diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 1278 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1220 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1314 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8806 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25842 |
5 files changed, 19230 insertions, 19230 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index ca8b2a89..62771912 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2282814 . 3443021571) +(2282835 . 3443721767) (-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."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . 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}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4404 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4400 . T) (-4405 . T) (-4399 . T)) +((-4405 . T) (-4403 . T) (-4402 . T) ((-4410 "*") . T) (-4401 . T) (-4406 . T) (-4400 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3191) +(-32 R -3195) ((|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 (-563))))) (-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 -4407))) +((|HasAttribute| |#1| (QUOTE -4408))) (-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}."))) -((-4407 . T) (-4408 . T)) +((-4408 . T) (-4409 . 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"))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . 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 -3191 UP UPUP -2995) +(-40 -3195 UP UPUP -3593) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-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))) (-4032 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4032 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4032 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-563)))) (-4032 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -3191) +((-4401 |has| (-407 |#2|) (-363)) (-4406 |has| (-407 |#2|) (-363)) (-4400 |has| (-407 |#2|) (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4034 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4034 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4034 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-563)))) (-4034 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -3195) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-307)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4404 |has| |#1| (-555)) (-4402 . T) (-4401 . T)) +((-4405 |has| |#1| (-555)) (-4403 . T) (-4402 . T)) ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-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."))) -((-4407 . T) (-4408 . T)) -((-4032 (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|))))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|))))))) +((-4408 . T) (-4409 . T)) +((-4034 (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#2|))))))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4404 . T)) +((-4405 . 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 -3191) +(-54 |Base| R -3195) ((|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"))) -((-4407 . T) (-4408 . T)) +((-4408 . T) (-4409 . 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}"))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|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}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) -(-61 -3348) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +(-61 -3352) ((|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 -3348) +(-62 -3352) ((|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 -3348) +(-63 -3352) ((|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 -3348) +(-64 -3352) ((|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 -3348) +(-65 -3352) ((|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 -3348) +(-66 -3352) ((|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 -3348) +(-67 -3352) ((|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 -3348) +(-68 -3352) ((|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 -3348) +(-69 -3352) ((|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 -3348) +(-70 -3352) ((|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 -3348) +(-71 -3352) ((|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 -3348) +(-72 -3352) ((|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 -3348) +(-73 -3352) ((|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 -3348) +(-74 -3352) ((|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 -3348) +(-77 -3352) ((|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 -3348) +(-78 -3352) ((|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 -3348) +(-79 -3352) ((|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 -3348) +(-80 -3352) ((|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 -3348) +(-81 -3352) ((|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 -3348) +(-82 -3352) ((|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 -3348) +(-83 -3352) ((|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 -3348) +(-84 -3352) ((|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 -3348) +(-85 -3352) ((|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 -3348) +(-86 -3352) ((|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 -3348) +(-87 -3352) ((|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 -3348) +(-88 -3352) ((|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 -3348) +(-89 -3352) ((|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}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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\"."))) -((-4407 . T)) +((-4408 . 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."))) -((-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)) +((-4408 . T) ((-4410 "*") . T) (-4409 . T) (-4405 . T) (-4403 . T) (-4402 . T) (-4401 . T) (-4406 . T) (-4400 . T) (-4399 . T) (-4398 . T) (-4397 . T) (-4396 . T) (-4404 . T) (-4407 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4395 . 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}."))) -((-4404 . T)) +((-4405 . 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}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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 (-4409 "*")))) +((|HasAttribute| |#1| (QUOTE (-4410 "*")))) (-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"))) -((-4407 . T)) +((-4408 . 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."))) -((-4408 . T)) +((-4409 . 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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4032 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145))))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4034 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (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| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -610) (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}"))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . 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| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3191 UP) +(-115 -3195 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}."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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}."))) -((-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 (-1169)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-4032 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (QUOTE (-1144))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (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)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-4034 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (QUOTE (-1144))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (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)))) (-4034 (-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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4408))) +((|HasAttribute| |#1| (QUOTE -4409))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4407 . T) (-4408 . T)) +((-4408 . T) (-4409 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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.}")) (|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'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4032 (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1093)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((|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."))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4034 (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1093)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4409 "*") . T)) +(((-4410 "*") . T)) NIL -(-135 |minix| -3304 S T$) +(-135 |minix| -3308 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -3304 R) +(-136 |minix| -3308 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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}."))) -((-4407 . T) (-4397 . T) (-4408 . T)) -((-4032 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4408 . T) (-4398 . T) (-4409 . T)) +((-4034 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|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."))) -((-4404 . T)) +((-4405 . 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."))) -((-4404 . T)) +((-4405 . T)) NIL -(-148 -3191 UP UPUP) +(-148 -3195 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 -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasAttribute| |#1| (QUOTE -4407))) +((|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasAttribute| |#1| (QUOTE -4408))) (-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."))) -((-4402 . T) (-4401 . T) (-4404 . T)) +((-4403 . T) (-4402 . T) (-4405 . 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 -3191) +(-158 R -3195) ((|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 (-1193))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-846)))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1193))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasAttribute| |#2| (QUOTE -4407)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-555))) (|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})"))) -((-4400 -4032 (|has| |#1| (-555)) (-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)) (-1413 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 -4034 (|has| |#1| (-555)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4407 |has| |#1| (-6 -4407)) (-1413 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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}."))) -((-4400 -4032 (|has| |#1| (-555)) (-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)) (-1413 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . 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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 -636) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-555)))) (-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 (-1193)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -611) (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 (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-4032 (-12 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(|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) +((-4401 -4034 (|has| |#1| (-555)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4407 |has| |#1| (-6 -4407)) (-1413 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4034 (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|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 -636) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-555)))) (-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 (-1193)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -611) (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 (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-4034 (-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))))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-555)))) (-4034 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|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 (-1193)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4407)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-4034 (-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."))) -(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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}."))) -(((-4409 "*") . T) (-4400 . T) (-4405 . T) (-4399 . T) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") . T) (-4401 . T) (-4406 . T) (-4400 . T) (-4402 . T) (-4403 . T) (-4405 . 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| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Symbol|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -3191) +(-188 R -3195) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -3191 UP UPUP R) +(-215 -3195 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 -3191 FP) +(-216 -3195 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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4032 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145))))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4034 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -3191) +(-219 R -3195) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -818,19 +818,19 @@ NIL NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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}."))) -((-4404 . T)) +((-4405 . T)) NIL -(-224 R -3191) +(-224 R -3195) ((|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}."))) -((-1403 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-1402 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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}"))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (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."))) -((-4408 . T)) +((-4409 . 