 2115539) (-916 2113160 2114135 2114163 "PID" 2114345 T PID (NIL) -9 NIL 2114479 NIL) (-915 2112885 2112922 2113010 "PICOERCE" 2113117 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2112205 2112344 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2019237 2020859 2020904 "PADIC" 2020909 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2016413 2017977 2018017 "PADICCT" 2018598 NIL PADICCT (NIL NIL) -9 NIL 2018880 NIL) (-864 2015370 2015570 2015838 "PADEPAC" 2016200 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2014582 2014715 2014921 "PADE" 2015232 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2012969 2013790 2014070 "OWP" 2014386 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2012462 2012675 2012772 "OVERSET" 2012892 T OVERSET (NIL) -8 NIL NIL NIL) (-860 2011508 2012067 2012239 "OVAR" 2012330 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 2010772 2010893 2011054 "OUT" 2011367 T OUT (NIL) -7 NIL NIL NIL) (-858 1999643 2001881 2004081 "OUTFORM" 2008592 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1998979 1999240 1999367 "OUTBFILE" 1999536 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1998286 1998451 1998479 "OUTBCON" 1998797 T OUTBCON (NIL) -9 NIL 1998963 NIL) (-855 1997887 1997999 1998156 "OUTBCON-" 1998161 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1997267 1997616 1997705 "OSI" 1997818 T OSI (NIL) -8 NIL NIL NIL) (-853 1996797 1997135 1997163 "OSGROUP" 1997168 T OSGROUP (NIL) -9 NIL 1997190 NIL) (-852 1995542 1995769 1996054 "ORTHPOL" 1996544 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1993093 1995377 1995498 "OREUP" 1995503 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1990496 1992784 1992911 "ORESUP" 1993035 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1988024 1988524 1989085 "OREPCTO" 1989985 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1981814 1984015 1984056 "OREPCAT" 1986404 NIL OREPCAT (NIL T) -9 NIL 1987508 NIL) (-847 1978961 1979743 1980801 "OREPCAT-" 1980806 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1978112 1978410 1978438 "ORDSET" 1978747 T ORDSET (NIL) -9 NIL 1978911 NIL) (-845 1977543 1977691 1977915 "ORDSET-" 1977920 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1976143 1976934 1976962 "ORDRING" 1977164 T ORDRING (NIL) -9 NIL 1977289 NIL) (-843 1975788 1975882 1976026 "ORDRING-" 1976031 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1975168 1975631 1975659 "ORDMON" 1975664 T ORDMON (NIL) -9 NIL 1975685 NIL) (-841 1974330 1974477 1974672 "ORDFUNS" 1975017 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1973668 1974087 1974115 "ORDFIN" 1974180 T ORDFIN (NIL) -9 NIL 1974254 NIL) (-839 1970227 1972254 1972663 "ORDCOMP" 1973292 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1969493 1969620 1969806 "ORDCOMP2" 1970087 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1966074 1966984 1967798 "OPTPROB" 1968699 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1962876 1963515 1964219 "OPTPACK" 1965390 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1960563 1961329 1961357 "OPTCAT" 1962176 T OPTCAT (NIL) -9 NIL 1962826 NIL) (-834 1959979 1960240 1960345 "OPSIG" 1960478 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1959747 1959786 1959852 "OPQUERY" 1959933 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1956878 1958058 1958562 "OP" 1959276 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1956387 1956584 1956625 "OPERCAT" 1956760 NIL OPERCAT (NIL T) -9 NIL 1956828 NIL) (-830 1956233 1956260 1956346 "OPERCAT-" 1956351 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1953045 1955030 1955399 "ONECOMP" 1955897 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1952350 1952465 1952639 "ONECOMP2" 1952917 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1951769 1951875 1952005 "OMSERVER" 1952240 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1948631 1951209 1951249 "OMSAGG" 1951310 NIL OMSAGG (NIL T) -9 NIL 1951374 NIL) (-825 1947254 1947517 1947799 "OMPKG" 1948369 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1946684 1946787 1946815 "OM" 1947114 T OM (NIL) -9 NIL NIL NIL) (-823 1945231 1946233 1946402 "OMLO" 1946565 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1944156 1944303 1944530 "OMEXPR" 1945057 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1943447 1943702 1943838 "OMERR" 1944040 T OMERR (NIL) -8 NIL NIL NIL) (-820 1942598 1942868 1943028 "OMERRK" 1943307 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1942049 1942275 1942383 "OMENC" 1942510 T OMENC (NIL) -8 NIL NIL NIL) (-818 1935944 1937129 1938300 "OMDEV" 1940898 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1935013 1935184 1935378 "OMCONN" 1935770 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1933600 1934576 1934604 "OINTDOM" 1934609 T OINTDOM (NIL) -9 NIL 1934630 NIL) (-815 1929379 1930590 1931306 "OFMONOID" 1932916 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1928790 1929316 1929361 "ODVAR" 1929366 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1926213 1928535 1928690 "ODR" 1928695 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1918522 1925989 1926115 "ODPOL" 1926120 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1912344 1918394 1918499 "ODP" 1918504 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1911110 1911325 1911600 "ODETOOLS" 1912118 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1908077 1908735 1909451 "ODESYS" 1910443 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1902959 1903867 1904892 "ODERTRIC" 1907152 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1902385 1902467 1902661 "ODERED" 1902871 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1899273 1899821 1900498 "ODERAT" 1901808 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1896230 1896697 1897294 "ODEPRRIC" 1898802 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1894173 1894769 1895255 "ODEPROB" 1895764 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1890693 1891178 1891825 "ODEPRIM" 1893652 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1889942 1890044 1890304 "ODEPAL" 1890585 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1886104 1886895 1887759 "ODEPACK" 1889098 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1885137 1885244 1885473 "ODEINT" 1885993 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1879238 1880663 1882110 "ODEIFTBL" 1883710 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1874573 1875359 1876318 "ODEEF" 1878397 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1873908 1873997 1874227 "ODECONST" 1874478 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1872033 1872694 1872722 "ODECAT" 1873327 T ODECAT (NIL) -9 NIL 1873858 NIL) (-795 1868905 1871745 1871864 "OCT" 1871946 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1868543 1868586 1868713 "OCTCT2" 1868856 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1863283 1865717 1865757 "OC" 1866854 NIL OC (NIL T) -9 NIL 1867712 NIL) (-792 1860510 1861258 1862248 "OC-" 1862342 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1859862 1860330 1860358 "OCAMON" 1860363 T OCAMON (NIL) -9 NIL 1860384 NIL) (-790 1859393 1859734 1859762 "OASGP" 1859767 T OASGP (NIL) -9 NIL 1859787 NIL) (-789 1858654 1859143 1859171 "OAMONS" 1859211 T OAMONS (NIL) -9 NIL 1859254 NIL) (-788 1858068 1858501 1858529 "OAMON" 1858534 T OAMON (NIL) -9 NIL 1858554 NIL) (-787 1857346 1857864 1857892 "OAGROUP" 1857897 T OAGROUP (NIL) -9 NIL 1857917 NIL) (-786 1857036 1857086 1857174 "NUMTUBE" 1857290 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1850609 1852127 1853663 "NUMQUAD" 1855520 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1846365 1847353 1848378 "NUMODE" 1849604 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1843720 1844600 1844628 "NUMINT" 1845551 T NUMINT (NIL) -9 NIL 1846315 NIL) (-782 1842668 1842865 1843083 "NUMFMT" 1843522 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1829027 1831972 1834504 "NUMERIC" 1840175 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1823397 1828476 1828571 "NTSCAT" 1828576 NIL NTSCAT (NIL T T T T) -9 NIL 1828615 NIL) (-779 1822591 1822756 1822949 "NTPOLFN" 1823236 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1810396 1819416 1820228 "NSUP" 1821812 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1810028 1810085 1810194 "NSUP2" 1810333 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1799984 1809802 1809935 "NSMP" 1809940 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1798416 1798717 1799074 "NREP" 1799672 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1797007 1797259 1797617 "NPCOEF" 1798159 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1796073 1796188 1796404 "NORMRETR" 1796888 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1794114 1794404 1794813 "NORMPK" 1795781 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1793799 1793827 1793951 "NORMMA" 1794080 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1793599 1793756 1793785 "NONE" 1793790 T NONE (NIL) -8 NIL NIL NIL) (-769 1793388 1793417 1793486 "NONE1" 1793563 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1792871 1792933 1793119 "NODE1" 1793320 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1791114 1791965 1792220 "NNI" 1792567 T NNI (NIL) -8 NIL NIL 1792802) (-766 1789534 1789847 1790211 "NLINSOL" 1790782 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1785775 1786770 1787669 "NIPROB" 1788655 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1784532 1784766 1785068 "NFINTBAS" 1785537 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1783706 1784182 1784223 "NETCLT" 1784395 NIL NETCLT (NIL T) -9 NIL 1784477 NIL) (-762 1782414 1782645 1782926 "NCODIV" 1783474 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1782176 1782213 1782288 "NCNTFRAC" 1782371 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1780356 1780720 1781140 "NCEP" 1781801 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1779227 1780000 1780028 "NASRING" 1780138 T NASRING (NIL) -9 NIL 1780218 NIL) (-758 1779022 1779066 1779160 "NASRING-" 1779165 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1778149 1778674 1778702 "NARNG" 1778819 T NARNG (NIL) -9 NIL 1778910 NIL) (-756 1777841 1777908 1778042 "NARNG-" 1778047 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1776720 1776927 1777162 "NAGSP" 1777626 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1767992 1769676 1771349 "NAGS" 1775067 T NAGS (NIL) -7 NIL NIL NIL) (-753 1766540 1766848 1767179 "NAGF07" 1767681 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1761078 1762369 1763676 "NAGF04" 1765253 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1754046 1755660 1757293 "NAGF02" 1759465 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1749270 1750370 1751487 "NAGF01" 1752949 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1742898 1744464 1746049 "NAGE04" 1747705 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1734067 1736188 1738318 "NAGE02" 1740788 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1730020 1730967 1731931 "NAGE01" 1733123 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1727815 1728349 1728907 "NAGD03" 1729482 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1719565 1721493 1723447 "NAGD02" 1725881 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1713376 1714801 1716241 "NAGD01" 1718145 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1709585 1710407 1711244 "NAGC06" 1712559 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1708050 1708382 1708738 "NAGC05" 1709249 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1707426 1707545 1707689 "NAGC02" 1707926 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1706460 1707043 1707083 "NAALG" 1707162 NIL NAALG (NIL T) -9 NIL 1707223 NIL) (-739 1706295 1706324 1706414 "NAALG-" 1706419 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1700245 1701353 1702540 "MULTSQFR" 1705191 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1699564 1699639 1699823 "MULTFACT" 1700157 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1692622 1696527 1696580 "MTSCAT" 1697650 NIL MTSCAT (NIL T T) -9 NIL 1698164 NIL) (-735 1692334 1692388 1692480 "MTHING" 1692562 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1692126 1692159 1692219 "MSYSCMD" 1692294 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1688208 1690881 1691201 "MSET" 1691839 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1685277 1687769 1687810 "MSETAGG" 1687815 NIL MSETAGG (NIL T) -9 NIL 1687849 NIL) (-731 1681118 1682656 1683401 "MRING" 1684577 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1680684 1680751 1680882 "MRF2" 1681045 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1680302 1680337 1680481 "MRATFAC" 1680643 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1677914 1678209 1678640 "MPRFF" 1680007 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1671939 1677768 1677865 "MPOLY" 1677870 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1671429 1671464 1671672 "MPCPF" 1671898 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1670943 1670986 1671170 "MPC3" 1671380 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1670138 1670219 1670440 "MPC2" 1670858 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1668439 1668776 1669166 "MONOTOOL" 1669798 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1667664 1667981 1668009 "MONOID" 1668228 T MONOID (NIL) -9 NIL 1668375 NIL) (-721 1667210 1667329 1667510 "MONOID-" 1667515 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1658034 1663977 1664036 "MONOGEN" 1664710 NIL MONOGEN (NIL T T) -9 NIL 1665166 NIL) (-719 1655252 1655987 1656987 "MONOGEN-" 1657106 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1654085 1654531 1654559 "MONADWU" 1654951 T MONADWU (NIL) -9 NIL 1655189 NIL) (-717 1653457 1653616 1653864 "MONADWU-" 1653869 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1652816 1653060 1653088 "MONAD" 1653295 T MONAD (NIL) -9 NIL 1653407 NIL) (-715 1652501 1652579 1652711 "MONAD-" 1652716 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1650790 1651414 1651693 "MOEBIUS" 1652254 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1650158 1650560 1650600 "MODULE" 1650605 NIL MODULE (NIL T) -9 NIL 1650631 NIL) (-712 1649726 1649822 1650012 "MODULE-" 1650017 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1647406 1648090 1648417 "MODRING" 1649550 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1644350 1645511 1646032 "MODOP" 1646935 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1642938 1643417 1643694 "MODMONOM" 1644213 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1632708 1641229 1641643 "MODMON" 1642575 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1629864 1631552 1631828 "MODFIELD" 1632583 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1628841 1629145 1629335 "MMLFORM" 1629694 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1628367 1628410 1628589 "MMAP" 1628792 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1626550 1627317 1627358 "MLO" 1627781 NIL MLO (NIL T) -9 NIL 1628023 NIL) (-703 1623916 1624432 1625034 "MLIFT" 1626031 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1623307 1623391 1623545 "MKUCFUNC" 1623827 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1622906 1622976 1623099 "MKRECORD" 1623230 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1621953 1622115 1622343 "MKFUNC" 1622717 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1621341 1621445 1621601 "MKFLCFN" 1621836 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1620618 1620720 1620905 "MKBCFUNC" 1621234 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1617325 1620172 1620308 "MINT" 1620502 T MINT (NIL) -8 NIL NIL NIL) (-696 1616137 1616380 1616657 "MHROWRED" 1617080 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1611517 1614672 1615077 "MFLOAT" 1615752 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1610874 1610950 1611121 "MFINFACT" 1611429 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1607189 1608037 1608921 "MESH" 1610010 T MESH (NIL) -7 NIL NIL NIL) (-692 1605579 1605891 1606244 "MDDFACT" 1606876 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1602374 1604738 1604779 "MDAGG" 1605034 NIL MDAGG (NIL T) -9 NIL 1605177 NIL) (-690 1592117 1601667 1601874 "MCMPLX" 1602187 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1591258 1591404 1591604 "MCDEN" 1591966 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1589148 1589418 1589798 "MCALCFN" 1590988 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1588073 1588313 1588546 "MAYBE" 1588954 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1585685 1586208 1586770 "MATSTOR" 1587544 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1581642 1585057 1585305 "MATRIX" 1585470 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1577406 1578115 1578851 "MATLIN" 1580999 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1567512 1570698 1570775 "MATCAT" 1575655 NIL MATCAT (NIL T T T) -9 NIL 1577072 NIL) (-682 1563868 1564889 1566245 "MATCAT-" 1566250 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1562462 1562615 1562948 "MATCAT2" 1563703 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1560574 1560898 1561282 "MAPPKG3" 1562137 