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 (-1169)))) (|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}."))) -((-4404 . T)) +((-4405 . 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4404 . T)) +((-4405 . T)) NIL (-234 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4407))) +((|HasAttribute| |#1| (QUOTE -4408))) (-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}."))) -((-4408 . T)) +((-4409 . 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 -3304 R) +(-237 S -3308 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 -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 (-1093)))) -(-238 -3304 R) +((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4405)) (|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 (-1093)))) +(-238 -3308 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"))) -((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) +((-4402 |has| |#2| (-1045)) (-4403 |has| |#2| (-1045)) (-4405 |has| |#2| (-6 -4405)) ((-4410 "*") |has| |#2| (-172)) (-4408 . T)) NIL -(-239 -3304 A B) +(-239 -3308 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 (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| (-563) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-4034 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|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}."))) -((-4400 . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) (-4402 . T) (-4403 . T) (-4405 . 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}"))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|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"))) -(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-555)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-555)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (-4034 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4034 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (-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."))) -((-4404 -4032 (-2190 (|has| |#4| (-1045)) (|has| |#4| (-233))) (-2190 (|has| |#4| (-1045)) (|has| |#4| (-896 (-1169)))) (|has| |#4| (-6 -4404)) (-2190 (|has| |#4| (-1045)) (|has| |#4| (-636 (-563))))) (-4401 |has| |#4| (-1045)) (-4402 |has| |#4| (-1045)) ((-4409 "*") |has| |#4| (-172)) (-4407 . 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(QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . 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}."))) -((-4407 . T) (-4408 . T)) +((-4408 . T) (-4409 . 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"))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#3| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#3| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (-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 -3191) +(-276 R -3195) ((|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 -3191) +(-277 R -3195) ((|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 (-1093)))) (-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}."))) -((-4408 . T)) +((-4409 . 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 -4408))) +((|HasAttribute| |#1| (QUOTE -4409))) (-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| -2472 -3164 |exactQuo|) +(-289 S R |Mod| -4219 -4300 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-290) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4400 . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-291) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -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."))) -((-4404 -4032 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-1045)) (-4402 |has| |#1| (-1045))) -((|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722)))) (|HasCategory| |#1| (QUOTE (-473))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|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 (-1105))) (|HasCategory| |#1| (QUOTE (-1093)))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-302))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-4032 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722)))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-172)))) +((-4405 -4034 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-1045)) (-4403 |has| |#1| (-1045))) +((|HasCategory| |#1| (QUOTE (-363))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4034 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722)))) (|HasCategory| |#1| (QUOTE (-473))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|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 (-1105))) (|HasCategory| |#1| (QUOTE (-1093)))) (-4034 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-302))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722)))) (-4034 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1105))) (|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."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#2|)))))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (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 -3191 S) +(-297 -3195 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 -3191) +(-298 E -3195) ((|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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-308 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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 -3191) +(-310 -3195) ((|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))}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-4032 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1144))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-4032 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-4034 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1144))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-4034 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1243 |#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."))) -((-4404 -4032 (-2190 (|has| |#1| (-1045)) (|has| |#1| (-636 (-563)))) (-12 (|has| |#1| (-555)) (-4032 (-2190 (|has| |#1| (-1045)) (|has| |#1| (-636 (-563)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-555)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-555)) (-4399 |has| |#1| (-555))) -((-4032 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555)))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1105)))) (-4032 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))))) (-4032 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1105)))) (-4032 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) -(-317 R -3191) +((-4405 -4034 (-2188 (|has| |#1| (-1045)) (|has| |#1| (-636 (-563)))) (-12 (|has| |#1| (-555)) (-4034 (-2188 (|has| |#1| (-1045)) (|has| |#1| (-636 (-563)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) ((-4410 "*") |has| |#1| (-555)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-555)) (-4400 |has| |#1| (-555))) +((-4034 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (QUOTE (-555))) (-4034 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555)))) (-4034 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1105)))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))))) (-4034 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1105)))) (-4034 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))))) (-4034 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4034 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) +(-317 R -3195) ((|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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4032 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3698) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2606) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1692) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4034 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2605) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|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."))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . T)) ((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1234,19 +1234,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172)))) (-326 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . 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."))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -3191) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -3195) ((|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 -3191) +(-329 -3195) ((|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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 -3191 UP UPUP R) +(-334 S -3195 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 -3191 UP UPUP R) +(-335 -3195 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 -3191 UP UPUP R) +(-336 -3195 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.}"))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-379)))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) (-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 -3191 UP UPUP) +(-341 S -3195 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 -3191 UP UPUP) +(-342 -3195 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."))) -((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 |has| (-407 |#2|) (-363)) (-4406 |has| (-407 |#2|) (-363)) (-4400 |has| (-407 |#2|) (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|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)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-350 R UP -3191) +(-350 R UP -3195) ((|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|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)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|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}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|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)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -3191 GF) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -3195 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 -3191 FP FPP) +(-358 -3195 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}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4404 . T)) +((-4405 . T)) NIL (-362 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1382,7 +1382,7 @@ NIL NIL (-363) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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 (-555)))) (-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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4404 |has| |#1| (-555)) (-4402 . T) (-4401 . T)) +((-4405 |has| |#1| (-555)) (-4403 . T) (-4402 . T)) NIL (-368) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) NIL (-371 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093)))) +((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093)))) (-373 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4407 . T)) +((-4408 . T)) NIL (-374 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4402 . T) (-4401 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4403 . T) (-4402 . 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 -636) (QUOTE (-563))))) (-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}"))) -((-4404 . T)) +((-4405 . 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}."))) -((-4390 . T) (-4398 . T) (-1403 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4391 . T) (-4399 . T) (-1402 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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}"))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . 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}."))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . 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."))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1478,7 +1478,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-846)))) (-387) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-388) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1490,13 +1490,13 @@ NIL NIL (-390 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . 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 -3191 UP UPUP R) +(-392 -3195 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 -3348 |returnType| -4093 |symbols|) +(-398 -3352 |returnType| -4094 |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 -3191 UP) +(-399 -3195 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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-403 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4390)) (|HasAttribute| |#1| (QUOTE -4398))) +((|HasAttribute| |#1| (QUOTE -4391)) (|HasAttribute| |#1| (QUOTE -4399))) (-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\"."))) -((-1403 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-1402 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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."))) -((-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 (-1169)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-4032 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|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 -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4395 -12 (|has| |#1| (-6 -4406)) (|has| |#1| (-452)) (|has| |#1| (-6 -4395))) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-4034 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|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 -4406)) (|HasAttribute| |#1| (QUOTE -4395)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (-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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) NIL (-410 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -3191 UP A) +(-413 R -3195 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4404 . T)) +((-4405 . T)) NIL -(-414 R -3191 UP A |ibasis|) +(-414 R -3195 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."))) -((-4404 |has| |#1| (-555)) (-4402 . T) (-4401 . T)) +((-4405 |has| |#1| (-555)) (-4403 . T) (-4402 . 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."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1212))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|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 (-1169)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1212))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|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 (-1169)))) (|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4407 . T) (-4397 . T) (-4408 . T)) +((-4408 . T) (-4398 . T) (-4409 . T)) NIL -(-426 R -3191) +(-426 R -3195) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-427 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-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 -3191) +((-4395 -12 (|has| |#1| (-6 -4395)) (|has| |#2| (-6 -4395))) (-4402 . T) (-4403 . T) (-4405 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4395)) (|HasAttribute| |#2| (QUOTE -4395)))) +(-428 R -3195) ((|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 (-563)))) (|HasCategory| |#2| (QUOTE (-555))) (|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 (-1105))) (|HasCategory| |#2| (LIST (QUOTE -611) (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}."))) -((-4404 -4032 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-555)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-555)) (-4399 |has| |#1| (-555))) +((-4405 -4034 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) ((-4410 "*") |has| |#1| (-555)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-555)) (-4400 |has| |#1| (-555))) NIL -(-431 R -3191) +(-431 R -3195) ((|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 -3191) +(-432 R -3195) ((|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 -3191) +(-433 R -3195) ((|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 -3191 UP) +(-435 R -3195 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 -3191) +(-443 R UP -3195) ((|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}."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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"))) -((-4404 |has| (-407 (-948 |#1|)) (-555)) (-4402 . T) (-4401 . T)) +((-4405 |has| (-407 (-948 |#1|)) (-555)) (-4403 . T) (-4402 . T)) ((|HasCategory| (-407 (-948 |#1|)) (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| (-407 (-948 |#1|)) (QUOTE (-555)))) (-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"))) -(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-555)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-555)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (-4034 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4034 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (-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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . T)) NIL (-462 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1782,7 +1782,7 @@ NIL NIL (-463 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#4| (LIST (QUOTE -610) (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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-471 |lv| -3191 R) +(-471 |lv| -3195 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1822,23 +1822,23 @@ NIL NIL (-473) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4404 . T)) +((-4405 . T)) NIL (-474 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4032 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3698) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2606) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1692) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4034 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2605) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|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."))) -((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093)))) +((-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#2|)))))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093)))) (-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)}"))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (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}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#2|)))))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (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 (-1169))))) (-4034 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|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}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) -(-485 -3191 UP UPUP R) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +(-485 -3195 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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4032 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145))))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4034 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (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 -4407)) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) +((|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,33 +1904,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -3191 UP |AlExt| |AlPol|) +(-494 -3195 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-495) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|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."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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 -3191) +(-499 R UP -3195) ((|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}."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -610) (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 -3191 |Expon| |VarSet| |DPoly|) +(-504 -3195 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-1169))))) @@ -1994,36 +1994,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-788)))) (-516 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|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}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((-4032 (|HasCategory| (-580 |#1|) (QUOTE (-145))) (|HasCategory| (-580 |#1|) (QUOTE (-368)))) (|HasCategory| (-580 |#1|) (QUOTE (-147))) (|HasCategory| (-580 |#1|) (QUOTE (-368))) (|HasCategory| (-580 |#1|) (QUOTE (-145)))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4034 (|HasCategory| (-580 |#1|) (QUOTE (-145))) (|HasCategory| (-580 |#1|) (QUOTE (-368)))) (|HasCategory| (-580 |#1|) (QUOTE (-147))) (|HasCategory| (-580 |#1|) (QUOTE (-368))) (|HasCategory| (-580 |#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}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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."))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|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 -4408))) +((|HasAttribute| |#3| (QUOTE -4409))) (-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 -4408))) +((|HasAttribute| |#7| (QUOTE -4409))) (-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."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (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 -3191 |Par|) +(-532 K -3195 |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 -3191 |Par|) +(-538 K -3195 |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."))) -((-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4406 . T) (-4407 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-546) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2126,13 +2126,13 @@ NIL NIL (-549 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) -(-550 R -3191) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#2|)))))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) +(-550 R -3195) ((|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 -(-551 R0 -3191 UP UPUP R) +(-551 R0 -3195 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 @@ -2142,7 +2142,7 @@ NIL NIL (-553 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."))) -((-1403 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-1402 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-554 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."))) @@ -2150,9 +2150,9 @@ NIL NIL (-555) ((|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."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-556 R -3191) +(-556 R -3195) ((|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 @@ -2164,7 +2164,7 @@ 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 -(-559 R -3191 L) +(-559 R -3195 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 -651) (|devaluate| |#2|)))) @@ -2172,31 +2172,31 @@ 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 -(-561 -3191 UP UPUP R) +(-561 -3195 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 -(-562 -3191 UP) +(-562 -3195 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 (-563) ((|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}."))) -((-4389 . T) (-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4390 . T) (-4396 . T) (-4400 . T) (-4395 . T) (-4406 . T) (-4407 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-564) ((|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 -(-565 R -3191 L) +(-565 R -3195 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 -651) (|devaluate| |#2|)))) -(-566 R -3191) +(-566 R -3195) ((|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 -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-626))))) -(-567 -3191 UP) +(-567 -3195 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 @@ -2204,27 +2204,27 @@ 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 -(-569 -3191) +(-569 -3195) ((|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 (-570 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."))) -((-1403 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-1402 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-571) ((|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 -(-572 R -3191) +(-572 R -3195) ((|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 -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-626))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-555)))) -(-573 -3191 UP) +(-573 -3195 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 -(-574 R -3191) +(-574 R -3195) ((|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 @@ -2246,27 +2246,27 @@ NIL NIL (-579 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-580 |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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) (-581) ((|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 -(-582 R -3191) +(-582 R -3195) ((|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 -(-583 E -3191) +(-583 E -3195) ((|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 -(-584 -3191) +(-584 -3195) ((|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}."))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . T)) ((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1169))))) (-585 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"))) @@ -2294,19 +2294,19 @@ NIL NIL (-591 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-4032 (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-4034 (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-592 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 (-593 |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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-563)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-563)) (|devaluate| |#1|)))) (|HasCategory| (-563) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-563)))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-563)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-563)) (|devaluate| |#1|)))) (|HasCategory| (-563) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -1692) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-563)))))) (-594 |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.}"))) -((-4402 |has| |#1| (-555)) (-4401 |has| |#1| (-555)) ((-4409 "*") |has| |#1| (-555)) (-4400 |has| |#1| (-555)) (-4404 . T)) +((-4403 |has| |#1| (-555)) (-4402 |has| |#1| (-555)) ((-4410 "*") |has| |#1| (-555)) (-4401 |has| |#1| (-555)) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-555)))) (-595 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),{}..]}."))) @@ -2316,7 +2316,7 @@ 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 -(-597 R -3191 FG) +(-597 R -3195 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 @@ -2326,12 +2326,12 @@ NIL NIL (-599 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|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 -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|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 -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-600 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 -4408)) (|HasCategory| |#2| (QUOTE (-846))) (|HasAttribute| |#1| (QUOTE -4407)) (|HasCategory| |#3| (QUOTE (-1093)))) +((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-846))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#3| (QUOTE (-1093)))) (-601 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2346,19 +2346,19 @@ NIL NIL (-604 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4404 -4032 (-2190 (|has| |#2| (-367 |#1|)) (|has| |#1| (-555))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-555)))) (-4402 . T) (-4401 . T)) -((-4032 (|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|)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4405 -4034 (-2188 (|has| |#2| (-367 |#1|)) (|has| |#1| (-555))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-555)))) (-4403 . T) (-4402 . T)) +((-4034 (|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|)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-605 |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."