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1559555 1559728 1559950 "MAPPKG2" 1560398 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1558054 1558338 1558665 "MAPPKG1" 1559261 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1557133 1557460 1557637 "MAPPAST" 1557897 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1556744 1556802 1556925 "MAPHACK3" 1557069 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1556336 1556397 1556511 "MAPHACK2" 1556676 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1555773 1555877 1556019 "MAPHACK1" 1556227 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1553852 1554473 1554777 "MAGMA" 1555501 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1553331 1553576 1553667 "MACROAST" 1553781 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1549749 1551570 1552031 "M3D" 1552903 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1543855 1548118 1548159 "LZSTAGG" 1548941 NIL LZSTAGG (NIL T) -9 NIL 1549236 NIL) (-669 1539812 1540986 1542443 "LZSTAGG-" 1542448 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1536899 1537703 1538190 "LWORD" 1539357 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1536475 1536703 1536778 "LSTAST" 1536844 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1529641 1536246 1536380 "LSQM" 1536385 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1528865 1529004 1529232 "LSPP" 1529496 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1526677 1526978 1527434 "LSMP" 1528554 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1523456 1524130 1524860 "LSMP1" 1525979 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1517333 1522623 1522664 "LSAGG" 1522726 NIL LSAGG (NIL T) -9 NIL 1522804 NIL) (-661 1514028 1514952 1516165 "LSAGG-" 1516170 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1511627 1513172 1513421 "LPOLY" 1513823 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1511209 1511294 1511417 "LPEFRAC" 1511536 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1509529 1510303 1510556 "LO" 1511041 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1509181 1509293 1509321 "LOGIC" 1509432 T LOGIC (NIL) -9 NIL 1509513 NIL) (-656 1509043 1509066 1509137 "LOGIC-" 1509142 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1508236 1508376 1508569 "LODOOPS" 1508899 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1505659 1508152 1508218 "LODO" 1508223 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1504197 1504432 1504785 "LODOF" 1505406 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1500519 1502950 1502991 "LODOCAT" 1503429 NIL LODOCAT (NIL T) -9 NIL 1503640 NIL) (-651 1500252 1500310 1500437 "LODOCAT-" 1500442 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1497572 1500093 1500211 "LODO2" 1500216 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1495007 1497509 1497554 "LODO1" 1497559 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1493867 1494032 1494344 "LODEEF" 1494830 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1489106 1491997 1492038 "LNAGG" 1492985 NIL LNAGG (NIL T) -9 NIL 1493429 NIL) (-646 1488253 1488467 1488809 "LNAGG-" 1488814 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1484389 1485178 1485817 "LMOPS" 1487668 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1483760 1484146 1484187 "LMODULE" 1484248 NIL LMODULE (NIL T) -9 NIL 1484290 NIL) (-643 1480958 1483405 1483528 "LMDICT" 1483670 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1480657 1480866 1480926 "LITERAL" 1480931 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1473840 1479603 1479901 "LIST" 1480392 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1473365 1473439 1473578 "LIST3" 1473760 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1472372 1472550 1472778 "LIST2" 1473183 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1470506 1470818 1471217 "LIST2MAP" 1472019 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1469202 1469872 1469913 "LINEXP" 1470168 NIL LINEXP (NIL T) -9 NIL 1470317 NIL) (-636 1467849 1468109 1468406 "LINDEP" 1468954 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1464616 1465335 1466112 "LIMITRF" 1467104 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1462891 1463187 1463603 "LIMITPS" 1464311 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1457319 1462402 1462630 "LIE" 1462712 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1456342 1456811 1456851 "LIECAT" 1456991 NIL LIECAT (NIL T) -9 NIL 1457142 NIL) (-631 1456183 1456210 1456298 "LIECAT-" 1456303 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1448679 1455632 1455797 "LIB" 1456038 T LIB (NIL) -8 NIL NIL NIL) (-629 1444314 1445197 1446132 "LGROBP" 1447796 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1442180 1442454 1442816 "LF" 1444035 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1441020 1441712 1441740 "LFCAT" 1441947 T LFCAT (NIL) -9 NIL 1442086 NIL) (-626 1437922 1438552 1439240 "LEXTRIPK" 1440384 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1434666 1435492 1435995 "LEXP" 1437502 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1434142 1434387 1434479 "LETAST" 1434594 T LETAST (NIL) -8 NIL NIL NIL) (-623 1432540 1432853 1433254 "LEADCDET" 1433824 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1431730 1431804 1432033 "LAZM3PK" 1432461 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1426647 1429807 1430345 "LAUPOL" 1431242 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1426212 1426256 1426424 "LAPLACE" 1426597 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1424151 1425313 1425564 "LA" 1426045 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1423198 1423782 1423823 "LALG" 1423885 NIL LALG (NIL T) -9 NIL 1423944 NIL) (-617 1422912 1422971 1423107 "LALG-" 1423112 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1422747 1422771 1422812 "KVTFROM" 1422874 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1421520 1421964 1422193 "KTVLOGIC" 1422538 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1421355 1421379 1421420 "KRCFROM" 1421482 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1420259 1420446 1420745 "KOVACIC" 1421155 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1420094 1420118 1420159 "KONVERT" 1420221 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1419929 1419953 1419994 "KOERCE" 1420056 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1417635 1418423 1418816 "KERNEL" 1419568 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1417137 1417218 1417348 "KERNEL2" 1417549 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1410907 1415676 1415730 "KDAGG" 1416107 NIL KDAGG (NIL T T) -9 NIL 1416313 NIL) (-607 1410436 1410560 1410765 "KDAGG-" 1410770 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1403584 1410097 1410252 "KAFILE" 1410314 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1398012 1403095 1403323 "JORDAN" 1403405 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1397391 1397661 1397782 "JOINAST" 1397911 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1397237 1397296 1397351 "JAVACODE" 1397356 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1393489 1395442 1395496 "IXAGG" 1396425 NIL IXAGG (NIL T T) -9 NIL 1396884 NIL) (-601 1392408 1392714 1393133 "IXAGG-" 1393138 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1387940 1392330 1392389 "IVECTOR" 1392394 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1386706 1386943 1387209 "ITUPLE" 1387707 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1385142 1385319 1385625 "ITRIGMNP" 1386528 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1383887 1384091 1384374 "ITFUN3" 1384918 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1383519 1383576 1383685 "ITFUN2" 1383824 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1381321 1382381 1382680 "ITAYLOR" 1383253 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1370266 1375458 1376621 "ISUPS" 1380191 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1369370 1369510 1369746 "ISUMP" 1370113 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1364584 1369171 1369250 "ISTRING" 1369323 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1364060 1364305 1364397 "ISAST" 1364512 T ISAST (NIL) -8 NIL NIL NIL) (-590 1363270 1363351 1363567 "IRURPK" 1363974 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1362206 1362407 1362647 "IRSN" 1363050 T IRSN (NIL) -7 NIL NIL NIL) (-588 1360235 1360590 1361026 "IRRF2F" 1361844 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1359982 1360020 1360096 "IRREDFFX" 1360191 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1358597 1358856 1359155 "IROOT" 1359715 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1355201 1356281 1356973 "IR" 1357937 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1352814 1353309 1353875 "IR2" 1354679 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1351886 1351999 1352220 "IR2F" 1352697 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1351677 1351711 1351771 "IPRNTPK" 1351846 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1348257 1351566 1351635 "IPF" 1351640 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1346584 1348182 1348239 "IPADIC" 1348244 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1345896 1346144 1346274 "IP4ADDR" 1346474 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1345369 1345600 1345710 "IOMODE" 1345806 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1344442 1344966 1345093 "IOBFILE" 1345262 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1343930 1344346 1344374 "IOBCON" 1344379 T IOBCON (NIL) -9 NIL 1344400 NIL) (-575 1343427 1343485 1343675 "INVLAPLA" 1343866 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1333075 1335429 1337815 "INTTR" 1341091 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1329419 1330161 1331025 "INTTOOLS" 1332260 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1329005 1329096 1329213 "INTSLPE" 1329322 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1326959 1328928 1328987 "INTRVL" 1328992 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1324561 1325073 1325648 "INTRF" 1326444 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1323972 1324069 1324211 "INTRET" 1324459 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1321969 1322358 1322828 "INTRAT" 1323580 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1319197 1319780 1320406 "INTPM" 1321454 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1315899 1316499 1317244 "INTPAF" 1318583 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1311078 1312040 1313091 "INTPACK" 1314868 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1307955 1310807 1310934 "INT" 1310971 T INT (NIL) -8 NIL NIL NIL) (-563 1307207 1307359 1307567 "INTHERTR" 1307797 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1306646 1306726 1306914 "INTHERAL" 1307121 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1304492 1304935 1305392 "INTHEORY" 1306209 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1295800 1297421 1299200 "INTG0" 1302844 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1276373 1281163 1285973 "INTFTBL" 1291010 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1275622 1275760 1275933 "INTFACT" 1276232 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1273007 1273453 1274017 "INTEF" 1275176 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1271440 1272179 1272207 "INTDOM" 1272508 T INTDOM (NIL) -9 NIL 1272715 NIL) (-555 1270809 1270983 1271225 "INTDOM-" 1271230 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1267269 1269193 1269247 "INTCAT" 1270046 NIL INTCAT (NIL T) -9 NIL 1270366 NIL) (-553 1266741 1266844 1266972 "INTBIT" 1267161 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1265412 1265566 1265880 "INTALG" 1266586 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1264869 1264959 1265129 "INTAF" 1265316 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1258212 1264679 1264819 "INTABL" 1264824 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1257516 1257982 1258047 "INT8" 1258081 T INT8 (NIL) -8 NIL NIL 1258126) (-548 1256819 1257285 1257350 "INT64" 1257384 T INT64 (NIL) -8 NIL NIL 1257429) (-547 1256122 1256588 1256653 "INT32" 1256687 T INT32 (NIL) -8 NIL NIL 1256732) (-546 1255425 1255891 1255956 "INT16" 1255990 T INT16 (NIL) -8 NIL NIL 1256035) (-545 1250405 1253114 1253142 "INS" 1254076 T INS (NIL) -9 NIL 1254741 NIL) (-544 1247645 1248416 1249390 "INS-" 1249463 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1246420 1246647 1246945 "INPSIGN" 1247398 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1245538 1245655 1245852 "INPRODPF" 1246300 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1244432 1244549 1244786 "INPRODFF" 1245418 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1243432 1243584 1243844 "INNMFACT" 1244268 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1242629 1242726 1242914 "INMODGCD" 1243331 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1241137 1241382 1241706 "INFSP" 1242374 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1240321 1240438 1240621 "INFPROD0" 1241017 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1237176 1238386 1238901 "INFORM" 1239814 T INFORM (NIL) -8 NIL NIL NIL) (-535 1236786 1236846 1236944 "INFORM1" 1237111 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1236309 1236398 1236512 "INFINITY" 1236692 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1235485 1236029 1236130 "INETCLTS" 1236228 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1234101 1234351 1234672 "INEP" 1235233 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1233350 1233998 1234063 "INDE" 1234068 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1232914 1232982 1233099 "INCRMAPS" 1233277 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1231732 1232183 1232389 "INBFILE" 1232728 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1227032 1227968 1228912 "INBFF" 1230820 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1225940 1226209 1226237 "INBCON" 1226750 T INBCON (NIL) -9 NIL 1227016 NIL) (-526 1225192 1225415 1225691 "INBCON-" 1225696 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1224671 1224916 1225007 "INAST" 1225121 T INAST (NIL) -8 NIL NIL NIL) (-524 1224098 1224350 1224456 "IMPTAST" 1224585 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1220544 1223942 1224046 "IMATRIX" 1224051 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1219256 1219379 1219694 "IMATQF" 1220400 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1217476 1217703 1218040 "IMATLIN" 1219012 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1212054 1217400 1217458 "ILIST" 1217463 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1209959 1211914 1212027 "IIARRAY2" 1212032 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1205357 1209870 1209934 "IFF" 1209939 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1204704 1204974 1205090 "IFAST" 1205261 T IFAST (NIL) -8 NIL NIL NIL) (-516 1199699 1203996 1204184 "IFARRAY" 1204561 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1198879 1199603 1199676 "IFAMON" 1199681 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1198463 1198528 1198582 "IEVALAB" 1198789 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1198138 1198206 1198366 "IEVALAB-" 1198371 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1197769 1198052 1198115 "IDPO" 1198120 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1197019 1197658 1197733 "IDPOAMS" 1197738 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1196326 1196908 1196983 "IDPOAM" 1196988 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1195385 1195661 1195714 "IDPC" 1196127 NIL IDPC (NIL T T) -9 NIL 1196276 NIL) (-508 1194854 1195277 1195350 "IDPAM" 1195355 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1194230 1194746 1194819 "IDPAG" 1194824 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1193875 1194066 1194141 "IDENT" 1194175 T IDENT (NIL) -8 NIL NIL NIL) (-505 1190130 1190978 1191873 "IDECOMP" 1193032 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1182967 1184053 1185100 "IDEAL" 1189166 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1182131 1182243 1182442 "ICDEN" 1182851 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1181202 1181611 1181758 "ICARD" 1182004 T ICARD (NIL) -8 NIL NIL NIL) (-501 1179262 1179575 1179980 "IBPTOOLS" 1180879 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1174869 1178882 1178995 "IBITS" 1179181 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1171592 1172168 1172863 "IBATOOL" 1174286 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1169371 1169833 1170366 "IBACHIN" 1171127 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1167200 1169217 1169320 "IARRAY2" 1169325 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1163306 1167126 1167183 "IARRAY1" 1167188 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1157263 1161718 1162199 "IAN" 1162845 T IAN (NIL) -8 NIL NIL NIL) (-494 1156774 1156831 1157004 "IALGFACT" 1157200 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1156302 1156415 1156443 "HYPCAT" 1156650 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1155840 1155957 1156143 "HYPCAT-" 1156148 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1155435 