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (LIST (QUOTE -610) (QUOTE (-858))))) (-606 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 (-607 |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}."))) -((-4408 . T)) +((-4409 . T)) NIL (-608 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"))) @@ -2376,7 +2376,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-612 -3191 UP) +(-612 -3195 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2398,19 +2398,19 @@ NIL NIL (-617 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."))) -((-4404 . T)) +((-4405 . T)) NIL (-618 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}."))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-844)))) -(-619 R -3191) +(-619 R -3195) ((|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 (-620 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"))) -((-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4400 . T) (-4404 . T)) +((-4403 . T) (-4402 . T) ((-4410 "*") . T) (-4401 . T) (-4405 . T)) ((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|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 (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (-621 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."))) @@ -2426,7 +2426,7 @@ NIL NIL (-624 |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}}."))) -((-4404 . T)) +((-4405 . T)) NIL (-625 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}}."))) @@ -2436,30 +2436,30 @@ 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 -(-627 R -3191) +(-627 R -3195) ((|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 -(-628 |lv| -3191) +(-628 |lv| -3195) ((|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 (-629) ((|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."))) -((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2557) (QUOTE (-52))))))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1151) (QUOTE (-846))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (QUOTE (-1093)))) +((-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2556) (QUOTE (-52))))))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1151) (QUOTE (-846))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (QUOTE (-1093)))) (-630 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-631 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4402 . T) (-4401 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4403 . T) (-4402 . T)) NIL (-632 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4404 -4032 (-2190 (|has| |#2| (-367 |#1|)) (|has| |#1| (-555))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-555)))) (-4402 . T) (-4401 . T)) -((-4032 (|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|)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4405 -4034 (-2188 (|has| |#2| (-367 |#1|)) (|has| |#1| (-555))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-555)))) (-4403 . T) (-4402 . T)) +((-4034 (|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|)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-633 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 @@ -2471,10 +2471,10 @@ NIL (-635 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 -((-2176 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-2174 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-636 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}."))) -((-4404 . T)) +((-4405 . T)) NIL (-637 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}."))) @@ -2490,16 +2490,16 @@ NIL NIL (-640 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."))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-641 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL (-642 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-643 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2511,22 +2511,22 @@ NIL (-645 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 -4408))) +((|HasAttribute| |#1| (QUOTE -4409))) (-646 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 -(-647 R -3191 L) +(-647 R -3195 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 (-648 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}}"))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-649 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-650 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2534,15 +2534,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-651 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}."))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-652 -3191 UP) +(-652 -3195 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)))) -(-653 A -3397) +(-653 A -4231) ((|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}}"))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-654 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."))) @@ -2558,7 +2558,7 @@ NIL NIL (-657 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}."))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . T)) ((|HasCategory| |#1| (QUOTE (-787)))) (-658 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."))) @@ -2566,7 +2566,7 @@ NIL NIL (-659 |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) (-4402 . T) (-4401 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4403 . T) (-4402 . T)) ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-172)))) (-660 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}."))) @@ -2574,13 +2574,13 @@ NIL NIL (-661 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}."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) NIL -(-662 -3191) +(-662 -3195) ((|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 -(-663 -3191 |Row| |Col| M) +(-663 -3195 |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 @@ -2590,8 +2590,8 @@ NIL NIL (-665 |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."))) -((-4404 . T) (-4407 . T) (-4401 . T) (-4402 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-555))) (-4032 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4405 . T) (-4408 . T) (-4402 . T) (-4403 . T)) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-555))) (-4034 (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-666) ((|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 @@ -2611,7 +2611,7 @@ NIL (-670 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 -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-671) ((|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 @@ -2655,10 +2655,10 @@ NIL (-681 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 (-4409 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-555)))) +((|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-555)))) (-682 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"))) -((-4407 . T) (-4408 . T)) +((-4408 . T) (-4409 . T)) NIL (-683 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."))) @@ -2666,8 +2666,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555)))) (-684 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."))) -((-4407 . T) (-4408 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4409 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-685 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 @@ -2676,7 +2676,7 @@ 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 -(-687 S -3191 FLAF FLAS) +(-687 S -3195 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 @@ -2686,11 +2686,11 @@ NIL NIL (-689) ((|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"))) -((-4400 . T) (-4405 |has| (-694) (-363)) (-4399 |has| (-694) (-363)) (-1413 . T) (-4406 |has| (-694) (-6 -4406)) (-4403 |has| (-694) (-6 -4403)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-694) (QUOTE (-147))) (|HasCategory| (-694) (QUOTE (-145))) (|HasCategory| (-694) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-694) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-694) (QUOTE (-368))) (|HasCategory| (-694) (QUOTE (-363))) (-4032 (|HasCategory| (-694) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-694) (QUOTE (-363)))) (|HasCategory| (-694) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-694) (QUOTE (-233))) (-4032 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-349)))) (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (LIST (QUOTE -286) (QUOTE (-694)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -309) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-694) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-694) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-694) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (-4032 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-349)))) (|HasCategory| (-694) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-694) (QUOTE (-1018))) (|HasCategory| (-694) (QUOTE (-1193))) (-12 (|HasCategory| (-694) (QUOTE (-998))) (|HasCategory| (-694) (QUOTE (-1193)))) (-4032 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-363))) (-12 (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (QUOTE (-905))))) (-4032 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (-12 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-905)))) (-12 (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (QUOTE (-905))))) (|HasCategory| (-694) (QUOTE (-545))) (-12 (|HasCategory| (-694) (QUOTE (-1054))) (|HasCategory| (-694) (QUOTE (-1193)))) (|HasCategory| (-694) (QUOTE (-1054))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905))) (-4032 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-363)))) (-4032 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-555)))) (-12 (|HasCategory| (-694) (QUOTE (-233))) (|HasCategory| (-694) (QUOTE (-363)))) (-12 (|HasCategory| (-694) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-694) (QUOTE (-363)))) (|HasCategory| (-694) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-694) (QUOTE (-846))) (|HasCategory| (-694) (QUOTE (-555))) (|HasAttribute| (-694) (QUOTE -4406)) (|HasAttribute| (-694) (QUOTE -4403)) (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-145)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-349))))) +((-4401 . T) (-4406 |has| (-694) (-363)) (-4400 |has| (-694) (-363)) (-1413 . T) (-4407 |has| (-694) (-6 -4407)) (-4404 |has| (-694) (-6 -4404)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-694) (QUOTE (-147))) (|HasCategory| (-694) (QUOTE (-145))) (|HasCategory| (-694) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-694) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-694) (QUOTE (-368))) (|HasCategory| (-694) (QUOTE (-363))) (-4034 (|HasCategory| (-694) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-694) (QUOTE (-363)))) (|HasCategory| (-694) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-694) (QUOTE (-233))) (-4034 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-349)))) (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (LIST (QUOTE -286) (QUOTE (-694)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -309) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-694) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-694) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-694) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (-4034 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-349)))) (|HasCategory| (-694) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-694) (QUOTE (-1018))) (|HasCategory| (-694) (QUOTE (-1193))) (-12 (|HasCategory| (-694) (QUOTE (-998))) (|HasCategory| (-694) (QUOTE (-1193)))) (-4034 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-363))) (-12 (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (QUOTE (-905))))) (-4034 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (-12 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-905)))) (-12 (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (QUOTE (-905))))) (|HasCategory| (-694) (QUOTE (-545))) (-12 (|HasCategory| (-694) (QUOTE (-1054))) (|HasCategory| (-694) (QUOTE (-1193)))) (|HasCategory| (-694) (QUOTE (-1054))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905))) (-4034 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-363)))) (-4034 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-555)))) (-12 (|HasCategory| (-694) (QUOTE (-233))) (|HasCategory| (-694) (QUOTE (-363)))) (-12 (|HasCategory| (-694) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-694) (QUOTE (-363)))) (|HasCategory| (-694) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-694) (QUOTE (-846))) (|HasCategory| (-694) (QUOTE (-555))) (|HasAttribute| (-694) (QUOTE -4407)) (|HasAttribute| (-694) (QUOTE -4404)) (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-145)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-349))))) (-690 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}."))) -((-4408 . T)) +((-4409 . T)) NIL (-691 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}."))) @@ -2700,13 +2700,13 @@ 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 -(-693 OV E -3191 PG) +(-693 OV E -3195 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 (-694) ((|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}"))) -((-1403 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-1402 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-695 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."))) @@ -2714,7 +2714,7 @@ NIL NIL (-696) ((|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}"))) -((-4406 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4407 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-697 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 -3209 I) +(-702 S -3213 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)}.}"))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . 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| -2472 -3164 |exactQuo|) +(-707 R |Mod| -4219 -4300 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-708 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|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)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (-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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) +((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-711 R |Mod| -2472 -3164 |exactQuo|) +(-711 R |Mod| -4219 -4300 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4404 . T)) +((-4405 . 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"))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . T)) NIL -(-714 -3191) +(-714 -3195) ((|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]]}."))) -((-4404 . T)) +((-4405 . 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."))) -((-4400 |has| |#1| (-363)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 |has| |#1| (-363)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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 -3191 UP) +(-723 -3195 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."))) -(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-555)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-555)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (-4034 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4034 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (-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}."))) -((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) +((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . 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."))) -((-4397 . T) (-4408 . T)) +((-4398 . T) (-4409 . 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}."))) -((-4407 . T) (-4397 . T) (-4408 . T)) +((-4408 . T) (-4398 . T) (-4409 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4402 . T) (-4401 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4403 . T) (-4402 . T) (-4405 . 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}."))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . 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 -3191) +(-761 -3195) ((|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 -3191) +(-762 P -3195) ((|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 -3191) +(-764 UP -3195) ((|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."))) -(((-4409 "*") . T)) +(((-4410 "*") . T)) NIL -(-768 R -3191) +(-768 R -3195) ((|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 -3191 |ExtF| |SUEx| |ExtP| |n|) +(-773 -3195 |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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . 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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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T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . 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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 (-563)))))) (-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.}"))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . 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 -611) (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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-794 -4032 R OS S) +(-794 -4034 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-795 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-4032 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4032 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) +((-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-4034 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4034 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (-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 -3191 L) +(-797 R -3195 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 -3191) +(-798 R -3195) ((|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 -3191) +(-800 R -3195) ((|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 -3191 UP UPUP R) +(-802 -3195 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 -3191 UP L LQ) +(-803 -3195 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 -3191 UP L LQ) +(-805 -3195 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 -3191 UP) +(-806 -3195 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 -3191 L UP A LO) +(-807 -3195 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 -3191 UP) +(-808 -3195 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 -3191 LO) +(-809 -3195 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 -3191 LODO) +(-810 -3195 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 -3304 S |f|) +(-811 -3308 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}."))) -((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST 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T)) +((|HasCategory| |#1| (QUOTE (-905))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (-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."))) -(((-4409 "*") |has| |#2| (-363)) (-4400 |has| |#2| (-363)) (-4405 |has| |#2| (-363)) (-4399 |has| |#2| (-363)) (-4404 . T) (-4402 . T) (-4401 . T)) +(((-4410 "*") |has| |#2| (-363)) (-4401 |has| |#2| (-363)) (-4406 |has| |#2| (-363)) (-4400 |has| |#2| (-363)) (-4405 . T) (-4403 . T) (-4402 . 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"))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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}."))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . 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}."))) -((-4407 . T) (-4397 . T) (-4408 . T)) +((-4408 . T) (-4398 . T) (-4409 . 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."))) -((-4404 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-4032 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4032 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4405 |has| |#1| (-844))) +((|HasCategory| |#1| (QUOTE (-844))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4034 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|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."))) -((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) +((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4404 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-4032 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4032 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4405 |has| |#1| (-844))) +((|HasCategory| |#1| (QUOTE (-844))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4034 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-840) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-841 -3304 S) +(-841 -3308 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3306,7 +3306,7 @@ NIL NIL (-844) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4404 . T)) +((-4405 . T)) NIL (-845 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3322,7 +3322,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172)))) (-848 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . 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."))) @@ -3330,11 +3330,11 @@ NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-850 R |sigma| -1648) ((|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."))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-851 |x| R |sigma| -1648) ((|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}."))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-555))) (|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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) +((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (-863 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3390,24 +3390,24 @@ NIL NIL (-865 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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)."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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)."))) -((-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 (-1169)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-4032 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (QUOTE (-1144))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (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)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-4034 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (QUOTE (-1144))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (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)))) (-4034 (-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)}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-4032 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1169)) (|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)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-4034 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1169)) (|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)))) (-4034 (-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 (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (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 (-2176 (|HasCategory| |#2| (QUOTE (-1045)))) (-2176 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2176 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169))))) +((-12 (-2174 (|HasCategory| |#2| (QUOTE (-1045)))) (-2174 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2174 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169))))) (-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 -3209) +(-886 R -3213) ((|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 -3191) +(-892 UP -3195) ((|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}."))) -((-4404 . T)) +((-4405 . 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 (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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."))) -((-4404 . T)) +((-4405 . 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."))) -((-4404 . T)) -((-4032 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) +((-4405 . T)) +((-4034 (|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}."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-907 R0 -3191 UP UPUP R) +(-907 R0 -3195 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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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 -3191) +(-914 -3195) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-917) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4409 "*") . T)) +(((-4410 "*") . T)) NIL -(-918 -3191 P) +(-918 -3195 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-919 |xx| -3191) +(-919 |xx| -3195) ((|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 -3191) +(-925 R -3195) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -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 -3191) +(-928 S R -3195) ((|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 -3191 -3209) +(-933 R -3195 -3213) ((|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 -3209) +(-934 -3213) ((|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"))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|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 -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|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 -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|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 -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 (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-846)))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasAttribute| |#2| (QUOTE -4406)) (|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 (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL -(-946 E V R P -3191) +(-946 E V R P -3195) ((|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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-949 E V R P -3191) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-949 E V R P -3195) ((|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"))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|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 -3191) +(-956 -3195) ((|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}"))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4405))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4406))) (-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"))) -((-4404 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-4032 (-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)))) (-4032 (-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)))) (-4032 (-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))))) +((-4405 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) +((-4034 (-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)))) (-4034 (-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)))) (-4034 (-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)))) (-4034 (-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)))) (-4034 (-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| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3786,7 +3786,7 @@ NIL NIL (-964 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4407 . T) (-4408 . T)) +((-4408 . T) (-4409 . 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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . 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 (-555)))) (-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."))) -((-4407 . T)) +((-4408 . 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}."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . 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 -3191) +(-981 K R UP -3195) ((|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 (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1144)))) (-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}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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."))) -((-4407 . T) (-4408 . T)) +((-4408 . T) (-4409 . 