1155635 1155718 "HOSTNAME" 1155777 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1155280 1155317 1155358 "HOMOTOP" 1155363 NIL HOMOTOP (NIL T) -9 NIL 1155396 NIL) (-489 1151912 1153290 1153331 "HOAGG" 1154312 NIL HOAGG (NIL T) -9 NIL 1154991 NIL) (-488 1150506 1150905 1151431 "HOAGG-" 1151436 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1144510 1150101 1150250 "HEXADEC" 1150377 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1143258 1143480 1143743 "HEUGCD" 1144287 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1142334 1143095 1143225 "HELLFDIV" 1143230 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1140513 1142111 1142199 "HEAP" 1142278 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1139776 1140065 1140199 "HEADAST" 1140399 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1133642 1139691 1139753 "HDP" 1139758 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1127358 1133277 1133429 "HDMP" 1133543 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1126682 1126822 1126986 "HB" 1127214 T HB (NIL) -7 NIL NIL NIL) (-479 1120068 1126528 1126632 "HASHTBL" 1126637 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1119544 1119789 1119881 "HASAST" 1119996 T HASAST (NIL) -8 NIL NIL NIL) (-477 1117322 1119166 1119348 "HACKPI" 1119382 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1112990 1117175 1117288 "GTSET" 1117293 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1106405 1112868 1112966 "GSTBL" 1112971 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1098683 1105436 1105701 "GSERIES" 1106196 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1097824 1098241 1098269 "GROUP" 1098472 T GROUP (NIL) -9 NIL 1098606 NIL) (-472 1097190 1097349 1097600 "GROUP-" 1097605 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1095557 1095878 1096265 "GROEBSOL" 1096867 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1094471 1094759 1094810 "GRMOD" 1095339 NIL GRMOD (NIL T T) -9 NIL 1095507 NIL) (-469 1094239 1094275 1094403 "GRMOD-" 1094408 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1089529 1090593 1091593 "GRIMAGE" 1093259 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1087995 1088256 1088580 "GRDEF" 1089225 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1087439 1087555 1087696 "GRAY" 1087874 T GRAY (NIL) -7 NIL NIL NIL) (-465 1086626 1087032 1087083 "GRALG" 1087236 NIL GRALG (NIL T T) -9 NIL 1087329 NIL) (-464 1086287 1086360 1086523 "GRALG-" 1086528 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1083064 1085872 1086050 "GPOLSET" 1086194 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1082418 1082475 1082733 "GOSPER" 1083001 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1078150 1078856 1079382 "GMODPOL" 1082117 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1077155 1077339 1077577 "GHENSEL" 1077962 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1071206 1072049 1073076 "GENUPS" 1076239 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1070903 1070954 1071043 "GENUFACT" 1071149 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1070315 1070392 1070557 "GENPGCD" 1070821 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1069789 1069824 1070037 "GENMFACT" 1070274 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1068355 1068612 1068919 "GENEEZ" 1069532 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1062229 1067966 1068128 "GDMP" 1068278 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1051571 1056000 1057106 "GCNAALG" 1061212 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1049964 1050826 1050854 "GCDDOM" 1051109 T GCDDOM (NIL) -9 NIL 1051266 NIL) (-451 1049434 1049561 1049776 "GCDDOM-" 1049781 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1048106 1048291 1048595 "GB" 1049213 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1036722 1039052 1041444 "GBINTERN" 1045797 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1034559 1034851 1035272 "GBF" 1036397 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1033340 1033505 1033772 "GBEUCLID" 1034375 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1032689 1032814 1032963 "GAUSSFAC" 1033211 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1031056 1031358 1031672 "GALUTIL" 1032408 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1029364 1029638 1029962 "GALPOLYU" 1030783 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1026729 1027019 1027426 "GALFACTU" 1029061 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1018535 1020034 1021642 "GALFACT" 1025161 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1015923 1016581 1016609 "FVFUN" 1017765 T FVFUN (NIL) -9 NIL 1018485 NIL) (-440 1015189 1015371 1015399 "FVC" 1015690 T FVC (NIL) -9 NIL 1015873 NIL) (-439 1014832 1015014 1015082 "FUNDESC" 1015141 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1014447 1014629 1014710 "FUNCTION" 1014784 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1012191 1012769 1013235 "FT" 1014001 T FT (NIL) -8 NIL NIL NIL) (-436 1010982 1011492 1011695 "FTEM" 1012008 T FTEM (NIL) -8 NIL NIL NIL) (-435 1009238 1009527 1009931 "FSUPFACT" 1010673 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1007635 1007924 1008256 "FST" 1008926 T FST (NIL) -8 NIL NIL NIL) (-433 1006806 1006912 1007107 "FSRED" 1007517 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1005484 1005740 1006094 "FSPRMELT" 1006521 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 1002569 1003007 1003506 "FSPECF" 1005047 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 984596 993072 993112 "FS" 996960 NIL FS (NIL T) -9 NIL 999249 NIL) (-429 973243 976236 980292 "FS-" 980589 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 972757 972811 972988 "FSINT" 973184 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 971049 971750 972053 "FSERIES" 972536 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 970063 970179 970410 "FSCINT" 970929 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 966271 969007 969048 "FSAGG" 969418 NIL FSAGG (NIL T) -9 NIL 969677 NIL) (-424 964033 964634 965430 "FSAGG-" 965525 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 963075 963218 963445 "FSAGG2" 963886 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 960729 961009 961563 "FS2UPS" 962793 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 960311 960354 960509 "FS2" 960680 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 959168 959339 959648 "FS2EXPXP" 960136 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 958594 958709 958861 "FRUTIL" 959048 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 950007 954089 955447 "FR" 957268 NIL FR (NIL T) -8 NIL NIL NIL) (-417 945055 947725 947765 "FRNAALG" 949161 NIL FRNAALG (NIL T) -9 NIL 949768 NIL) (-416 940728 941804 943079 "FRNAALG-" 943829 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 940366 940409 940536 "FRNAAF2" 940679 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 938746 939220 939515 "FRMOD" 940178 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 936497 937129 937446 "FRIDEAL" 938537 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 935692 935779 936068 "FRIDEAL2" 936404 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 934825 935239 935280 "FRETRCT" 935285 NIL FRETRCT (NIL T) -9 NIL 935461 NIL) (-410 933937 934168 934519 "FRETRCT-" 934524 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 931115 932325 932384 "FRAMALG" 933266 NIL FRAMALG (NIL T T) -9 NIL 933558 NIL) (-408 929249 929704 930334 "FRAMALG-" 930557 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 923170 928724 929000 "FRAC" 929005 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 922806 922863 922970 "FRAC2" 923107 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 922442 922499 922606 "FR2" 922743 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 917080 919967 919995 "FPS" 921114 T FPS (NIL) -9 NIL 921671 NIL) (-403 916529 916638 916802 "FPS-" 916948 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 913949 915618 915646 "FPC" 915871 T FPC (NIL) -9 NIL 916013 NIL) (-401 913742 913782 913879 "FPC-" 913884 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 912532 913230 913271 "FPATMAB" 913276 NIL FPATMAB (NIL T) -9 NIL 913428 NIL) (-399 910205 910708 911134 "FPARFRAC" 912169 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 905598 906097 906779 "FORTRAN" 909637 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 903314 903814 904353 "FORT" 905079 T FORT (NIL) -7 NIL NIL NIL) (-396 900990 901552 901580 "FORTFN" 902640 T FORTFN (NIL) -9 NIL 903264 NIL) (-395 900754 900804 900832 "FORTCAT" 900891 T FORTCAT (NIL) -9 NIL 900953 NIL) (-394 898860 899370 899760 "FORMULA" 900384 T FORMULA (NIL) -8 NIL NIL NIL) (-393 898648 898678 898747 "FORMULA1" 898824 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 898171 898223 898396 "FORDER" 898590 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 897267 897431 897624 "FOP" 897998 T FOP (NIL) -7 NIL NIL NIL) (-390 895848 896547 896721 "FNLA" 897149 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 894577 894992 895020 "FNCAT" 895480 T FNCAT (NIL) -9 NIL 895740 NIL) (-388 894116 894536 894564 "FNAME" 894569 T FNAME (NIL) -8 NIL NIL NIL) (-387 892745 893708 893736 "FMTC" 893741 T FMTC (NIL) -9 NIL 893777 NIL) (-386 889078 890268 890897 "FMONOID" 892149 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 888270 888820 888969 "FM" 888974 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 885694 886340 886368 "FMFUN" 887512 T FMFUN (NIL) -9 NIL 888220 NIL) (-383 884963 885144 885172 "FMC" 885462 T FMC (NIL) -9 NIL 885644 NIL) (-382 882131 882991 883045 "FMCAT" 884240 NIL FMCAT (NIL T T) -9 NIL 884735 NIL) (-381 880997 881897 881997 "FM1" 882076 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 878771 879187 879681 "FLOATRP" 880548 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 872345 876500 877121 "FLOAT" 878170 T FLOAT (NIL) -8 NIL NIL NIL) (-378 869783 870283 870861 "FLOATCP" 871812 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 868558 869396 869437 "FLINEXP" 869442 NIL FLINEXP (NIL T) -9 NIL 869535 NIL) (-376 867712 867947 868275 "FLINEXP-" 868280 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 866788 866932 867156 "FLASORT" 867564 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 863979 864847 864899 "FLALG" 866126 NIL FLALG (NIL T T) -9 NIL 866593 NIL) (-373 857715 861465 861506 "FLAGG" 862768 NIL FLAGG (NIL T) -9 NIL 863420 NIL) (-372 856441 856780 857270 "FLAGG-" 857275 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 855483 855626 855853 "FLAGG2" 856294 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 852424 853432 853491 "FINRALG" 854619 NIL FINRALG (NIL T T) -9 NIL 855127 NIL) (-369 851584 851813 852152 "FINRALG-" 852157 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 850966 851203 851231 "FINITE" 851427 T FINITE (NIL) -9 NIL 851534 NIL) (-367 843398 845585 845625 "FINAALG" 849292 NIL FINAALG (NIL T) -9 NIL 850745 NIL) (-366 838730 839780 840924 "FINAALG-" 842303 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 838098 838485 838588 "FILE" 838660 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 836756 837094 837148 "FILECAT" 837832 NIL FILECAT (NIL T T) -9 NIL 838048 NIL) (-363 834590 836118 836146 "FIELD" 836186 T FIELD (NIL) -9 NIL 836266 NIL) (-362 833210 833595 834106 "FIELD-" 834111 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 831060 831845 832192 "FGROUP" 832896 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 830150 830314 830534 "FGLMICPK" 830892 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 825982 830075 830132 "FFX" 830137 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 825583 825644 825779 "FFSLPE" 825915 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 821572 822355 823151 "FFPOLY" 824819 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 821076 821112 821321 "FFPOLY2" 821530 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 816919 820995 821058 "FFP" 821063 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 812317 816830 816894 "FF" 816899 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 807443 811660 811850 "FFNBX" 812171 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 802372 806578 806836 "FFNBP" 807297 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 797005 801656 801867 "FFNB" 802205 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 795837 796035 796350 "FFINTBAS" 796802 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 792030 794244 794272 "FFIELDC" 794892 T FFIELDC (NIL) -9 NIL 795268 NIL) (-348 790692 791063 791560 "FFIELDC-" 791565 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 790261 790307 790431 "FFHOM" 790634 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 787956 788443 788960 "FFF" 789776 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 783574 787698 787799 "FFCGX" 787899 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 779195 783306 783413 "FFCGP" 783517 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 774378 778922 779030 "FFCG" 779131 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 756176 765249 765335 "FFCAT" 770500 NIL FFCAT (NIL T T T) -9 NIL 771951 NIL) (-341 751374 752421 753735 "FFCAT-" 754965 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 750785 750828 751063 "FFCAT2" 751325 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 739955 743757 744977 "FEXPR" 749637 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 738955 739390 739431 "FEVALAB" 739515 NIL FEVALAB (NIL T) -9 NIL 739776 NIL) (-337 738114 738324 738662 "FEVALAB-" 738667 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 736680 737497 737700 "FDIV" 738013 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 733720 734461 734576 "FDIVCAT" 736144 NIL FDIVCAT (NIL T T T T) -9 NIL 736581 NIL) (-334 733482 733509 733679 "FDIVCAT-" 733684 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 732702 732789 733066 "FDIV2" 733389 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 731388 731647 731936 "FCPAK1" 732433 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 730487 730888 731029 "FCOMP" 731279 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 714189 717637 721175 "FC" 726969 T FC (NIL) -8 NIL NIL NIL) (-329 706733 710753 710793 "FAXF" 712595 NIL FAXF (NIL T) -9 NIL 713287 NIL) (-328 704009 704667 705492 "FAXF-" 705957 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 699061 703385 703561 "FARRAY" 703866 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 694280 696346 696399 "FAMR" 697422 NIL FAMR (NIL T T) -9 NIL 697882 NIL) (-325 693170 693472 693907 "FAMR-" 693912 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 692339 693092 693145 "FAMONOID" 693150 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 690125 690835 690888 "FAMONC" 691829 NIL FAMONC (NIL T T) -9 NIL 692215 NIL) (-322 688790 689879 690016 "FAGROUP" 690021 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 686585 686904 687307 "FACUTIL" 688471 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 685684 685869 686091 "FACTFUNC" 686395 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 678054 684935 685147 "EXPUPXS" 685540 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 675537 676077 676663 "EXPRTUBE" 677488 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 671731 672323 673060 "EXPRODE" 674876 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 657070 670386 670814 "EXPR" 671335 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 651477 652064 652877 "EXPR2UPS" 656368 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 651113 651170 651277 "EXPR2" 651414 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 642483 650245 650542 "EXPEXPAN" 650950 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 642283 642440 642469 "EXIT" 642474 T EXIT (NIL) -8 NIL NIL NIL) (-311 641763 642007 642098 "EXITAST" 642212 T EXITAST (NIL) -8 NIL NIL NIL) (-310 641390 641452 641565 "EVALCYC" 641695 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 640931 641049 641090 "EVALAB" 641260 NIL EVALAB (NIL T) -9 NIL 641364 NIL) (-308 640412 640534 640755 "EVALAB-" 640760 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 637846 639148 639176 "EUCDOM" 639731 T EUCDOM (NIL) -9 NIL 640081 NIL) (-306 636251 636693 637283 "EUCDOM-" 637288 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 623789 626549 629299 "ESTOOLS" 633521 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 623421 623478 623587 "ESTOOLS2" 623726 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 623172 623214 623294 "ESTOOLS1" 623373 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 617051 618805 618833 "ES" 621601 T ES (NIL) -9 NIL 623010 NIL) (-301 611998 613285 615102 "ES-" 615266 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 608372 609133 609913 "ESCONT" 611238 T ESCONT (NIL) -7 NIL NIL NIL) (-299 608117 608149 608231 "ESCONT1" 608334 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 607792 607842 607942 "ES2" 608061 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 607422 607480 607589 "ES1" 607728 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 606638 606767 606943 "ERROR" 607266 T ERROR (NIL) -7 NIL NIL NIL) (-295 600030 606497 606588 "EQTBL" 606593 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 