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 -611) (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}."))) -((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 |has| |#1| (-290)) (-4402 . T) (-4403 . T) (-4405 . 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.}"))) -((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|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 (-1169)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) +((-4401 |has| |#1| (-290)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|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 (-1169)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|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}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (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 -3191 UP UPUP |radicnd| |n|) +(-999 -3195 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-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))) (-4032 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4032 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4032 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-563)))) (-4032 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +((-4401 |has| (-407 |#2|) (-363)) (-4406 |has| (-407 |#2|) (-363)) (-4400 |has| (-407 |#2|) (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4034 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4034 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4034 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-563)))) (-4034 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4032 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145))))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4034 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (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 -4408)) (|HasCategory| |#2| (QUOTE (-1093)))) +((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-1093)))) (-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}}"))) -((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) +((-4401 . T) (-4406 . T) (-4400 . T) (-4403 . T) (-4402 . T) ((-4410 "*") . T) (-4405 . T)) NIL -(-1009 R -3191) +(-1009 R -3195) ((|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 -3191) +(-1010 R -3195) ((|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 -3191 UP) +(-1011 -3195 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 -3191 UP) +(-1012 -3195 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"))) -((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) -((-4032 (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (QUOTE (-563))))) -(-1021 -3191 L) +((-4401 . T) (-4406 . T) (-4400 . T) (-4403 . T) (-4402 . T) ((-4410 "*") . T) (-4405 . T)) +((-4034 (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (QUOTE (-563))))) +(-1021 -3195 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 (-1093)))) (-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."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (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 (-4409 "*")))) +((|HasAttribute| |#1| (QUOTE (-4410 "*")))) (-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 -3191 |Expon| |VarSet| |FPol| |LFPol|) +(-1030 -3195 |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"))) -(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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.}"))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -2557) (QUOTE (-52))))))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -2556) (QUOTE (-52))))))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1093))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -610) (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}."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) ((-12 (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1093))) (|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 -611) (QUOTE (-536)))) (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| (-860 |#2|) (QUOTE (-368))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -610) (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."))) -((-4404 . T)) +((-4405 . T)) NIL -(-1046 |xx| -3191) +(-1046 |xx| -3195) ((|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 (-555))) (|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"))) -((-4407 . T) (-4402 . T) (-4401 . T)) +((-4408 . T) (-4403 . T) (-4402 . 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}."))) -((-4407 . T) (-4402 . T) (-4401 . T)) -((-4032 (-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 (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4403 . T) (-4402 . T)) +((-4034 (-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 (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -610) (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."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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."))) -((-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4396 . T) (-4400 . T) (-4395 . T) (-4406 . T) (-4407 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . 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}"))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -2557) (QUOTE (-52))))))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -2556) (QUOTE (-52))))))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (QUOTE (-1093))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1093))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (LIST (QUOTE -610) (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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -988) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-1169))))) (-1059 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . 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}."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . 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."))) @@ -4204,11 +4204,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1069 |Base| R -3191) +(-1069 |Base| R -3195) ((|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 -(-1070 |Base| R -3191) +(-1070 |Base| R -3195) ((|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 @@ -4222,8 +4222,8 @@ NIL NIL (-1073 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."))) -((-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))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((-4401 |has| |#1| (-363)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1074 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 @@ -4250,8 +4250,8 @@ NIL NIL (-1080 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"))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1081 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 @@ -4294,7 +4294,7 @@ NIL NIL (-1091 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}."))) -((-4397 . T)) +((-4398 . T)) NIL (-1092 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}."))) @@ -4310,8 +4310,8 @@ NIL NIL (-1095 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)}}"))) -((-4407 . T) (-4397 . T) (-4408 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4408 . T) (-4398 . T) (-4409 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1096 |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 @@ -4338,7 +4338,7 @@ NIL NIL (-1102 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.}"))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) NIL (-1103) ((|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."))) @@ -4354,8 +4354,8 @@ NIL NIL (-1106 |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}."))) -((-4401 |has| |#3| (-1045)) (-4402 |has| |#3| (-1045)) (-4404 |has| |#3| (-6 -4404)) ((-4409 "*") |has| |#3| (-172)) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST 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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 @@ -4364,7 +4364,7 @@ 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 -(-1109 R -3191) +(-1109 R -3195) ((|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 @@ -4382,19 +4382,19 @@ NIL NIL (-1113) ((|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."))) -((-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4396 . T) (-4400 . T) (-4395 . T) (-4406 . T) (-4407 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1114 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4407 . T) (-4408 . T)) +((-4408 . T) (-4409 . T)) NIL (-1115 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-4409 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) +((|HasCategory| |#3| (QUOTE (-363))) (|HasAttribute| |#3| (QUOTE (-4410 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) (-1116 |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."))) -((-4407 . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4408 . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1117 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}."))) @@ -4402,17 +4402,17 @@ NIL NIL (-1118 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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1119 |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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363)))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363)))) (-1120 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}"))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) NIL -(-1121 UP -3191) +(-1121 UP -3195) ((|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 @@ -4466,19 +4466,19 @@ NIL NIL (-1134 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093))) (-4032 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093))))) (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093))) (-4034 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093))))) (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-858))))) (-1135 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4404 . T) (-4396 |has| |#2| (-6 (-4409 "*"))) (-4407 . T) (-4401 . T) (-4402 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-363))) (-4032 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4405 . T) (-4397 |has| |#2| (-6 (-4410 "*"))) (-4408 . T) (-4402 . T) (-4403 . T)) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-363))) (-4034 (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1136 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1137) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) NIL (-1138 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.}"))) @@ -4486,12 +4486,12 @@ NIL NIL (-1139 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."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858))))) (-1140 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}."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-1141 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 @@ -4502,8 +4502,8 @@ NIL NIL (-1143 |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."))) -((-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093)))) +((-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#2|)))))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093)))) (-1144) ((|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 @@ -4526,20 +4526,20 @@ NIL NIL (-1149 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."))) -((-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-1150) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) NIL (-1151) NIL -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1152 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4407 . T) (-4408 . T)) -((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#1|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -610) (QUOTE (-858))))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#1|)))))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (QUOTE (-1093))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (LIST (QUOTE -610) (QUOTE (-858))))) (-1153 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 @@ -4570,9 +4570,9 @@ NIL NIL (-1160 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|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 (-1105))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3698) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2606) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|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 (-1105))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -1692) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2605) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) (-1168) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4614,8 +4614,8 @@ NIL NIL (-1171 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasAttribute| |#1| (QUOTE -4405))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4034 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasAttribute| |#1| (QUOTE -4406))) (-1172) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4641,7 +4641,7 @@ NIL NIL NIL (-1178) -((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension()} returns a string representation of a filename extension for native modules.")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform()} returns a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) +((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL (-1179 S) @@ -4654,8 +4654,8 @@ NIL NIL (-1181 |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}"))) -((-4407 . T) (-4408 . 