592533 595344 596793 "EQ" 598614 NIL -2077 (NIL T) -8 NIL NIL NIL) (-293 592165 592222 592331 "EQ2" 592470 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 587454 588503 589596 "EP" 591104 NIL EP (NIL T) -7 NIL NIL NIL) (-291 586054 586345 586651 "ENV" 587168 T ENV (NIL) -8 NIL NIL NIL) (-290 585199 585753 585781 "ENTIRER" 585786 T ENTIRER (NIL) -9 NIL 585832 NIL) (-289 581666 583154 583524 "EMR" 584998 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 580810 580995 581049 "ELTAGG" 581429 NIL ELTAGG (NIL T T) -9 NIL 581640 NIL) (-287 580529 580591 580732 "ELTAGG-" 580737 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 580318 580347 580401 "ELTAB" 580485 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 579444 579590 579789 "ELFUTS" 580169 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 579186 579242 579270 "ELEMFUN" 579375 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 579056 579077 579145 "ELEMFUN-" 579150 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 573900 577156 577197 "ELAGG" 578137 NIL ELAGG (NIL T) -9 NIL 578600 NIL) (-281 572185 572619 573282 "ELAGG-" 573287 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 570850 571128 571421 "ELABEXPR" 571912 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 563714 565517 566344 "EFUPXS" 570126 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 557164 558965 559775 "EFULS" 562990 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 554586 554944 555423 "EFSTRUC" 556796 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 543657 545223 546783 "EF" 553101 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 542731 543142 543291 "EAB" 543528 T EAB (NIL) -8 NIL NIL NIL) (-274 541913 542690 542718 "E04UCFA" 542723 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 541095 541872 541900 "E04NAFA" 541905 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 540277 541054 541082 "E04MBFA" 541087 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 539459 540236 540264 "E04JAFA" 540269 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 538643 539418 539446 "E04GCFA" 539451 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 537827 538602 538630 "E04FDFA" 538635 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 537009 537786 537814 "E04DGFA" 537819 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 531182 532534 533898 "E04AGNT" 535665 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 529862 530368 530408 "DVARCAT" 530883 NIL DVARCAT (NIL T) -9 NIL 531082 NIL) (-265 529066 529278 529592 "DVARCAT-" 529597 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 521931 528865 528994 "DSMP" 528999 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 516713 517876 518944 "DROPT" 520883 T DROPT (NIL) -8 NIL NIL NIL) (-262 516378 516437 516535 "DROPT1" 516648 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 511493 512619 513756 "DROPT0" 515261 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 509838 510163 510549 "DRAWPT" 511127 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 504425 505348 506427 "DRAW" 508812 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 504058 504111 504229 "DRAWHACK" 504366 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 502789 503058 503349 "DRAWCX" 503787 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 502304 502373 502524 "DRAWCURV" 502715 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 492772 494734 496849 "DRAWCFUN" 500209 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 489538 491467 491508 "DQAGG" 492137 NIL DQAGG (NIL T) -9 NIL 492410 NIL) (-253 477782 484516 484599 "DPOLCAT" 486451 NIL DPOLCAT (NIL T T T T) -9 NIL 486996 NIL) (-252 472618 473967 475925 "DPOLCAT-" 475930 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 465740 472479 472577 "DPMO" 472582 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 458765 465520 465687 "DPMM" 465692 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 458370 458684 458732 "DOMCTOR" 458737 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 457638 457892 458029 "DOMAIN" 458253 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 451354 457273 457425 "DMP" 457539 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450954 451010 451154 "DLP" 451292 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 444776 450281 450471 "DLIST" 450796 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 441573 443629 443670 "DLAGG" 444220 NIL DLAGG (NIL T) -9 NIL 444450 NIL) (-243 440352 441016 441044 "DIVRING" 441136 T DIVRING (NIL) -9 NIL 441219 NIL) (-242 439589 439779 440079 "DIVRING-" 440084 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 437691 438048 438454 "DISPLAY" 439203 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 431579 437605 437668 "DIRPROD" 437673 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 430427 430630 430895 "DIRPROD2" 431372 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 419636 425642 425695 "DIRPCAT" 426105 NIL DIRPCAT (NIL NIL T) -9 NIL 426945 NIL) (-237 416962 417604 418485 "DIRPCAT-" 418822 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 416249 416409 416595 "DIOSP" 416796 T DIOSP (NIL) -7 NIL NIL NIL) (-235 412904 415161 415202 "DIOPS" 415636 NIL DIOPS (NIL T) -9 NIL 415865 NIL) (-234 412453 412567 412758 "DIOPS-" 412763 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 411311 411939 411967 "DIFRING" 412154 T DIFRING (NIL) -9 NIL 412264 NIL) (-232 410957 411034 411186 "DIFRING-" 411191 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 408728 410000 410041 "DIFEXT" 410404 NIL DIFEXT (NIL T) -9 NIL 410698 NIL) (-230 407013 407441 408107 "DIFEXT-" 408112 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 404288 406545 406586 "DIAGG" 406591 NIL DIAGG (NIL T) -9 NIL 406611 NIL) (-228 403672 403829 404081 "DIAGG-" 404086 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 399089 402631 402908 "DHMATRIX" 403441 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 394701 395610 396620 "DFSFUN" 398099 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 389779 393632 393944 "DFLOAT" 394409 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 388007 388288 388684 "DFINTTLS" 389487 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 385036 386028 386428 "DERHAM" 387673 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 382837 384811 384900 "DEQUEUE" 384980 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 382052 382185 382381 "DEGRED" 382699 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 378447 379192 380045 "DEFINTRF" 381280 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 375974 376443 377042 "DEFINTEF" 377966 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 375324 375594 375709 "DEFAST" 375879 T DEFAST (NIL) -8 NIL NIL NIL) (-217 369328 374919 375068 "DECIMAL" 375195 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 366838 367298 367804 "DDFACT" 368872 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 366434 366477 366628 "DBLRESP" 366789 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 364306 364667 365027 "DBASE" 366201 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 363548 363786 363932 "DATAARY" 364205 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 362654 363507 363535 "D03FAFA" 363540 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 361761 362613 362641 "D03EEFA" 362646 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 359711 360177 360666 "D03AGNT" 361292 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 359000 359670 359698 "D02EJFA" 359703 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 358289 358959 358987 "D02CJFA" 358992 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 357578 358248 358276 "D02BHFA" 358281 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 356867 357537 357565 "D02BBFA" 357570 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 350064 351653 353259 "D02AGNT" 355281 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 347832 348355 348901 "D01WGTS" 349538 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 346899 347791 347819 "D01TRNS" 347824 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 345967 346858 346886 "D01GBFA" 346891 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 345035 345926 345954 "D01FCFA" 345959 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 344103 344994 345022 "D01ASFA" 345027 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 343171 344062 344090 "D01AQFA" 344095 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 342239 343130 343158 "D01APFA" 343163 T D01APFA (NIL) -8 NIL NIL NIL) (-197 341307 342198 342226 "D01ANFA" 342231 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 340375 341266 341294 "D01AMFA" 341299 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 339443 340334 340362 "D01ALFA" 340367 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 338511 339402 339430 "D01AKFA" 339435 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 337579 338470 338498 "D01AJFA" 338503 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 330874 332427 333988 "D01AGNT" 336038 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 330211 330339 330491 "CYCLOTOM" 330742 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 326946 327659 328386 "CYCLES" 329504 T CYCLES (NIL) -7 NIL NIL NIL) (-189 326258 326392 326563 "CVMP" 326807 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 324029 324287 324663 "CTRIGMNP" 325986 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 323497 323823 323896 "CTOR" 323976 T CTOR (NIL) -8 NIL NIL NIL) (-186 323006 323228 323329 "CTORKIND" 323416 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 322328 322613 322641 "CTORCAT" 322823 T CTORCAT (NIL) -9 NIL 322936 NIL) (-184 321926 322037 322196 "CTORCAT-" 322201 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 321415 321629 321727 "CTORCALL" 321848 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 320789 320888 321041 "CSTTOOLS" 321312 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 316588 317245 318003 "CRFP" 320101 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 316063 316309 316401 "CRCEAST" 316516 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 315110 315295 315523 "CRAPACK" 315867 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 314494 314595 314799 "CPMATCH" 314986 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 314219 314247 314353 "CPIMA" 314460 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 310583 311255 311973 "COORDSYS" 313554 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 309995 310116 310258 "CONTOUR" 310461 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 305886 307998 308490 "CONTFRAC" 309535 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 305766 305787 305815 "CONDUIT" 305852 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 304905 305459 305487 "COMRING" 305492 T COMRING (NIL) -9 NIL 305544 NIL) (-171 303959 304263 304447 "COMPPROP" 304741 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 303620 303655 303783 "COMPLPAT" 303918 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 293642 303429 303538 "COMPLEX" 303543 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 293278 293335 293442 "COMPLEX2" 293579 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 292996 293031 293129 "COMPFACT" 293237 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 277123 287378 287418 "COMPCAT" 288422 NIL COMPCAT (NIL T) -9 NIL 289818 NIL) (-165 266634 269562 273189 "COMPCAT-" 273545 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 266363 266391 266494 "COMMUPC" 266600 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 266157 266191 266250 "COMMONOP" 266324 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 265713 265908 265995 "COMM" 266090 T COMM (NIL) -8 NIL NIL NIL) (-161 265289 265517 265592 "COMMAAST" 265658 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 264538 264732 264760 "COMBOPC" 265098 T COMBOPC (NIL) -9 NIL 265273 NIL) (-159 263434 263644 263886 "COMBINAT" 264328 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 259631 260205 260845 "COMBF" 262856 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 258389 258747 258982 "COLOR" 259416 T COLOR (NIL) -8 NIL NIL NIL) (-156 257865 258110 258202 "COLONAST" 258317 T COLONAST (NIL) -8 NIL NIL NIL) (-155 257505 257552 257677 "CMPLXRT" 257812 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256953 257205 257304 "CLLCTAST" 257426 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 252453 253483 254563 "CLIP" 255893 T CLIP (NIL) -7 NIL NIL NIL) (-152 250799 251559 251798 "CLIF" 252280 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246974 248945 248986 "CLAGG" 249915 NIL CLAGG (NIL T) -9 NIL 250451 NIL) (-150 245396 245853 246436 "CLAGG-" 246441 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244940 245025 245165 "CINTSLPE" 245305 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 242441 242912 243460 "CHVAR" 244468 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 241650 242204 242232 "CHARZ" 242237 T CHARZ (NIL) -9 NIL 242252 NIL) (-146 241404 241444 241522 "CHARPOL" 241604 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 240497 241084 241112 "CHARNZ" 241159 T CHARNZ (NIL) -9 NIL 241215 NIL) (-144 238459 239187 239522 "CHAR" 240182 T CHAR (NIL) -8 NIL NIL NIL) (-143 238185 238246 238274 "CFCAT" 238385 T CFCAT (NIL) -9 NIL NIL NIL) (-142 237430 237541 237723 "CDEN" 238069 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 233395 236583 236863 "CCLASS" 237170 T CCLASS (NIL) -8 NIL NIL NIL) (-140 232702 232845 233008 "CATEGORY" 233252 T -10 (NIL) -8 NIL NIL NIL) (-139 232307 232621 232669 "CATCTOR" 232674 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 231758 232010 232108 "CATAST" 232229 T CATAST (NIL) -8 NIL NIL NIL) (-137 231234 231479 231571 "CASEAST" 231686 T CASEAST (NIL) -8 NIL NIL NIL) (-136 226243 227263 228016 "CARTEN" 230537 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 225351 225499 225720 "CARTEN2" 226090 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 223666 224501 224758 "CARD" 225114 T CARD (NIL) -8 NIL NIL NIL) (-133 223242 223470 223545 "CAPSLAST" 223611 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 222588 222942 222970 "CACHSET" 223102 T CACHSET (NIL) -9 NIL 223179 NIL) (-131 222058 222380 222408 "CABMON" 222458 T CABMON (NIL) -9 NIL 222514 NIL) (-130 221531 221762 221872 "BYTEORD" 221968 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 220507 221065 221207 "BYTE" 221370 T BYTE (NIL) -8 NIL NIL 221492) (-128 215857 220012 220184 "BYTEBUF" 220355 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 213366 215549 215656 "BTREE" 215783 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 210815 213014 213136 "BTOURN" 213276 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 208185 210285 210326 "BTCAT" 210394 NIL BTCAT (NIL T) -9 NIL 210471 NIL) (-124 207852 207932 208081 "BTCAT-" 208086 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 203117 206995 207023 "BTAGG" 207245 T BTAGG (NIL) -9 NIL 207406 NIL) (-122 202607 202732 202938 "BTAGG-" 202943 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 199602 201885 202100 "BSTREE" 202424 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 198740 198866 199050 "BRILL" 199458 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 195392 197466 197507 "BRAGG" 198156 NIL BRAGG (NIL T) -9 NIL 198414 NIL) (-118 193921 194327 194882 "BRAGG-" 194887 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 187150 193267 193451 "BPADICRT" 193769 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 185465 187087 187132 "BPADIC" 187137 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 185163 185193 185307 "BOUNDZRO" 185429 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 180255 181453 182396 "BOP" 184240 T BOP (NIL) -8 NIL NIL NIL) (-113 177876 178320 178840 "BOP1" 179768 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176551 177300 177493 "BOOLEAN" 177703 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175889 176291 176345 "BMODULE" 176350 NIL BMODULE (NIL T T) -9 NIL 176415 NIL) (-110 171690 175687 175760 "BITS" 175836 T BITS (NIL) -8 NIL NIL NIL) (-109 171111 171230 171370 "BINDING" 171570 T BINDING (NIL) -8 NIL NIL NIL) (-108 165118 170708 170856 "BINARY" 170983 T BINARY (NIL) -8 NIL NIL NIL) (-107 162898 164373 164414 "BGAGG" 164674 NIL BGAGG (NIL T) -9 NIL 164811 NIL) (-106 162729 162761 162852 "BGAGG-" 162857 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161800 162113 162318 "BFUNCT" 162544 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 160490 160668 160956 "BEZOUT" 161624 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156959 159342 159672 "BBTREE" 160193 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156693 156746 156774 "BASTYPE" 156893 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156546 156574 156647 "BASTYPE-" 156652 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155980 156056 156208 "BALFACT" 156457 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154836 155395 155581 "AUTOMOR" 155825 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154562 154567 154593 "ATTREG" 154598 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152814 153259 153611 "ATTRBUT" 154228 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 152422 152642 152708 "ATTRAST" 152766 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151958 152071 152097 "ATRIG" 152298 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151767 151808 151895 "ATRIG-" 151900 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 151412 151598 151624 "ASTCAT" 151629 T ASTCAT (NIL) -9 NIL 151659 NIL) (-92 151139 151198 151317 "ASTCAT-" 151322 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 149288 150915 151003 "ASTACK" 151082 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147793 148090 148455 "ASSOCEQ" 148970 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146825 147452 147576 "ASP9" 147700 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146588 146773 146812 "ASP8" 146817 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 145456 146193 146335 "ASP80" 146477 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 144354 145091 145223 "ASP7" 145355 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 143308 144031 144149 "ASP78" 144267 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 142277 142988 143105 "ASP77" 143222 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 141189 141915 142046 "ASP74" 142177 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 140089 140824 140956 "ASP73" 141088 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 139193 139915 140015 "ASP6" 140020 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 138137 138870 138988 "ASP55" 139106 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 137086 137811 137930 "ASP50" 138049 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 136174 136787 136897 "ASP4" 137007 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 135262 135875 135985 "ASP49" 136095 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 134046 134801 134969 "ASP42" 135151 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132822 133579 133749 "ASP41" 133933 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131772 132499 132617 "ASP35" 132735 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 131537 131720 131759 "ASP34" 131764 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 131274 131341 131417 "ASP33" 131492 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 130167 130909 131041 "ASP31" 131173 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129932 130115 130154 "ASP30" 130159 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129667 129736 129812 "ASP29" 129887 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 129432 129615 129654 "ASP28" 129659 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 129197 129380 129419 "ASP27" 129424 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 128281 128895 129006 "ASP24" 129117 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 127357 128083 128195 "ASP20" 128200 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 126445 127058 127168 "ASP1" 127278 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 125387 126119 126238 "ASP19" 126357 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 125124 125191 125267 "ASP12" 125342 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123976 124723 124867 "ASP10" 125011 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121827 123820 123911 "ARRAY2" 123916 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117592 121475 121589 "ARRAY1" 121744 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116624 116797 117018 "ARRAY12" 117415 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110936 112854 112929 "ARR2CAT" 115559 NIL ARR2CAT (NIL T T T) -9 NIL 116317 NIL) (-56 108370 109114 110068 "ARR2CAT-" 110073 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107687 107997 108122 "ARITY" 108263 T ARITY (NIL) -8 NIL NIL NIL) (-54 106435 106587 106893 "APPRULE" 107523 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 106086 106134 106253 "APPLYORE" 106381 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 105033 105351 105546 "ANY" 105909 T ANY (NIL) -8 NIL NIL NIL) (-51 104311 104434 104591 "ANY1" 104907 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101841 102748 103075 "ANTISYM" 104035 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101333 101548 101644 "ANON" 101763 T ANON (NIL) -8 NIL NIL NIL) (-48 95430 99872 100326 "AN" 100897 T AN (NIL) -8 NIL NIL NIL) (-47 91652 93040 93091 "AMR" 93839 NIL AMR (NIL T T) -9 NIL 94439 NIL) (-46 90764 90985 91348 "AMR-" 91353 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 75203 90681 90742 "ALIST" 90747 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 72005 74797 74966 "ALGSC" 75121 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68560 69115 69722 "ALGPKG" 71445 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67837 67938 68122 "ALGMFACT" 68446 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63575 64261 64916 "ALGMANIP" 67360 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54945 63201 63351 "ALGFF" 63508 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54141 54272 54451 "ALGFACT" 54803 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53174 53772 53810 "ALGEBRA" 53815 NIL ALGEBRA (NIL T) -9 NIL 53856 NIL) (-37 52892 52951 53083 "ALGEBRA-" 53088 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34985 50894 50946 "ALAGG" 51082 NIL ALAGG (NIL T T) -9 NIL 51243 NIL) (-35 34521 34634 34660 "AHYP" 34861 T AHYP (NIL) -9 NIL NIL NIL) (-34 33452 33700 33726 "AGG" 34225 T AGG (NIL) -9 NIL 34504 NIL) (-33 32886 33048 33262 "AGG-" 33267 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30562 30985 31403 "AF" 32528 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30042 30287 30377 "ADDAST" 30490 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29310 29569 29725 "ACPLOT" 29904 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18568 26523 26574 "ACFS" 27285 NIL ACFS (NIL T) -9 NIL 27524 NIL) (-28 16582 17072 17847 "ACFS-" 17852 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12821 14749 14775 "ACF" 15654 T ACF (NIL) -9 NIL 16066 NIL) (-26 11525 11859 12352 "ACF-" 12357 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11099 11292 11318 "ABELSG" 11410 T ABELSG (NIL) -9 NIL 11475 NIL) (-24 10966 10991 11057 "ABELSG-" 11062 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10309 10596 10622 "ABELMON" 10792 T ABELMON (NIL) -9 NIL 10904 NIL) (-22 9973 10057 10195 "ABELMON-" 10200 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9804 T ABELGRP (NIL) -9 NIL 9886 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 07bdf710..211dd76c 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,26 +1,59 @@ -(735605 . 3451578538) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-556)) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *2 (-641 *1)) (-4 *1 (-1059 *3 *4 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-670 *3)) (-4 *3 (-1209)) (-5 *2 (-112))))) -(((*1 *2 *3) (-12 (-5 *2 (-564)) (-5 *1 (-569 *3)) (-4 *3 (-1034 *2)))) +(735661 . 3451919710) +(((*1 *2 *1) + (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1209)) (-4 *4 (-373 *3)) + (-4 *5 (-373 *3)) (-5 *2 (-767)))) ((*1 *2 *1) - (-12 (-4 *1 (-1097 *3 *4 *2 *5 *6)) (-4 *3 (-1094)) (-4 *4 (-1094)) - (-4 *5 (-1094)) (-4 *6 (-1094)) (-4 *2 (-1094))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1166 *6)) (-4 *6 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *2 (-1166 *7)) (-5 *1 (-321 *4 *5 *6 *7)) - (-4 *7 (-945 *6 *4 *5))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998)))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-917)) (-5 *2 (-468)) (-5 *1 (-1260))))) -(((*1 *2 *1) (-12 (-5 *2 (-1150 *3)) (-5 *1 (-174 *3)) (-4 *3 (-307))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-767)) (-4 *5 (-556)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-965 *5 *3)) (-4 *3 (-1235 *5))))) + (-12 (-4 *1 (-1048 *3 *4 *5 *6 *7)) (-4 *5 (-1045)) + (-4 *6 (-238 *4 *5)) (-4 *7 (-238 *3 *5)) (-5 *2 (-767))))) +(((*1 *1 *1) (-12 (-5 *1 (-606 *2)) (-4 *2 (-1094)))) + ((*1 *1 *1) (-5 *1 (-630)))) +(((*1 *2 *1) + (-12 (-4 *1 (-335 *3 *4 *5 *6)) (-4 *3 (-363)) (-4 *4 (-1235 *3)) + (-4 *5 (-1235 (-407 *4))) (-4 *6 (-342 *3 *4 *5)) + (-5 *2 (-413 *4 (-407 *4) *5 *6)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1259 *6)) (-4 *6 (-13 (-409 *4 *5) (-1034 *4))) + (-4 *4 (-988 *3)) (-4 *5 (-1235 *4)) (-4 *3 (-307)) + (-5 *1 (-413 *3 *4 *5 *6)))) + ((*1 *1 *2) + (-12 (-5 *2 (-641 *6)) (-4 *6 (-945 *3 *4 *5)) (-4 *3 (-363)) + (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-504 *3 *4 *5 *6))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-363)) (-5 *2 (-2 (|:| -1876 *3) (|:| -2786 *3))) + (-5 *1 (-762 *3 *4)) (-4 *3 (-704 *4)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-363)) (-4 *3 (-1045)) + (-5 *2 (-2 (|:| -1876 *1) (|:| -2786 *1))) (-4 *1 (-848 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-363)) (-4 *5 (-1045)) + (-5 *2 (-2 (|:| -1876 *3) (|:| -2786 *3))) (-5 *1 (-849 *5 *3)) + (-4 *3 (-848 *5))))) +(((*1 *1) (-5 *1 (-468)))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-767)) (-5 *1 (-873 *2)) (-4 *2 (-1209)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-767)) (-5 *1 (-875 *2)) (-4 *2 (-1209)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-767)) (-5 *1 (-878 *2)) (-4 *2 (-1209))))) +(((*1 *1 *2) + (-12 (-5 *2 (-641 (-641 *3))) (-4 *3 (-1094)) (-4 *1 (-899 *3))))) +(((*1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-1036))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-610 *6)) (-4 *6 (-13 (-430 *5) (-27) (-1194))) + (-4 *5 (-13 (-452) (-1034 (-564)) (-846) (-147) (-637 (-564)))) + (-5 *2 (-1166 (-407 (-1166 *6)))) (-5 *1 (-560 *5 *6 *7)) + (-5 *3 (-1166 *6)) (-4 *7 (-1094)))) + ((*1 *2 *1) + (-12 (-4 *2 (-1235 *3)) (-5 *1 (-708 *3 *2)) (-4 *3 (-1045)))) + ((*1 *2 *1) + (-12 (-4 *1 (-720 *3 *2)) (-4 *3 (-172)) (-4 *2 (-1235 *3)))) + ((*1 *2 *3 *4 *4 *5 *6 *7 *8) + (|partial| -12 (-5 *4 (-1166 *11)) (-5 *6 (-641 *10)) + (-5 *7 (-641 (-767))) (-5 *8 (-641 *11)) (-4 *10 (-846)) + (-4 *11 (-307)) (-4 *9 (-789)) (-4 *5 (-945 *11 *9 *10)) + (-5 *2 (-641 (-1166 *5))) (-5 *1 (-738 *9 *10 *11 *5)) + (-5 *3 (-1166 *5)))) + ((*1 *2 *1) + (-12 (-4 *2 (-945 *3 *4 *5)) (-5 *1 (-1030 *3 *4 *5 *2 *6)) + (-4 *3 (-363)) (-4 *4 (-789)) (-4 *5 (-846)) (-14 *6 (-641 *2))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) @@ -37,57 +70,41 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-4 *3 (-1059 *5 *6 *7)) (-5 *2 (-112)) - (-5 *1 (-1066 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-4 *3 (-1059 *5 *6 *7)) - (-5 *2 (-641 (-2 (|:| |val| (-112)) (|:| -3461 *4)))) - (-5 *1 (-1066 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-1 (-225) (-225) (-225))) + (-5 *4 (-1 (-225) (-225) (-225) (-225))) + (-5 *2 (-1 (-939 (-225)) (-225) (-225))) (-5 *1 (-693))))) +(((*1 *2 *1 *2) + (-12 (-4 *1 (-364 *3 *2)) (-4 *3 (-1094)) (-4 *2 (-1094))))) +(((*1 *2 *3 *4 *5 *4 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *7 *4) + (-12 (-5 *3 (-1152)) (-5 *5 (-685 (-225))) (-5 *6 (-225)) + (-5 *7 (-685 (-564))) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-748))))) +(((*1 *2 *3) (-12 (-5 *3 (-948 (-225))) (-5 *2 (-225)) (-5 *1 (-305))))) +(((*1 *2 *2 *2 *2 *3) + (-12 (-4 *3 (-556)) (-5 *1 (-965 *3 *2)) (-4 *2 (-1235 *3))))) (((*1 *2 *1) - (-12 (-5 *2 (-641 (-641 (-767)))) (-5 *1 (-900 *3)) (-4 *3 (-1094))))) -(((*1 *2 *3 *4 *4 *2 *2 *2) - (-12 (-5 *2 (-564)) - (-5 *3 - (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-767)) (|:| |poli| *4) - (|:| |polj| *4))) - (-4 *6 (-789)) (-4 *4 (-945 *5 *6 *7)) (-4 *5 (-452)) (-4 *7 (-846)) - (-5 *1 (-449 *5 *6 *7 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-180)))) - ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-311)))) - ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-966)))) - ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-990)))) - ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1032)))) - ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1067))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-641 (-948 *4))) (-5 *3 (-641 (-1170))) (-4 *4 (-452)) - (-5 *1 (-914 *4))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-641 (-1152))) (-5 *1 (-394)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-641 (-1152))) (-5 *1 (-1189))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-984 *4 *5 *6 *7 *3)) (-4 *3 (-1065 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-1101 *4 *5 *6 *7 *3)) (-4 *3 (-1065 *4 *5 *6 *7))))) -(((*1 *2 *2) - (-12 (-4 *3 (-556)) (-4 *4 (-988 *3)) (-5 *1 (-142 *3 *4 *2)) - (-4 *2 (-373 *4)))) - ((*1 *2 *3) - (-12 (-4 *4 (-556)) (-4 *5 (-988 *4)) (-4 *2 (-373 *4)) - (-5 *1 (-503 *4 *5 *2 *3)) (-4 *3 (-373 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-685 *5)) (-4 *5 (-988 *4)) (-4 *4 (-556)) - (-5 *2 (-685 *4)) (-5 *1 (-689 *4 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-556)) (-4 *4 (-988 *3)) (-5 *1 (-1228 *3 *4 *2)) - (-4 *2 (-1235 *4))))) + (-12 (-14 *3 (-641 (-1170))) (-4 *4 (-172)) + (-14 *6 + (-1 (-112) (-2 (|:| -2014 *5) (|:| -4165 *2)) + (-2 (|:| -2014 *5) (|:| -4165 *2)))) + (-4 *2 (-238 (-2069 *3) (-767))) (-5 *1 (-461 *3 *4 *5 *2 *6 *7)) + (-4 *5 (-846)) (-4 *7 (-945 *4 *2 (-860 *3)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-554 *3)) (-4 *3 (-13 (-404) (-1194))) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-844)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1062 *4 *3)) (-4 *4 (-13 (-844) (-363))) + (-4 *3 (-1235 *4)) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-31)))) + ((*1 *2) (-12 (-4 *1 (-404)) (-5 *2 (-917)))) ((*1 *1) (-4 *1 (-545))) + ((*1 *2 *2) (-12 (-5 *2 (-917)) (-5 *1 (-695)))) + ((*1 *2 *1) (-12 (-5 *2 (-641 *3)) (-5 *1 (-900 *3)) (-4 *3 (-1094))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-819)) (-5 *2 (-1264)) (-5 *1 (-818))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1209)) (-5 *2 (-641 *1)) (-4 *1 (-1006 *3))))) +(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) + (-12 (-5 *3 (-1152)) (-5 *4 (-564)) (-5 *5 (-685 (-169 (-225)))) + (-5 *2 (-1031)) (-5 *1 (-750))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) @@ -104,21 +121,41 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *1) - (-12 (-4 *3 (-363)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-641 *6)) - (-5 *1 (-504 *3 *4 *5 *6)) (-4 *6 (-945 *3 *4 *5)))) - ((*1 *2 *1) - (-12 (-5 *2 (-641 (-901 *3))) (-5 *1 (-900 *3)) (-4 *3 (-1094))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) (((*1 *2 *3) - (-12 (-5 *3 (-564)) (-4 *4 (-789)) (-4 *5 (-846)) (-4 *2 (-1045)) - (-5 *1 (-321 *4 *5 *2 *6)) (-4 *6 (-945 *2 *4 *5))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-564)) (-5 *1 (-316 *3)) (-4 *3 (-556)) (-4 *3 (-846))))) + (-12 (-5 *3 (-948 (-564))) (-5 *2 (-641 *1)) (-4 *1 (-1008)))) + ((*1 *2 *3) + (-12 (-5 *3 (-948 (-407 (-564)))) (-5 *2 (-641 *1)) (-4 *1 (-1008)))) + ((*1 *2 *3) (-12 (-5 *3 (-948 *1)) (-4 *1 (-1008)) (-5 *2 (-641 *1)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1166 (-564))) (-5 *2 (-641 *1)) (-4 *1 (-1008)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1166 (-407 (-564)))) (-5 *2 (-641 *1)) (-4 *1 (-1008)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1166 *1)) (-4 *1 (-1008)) (-5 *2 (-641 *1)))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-844) (-363))) (-4 *3 (-1235 *4)) (-5 *2 (-641 *1)) + (-4 *1 (-1062 *4 *3))))) (((*1 *2 *1) - (-12 (-4 *1 (-1097 *3 *2 *4 *5 *6)) (-4 *3 (-1094)) (-4 *4 (-1094)) + (-12 (-5 *2 (-641 (-2 (|:| |k| (-1170)) (|:| |c| (-1281 *3))))) + (-5 *1 (-1281 *3)) (-4 *3 (-1045)))) + ((*1 *2 *1) + (-12 (-5 *2 (-641 (-2 (|:| |k| *3) (|:| |c| (-1283 *3 *4))))) + (-5 *1 (-1283 *3 *4)) (-4 *3 (-846)) (-4 *4 (-1045))))) +(((*1 *2 *3) (-12 (-5 *2 (-564)) (-5 *1 (-569 *3)) (-4 *3 (-1034 *2)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1097 *3 *4 *2 *5 *6)) (-4 *3 (-1094)) (-4 *4 (-1094)) (-4 *5 (-1094)) (-4 *6 (-1094)) (-4 *2 (-1094))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-778 *2)) (-4 *2 (-556)) (-4 *2 (-1045)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-556)) (-5 *1 (-965 *3 *2)) (-4 *2 (-1235 *3)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) + (-4 *4 (-846)) (-4 *2 (-556)))) + ((*1 *2 *3 *3 *1) + (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *3 (-1059 *4 *5 *6)) + (-5 *2 (-641 (-2 (|:| |val| *3) (|:| -3418 *1)))) + (-4 *1 (-1065 *4 *5 *6 *3))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-564)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1209)) (-4 *4 (-373 *2)) (-4 *5 (-373 *2)))) @@ -150,14 +187,14 @@ (-12 (-5 *3 (-1170)) (-5 *2 (-245 (-1152))) (-5 *1 (-214 *4)) (-4 *4 (-13 (-846) - (-10 -8 (-15 -4362 ((-1152) $ *3)) (-15 -1667 ((-1264) $)) - (-15 -3858 ((-1264) $))))))) + (-10 -8 (-15 -4361 ((-1152) $ *3)) (-15 -1682 ((-1264) $)) + (-15 -3141 ((-1264) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-985)) (-5 *1 (-214 *3)) (-4 *3 (-13 (-846) - (-10 -8 (-15 -4362 ((-1152) $ (-1170))) (-15 -1667 ((-1264) $)) - (-15 -3858 ((-1264) $))))))) + (-10 -8 (-15 -4361 ((-1152) $ (-1170))) (-15 -1682 ((-1264) $)) + (-15 -3141 ((-1264) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-767)) (-5 *1 (-245 *4)) (-4 *4 (-846)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-245 *3)) (-4 *3 (-846)))) @@ -243,16 +280,81 @@ (-12 (-5 *2 "rest") (-4 *1 (-1247 *3)) (-4 *3 (-1209)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) +(((*1 *2 *3 *4) + (-12 (-5 *2 (-641 (-169 *4))) (-5 *1 (-155 *3 *4)) + (-4 *3 (-1235 (-169 (-564)))) (-4 *4 (-13 (-363) (-844))))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-363) (-844))) (-5 *2 (-641 (-169 *4))) + (-5 *1 (-181 *4 *3)) (-4 *3 (-1235 (-169 *4))))) + ((*1 *2 *3 *4) + (-12 (-4 *4 (-13 (-363) (-844))) (-5 *2 (-641 (-169 *4))) + (-5 *1 (-181 *4 *3)) (-4 *3 (-1235 (-169 *4)))))) +(((*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1209))))) +(((*1 *2 *1) (-12 (-5 *2 (-858)) (-5 *1 (-52))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1128 *3)) (-4 *3 (-1045)) + (-5 *2 + (-2 (|:| -1707 (-767)) (|:| |curves| (-767)) + (|:| |polygons| (-767)) (|:| |constructs| (-767))))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-1259 (-564))) (-5 *3 (-564)) (-5 *1 (-1104)))) + ((*1 *2 *3 *2 *4) + (-12 (-5 *2 (-1259 (-564))) (-5 *3 (-641 (-564))) (-5 *4 (-564)) + (-5 *1 (-1104))))) (((*1 *2 *1 *1) - (-12 (-4 *3 (-363)) (-4 *3 (-1045)) - (-5 *2 (-2 (|:| -3783 *1) (|:| -1673 *1))) (-4 *1 (-848 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-363)) (-4 *5 (-1045)) - (-5 *2 (-2 (|:| -3783 *3) (|:| -1673 *3))) (-5 *1 (-849 *5 *3)) - (-4 *3 (-848 *5))))) -(((*1 *2 *3 *3 *2) - (-12 (-5 *2 (-685 (-564))) (-5 *3 (-641 (-564))) (-5 *1 (-1104))))) -(((*1 *2 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-755))))) + (-12 (-5 *2 (-641 (-778 *3))) (-5 *1 (-778 *3)) (-4 *3 (-556)) + (-4 *3 (-1045))))) +(((*1 *1) (-5 *1 (-141)))) +(((*1 *1 *1) (-4 *1 (-95))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) + (-4 *2 (-13 (-430 *3) (-998))))) + ((*1 *2 *2) + (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1250 *3)) + (-5 *1 (-278 *3 *4 *2)) (-4 *2 (-1221 *3 *4)))) + ((*1 *2 *2) + (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1219 *3)) + (-5 *1 (-279 *3 *4 *2 *5)) (-4 *2 (-1242 *3 *4)) (-4 *5 (-979 *4)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) + (-5 *1 (-1155 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) + (-5 *1 (-1156 *3))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1259 (-1259 (-564)))) (-5 *3 (-917)) (-5 *1 (-466))))) +(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-180)))) + ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-311)))) + ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-966)))) + ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-990)))) + ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1032)))) + ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1067))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-972 *3 *4 *2 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *2 (-846)) (-4 *5 (-1059 *3 *4 *2))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-685 *3)) (-4 *3 (-1045)) (-5 *1 (-1024 *3)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-641 (-685 *3))) (-4 *3 (-1045)) (-5 *1 (-1024 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-685 *3)) (-4 *3 (-1045)) (-5 *1 (-1024 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-641 (-685 *3))) (-4 *3 (-1045)) (-5 *1 (-1024 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 *5)) (-5 *4 (-917)) (-4 *5 (-846)) + (-5 *2 (-59 (-641 (-668 *5)))) (-5 *1 (-668 *5))))) +(((*1 *2 *1) (-12 (-4 *1 (-991 *2)) (-4 *2 (-1209))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-1166 *1)) (-5 *3 (-1170)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-1166 *1)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-948 *1)) (-4 *1 (-27)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1170)) (-4 *1 (-29 *3)) (-4 *3 (-13 (-846) (-556))))) + ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-13 (-846) (-556)))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-585 *3)) (-4 *3 (-363))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-363)) (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-112)) + (-5 *1 (-504 *4 *5 *6 *3)) (-4 *3 (-945 *4 *5 *6))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-132)) (-5 *3 (-767)) (-5 *2 (-1264))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-225))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) @@ -274,41 +376,39 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) -(((*1 *2) - (-12 (-4 *3 (-556)) (-5 *2 (-641 (-685 *3))) (-5 *1 (-43 *3 *4)) - (-4 *4 (-417 *3))))) + (-12 (-5 *4 (-641 *3)) (-4 *3 (-1235 *5)) (-4 *5 (-307)) + (-5 *2 (-767)) (-5 *1 (-455 *5 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-641 (-1152))) (-5 *1 (-394))))) (((*1 *2 *1) - (-12 (-4 *1 (-1128 *3)) (-4 *3 (-1045)) - (-5 *2 (-641 (-641 (-939 *3)))))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *2 (-641 (-641 (-939 *4)))) (-5 *3 (-112)) (-4 *4 (-1045)) - (-4 *1 (-1128 *4)))) - ((*1 *1 *2) - (-12 (-5 *2 (-641 (-641 (-939 *3)))) (-4 *3 (-1045)) - (-4 *1 (-1128 *3)))) - ((*1 *1 *1 *2 *3 *3) - (-12 (-5 *2 (-641 (-641 (-641 *4)))) (-5 *3 (-112)) - (-4 *1 (-1128 *4)) (-4 *4 (-1045)))) - ((*1 *1 *1 *2 *3 *3) - (-12 (-5 *2 (-641 (-641 (-939 *4)))) (-5 *3 (-112)) - (-4 *1 (-1128 *4)) (-4 *4 (-1045)))) - ((*1 *1 *1 *2 *3 *4) - (-12 (-5 *2 (-641 (-641 (-641 *5)))) (-5 *3 (-641 (-171))) - (-5 *4 (-171)) (-4 *1 (-1128 *5)) (-4 *5 (-1045)))) - ((*1 *1 *1 *2 *3 *4) - (-12 (-5 *2 (-641 (-641 (-939 *5)))) (-5 *3 (-641 (-171))) - (-5 *4 (-171)) (-4 *1 (-1128 *5)) (-4 *5 (-1045))))) -(((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-144))))) -(((*1 *2 *2 *2 *3 *3) - (-12 (-5 *3 (-767)) (-4 *4 (-1045)) (-5 *1 (-1231 *4 *2)) - (-4 *2 (-1235 *4))))) -(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-922))))) + (-12 (-4 *1 (-1097 *3 *2 *4 *5 *6)) (-4 *3 (-1094)) (-4 *4 (-1094)) + (-4 *5 (-1094)) (-4 *6 (-1094)) (-4 *2 (-1094))))) +(((*1 *1 *2 *3 *1) + (-12 (-14 *4 (-641 (-1170))) (-4 *2 (-172)) + (-4 *3 (-238 (-2069 *4) (-767))) + (-14 *6 + (-1 (-112) (-2 (|:| -2014 *5) (|:| -4165 *3)) + (-2 (|:| -2014 *5) (|:| -4165 *3)))) + (-5 *1 (-461 *4 *2 *5 *3 *6 *7)) (-4 *5 (-846)) + (-4 *7 (-945 *2 *3 (-860 *4)))))) +(((*1 *2 *1) (-12 (-4 *1 (-793 *2)) (-4 *2 (-172))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-442 *3)) (-4 *3 (-1235 (-564)))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-1202 *4 *5 *3 *6)) (-4 *4 (-556)) (-4 *5 (-789)) + (-4 *3 (-846)) (-4 *6 (-1059 *4 *5 *3)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-1278 *3)) (-4 *3 (-363)) (-5 *2 (-112))))) (((*1 *2 *3 *4) - (-12 (-4 *6 (-556)) (-4 *2 (-945 *3 *5 *4)) - (-5 *1 (-728 *5 *4 *6 *2)) (-5 *3 (-407 (-948 *6))) (-4 *5 (-789)) - (-4 *4 (-13 (-846) (-10 -8 (-15 -4344 ((-1170) $)))))))) -(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-517))))) + (-12 (-5 *3 (-1170)) (-5 *4 (-948 (-564))) (-5 *2 (-330)) + (-5 *1 (-332))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-529))))) +(((*1 *2 *1) (-12 (-5 *2 (-1098)) (-5 *1 (-52))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-564)) (-4 *1 (-57 *4 *5 *2)) (-4 *4 (-1209)) + (-4 *5 (-373 *4)) (-4 *2 (-373 *4)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-564)) (-4 *1 (-1048 *4 *5 *6 *7 *2)) (-4 *6 (-1045)) + (-4 *7 (-238 *5 *6)) (-4 *2 (-238 *4 *6))))) +(((*1 *2 *1) (-12 (-4 *1 (-389)) (-5 *2 (-112))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) @@ -328,14 +428,8 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *1 *1) - (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1045))))) -(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-561))))) -(((*1 *2 *3) - (|partial| -12 (-4 *4 (-13 (-556) (-147))) - (-5 *2 (-2 (|:| -4242 *3) (|:| -4251 *3))) (-5 *1 (-1229 *4 *3)) - (-4 *3 (-1235 *4))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) +(((*1 *2 *1) (-12 (-4 *1 (-988 *2)) (-4 *2 (-556)) (-4 *2 (-545)))) + ((*1 *1 *1) (-4 *1 (-1054)))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-612 *2) (-172))) (-5 *2 (-888 *4)) (-5 *1 (-170 *4 *5 *3)) (-4 *4 (-1094)) (-4 *3 (-166 *5)))) @@ -368,9 +462,9 @@ (-12 (-5 *2 (-948 *3)) (-4 *3 (-1045)) (-4 *1 (-1059 *3 *4 *5)) (-4 *5 (-612 (-1170))) (-4 *4 (-789)) (-4 *5 (-846)))) ((*1 *1 *2) - (-2750 + (-2733 (-12 (-5 *2 (-948 (-564))) (-4 *1 (-1059 *3 *4 *5)) - (-12 (-2356 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) + (-12 (-2354 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) (-4 *5 (-612 (-1170)))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846))) (-12 (-5 *2 (-948 (-564))) (-4 *1 (-1059 *3 *4 *5)) @@ -381,12 +475,12 @@ (-4 *3 (-38 (-407 (-564)))) (-4 *5 (-612 (-1170))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3461 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3418 *8))) (-4 *7 (-1059 *4 *5 *6)) (-4 *8 (-1065 *4 *5 *6 *7)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-1152)) (-5 *1 (-1063 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3461 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3418 *8))) (-4 *7 (-1059 *4 *5 *6)) (-4 *8 (-1103 *4 *5 *6 *7)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-1152)) (-5 *1 (-1139 *4 *5 *6 *7 *8)))) @@ -419,50 +513,48 @@ (-5 *2 (-641 (-776 *4 (-860 *6)))) (-5 *1 (-1285 *4 *5 *6)) (-14 *5 (-641 (-1170)))))) (((*1 *1 *2) - (-12 (-5 *2 (-1166 *3)) (-4 *3 (-1045)) (-4 *1 (-1235 *3))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-972 *4 *5 *3 *6)) (-4 *4 (-1045)) (-4 *5 (-789)) - (-4 *3 (-846)) (-4 *6 (-1059 *4 *5 *3)) (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-641 - (-2 (|:| -2828 (-767)) - (|:| |eqns| - (-641 - (-2 (|:| |det| *7) (|:| |rows| (-641 (-564))) - (|:| |cols| (-641 (-564)))))) - (|:| |fgb| (-641 *7))))) - (-4 *7 (-945 *4 *6 *5)) (-4 *4 (-13 (-307) (-147))) - (-4 *5 (-13 (-846) (-612 (-1170)))) (-4 *6 (-789)) (-5 *2 (-767)) - (-5 *1 (-920 *4 *5 *6 *7))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-641 (-948 (-564)))) (-5 *4 (-641 (-1170))) - (-5 *2 (-641 (-641 (-379)))) (-5 *1 (-1019)) (-5 *5 (-379)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1042 *4 *5)) (-4 *4 (-13 (-844) (-307) (-147) (-1018))) - (-14 *5 (-641 (-1170))) (-5 *2 (-641 (-641 (-1020 (-407 *4))))) - (-5 *1 (-1285 *4 *5 *6)) (-14 *6 (-641 (-1170))))) - ((*1 *2 *3 *4 *4 *4) - (-12 (-5 *3 (-641 (-948 *5))) (-5 *4 (-112)) - (-4 *5 (-13 (-844) (-307) (-147) (-1018))) - (-5 *2 (-641 (-641 (-1020 (-407 *5))))) (-5 *1 (-1285 *5 *6 *7)) - (-14 *6 (-641 (-1170))) (-14 *7 (-641 (-1170))))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 (-948 *5))) (-5 *4 (-112)) - (-4 *5 (-13 (-844) (-307) (-147) (-1018))) - (-5 *2 (-641 (-641 (-1020 (-407 *5))))) (-5 *1 (-1285 *5 *6 *7)) - (-14 *6 (-641 (-1170))) (-14 *7 (-641 (-1170))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-948 *5))) (-5 *4 (-112)) - (-4 *5 (-13 (-844) (-307) (-147) (-1018))) - (-5 *2 (-641 (-641 (-1020 (-407 *5))))) (-5 *1 (-1285 *5 *6 *7)) - (-14 *6 (-641 (-1170))) (-14 *7 (-641 (-1170))))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 (-948 *4))) - (-4 *4 (-13 (-844) (-307) (-147) (-1018))) - (-5 *2 (-641 (-641 (-1020 (-407 *4))))) (-5 *1 (-1285 *4 *5 *6)) - (-14 *5 (-641 (-1170))) (-14 *6 (-641 (-1170)))))) + (|partial| -12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) + (-4 *3 (-556)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *1 (-1272 *3 *4 *5 *6)))) + ((*1 *1 *2 *3 *4) + (|partial| -12 (-5 *2 (-641 *8)) (-5 *3 (-1 (-112) *8 *8)) + (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1059 *5 *6 *7)) (-4 *5 (-556)) + (-4 *6 (-789)) (-4 *7 (-846)) (-5 *1 (-1272 *5 *6 *7 *8))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1096 *3)) (-5 *1 (-900 *3)) (-4 *3 (-1094)))) + ((*1 *2 *1) + (-12 (-5 *2 (-1096 *3)) (-5 *1 (-901 *3)) (-4 *3 (-1094))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-1094)) (-4 *3 (-896 *5)) (-5 *2 (-1259 *3)) + (-5 *1 (-688 *5 *3 *6 *4)) (-4 *6 (-373 *3)) + (-4 *4 (-13 (-373 *5) (-10 -7 (-6 -4407))))))) +(((*1 *2 *1) + (-12 (-4 *4 (-1094)) (-5 *2 (-885 *3 *5)) (-5 *1 (-881 *3 *4 *5)) + (-4 *3 (-1094)) (-4 *5 (-662 *4))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-1059 *3 *4 *2)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *2 (-846)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) + (-4 *4 (-846))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1166 *1)) (-5 *4 (-1170)) (-4 *1 (-27)) + (-5 *2 (-641 *1)))) + ((*1 *2 *3) (-12 (-5 *3 (-1166 *1)) (-4 *1 (-27)) (-5 *2 (-641 *1)))) + ((*1 *2 *3) (-12 (-5 *3 (-948 *1)) (-4 *1 (-27)) (-5 *2 (-641 *1)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-1170)) (-4 *4 (-13 (-846) (-556))) (-5 *2 (-641 *1)) + (-4 *1 (-29 *4)))) + ((*1 *2 *1) + (-12 (-4 *3 (-13 (-846) (-556))) (-5 *2 (-641 *1)) (-4 *1 (-29 *3)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-316 (-225))) (-5 *4 (-641 (-1170))) + (-5 *5 (-1088 (-839 (-225)))) (-5 *2 (-1150 (-225))) (-5 *1 (-300))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-1172 (-407 (-564)))) (-5 *1 (-190))))) +(((*1 *2 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) + (-5 *1 (-752))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1098)) (-5 *1 (-280))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) @@ -482,13 +574,9 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2) (-12 (-5 *2 (-1170)) (-5 *1 (-1173))))) -(((*1 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) - ((*1 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-431 *3 *2)) - (-4 *2 (-430 *3)))) - ((*1 *1 *1) (-4 *1 (-1133)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1094)) (-4 *4 (-1094)) + (-4 *6 (-1094)) (-5 *2 (-1 *6 *5)) (-5 *1 (-680 *5 *4 *6))))) (((*1 *2 *1) (-12 (-4 *1 (-254 *3)) (-4 *3 (-1209)) (-5 *2 (-767)))) ((*1 *2 *1) (-12 (-4 *1 (-302)) (-5 *2 (-767)))) ((*1 *2 *3) @@ -498,23 +586,46 @@ ((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-610 *3)) (-4 *3 (-846)))) ((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-858)))) ((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-858))))) -(((*1 *2 *1 *3 *3 *2) - (-12 (-5 *3 (-564)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1209)) - (-4 *4 (-373 *2)) (-4 *5 (-373 *2)))) - ((*1 *2 *1 *3 *2) - (-12 (|has| *1 (-6 -4407)) (-4 *1 (-288 *3 *2)) (-4 *3 (-1094)) - (-4 *2 (-1209))))) -(((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-846))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-114))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-767)) (-4 *4 (-556)) (-5 *1 (-965 *4 *2)) - (-4 *2 (-1235 *4))))) -(((*1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-1036))))) -(((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-418 *3)) (-4 *3 (-556)))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 (-2 (|:| -3595 *4) (|:| -2762 (-564))))) - (-4 *4 (-1235 (-564))) (-5 *2 (-767)) (-5 *1 (-442 *4))))) -(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-923))))) +(((*1 *2 *3 *3 *3 *3 *3 *3 *3 *3 *4 *5 *5 *5 *5 *5 *5 *6 *6 *6 *3 *3 *5 + *7 *3 *8) + (-12 (-5 *5 (-685 (-225))) (-5 *6 (-112)) (-5 *7 (-685 (-564))) + (-5 *8 (-3 (|:| |fn| (-388)) (|:| |fp| (-65 QPHESS)))) + (-5 *3 (-564)) (-5 *4 (-225)) (-5 *2 (-1031)) (-5 *1 (-749))))) +(((*1 *1 *2 *2 *3 *1) + (-12 (-5 *2 (-506)) (-5 *3 (-1098)) (-5 *1 (-291))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-917)) (-5 *2 (-1264)) (-5 *1 (-1260)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-917)) (-5 *2 (-1264)) (-5 *1 (-1261))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-641 *1)) (-4 *1 (-1059 *4 *5 *6)) (-4 *4 (-1045)) + (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-112)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1059 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *5 (-846)) (-5 *2 (-112)))) + ((*1 *2 *3 *1 *4) + (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *1 (-1202 *5 *6 *7 *3)) + (-4 *5 (-556)) (-4 *6 (-789)) (-4 *7 (-846)) + (-4 *3 (-1059 *5 *6 *7)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-307) (-147))) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *7 (-945 *4 *5 *6)) (-5 *2 (-641 (-641 *7))) + (-5 *1 (-448 *4 *5 *6 *7)) (-5 *3 (-641 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-307) (-147))) (-4 *6 (-789)) + (-4 *7 (-846)) (-4 *8 (-945 *5 *6 *7)) (-5 *2 (-641 (-641 *8))) + (-5 *1 (-448 *5 *6 *7 *8)) (-5 *3 (-641 *8))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *1) (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1209)) (-5 *2 (-112))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-776 *5 (-860 *6)))) (-5 *4 (-112)) (-4 *5 (-452)) + (-14 *6 (-641 (-1170))) + (-5 *2 + (-641 (-1140 *5 (-531 (-860 *6)) (-860 *6) (-776 *5 (-860 *6))))) + (-5 *1 (-626 *5 *6))))) +(((*1 *2 *2) (-12 (-5 *2 (-917)) (-5 *1 (-1262)))) + ((*1 *2) (-12 (-5 *2 (-917)) (-5 *1 (-1262))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -532,46 +643,36 @@ (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) (((*1 *2 *3) - (-12 (-5 *3 (-917)) (-5 *2 (-1166 *4)) (-5 *1 (-587 *4)) - (-4 *4 (-349))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1209)) - (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4407)) (-4 *1 (-489 *3)) - (-4 *3 (-1209))))) + (-12 (-5 *3 (-3 (|:| |fst| (-434)) (|:| -1835 "void"))) + (-5 *2 (-1264)) (-5 *1 (-1173)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1170)) + (-5 *4 (-3 (|:| |fst| (-434)) (|:| -1835 "void"))) (-5 *2 (-1264)) + (-5 *1 (-1173)))) + ((*1 *2 *3 *4 *1) + (-12 (-5 *3 (-1170)) + (-5 *4 (-3 (|:| |fst| (-434)) (|:| -1835 "void"))) (-5 *2 (-1264)) + (-5 *1 (-1173))))) (((*1 *2 *1) - (-12 (-4 *1 (-326 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-788)) - (-5 *2 (-641 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-382 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-1094)) - (-5 *2 (-641 *3)))) - ((*1 *2 *1) - (-12 (-5 *2 (-1150 *3)) (-5 *1 (-595 *3)) (-4 *3 (-1045)))) - ((*1 *2 *1) - (-12 (-5 *2 (-641 *3)) (-5 *1 (-731 *3 *4)) (-4 *3 (-1045)) - (-4 *4 (-722)))) - ((*1 *2 *1) (-12 (-4 *1 (-848 *3)) (-4 *3 (-1045)) (-5 *2 (-641 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1250 *3)) (-4 *3 (-1045)) (-5 *2 (-1150 *3))))) -(((*1 *2 *3 *3 *4 *5 *5 *5 *4 *4 *4 *3 *4 *4 *6) - (-12 (-5 *3 (-685 (-225))) (-5 *4 (-564)) (-5 *5 (-225)) - (-5 *6 (-3 (|:| |fn| (-388)) (|:| |fp| (-86 FCN)))) (-5 *2 (-1031)) - (-5 *1 (-745))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998)))))) + (-12 (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-641 *1)) + (-4 *1 (-1059 *3 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *1 (-174 *2)) (-4 *2 (-307)))) + ((*1 *2 *1) (-12 (-5 *1 (-910 *2)) (-4 *2 (-307)))) + ((*1 *2 *1) (-12 (-4 *1 (-988 *2)) (-4 *2 (-556)) (-4 *2 (-307)))) + ((*1 *2 *1) (-12 (-4 *1 (-1054)) (-5 *2 (-564))))) +(((*1 *2 *3) + (-12 (-4 *1 (-349)) (-5 *3 (-564)) (-5 *2 (-1182 (-917) (-767)))))) +(((*1 *2) + (-12 (-4 *4 (-172)) (-5 *2 (-112)) (-5 *1 (-366 *3 *4)) + (-4 *3 (-367 *4)))) + ((*1 *2) (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-5 *2 (-112))))) +(((*1 *2 *3) (-12 (-5 *3 (-379)) (-5 *2 (-225)) (-5 *1 (-1262)))) + ((*1 *2) (-12 (-5 *2 (-225)) (-5 *1 (-1262))))) (((*1 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-147)) - (-4 *3 (-307)) (-4 *3 (-556)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *1 (-973 *3 *4 *5 *6))))) -(((*1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-330))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1226 (-564))) (-4 *1 (-282 *3)) (-4 *3 (-1209)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-282 *3)) (-4 *3 (-1209))))) -(((*1 *1 *1 *2 *2 *1) - (-12 (-5 *2 (-564)) (-4 *1 (-683 *3 *4 *5)) (-4 *3 (-1045)) - (-4 *4 (-373 *3)) (-4 *5 (-373 *3))))) + (-12 (-5 *2 (-1259 *1)) (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) + (-4 *4 (-1235 *3)) (-4 *5 (-1235 (-407 *4)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1150 (-407 *3))) (-5 *1 (-174 *3)) (-4 *3 (-307))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -588,30 +689,28 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-373 *2)) (-4 *2 (-1209)) (-4 *2 (-846)))) - ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-373 *3)) (-4 *3 (-1209)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-964 *2)) (-4 *2 (-846)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1128 *2)) (-4 *2 (-1045)))) - ((*1 *1 *2) - (-12 (-5 *2 (-641 *1)) (-4 *1 (-1128 *3)) (-4 *3 (-1045)))) - ((*1 *1 *2) - (-12 (-5 *2 (-641 (-1158 *3 *4))) (-5 *1 (-1158 *3 *4)) - (-14 *3 (-917)) (-4 *4 (-1045)))) - ((*1 *1 *1 *1) - (-12 (-5 *1 (-1158 *2 *3)) (-14 *2 (-917)) (-4 *3 (-1045))))) -(((*1 *2 *1) (-12 (-4 *1 (-970)) (-5 *2 (-1088 (-225)))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-778 *2)) (-4 *2 (-1045))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-192)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-300)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-305))))) -(((*1 *2 *1) (-12 (-4 *1 (-865 *3)) (-5 *2 (-564))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998)))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-363)) (-5 *1 (-762 *2 *3)) (-4 *2 (-704 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-848 *2)) (-4 *2 (-1045)) (-4 *2 (-363))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-556)) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *2 (-641 *1)) (-4 *1 (-1059 *3 *4 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-922))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-685 *8)) (-4 *8 (-945 *5 *7 *6)) + (-4 *5 (-13 (-307) (-147))) (-4 *6 (-13 (-846) (-612 (-1170)))) + (-4 *7 (-789)) + (-5 *2 + (-641 + (-2 (|:| -4242 (-767)) + (|:| |eqns| + (-641 + (-2 (|:| |det| *8) (|:| |rows| (-641 (-564))) + (|:| |cols| (-641 (-564)))))) + (|:| |fgb| (-641 *8))))) + (-5 *1 (-920 *5 *6 *7 *8)) (-5 *4 (-767))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1283 *4 *2)) (-4 *1 (-374 *4 *2)) (-4 *4 (-846)) (-4 *2 (-172)))) @@ -622,16 +721,17 @@ (-4 *2 (-1045)))) ((*1 *2 *1 *3) (-12 (-4 *2 (-1045)) (-5 *1 (-1282 *2 *3)) (-4 *3 (-842))))) -(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-767)) (-4 *5 (-556)) - (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-965 *5 *3)) (-4 *3 (-1235 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 (-564))) (-5 *2 (-900 (-564))) (-5 *1 (-913)))) - ((*1 *2) (-12 (-5 *2 (-900 (-564))) (-5 *1 (-913))))) -(((*1 *1) (-5 *1 (-130)))) +(((*1 *2 *2) (|partial| -12 (-5 *2 (-316 (-225))) (-5 *1 (-267))))) +(((*1 *2 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1031)) + (-5 *1 (-747))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-294 *2)) (-4 *2 (-302)) (-4 *2 (-1209)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-641 (-610 *1))) (-5 *3 (-641 *1)) (-4 *1 (-302)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-641 (-294 *1))) (-4 *1 (-302)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-294 *1)) (-4 *1 (-302))))) +(((*1 *2 *1) (-12 (-4 *1 (-1278 *3)) (-4 *3 (-363)) (-5 *2 (-112))))) +(((*1 *1 *2) (-12 (-5 *1 (-1022 *2)) (-4 *2 (-1209))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -648,96 +748,60 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) -(((*1 *1) (-5 *1 (-291)))) -(((*1 *1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-117 *3)) (-14 *3 *2))) - ((*1 *1 *1) (-12 (-5 *1 (-117 *2)) (-14 *2 (-564)))) - ((*1 *1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-867 *3)) (-14 *3 *2))) - ((*1 *1 *1) (-12 (-5 *1 (-867 *2)) (-14 *2 (-564)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-564)) (-14 *3 *2) (-5 *1 (-868 *3 *4)) - (-4 *4 (-865 *3)))) - ((*1 *1 *1) - (-12 (-14 *2 (-564)) (-5 *1 (-868 *2 *3)) (-4 *3 (-865 *2)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-564)) (-4 *1 (-1221 *3 *4)) (-4 *3 (-1045)) - (-4 *4 (-1250 *3)))) - ((*1 *1 *1) - 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*6)) (-5 *2 (-112)) + (-5 *1 (-1101 *4 *5 *6 *7 *3)) (-4 *3 (-1065 *4 *5 *6 *7))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-939 *3) (-939 *3))) (-5 *1 (-176 *3)) + (-4 *3 (-13 (-363) (-1194) (-998))))) + ((*1 *2) + (|partial| -12 (-4 *4 (-1213)) (-4 *5 (-1235 (-407 *2))) + (-4 *2 (-1235 *4)) (-5 *1 (-341 *3 *4 *2 *5)) + (-4 *3 (-342 *4 *2 *5)))) + ((*1 *2) + (|partial| -12 (-4 *1 (-342 *3 *2 *4)) (-4 *3 (-1213)) + (-4 *4 (-1235 (-407 *2))) (-4 *2 (-1235 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1221 *3 *2)) (-4 *3 (-1045)) (-4 *2 (-1250 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -757,17 +821,6 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) -(((*1 *2 *1) (-12 (-4 *1 (-793 *2)) (-4 *2 (-172)))) - ((*1 *2 *1) (-12 (-4 *1 (-993 *2)) (-4 *2 (-172))))) -(((*1 *2 *1) (-12 (-4 *1 (-951)) (-5 *2 (-1088 (-225))))) - ((*1 *2 *1) (-12 (-4 *1 (-970)) (-5 *2 (-1088 (-225)))))) -(((*1 *2 *1) - (-12 (-5 *2 (-641 (-2 (|:| |integrand| *3) (|:| |intvar| *3)))) - (-5 *1 (-585 *3)) (-4 *3 (-363))))) -(((*1 *2 *3 *4 *5 *6) - (-12 (-5 *6 (-917)) (-4 *5 (-307)) (-4 *3 (-1235 *5)) - (-5 *2 (-2 (|:| |plist| (-641 *3)) (|:| |modulo| *5))) - (-5 *1 (-460 *5 *3)) (-5 *4 (-641 *3))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-788)))) @@ -875,9 +928,9 @@ (-4 *6 (-363)) (-5 *2 (-585 *6)) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -2656 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -3139 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-363)) (-4 *6 (-363)) - (-5 *2 (-2 (|:| -2656 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -3139 *6) (|:| |coeff| *6))) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -996,7 +1049,7 @@ (-4 *8 (-1045)) (-4 *6 (-789)) (-4 *2 (-13 (-1094) - (-10 -8 (-15 -2980 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-767)))))) + (-10 -8 (-15 -2968 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-767)))))) (-5 *1 (-947 *6 *7 *8 *5 *2)) (-4 *5 (-945 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-954 *5)) (-4 *5 (-1209)) @@ -1009,8 +1062,8 @@ (-4 *2 (-945 (-948 *4) *5 *6)) (-4 *5 (-789)) (-4 *6 (-13 (-846) - (-10 -8 (-15 -4344 ((-1170) $)) - (-15 -3257 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -4327 ((-1170) $)) + (-15 -3229 ((-3 $ "failed") (-1170)))))) (-5 *1 (-980 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-556)) (-4 *6 (-556)) @@ -1097,15 +1150,32 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1045)) (-5 *1 (-1282 *3 *4)) (-4 *4 (-842))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-641 *6)) (-5 *4 (-641 (-1170))) (-4 *6 (-363)) - (-5 *2 (-641 (-294 (-948 *6)))) (-5 *1 (-538 *5 *6 *7)) - (-4 *5 (-452)) (-4 *7 (-13 (-363) (-844)))))) -(((*1 *2) - (-12 (-4 *3 (-556)) (-5 *2 (-641 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-417 *3))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1045)) (-5 *2 (-641 *1)) (-4 *1 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*1) (-4 *1 (-1133)))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-875 (-1 (-225) (-225)))) (-5 *4 (-1088 (-379))) (-5 *5 (-641 (-263))) (-5 *2 (-1127 (-225))) (-5 *1 (-255)))) @@ -1159,14 +1229,19 @@ (-12 (-5 *3 (-878 *5)) (-5 *4 (-1086 (-379))) (-4 *5 (-13 (-612 (-536)) (-1094))) (-5 *2 (-1127 (-225))) (-5 *1 (-259 *5))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-767)) (-4 *4 (-13 (-1045) (-713 (-407 (-564))))) - (-4 *5 (-846)) (-5 *1 (-1275 *4 *5 *2)) (-4 *2 (-1280 *5 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-307) (-147))) (-4 *4 (-13 (-846) (-612 (-1170)))) - (-4 *5 (-789)) (-5 *1 (-920 *3 *4 *5 *2)) (-4 *2 (-945 *3 *5 *4))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) -(((*1 *1 *1) (-4 *1 (-545)))) +(((*1 *1 *1 *2 *1) (-12 (-5 *1 (-127 *2)) (-4 *2 (-1094)))) + ((*1 *1 *2) (-12 (-5 *1 (-127 *2)) (-4 *2 (-1094))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-506)) (-5 *3 (-641 (-961))) (-5 *1 (-109))))) +(((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1158 *3 *4)) (-14 *3 (-917)) + (-4 *4 (-1045))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1152)) (-5 *2 (-564)) (-5 *1 (-1191 *4)) + (-4 *4 (-1045))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1094)) + (-4 *6 (-1094)) (-4 *2 (-1094)) (-5 *1 (-676 *5 *6 *2))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -1187,47 +1262,35 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) -(((*1 *2 *1) - (-12 (-4 *1 (-1097 *3 *4 *5 *6 *7)) (-4 *3 (-1094)) (-4 *4 (-1094)) - (-4 *5 (-1094)) (-4 *6 (-1094)) (-4 *7 (-1094)) (-5 *2 (-112))))) +(((*1 *2 *3) (-12 (-5 *3 (-939 *2)) (-5 *1 (-978 *2)) (-4 *2 (-1045))))) (((*1 *2 *2) (|partial| -12 (-5 *2 (-316 (-225))) (-5 *1 (-305)))) ((*1 *2 *1) (|partial| -12 (-5 *2 (-2 (|:| |num| (-888 *3)) (|:| |den| (-888 *3)))) (-5 *1 (-888 *3)) (-4 *3 (-1094))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-641 (-564))) (-5 *1 (-136 *3 *4 *5)) (-14 *3 (-564)) + (-14 *4 (-767)) (-4 *5 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(|:| -4249 (-1150 *4)) (|:| -4261 (-1150 *4)))) + (-5 *1 (-1156 *4)) (-5 *3 (-1150 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-418 *3)) (-4 *3 (-556)))) + ((*1 *2 *3) + (-12 (-5 *3 (-641 (-2 (|:| -3546 *4) (|:| -3258 (-564))))) + (-4 *4 (-1235 (-564))) (-5 *2 (-767)) (-5 *1 (-442 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -1248,80 +1311,108 @@ (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3)))) ((*1 *1 *1) (-4 *1 (-1197)))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-452)) - (-4 *3 (-556)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *1 (-973 *3 *4 *5 *6))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-564)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-373 *2)) - (-4 *5 (-373 *2)) (-4 *2 (-1209)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-767)) (-4 *2 (-1094)) (-5 *1 (-213 *4 *2)) - (-14 *4 (-917)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-288 *3 *2)) (-4 *3 (-1094)) (-4 *2 (-1209)))) - ((*1 *2 *1 *3 *3) 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(((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1166 (-407 (-1166 *2)))) (-5 *4 (-610 *2)) (-4 *2 (-13 (-430 *5) (-27) (-1194))) @@ -4191,57 +4276,27 @@ (-4 *6 (-1045)) (-4 *2 (-13 (-363) - (-10 -8 (-15 -2350 ($ *7)) (-15 -2261 (*7 $)) (-15 -2272 (*7 $))))) + (-10 -8 (-15 -2326 ($ *7)) (-15 -2254 (*7 $)) (-15 -2264 (*7 $))))) (-5 *1 (-946 *5 *4 *6 *7 *2)) (-4 *7 (-945 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-407 (-1166 (-407 (-948 *5))))) (-5 *4 (-1170)) (-5 *2 (-407 (-948 *5))) (-5 *1 (-1039 *5)) (-4 *5 (-556))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-1170))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) -(((*1 *2 *1) (-12 (-5 *1 (-910 *2)) (-4 *2 (-307))))) -(((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-818))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-294 (-839 *3))) (-4 *3 (-13 (-27) (-1194) (-430 *5))) - (-4 *5 (-13 (-452) (-846) (-1034 (-564)) (-637 (-564)))) - (-5 *2 - (-3 (-839 *3) - (-2 (|:| |leftHandLimit| (-3 (-839 *3) "failed")) - (|:| 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(-5 *1 (-635 *6))))) -(((*1 *2 *1) (-12 (-5 *2 (-641 (-641 (-225)))) (-5 *1 (-922))))) +(((*1 *1) (-5 *1 (-291)))) +(((*1 *2 *3 *1) + (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1094)) (-4 *4 (-1094)) + (-5 *2 (-2 (|:| -3026 *3) (|:| -3683 *4)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1045))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-114) (-114))) (-5 *1 (-114))))) +(((*1 *2 *3) (-12 (-5 *3 (-1170)) (-5 *2 (-1264)) (-5 *1 (-1173))))) +(((*1 *1 *1) (-5 *1 (-1057)))) +(((*1 *2 *3) + (-12 (-5 *2 (-112)) (-5 *1 (-39 *3)) (-4 *3 (-1235 (-48)))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -2029 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3374 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-2 @@ -4259,7 +4314,7 @@ (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2029 + (|:| -3374 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -4268,24 +4323,13 @@ (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-559))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1166 *5)) (-4 *5 (-452)) (-5 *2 (-641 *6)) - (-5 *1 (-538 *5 *6 *4)) (-4 *6 (-363)) (-4 *4 (-13 (-363) (-844))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-948 *5)) (-4 *5 (-452)) (-5 *2 (-641 *6)) - (-5 *1 (-538 *5 *6 *4)) (-4 *6 (-363)) (-4 *4 (-13 (-363) (-844)))))) -(((*1 *1 *2) - (-12 (-5 *2 (-641 *3)) (-4 *3 (-1209)) (-5 *1 (-1259 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-917)) (|has| *1 (-6 -4397)) (-4 *1 (-404)))) - ((*1 *2) (-12 (-4 *1 (-404)) (-5 *2 (-917)))) - ((*1 *2 *2) (-12 (-5 *2 (-917)) (-5 *1 (-695)))) - ((*1 *2) (-12 (-5 *2 (-917)) (-5 *1 (-695))))) -(((*1 *2 *3) (-12 (-5 *3 (-948 (-225))) (-5 *2 (-225)) (-5 *1 (-305))))) + (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1097 *3 *4 *5 *6 *7)) (-4 *3 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(-860 *4))))) ((*1 *1 *2 *3) @@ -4326,63 +4370,10 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-969 *4 *3 *2)) (-4 *4 (-1045)) (-4 *3 (-788)) (-4 *2 (-846))))) -(((*1 *2 *3 *4 *4 *3 *3 *5) - (|partial| -12 (-5 *4 (-610 *3)) (-5 *5 (-1166 *3)) - (-4 *3 (-13 (-430 *6) (-27) (-1194))) - (-4 *6 (-13 (-452) (-1034 (-564)) (-846) (-147) (-637 (-564)))) - (-5 *2 (-2 (|:| -2656 *3) (|:| |coeff| *3))) - (-5 *1 (-560 *6 *3 *7)) (-4 *7 (-1094)))) - ((*1 *2 *3 *4 *4 *3 *4 *3 *5) - (|partial| -12 (-5 *4 (-610 *3)) (-5 *5 (-407 (-1166 *3))) - (-4 *3 (-13 (-430 *6) (-27) (-1194))) - (-4 *6 (-13 (-452) (-1034 (-564)) (-846) (-147) (-637 (-564)))) - (-5 *2 (-2 (|:| -2656 *3) (|:| |coeff| *3))) - (-5 *1 (-560 *6 *3 *7)) (-4 *7 (-1094))))) -(((*1 *1 *1) (-4 *1 (-173))) - ((*1 *1 *1) - (-12 (-4 *1 (-364 *2 *3)) (-4 *2 (-1094)) (-4 *3 (-1094))))) -(((*1 *2 *3) - (-12 (-4 *4 (-556)) (-5 *2 (-767)) (-5 *1 (-43 *4 *3)) - (-4 *3 (-417 *4))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-641 (-641 (-641 *4)))) (-5 *2 (-641 (-641 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*2 *1) - (-12 (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-641 *1)) - (-4 *1 (-1059 *3 *4 *5))))) -(((*1 *2 *3 *1) - (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-3 (-112) (-641 *1))) - (-4 *1 (-1065 *4 *5 *6 *3))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-685 *5))) (-5 *4 (-564)) (-4 *5 (-363)) - (-4 *5 (-1045)) (-5 *2 (-112)) (-5 *1 (-1025 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 (-685 *4))) (-4 *4 (-363)) (-4 *4 (-1045)) - (-5 *2 (-112)) (-5 *1 (-1025 *4))))) + (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1094)) (-4 *5 (-1094)) + (-4 *6 (-1094)) (-5 *2 (-1 *6 *5)) (-5 *1 (-680 *4 *5 *6))))) +(((*1 *1) (-5 *1 (-141)))) (((*1 *2 *1) (-12 (-4 *1 (-244 *2)) (-4 *2 (-1209)))) ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-1090)))) ((*1 *2 *1) @@ -4391,93 +4382,138 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-767)) (-4 *1 (-1247 *3)) (-4 *3 (-1209)))) ((*1 *2 *1) (-12 (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1045)) (-5 *1 (-1231 *3 *2)) (-4 *2 (-1235 *3))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-939 *5)) (-4 *5 (-1045)) (-5 *2 (-767)) + (-5 *1 (-1158 *4 *5)) (-14 *4 (-917)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-641 (-767))) (-5 *3 (-767)) (-5 *1 (-1158 *4 *5)) + (-14 *4 (-917)) (-4 *5 (-1045)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-641 (-767))) (-5 *3 (-939 *5)) (-4 *5 (-1045)) + (-5 *1 (-1158 *4 *5)) (-14 *4 (-917))))) +(((*1 *2 *3) + (-12 (-4 *4 (-846)) (-5 *2 (-1181 (-641 *4))) (-5 *1 (-1180 *4)) + (-5 *3 (-641 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1170)) + (-5 *2 + (-2 (|:| |zeros| (-1150 (-225))) (|:| |ones| (-1150 (-225))) + (|:| |singularities| (-1150 (-225))))) + (-5 *1 (-105))))) (((*1 *2 *1) - (-12 (-4 *1 (-1235 *3)) (-4 *3 (-1045)) (-5 *2 (-1166 *3))))) -(((*1 *1 *1 *2) - (-12 (-5 *1 (-1134 *3 *2)) (-4 *3 (-13 (-1094) (-34))) - (-4 *2 (-13 (-1094) (-34)))))) -(((*1 *1 *1) (-12 (-4 *1 (-373 *2)) (-4 *2 (-1209)))) - ((*1 *2 *2) - (-12 (-4 *3 (-1045)) (-5 *1 (-444 *3 *2)) (-4 *2 (-1235 *3)))) - ((*1 *1 *1) - (-12 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((*1 *2 *1) (-12 (-5 *1 (-294 *2)) (-4 *2 (-1209)))) @@ -11343,89 +11356,51 @@ (-4 *4 (-13 (-1045) (-882 *3) (-846) (-612 (-888 *3)))))) ((*1 *2 *1) (-12 (-4 *2 (-1094)) (-5 *1 (-1159 *3 *2)) (-4 *3 (-1094))))) -(((*1 *2 *3) - (-12 (-5 *3 (-948 *4)) (-4 *4 (-13 (-307) (-147))) - (-4 *2 (-945 *4 *6 *5)) (-5 *1 (-920 *4 *5 *6 *2)) - (-4 *5 (-13 (-846) (-612 (-1170)))) (-4 *6 (-789))))) -(((*1 *2 *3 *4 *4 *5 *3 *3) - (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *5 (-225)) - (-5 *2 (-1031)) (-5 *1 (-748))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1170)) (-5 *2 (-1 *6 *5)) (-5 *1 (-702 *4 *5 *6)) - (-4 *4 (-612 (-536))) (-4 *5 (-1209)) (-4 *6 (-1209))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-556)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-965 *4 *3)) (-4 *3 (-1235 *4))))) -(((*1 *2 *3 *1 *4 *4 *4 *4 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-641 (-1023 *5 *6 *7 *3))) (-5 *1 (-1023 *5 *6 *7 *3)) - (-4 *3 (-1059 *5 *6 *7)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-641 *6)) (-4 *1 (-1065 *3 *4 *5 *6)) (-4 *3 (-452)) - (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)))) - ((*1 *1 *2 *1) - (-12 (-4 *1 (-1065 *3 *4 *5 *2)) (-4 *3 (-452)) (-4 *4 (-789)) - (-4 *5 (-846)) (-4 *2 (-1059 *3 *4 *5)))) - ((*1 *2 *3 *1 *4 *4 *4 *4 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-641 (-1140 *5 *6 *7 *3))) (-5 *1 (-1140 *5 *6 *7 *3)) - (-4 *3 (-1059 *5 *6 *7))))) -(((*1 *2) - (-12 (-4 *3 (-556)) (-5 *2 (-641 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-417 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) -(((*1 *2 *3 *4 *5 *6) - (-12 (-5 *5 (-641 (-641 (-3 (|:| |array| *6) (|:| |scalar| *3))))) - (-5 *4 (-641 (-3 (|:| |array| (-641 *3)) (|:| |scalar| (-1170))))) - (-5 *6 (-641 (-1170))) (-5 *3 (-1170)) (-5 *2 (-1098)) - (-5 *1 (-397)))) - ((*1 *2 *3 *4 *5 *6 *3) - (-12 (-5 *5 (-641 (-641 (-3 (|:| |array| *6) (|:| |scalar| *3))))) - (-5 *4 (-641 (-3 (|:| |array| (-641 *3)) (|:| |scalar| (-1170))))) - (-5 *6 (-641 (-1170))) (-5 *3 (-1170)) (-5 *2 (-1098)) - (-5 *1 (-397)))) - ((*1 *2 *3 *4 *5 *4) - (-12 (-5 *4 (-641 (-1170))) (-5 *5 (-1173)) (-5 *3 (-1170)) - (-5 *2 (-1098)) (-5 *1 (-397))))) -(((*1 *1) (-12 (-4 *1 (-465 *2 *3)) (-4 *2 (-172)) (-4 *3 (-23)))) - ((*1 *1) (-5 *1 (-536))) ((*1 *1) (-4 *1 (-718))) - ((*1 *1) (-4 *1 (-722))) - ((*1 *1) (-12 (-5 *1 (-888 *2)) (-4 *2 (-1094)))) - ((*1 *1) (-12 (-5 *1 (-889 *2)) (-4 *2 (-846))))) -(((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -2029 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) - (|:| |relerr| (-225)))) - (-5 *2 - (-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| (-1150 (-225))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2029 - (-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 (-559))))) -(((*1 *2 *1) (-12 (-4 *1 (-763 *3)) (-4 *3 (-1094)) (-5 *2 (-112))))) -(((*1 *1) (-5 *1 (-130)))) -(((*1 *2 *2) (-12 (-5 *2 (-1150 (-641 (-564)))) (-5 *1 (-879))))) + (-12 (-5 *3 (-1259 *5)) (-4 *5 (-788)) (-5 *2 (-112)) + (-5 *1 (-841 *4 *5)) (-14 *4 (-767))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-976 *2)) (-4 *2 (-1045)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-939 (-225))) (-5 *1 (-1205)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1257 *2)) (-4 *2 (-1209)) (-4 *2 (-1045))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-564)) (-5 *1 (-418 *2)) (-4 *2 (-556))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-379)) (-5 *2 (-1264)) (-5 *1 (-1261))))) +(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-96)))) + ((*1 *2 *1) (-12 (-5 *2 (-506)) (-5 *1 (-109)))) + ((*1 *2 *1) + (-12 (-4 *1 (-364 *2 *3)) (-4 *3 (-1094)) (-4 *2 (-1094)))) + ((*1 *2 *1) (-12 (-4 *1 (-389)) (-5 *2 (-1152)))) + ((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-438 *3)) (-14 *3 *2))) + ((*1 *2 *1) (-12 (-5 *2 (-506)) (-5 *1 (-483)))) + ((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-610 *3)) (-4 *3 (-846)))) + ((*1 *2 *1) (-12 (-4 *1 (-831 *2)) (-4 *2 (-1094)))) + ((*1 *2 *1) (-12 (-5 *2 (-506)) (-5 *1 (-861)))) + ((*1 *2 *1) (-12 (-5 *2 (-506)) (-5 *1 (-961)))) + ((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-1069 *3)) (-14 *3 *2))) + ((*1 *2 *1) (-12 (-5 *2 (-506)) (-5 *1 (-1109)))) + ((*1 *1 *1) (-5 *1 (-1170)))) +(((*1 *1) (-4 *1 (-23))) + ((*1 *1) (-12 (-4 *1 (-470 *2 *3)) (-4 *2 (-172)) (-4 *3 (-23)))) + ((*1 *1) (-5 *1 (-536))) + ((*1 *1) (-12 (-5 *1 (-888 *2)) (-4 *2 (-1094))))) +(((*1 *1 *2) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-487))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-685 *3)) (-4 *3 (-1045)) (-5 *1 (-686 *3)))) + ((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-685 *3)) (-4 *3 (-1045)) (-5 *1 (-686 *3))))) +(((*1 *2 *3 *4 *4 *3 *5) + (-12 (-5 *4 (-610 *3)) (-5 *5 (-1166 *3)) + (-4 *3 (-13 (-430 *6) (-27) (-1194))) + (-4 *6 (-13 (-452) (-1034 (-564)) (-846) (-147) (-637 (-564)))) + (-5 *2 (-585 *3)) (-5 *1 (-560 *6 *3 *7)) (-4 *7 (-1094)))) + ((*1 *2 *3 *4 *4 *4 *3 *5) + (-12 (-5 *4 (-610 *3)) (-5 *5 (-407 (-1166 *3))) + (-4 *3 (-13 (-430 *6) (-27) (-1194))) + (-4 *6 (-13 (-452) (-1034 (-564)) (-846) (-147) (-637 (-564)))) + (-5 *2 (-585 *3)) (-5 *1 (-560 *6 *3 *7)) (-4 *7 (-1094))))) +(((*1 *2) (-12 (-5 *2 (-641 *3)) (-5 *1 (-1078 *3)) (-4 *3 (-132))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-917)) (-5 *4 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1260))))) (((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-137)))) ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-156)))) ((*1 *2 *1) (-12 (-5 *1 (-294 *2)) (-4 *2 (-1209)))) @@ -11439,111 +11414,25 @@ (-4 *4 (-13 (-1045) (-882 *3) (-846) (-612 (-888 *3)))))) ((*1 *2 *1) (-12 (-4 *2 (-1094)) (-5 *1 (-1159 *2 *3)) (-4 *3 (-1094))))) -(((*1 *2 *1) - (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) - (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-112))))) -(((*1 *2 *3 *1) - (|partial| -12 (-5 *3 (-1 (-112) *2)) (-4 *1 (-151 *2)) - (-4 *2 (-1209))))) -(((*1 *2 *1) (-12 (-5 *2 (-770)) (-5 *1 (-52))))) -(((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-910 *3)) (-4 *3 (-307))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) (-5 *2 (-641 *10)) - (-5 *1 (-622 *5 *6 *7 *8 *9 *10)) (-4 *9 (-1065 *5 *6 *7 *8)) - (-4 *10 (-1103 *5 *6 *7 *8)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-776 *5 (-860 *6)))) (-5 *4 (-112)) (-4 *5 (-452)) - (-14 *6 (-641 (-1170))) (-5 *2 (-641 (-1042 *5 *6))) - (-5 *1 (-626 *5 *6)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-776 *5 (-860 *6)))) (-5 *4 (-112)) (-4 *5 (-452)) - (-14 *6 (-641 (-1170))) - (-5 *2 - (-641 (-1140 *5 (-531 (-860 *6)) (-860 *6) (-776 *5 (-860 *6))))) - (-5 *1 (-626 *5 *6)))) - ((*1 *2 *3 *4 *4 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-641 (-1023 *5 *6 *7 *8))) (-5 *1 (-1023 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-641 (-1023 *5 *6 *7 *8))) (-5 *1 (-1023 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 (-776 *5 (-860 *6)))) (-5 *4 (-112)) (-4 *5 (-452)) - (-14 *6 (-641 (-1170))) (-5 *2 (-641 (-1042 *5 *6))) - (-5 *1 (-1042 *5 *6)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) (-5 *2 (-641 *1)) - (-4 *1 (-1065 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-641 (-1140 *5 *6 *7 *8))) (-5 *1 (-1140 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1059 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-5 *2 (-641 (-1140 *5 *6 *7 *8))) (-5 *1 (-1140 *5 *6 *7 *8)))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 *7)) (-4 *7 (-1059 *4 *5 *6)) (-4 *4 (-556)) - (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-641 *1)) - (-4 *1 (-1202 *4 *5 *6 *7))))) +(((*1 *1 *2) (-12 (-5 *1 (-227 *2)) (-4 *2 (-13 (-363) (-1194)))))) +(((*1 *1) (-5 *1 (-1057)))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-4 *1 (-326 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-788))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1170)) - (-4 *5 (-13 (-307) (-846) (-147) (-1034 (-564)) (-637 (-564)))) - (-5 *2 (-585 *3)) (-5 *1 (-426 *5 *3)) - (-4 *3 (-13 (-1194) (-29 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1170)) (-4 *5 (-13 (-556) (-1034 (-564)) (-147))) - (-5 *2 (-585 (-407 (-948 *5)))) (-5 *1 (-570 *5)) - (-5 *3 (-407 (-948 *5)))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1261))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-641 (-564))) (-5 *2 (-685 (-564))) (-5 *1 (-1104))))) -(((*1 *1) (-4 *1 (-23))) - ((*1 *1) (-12 (-4 *1 (-470 *2 *3)) (-4 *2 (-172)) (-4 *3 (-23)))) - ((*1 *1) (-5 *1 (-536))) - ((*1 *1) (-12 (-5 *1 (-888 *2)) (-4 *2 (-1094))))) -(((*1 *2 *1) (-12 (-4 *1 (-1278 *3)) (-4 *3 (-363)) (-5 *2 (-112))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-610 *2)) (-4 *2 (-13 (-27) (-1194) (-430 *4))) - (-4 *4 (-13 (-556) (-846) (-1034 (-564)) (-637 (-564)))) - (-5 *1 (-277 *4 *2))))) -(((*1 *2) (-12 (-5 *2 (-1264)) (-5 *1 (-1211))))) -(((*1 *2 *1) (-12 (-5 *2 (-641 (-1208))) (-5 *1 (-524))))) -(((*1 *2 *1) (-12 (-5 *2 (-967)) (-5 *1 (-901 *3)) (-4 *3 (-1094))))) -(((*1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-858)))) - ((*1 *1 *1) (-5 *1 (-858)))) -(((*1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-858))))) -(((*1 *2 *3 *4 *5 *5 *6) - (-12 (-5 *4 (-1170)) (-5 *6 (-112)) - (-4 *7 (-13 (-307) (-846) (-147) (-1034 (-564)) (-637 (-564)))) - (-4 *3 (-13 (-1194) (-955) (-29 *7))) - (-5 *2 - (-3 (|:| |f1| (-839 *3)) (|:| |f2| (-641 (-839 *3))) - (|:| |fail| "failed") (|:| |pole| "potentialPole"))) - (-5 *1 (-219 *7 *3)) (-5 *5 (-839 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-683 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-373 *3)) - (-4 *5 (-373 *3)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1048 *3 *4 *5 *6 *7)) (-4 *5 (-1045)) - (-4 *6 (-238 *4 *5)) (-4 *7 (-238 *3 *5)) (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-641 (-2 (|:| -4242 (-407 (-564))) (|:| -4251 (-407 (-564)))))) - (-5 *2 (-641 (-225))) (-5 *1 (-305))))) + (-12 (-4 *5 (-556)) + (-5 *2 (-2 (|:| -3116 (-685 *5)) (|:| |vec| (-1259 (-641 (-917)))))) + (-5 *1 (-90 *5 *3)) (-5 *4 (-917)) (-4 *3 (-652 *5))))) +(((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-467)))) + ((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-467)))) + ((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-923))))) (((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -1931)) (-5 *2 (-112)) (-5 *1 (-615)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -1384)) (-5 *2 (-112)) (-5 *1 (-615)))) + (-12 (-5 *3 (|[\|\|]| -1388)) (-5 *2 (-112)) (-5 *1 (-615)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -2017)) (-5 *2 (-112)) (-5 *1 (-615)))) + (-12 (-5 *3 (|[\|\|]| -3219)) (-5 *2 (-112)) (-5 *1 (-615)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -3261)) (-5 *2 (-112)) (-5 *1 (-687 *4)) + (-12 (-5 *3 (|[\|\|]| -3231)) (-5 *2 (-112)) (-5 *1 (-687 *4)) (-4 *4 (-611 (-858))))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| *4)) (-4 *4 (-611 (-858))) (-5 *2 (-112)) @@ -11618,263 +11507,322 @@ (-12 (-5 *3 (|[\|\|]| (-225))) (-5 *2 (-112)) (-5 *1 (-1175)))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| (-564))) (-5 *2 (-112)) (-5 *1 (-1175))))) -(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-248))))) -(((*1 *2 *3) - (-12 (-4 *4 (-373 *2)) (-4 *5 (-373 *2)) (-4 *2 (-363)) - (-5 *1 (-521 *2 *4 *5 *3)) (-4 *3 (-683 *2 *4 *5)))) - ((*1 *2 *1) - (-12 (-4 *1 (-683 *2 *3 *4)) (-4 *3 (-373 *2)) (-4 *4 (-373 *2)) - (|has| *2 (-6 (-4408 "*"))) (-4 *2 (-1045)))) - 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(-1170))) (-14 *6 (-1259 (-685 *3)))))) + (|partial| -12 + (-5 *3 + (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) + (|:| -3374 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (-5 *2 + (-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| (-1150 (-225))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3374 + (-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 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*2 (-2 (|:| |localSymbols| (-1174)) (|:| -3063 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3027 (-641 (-330))))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-1259 (-695))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3063 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3027 (-641 (-330))))) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-441)))) @@ -12280,7 +12317,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-641 (-2 (|:| -4311 *3) (|:| -3144 *4)))) + (-12 (-5 *2 (-641 (-2 (|:| -4290 *3) (|:| -3124 *4)))) (-4 *3 (-1045)) (-4 *4 (-722)) (-5 *1 (-731 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-759)))) ((*1 *1 *2) @@ -12289,25 +12326,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -2029 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3374 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-316 (-225))) - (|:| -2029 (-641 (-1088 (-839 (-225))))) + (|:| -3374 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-316 (-225))) - (|:| -2029 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) + (|:| -3374 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -2029 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3374 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *2 *3) (-12 (-5 *2 (-770)) (-5 *1 (-769 *3)) (-4 *3 (-1209)))) @@ -12325,23 +12362,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -3978 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3958 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-641 (-316 (-225)))) - (|:| -3978 (-641 (-225))))))) + (|:| -3958 (-641 (-225))))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3978 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3958 (-641 (-225))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-316 (-225))) (|:| -3978 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3958 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (-5 *1 (-837)))) @@ -12442,194 +12479,240 @@ ((*1 *1 *2) (-12 (-5 *2 (-660 *3 *4)) (-4 *3 (-846)) (-4 *4 (-172)) (-5 *1 (-1279 *3 *4))))) -(((*1 *2 *1) - (-12 (-4 *1 (-166 *3)) (-4 *3 (-172)) (-4 *3 (-1054)) (-4 *3 (-1194)) - (-5 *2 (-2 (|:| |r| *3) (|:| |phi| *3)))))) (((*1 *2 *3) - (-12 (-4 *4 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*3 (-13 (-556) (-147))) (-5 *1 (-1229 *3 *2)) + (-4 *2 (-1235 *3))))) +(((*1 *2 *2 *1) + (-12 (-5 *2 (-641 *6)) (-4 *1 (-972 *3 *4 *5 *6)) (-4 *3 (-1045)) + (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) + (-4 *3 (-556))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-767)) (-4 *4 (-556)) (-5 *1 (-965 *4 *2)) + (-4 *2 (-1235 *4))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) @@ -16935,47 +16782,49 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 (-641 (-939 (-225))))) (-5 *2 (-641 (-225))) - (-5 *1 (-468))))) -(((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1045)) - (-14 *4 (-641 (-1170))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1 (-939 (-225)) (-225) (-225))) + (-5 *3 (-1 (-225) (-225) (-225) (-225))) (-5 *1 (-255))))) +(((*1 *2 *2) + (-12 (-4 *3 (-556)) (-4 *4 (-988 *3)) (-5 *1 (-142 *3 *4 *2)) + (-4 *2 (-373 *4)))) ((*1 *2 *3) - (-12 (-5 *3 (-52)) 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*2 (-13 (-430 *3) (-998))))) @@ -17460,34 +17346,33 @@ ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-789)) (-4 *6 (-846)) (-4 *3 (-556)) - (-4 *7 (-945 *3 *5 *6)) - (-5 *2 (-2 (|:| -1377 (-767)) (|:| -4311 *8) (|:| |radicand| *8))) - (-5 *1 (-949 *5 *6 *3 *7 *8)) (-5 *4 (-767)) - (-4 *8 - (-13 (-363) - (-10 -8 (-15 -2350 ($ *7)) (-15 -2261 (*7 $)) (-15 -2272 (*7 $)))))))) -(((*1 *1) (-5 *1 (-559)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *2 (-641 *2))) (-5 *4 (-641 *5)) - (-4 *5 (-38 (-407 (-564)))) (-4 *2 (-1250 *5)) - (-5 *1 (-1252 *5 *2))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-685 (-407 (-564)))) - (-5 *2 - (-641 - (-2 (|:| |outval| *4) (|:| |outmult| (-564)) - (|:| |outvect| (-641 (-685 *4)))))) - (-5 *1 (-775 *4)) (-4 *4 (-13 (-363) (-844)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1031)) (-5 *1 (-754))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-452))) (-5 *1 (-1200 *3 *2)) - (-4 *2 (-13 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