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T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2556) (|devaluate| |#2|)))))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4034 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) (-1182 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 @@ -4666,7 +4666,7 @@ NIL NIL (-1184 |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})}."))) -((-4408 . T)) +((-4409 . T)) NIL (-1185 |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."))) @@ -4706,8 +4706,8 @@ NIL NIL (-1194 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4408 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +((-4409 . T) (-4408 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-1195 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4716,7 +4716,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1197 R -3191) +(-1197 R -3195) ((|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 @@ -4724,7 +4724,7 @@ 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 -(-1199 R -3191) +(-1199 R -3195) ((|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 -611) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) @@ -4734,12 +4734,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-368)))) (-1201 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) NIL (-1202 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363)))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363)))) (-1203 |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 @@ -4752,7 +4752,7 @@ 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 (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) -(-1206 -3191) +(-1206 -3195) ((|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 @@ -4778,7 +4778,7 @@ NIL NIL (-1212) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1213) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4798,7 +4798,7 @@ NIL NIL (-1217 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1218 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)}."))) @@ -4806,16 +4806,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-1219 |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)}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1220 |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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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 @@ -4850,8 +4850,8 @@ NIL NIL (-1230 |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}"))) -(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-555)) (-4403 |has| |#2| (-363)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-555)) (-4404 |has| |#2| (-363)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4034 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4034 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4034 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1231 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 @@ -4862,15 +4862,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1144)))) (-1233 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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL (-1234 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 (-1169)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1105))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1693) (LIST (|devaluate| |#2|) (QUOTE (-1169)))))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1105))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1692) (LIST (|devaluate| |#2|) (QUOTE (-1169)))))) (-1235 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1236 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4882,7 +4882,7 @@ NIL NIL (-1238 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1239 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)}."))) @@ -4890,24 +4890,24 @@ NIL NIL (-1240 |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)}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1241 |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)}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4032 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3698) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2606) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1692) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4034 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2605) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-1242 |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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4032 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3698) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2606) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4034 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1692) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4034 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2605) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) (-1243 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))}."))) -(((-4409 "*") |has| (-1242 |#2| |#3| |#4|) (-172)) (-4400 |has| (-1242 |#2| |#3| |#4|) (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-172))) (-4032 (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-555)))) +(((-4410 "*") |has| (-1242 |#2| |#3| |#4|) (-172)) (-4401 |has| (-1242 |#2| |#3| |#4|) (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-172))) (-4034 (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-555)))) (-1244 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4408))) +((|HasAttribute| |#1| (QUOTE -4409))) (-1245 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4919,20 +4919,20 @@ NIL (-1247 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-563)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1193))) (|HasSignature| |#2| (LIST (QUOTE -2606) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3698) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1193))) (|HasSignature| |#2| (LIST (QUOTE -2605) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2062) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1248 |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."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1249 |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}."))) -(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|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 (-1105))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3698) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2606) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4034 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|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 (-1105))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -1692) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2605) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) (-1250 |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 -(-1251 -3191 UP L UTS) +(-1251 -3195 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 (-555)))) @@ -4950,7 +4950,7 @@ 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)))) (-1255 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) NIL (-1256 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4958,8 +4958,8 @@ NIL NIL (-1257 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4408 . T) (-4407 . T)) -((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|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 -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4409 . T) (-4408 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4034 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|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 -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1258) ((|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|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4986,13 +4986,13 @@ NIL NIL (-1264 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4402 . T) (-4401 . T)) +((-4403 . T) (-4402 . T)) NIL (-1265 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 -(-1266 K R UP -3191) +(-1266 K R UP -3195) ((|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 @@ -5006,56 +5006,56 @@ NIL NIL (-1269 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)"))) -((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) +((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (-1270 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}}."))) -((-4408 . T) (-4407 . T)) +((-4409 . T) (-4408 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858))))) (-1271 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})"))) -((-4401 . T) (-4402 . T) (-4404 . T)) +((-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1272 |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."))) -((-4404 . T) (-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4400))) +((-4405 . T) (-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4401))) (-1273 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 (-1274 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) +((-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL -(-1275 S -3191) +(-1275 S -3195) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1276 -3191) +(-1276 -3195) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1277 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasAttribute| |#2| (QUOTE -4400))) +((-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasAttribute| |#2| (QUOTE -4401))) (-1278 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) +((-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL (-1279 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4400 |has| |#1| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4400))) +((-4401 |has| |#1| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4401))) (-1280 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-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))) +((-4405 . T) (-4406 |has| |#1| (-6 -4406)) (-4401 |has| |#1| (-6 -4401)) (-4403 . T) (-4402 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4406)) (|HasAttribute| |#1| (QUOTE -4401))) (-1281 |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."))) -((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4400))) +((-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4401))) (-1282 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 @@ -5070,7 +5070,7 @@ NIL NIL (-1285 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) +(((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL NIL NIL @@ -5088,4 +5088,4 @@ NIL NIL NIL NIL -((-3 NIL 2282794 2282799 2282804 2282809) (-2 NIL 2282774 2282779 2282784 2282789) (-1 NIL 2282754 2282759 2282764 2282769) (0 NIL 2282734 2282739 2282744 2282749) (-1285 "ZMOD.spad" 2282543 2282556 2282672 2282729) (-1284 "ZLINDEP.spad" 2281587 2281598 2282533 2282538) (-1283 "ZDSOLVE.spad" 2271436 2271458 2281577 2281582) (-1282 "YSTREAM.spad" 2270929 2270940 2271426 2271431) (-1281 "XRPOLY.spad" 2270149 2270169 2270785 2270854) (-1280 "XPR.spad" 2267940 2267953 2269867 2269966) (-1279 "XPOLY.spad" 2267495 2267506 2267796 2267865) (-1278 "XPOLYC.spad" 2266812 2266828 2267421 2267490) (-1277 "XPBWPOLY.spad" 2265249 2265269 2266592 2266661) (-1276 "XF.spad" 2263710 2263725 2265151 2265244) (-1275 "XF.spad" 2262151 2262168 2263594 2263599) (-1274 "XFALG.spad" 2259175 2259191 2262077 2262146) (-1273 "XEXPPKG.spad" 2258426 2258452 2259165 2259170) (-1272 "XDPOLY.spad" 2258040 2258056 2258282 2258351) (-1271 "XALG.spad" 2257700 2257711 2257996 2258035) (-1270 "WUTSET.spad" 2253539 2253556 2257346 2257373) (-1269 "WP.spad" 2252738 2252782 2253397 2253464) (-1268 "WHILEAST.spad" 2252536 2252545 2252728 2252733) (-1267 "WHEREAST.spad" 2252207 2252216 2252526 2252531) (-1266 "WFFINTBS.spad" 2249770 2249792 2252197 2252202) (-1265 "WEIER.spad" 2247984 2247995 2249760 2249765) (-1264 "VSPACE.spad" 2247657 2247668 2247952 2247979) (-1263 "VSPACE.spad" 2247350 2247363 2247647 2247652) (-1262 "VOID.spad" 2247027 2247036 2247340 2247345) (-1261 "VIEW.spad" 2244649 2244658 2247017 2247022) (-1260 "VIEWDEF.spad" 2239846 2239855 2244639 2244644) (-1259 "VIEW3D.spad" 2223681 2223690 2239836 2239841) (-1258 "VIEW2D.spad" 2211418 2211427 2223671 2223676) (-1257 "VECTOR.spad" 2210093 2210104 2210344 2210371) (-1256 "VECTOR2.spad" 2208720 2208733 2210083 2210088) (-1255 "VECTCAT.spad" 2206620 2206631 2208688 2208715) (-1254 "VECTCAT.spad" 2204328 2204341 2206398 2206403) (-1253 "VARIABLE.spad" 2204108 2204123 2204318 2204323) (-1252 "UTYPE.spad" 2203752 2203761 2204098 2204103) (-1251 "UTSODETL.spad" 2203045 2203069 2203708 2203713) (-1250 "UTSODE.spad" 2201233 2201253 2203035 2203040) (-1249 "UTS.spad" 2196022 2196050 2199700 2199797) (-1248 "UTSCAT.spad" 2193473 2193489 2195920 2196017) (-1247 "UTSCAT.spad" 2190568 2190586 2193017 2193022) (-1246 "UTS2.spad" 2190161 2190196 2190558 2190563) (-1245 "URAGG.spad" 2184793 2184804 2190151 2190156) (-1244 "URAGG.spad" 2179389 2179402 2184749 2184754) (-1243 "UPXSSING.spad" 2177032 2177058 2178470 2178603) (-1242 "UPXS.spad" 2174180 2174208 2175164 2175313) (-1241 "UPXSCONS.spad" 2171937 2171957 2172312 2172461) (-1240 "UPXSCCA.spad" 2170502 2170522 2171783 2171932) (-1239 "UPXSCCA.spad" 2169209 2169231 2170492 2170497) (-1238 "UPXSCAT.spad" 2167790 2167806 2169055 2169204) (-1237 "UPXS2.spad" 2167331 2167384 2167780 2167785) (-1236 "UPSQFREE.spad" 2165743 2165757 2167321 2167326) (-1235 "UPSCAT.spad" 2163336 2163360 2165641 2165738) (-1234 "UPSCAT.spad" 2160635 2160661 2162942 2162947) (-1233 "UPOLYC.spad" 2155613 2155624 2160477 2160630) (-1232 "UPOLYC.spad" 2150483 2150496 2155349 2155354) (-1231 "UPOLYC2.spad" 2149952 2149971 2150473 2150478) (-1230 "UP.spad" 2147109 2147124 2147502 2147655) (-1229 "UPMP.spad" 2145999 2146012 2147099 2147104) (-1228 "UPDIVP.spad" 2145562 2145576 2145989 2145994) (-1227 "UPDECOMP.spad" 2143799 2143813 2145552 2145557) (-1226 "UPCDEN.spad" 2143006 2143022 2143789 2143794) (-1225 "UP2.spad" 2142368 2142389 2142996 2143001) (-1224 "UNISEG.spad" 2141721 2141732 2142287 2142292) (-1223 "UNISEG2.spad" 2141214 2141227 2141677 2141682) (-1222 "UNIFACT.spad" 2140315 2140327 2141204 2141209) (-1221 "ULS.spad" 2130867 2130895 2131960 2132389) (-1220 "ULSCONS.spad" 2123261 2123281 2123633 2123782) (-1219 "ULSCCAT.spad" 2120990 2121010 2123107 2123256) (-1218 "ULSCCAT.spad" 2118827 2118849 2120946 2120951) (-1217 "ULSCAT.spad" 2117043 2117059 2118673 2118822) (-1216 "ULS2.spad" 2116555 2116608 2117033 2117038) (-1215 "UINT8.spad" 2116432 2116441 2116545 2116550) (-1214 "UINT32.spad" 2116308 2116317 2116422 2116427) (-1213 "UINT16.spad" 2116184 2116193 2116298 2116303) (-1212 "UFD.spad" 2115249 2115258 2116110 2116179) (-1211 "UFD.spad" 2114376 2114387 2115239 2115244) (-1210 "UDVO.spad" 2113223 2113232 2114366 2114371) (-1209 "UDPO.spad" 2110650 2110661 2113179 2113184) (-1208 "TYPE.spad" 2110582 2110591 2110640 2110645) (-1207 "TYPEAST.spad" 2110501 2110510 2110572 2110577) (-1206 "TWOFACT.spad" 2109151 2109166 2110491 2110496) (-1205 "TUPLE.spad" 2108635 2108646 2109050 2109055) (-1204 "TUBETOOL.spad" 2105472 2105481 2108625 2108630) (-1203 "TUBE.spad" 2104113 2104130 2105462 2105467) (-1202 "TS.spad" 2102702 2102718 2103678 2103775) (-1201 "TSETCAT.spad" 2089829 2089846 2102670 2102697) (-1200 "TSETCAT.spad" 2076942 2076961 2089785 2089790) (-1199 "TRMANIP.spad" 2071308 2071325 2076648 2076653) (-1198 "TRIMAT.spad" 2070267 2070292 2071298 2071303) (-1197 "TRIGMNIP.spad" 2068784 2068801 2070257 2070262) (-1196 "TRIGCAT.spad" 2068296 2068305 2068774 2068779) (-1195 "TRIGCAT.spad" 2067806 2067817 2068286 2068291) (-1194 "TREE.spad" 2066377 2066388 2067413 2067440) (-1193 "TRANFUN.spad" 2066208 2066217 2066367 2066372) (-1192 "TRANFUN.spad" 2066037 2066048 2066198 2066203) (-1191 "TOPSP.spad" 2065711 2065720 2066027 2066032) (-1190 "TOOLSIGN.spad" 2065374 2065385 2065701 2065706) (-1189 "TEXTFILE.spad" 2063931 2063940 2065364 2065369) (-1188 "TEX.spad" 2061063 2061072 2063921 2063926) (-1187 "TEX1.spad" 2060619 2060630 2061053 2061058) (-1186 "TEMUTL.spad" 2060174 2060183 2060609 2060614) (-1185 "TBCMPPK.spad" 2058267 2058290 2060164 2060169) (-1184 "TBAGG.spad" 2057303 2057326 2058247 2058262) (-1183 "TBAGG.spad" 2056347 2056372 2057293 2057298) (-1182 "TANEXP.spad" 2055723 2055734 2056337 2056342) (-1181 "TABLE.spad" 2054134 2054157 2054404 2054431) (-1180 "TABLEAU.spad" 2053615 2053626 2054124 2054129) (-1179 "TABLBUMP.spad" 2050398 2050409 2053605 2053610) (-1178 "SYSTEM.spad" 2049672 2049681 2050388 2050393) (-1177 "SYSSOLP.spad" 2047145 2047156 2049662 2049667) (-1176 "SYSNNI.spad" 2046321 2046332 2047135 2047140) (-1175 "SYSINT.spad" 2045794 2045805 2046311 2046316) (-1174 "SYNTAX.spad" 2042064 2042073 2045784 2045789) (-1173 "SYMTAB.spad" 2040120 2040129 2042054 2042059) (-1172 "SYMS.spad" 2036105 2036114 2040110 2040115) (-1171 "SYMPOLY.spad" 2035112 2035123 2035194 2035321) (-1170 "SYMFUNC.spad" 2034587 2034598 2035102 2035107) (-1169 "SYMBOL.spad" 2032014 2032023 2034577 2034582) (-1168 "SWITCH.spad" 2028771 2028780 2032004 2032009) (-1167 "SUTS.spad" 2025670 2025698 2027238 2027335) (-1166 "SUPXS.spad" 2022805 2022833 2023802 2023951) (-1165 "SUP.spad" 2019574 2019585 2020355 2020508) (-1164 "SUPFRACF.spad" 2018679 2018697 2019564 2019569) (-1163 "SUP2.spad" 2018069 2018082 2018669 2018674) (-1162 "SUMRF.spad" 2017035 2017046 2018059 2018064) (-1161 "SUMFS.spad" 2016668 2016685 2017025 2017030) (-1160 "SULS.spad" 2007207 2007235 2008313 2008742) (-1159 "SUCHTAST.spad" 2006976 2006985 2007197 2007202) (-1158 "SUCH.spad" 2006656 2006671 2006966 2006971) (-1157 "SUBSPACE.spad" 1998663 1998678 2006646 2006651) (-1156 "SUBRESP.spad" 1997823 1997837 1998619 1998624) (-1155 "STTF.spad" 1993922 1993938 1997813 1997818) (-1154 "STTFNC.spad" 1990390 1990406 1993912 1993917) (-1153 "STTAYLOR.spad" 1982788 1982799 1990271 1990276) (-1152 "STRTBL.spad" 1981293 1981310 1981442 1981469) (-1151 "STRING.spad" 1980702 1980711 1980716 1980743) (-1150 "STRICAT.spad" 1980490 1980499 1980670 1980697) (-1149 "STREAM.spad" 1977348 1977359 1980015 1980030) (-1148 "STREAM3.spad" 1976893 1976908 1977338 1977343) (-1147 "STREAM2.spad" 1975961 1975974 1976883 1976888) (-1146 "STREAM1.spad" 1975665 1975676 1975951 1975956) (-1145 "STINPROD.spad" 1974571 1974587 1975655 1975660) (-1144 "STEP.spad" 1973772 1973781 1974561 1974566) (-1143 "STBL.spad" 1972298 1972326 1972465 1972480) (-1142 "STAGG.spad" 1971373 1971384 1972288 1972293) (-1141 "STAGG.spad" 1970446 1970459 1971363 1971368) (-1140 "STACK.spad" 1969797 1969808 1970053 1970080) (-1139 "SREGSET.spad" 1967501 1967518 1969443 1969470) (-1138 "SRDCMPK.spad" 1966046 1966066 1967491 1967496) (-1137 "SRAGG.spad" 1961143 1961152 1966014 1966041) (-1136 "SRAGG.spad" 1956260 1956271 1961133 1961138) (-1135 "SQMATRIX.spad" 1953876 1953894 1954792 1954879) (-1134 "SPLTREE.spad" 1948428 1948441 1953312 1953339) (-1133 "SPLNODE.spad" 1945016 1945029 1948418 1948423) (-1132 "SPFCAT.spad" 1943793 1943802 1945006 1945011) (-1131 "SPECOUT.spad" 1942343 1942352 1943783 1943788) (-1130 "SPADXPT.spad" 1934482 1934491 1942333 1942338) (-1129 "spad-parser.spad" 1933947 1933956 1934472 1934477) (-1128 "SPADAST.spad" 1933648 1933657 1933937 1933942) (-1127 "SPACEC.spad" 1917661 1917672 1933638 1933643) (-1126 "SPACE3.spad" 1917437 1917448 1917651 1917656) (-1125 "SORTPAK.spad" 1916982 1916995 1917393 1917398) (-1124 "SOLVETRA.spad" 1914739 1914750 1916972 1916977) (-1123 "SOLVESER.spad" 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(-1104 "SGROUP.spad" 1879427 1879438 1879811 1879816) (-1103 "SGCF.spad" 1872308 1872317 1879417 1879422) (-1102 "SFRTCAT.spad" 1871236 1871253 1872276 1872303) (-1101 "SFRGCD.spad" 1870299 1870319 1871226 1871231) (-1100 "SFQCMPK.spad" 1864936 1864956 1870289 1870294) (-1099 "SFORT.spad" 1864371 1864385 1864926 1864931) (-1098 "SEXOF.spad" 1864214 1864254 1864361 1864366) (-1097 "SEX.spad" 1864106 1864115 1864204 1864209) (-1096 "SEXCAT.spad" 1861657 1861697 1864096 1864101) (-1095 "SET.spad" 1859957 1859968 1861078 1861117) (-1094 "SETMN.spad" 1858391 1858408 1859947 1859952) (-1093 "SETCAT.spad" 1857876 1857885 1858381 1858386) (-1092 "SETCAT.spad" 1857359 1857370 1857866 1857871) (-1091 "SETAGG.spad" 1853880 1853891 1857339 1857354) (-1090 "SETAGG.spad" 1850409 1850422 1853870 1853875) (-1089 "SEQAST.spad" 1850112 1850121 1850399 1850404) (-1088 "SEGXCAT.spad" 1849234 1849247 1850102 1850107) (-1087 "SEG.spad" 1849047 1849058 1849153 1849158) (-1086 "SEGCAT.spad" 1847954 1847965 1849037 1849042) (-1085 "SEGBIND.spad" 1847026 1847037 1847909 1847914) (-1084 "SEGBIND2.spad" 1846722 1846735 1847016 1847021) (-1083 "SEGAST.spad" 1846436 1846445 1846712 1846717) (-1082 "SEG2.spad" 1845861 1845874 1846392 1846397) (-1081 "SDVAR.spad" 1845137 1845148 1845851 1845856) (-1080 "SDPOL.spad" 1842527 1842538 1842818 1842945) (-1079 "SCPKG.spad" 1840606 1840617 1842517 1842522) (-1078 "SCOPE.spad" 1839751 1839760 1840596 1840601) (-1077 "SCACHE.spad" 1838433 1838444 1839741 1839746) (-1076 "SASTCAT.spad" 1838342 1838351 1838423 1838428) (-1075 "SAOS.spad" 1838214 1838223 1838332 1838337) (-1074 "SAERFFC.spad" 1837927 1837947 1838204 1838209) (-1073 "SAE.spad" 1836102 1836118 1836713 1836848) (-1072 "SAEFACT.spad" 1835803 1835823 1836092 1836097) (-1071 "RURPK.spad" 1833444 1833460 1835793 1835798) (-1070 "RULESET.spad" 1832885 1832909 1833434 1833439) (-1069 "RULE.spad" 1831089 1831113 1832875 1832880) (-1068 "RULECOLD.spad" 1830941 1830954 1831079 1831084) (-1067 "RSTRCAST.spad" 1830658 1830667 1830931 1830936) (-1066 "RSETGCD.spad" 1827036 1827056 1830648 1830653) (-1065 "RSETCAT.spad" 1816820 1816837 1827004 1827031) (-1064 "RSETCAT.spad" 1806624 1806643 1816810 1816815) (-1063 "RSDCMPK.spad" 1805076 1805096 1806614 1806619) (-1062 "RRCC.spad" 1803460 1803490 1805066 1805071) (-1061 "RRCC.spad" 1801842 1801874 1803450 1803455) (-1060 "RPTAST.spad" 1801544 1801553 1801832 1801837) (-1059 "RPOLCAT.spad" 1780904 1780919 1801412 1801539) (-1058 "RPOLCAT.spad" 1759978 1759995 1780488 1780493) (-1057 "ROUTINE.spad" 1755841 1755850 1758625 1758652) (-1056 "ROMAN.spad" 1755169 1755178 1755707 1755836) (-1055 "ROIRC.spad" 1754249 1754281 1755159 1755164) (-1054 "RNS.spad" 1753152 1753161 1754151 1754244) (-1053 "RNS.spad" 1752141 1752152 1753142 1753147) (-1052 "RNG.spad" 1751876 1751885 1752131 1752136) (-1051 "RMODULE.spad" 1751514 1751525 1751866 1751871) (-1050 "RMCAT2.spad" 1750922 1750979 1751504 1751509) (-1049 "RMATRIX.spad" 1749746 1749765 1750089 1750128) (-1048 "RMATCAT.spad" 1745279 1745310 1749702 1749741) (-1047 "RMATCAT.spad" 1740702 1740735 1745127 1745132) (-1046 "RINTERP.spad" 1740590 1740610 1740692 1740697) (-1045 "RING.spad" 1740060 1740069 1740570 1740585) (-1044 "RING.spad" 1739538 1739549 1740050 1740055) (-1043 "RIDIST.spad" 1738922 1738931 1739528 1739533) (-1042 "RGCHAIN.spad" 1737501 1737517 1738407 1738434) (-1041 "RGBCSPC.spad" 1737282 1737294 1737491 1737496) (-1040 "RGBCMDL.spad" 1736812 1736824 1737272 1737277) (-1039 "RF.spad" 1734426 1734437 1736802 1736807) (-1038 "RFFACTOR.spad" 1733888 1733899 1734416 1734421) (-1037 "RFFACT.spad" 1733623 1733635 1733878 1733883) (-1036 "RFDIST.spad" 1732611 1732620 1733613 1733618) (-1035 "RETSOL.spad" 1732028 1732041 1732601 1732606) (-1034 "RETRACT.spad" 1731456 1731467 1732018 1732023) (-1033 "RETRACT.spad" 1730882 1730895 1731446 1731451) (-1032 "RETAST.spad" 1730694 1730703 1730872 1730877) (-1031 "RESULT.spad" 1728754 1728763 1729341 1729368) (-1030 "RESRING.spad" 1728101 1728148 1728692 1728749) (-1029 "RESLATC.spad" 1727425 1727436 1728091 1728096) (-1028 "REPSQ.spad" 1727154 1727165 1727415 1727420) (-1027 "REP.spad" 1724706 1724715 1727144 1727149) (-1026 "REPDB.spad" 1724411 1724422 1724696 1724701) (-1025 "REP2.spad" 1713983 1713994 1724253 1724258) (-1024 "REP1.spad" 1707973 1707984 1713933 1713938) (-1023 "REGSET.spad" 1705770 1705787 1707619 1707646) (-1022 "REF.spad" 1705099 1705110 1705725 1705730) (-1021 "REDORDER.spad" 1704275 1704292 1705089 1705094) (-1020 "RECLOS.spad" 1703058 1703078 1703762 1703855) (-1019 "REALSOLV.spad" 1702190 1702199 1703048 1703053) (-1018 "REAL.spad" 1702062 1702071 1702180 1702185) (-1017 "REAL0Q.spad" 1699344 1699359 1702052 1702057) (-1016 "REAL0.spad" 1696172 1696187 1699334 1699339) (-1015 "RDUCEAST.spad" 1695893 1695902 1696162 1696167) (-1014 "RDIV.spad" 1695544 1695569 1695883 1695888) (-1013 "RDIST.spad" 1695107 1695118 1695534 1695539) (-1012 "RDETRS.spad" 1693903 1693921 1695097 1695102) (-1011 "RDETR.spad" 1692010 1692028 1693893 1693898) (-1010 "RDEEFS.spad" 1691083 1691100 1692000 1692005) (-1009 "RDEEF.spad" 1690079 1690096 1691073 1691078) (-1008 "RCFIELD.spad" 1687265 1687274 1689981 1690074) (-1007 "RCFIELD.spad" 1684537 1684548 1687255 1687260) (-1006 "RCAGG.spad" 1682449 1682460 1684527 1684532) (-1005 "RCAGG.spad" 1680288 1680301 1682368 1682373) (-1004 "RATRET.spad" 1679648 1679659 1680278 1680283) (-1003 "RATFACT.spad" 1679340 1679352 1679638 1679643) (-1002 "RANDSRC.spad" 1678659 1678668 1679330 1679335) (-1001 "RADUTIL.spad" 1678413 1678422 1678649 1678654) (-1000 "RADIX.spad" 1675314 1675328 1676880 1676973) (-999 "RADFF.spad" 1673728 1673764 1673846 1674002) (-998 "RADCAT.spad" 1673322 1673330 1673718 1673723) (-997 "RADCAT.spad" 1672914 1672924 1673312 1673317) (-996 "QUEUE.spad" 1672257 1672267 1672521 1672548) (-995 "QUAT.spad" 1670839 1670849 1671181 1671246) (-994 "QUATCT2.spad" 1670458 1670476 1670829 1670834) (-993 "QUATCAT.spad" 1668623 1668633 1670388 1670453) (-992 "QUATCAT.spad" 1666539 1666551 1668306 1668311) (-991 "QUAGG.spad" 1665365 1665375 1666507 1666534) (-990 "QQUTAST.spad" 1665134 1665142 1665355 1665360) (-989 "QFORM.spad" 1664597 1664611 1665124 1665129) (-988 "QFCAT.spad" 1663300 1663310 1664499 1664592) (-987 "QFCAT.spad" 1661594 1661606 1662795 1662800) (-986 "QFCAT2.spad" 1661285 1661301 1661584 1661589) (-985 "QEQUAT.spad" 1660842 1660850 1661275 1661280) (-984 "QCMPACK.spad" 1655589 1655608 1660832 1660837) (-983 "QALGSET.spad" 1651664 1651696 1655503 1655508) (-982 "QALGSET2.spad" 1649660 1649678 1651654 1651659) (-981 "PWFFINTB.spad" 1646970 1646991 1649650 1649655) (-980 "PUSHVAR.spad" 1646299 1646318 1646960 1646965) (-979 "PTRANFN.spad" 1642425 1642435 1646289 1646294) (-978 "PTPACK.spad" 1639513 1639523 1642415 1642420) (-977 "PTFUNC2.spad" 1639334 1639348 1639503 1639508) (-976 "PTCAT.spad" 1638583 1638593 1639302 1639329) (-975 "PSQFR.spad" 1637890 1637914 1638573 1638578) (-974 "PSEUDLIN.spad" 1636748 1636758 1637880 1637885) (-973 "PSETPK.spad" 1622181 1622197 1636626 1636631) (-972 "PSETCAT.spad" 1616101 1616124 1622161 1622176) (-971 "PSETCAT.spad" 1609995 1610020 1616057 1616062) (-970 "PSCURVE.spad" 1608978 1608986 1609985 1609990) (-969 "PSCAT.spad" 1607745 1607774 1608876 1608973) (-968 "PSCAT.spad" 1606602 1606633 1607735 1607740) (-967 "PRTITION.spad" 1605547 1605555 1606592 1606597) (-966 "PRTDAST.spad" 1605266 1605274 1605537 1605542) (-965 "PRS.spad" 1594828 1594845 1605222 1605227) (-964 "PRQAGG.spad" 1594259 1594269 1594796 1594823) (-963 "PROPLOG.spad" 1593662 1593670 1594249 1594254) (-962 "PROPFRML.spad" 1591580 1591591 1593652 1593657) (-961 "PROPERTY.spad" 1591074 1591082 1591570 1591575) (-960 "PRODUCT.spad" 1588754 1588766 1589040 1589095) (-959 "PR.spad" 1587140 1587152 1587845 1587972) (-958 "PRINT.spad" 1586892 1586900 1587130 1587135) (-957 "PRIMES.spad" 1585143 1585153 1586882 1586887) (-956 "PRIMELT.spad" 1583124 1583138 1585133 1585138) (-955 "PRIMCAT.spad" 1582747 1582755 1583114 1583119) (-954 "PRIMARR.spad" 1581752 1581762 1581930 1581957) (-953 "PRIMARR2.spad" 1580475 1580487 1581742 1581747) (-952 "PREASSOC.spad" 1579847 1579859 1580465 1580470) (-951 "PPCURVE.spad" 1578984 1578992 1579837 1579842) (-950 "PORTNUM.spad" 1578759 1578767 1578974 1578979) (-949 "POLYROOT.spad" 1577588 1577610 1578715 1578720) (-948 "POLY.spad" 1574885 1574895 1575402 1575529) (-947 "POLYLIFT.spad" 1574146 1574169 1574875 1574880) (-946 "POLYCATQ.spad" 1572248 1572270 1574136 1574141) (-945 "POLYCAT.spad" 1565654 1565675 1572116 1572243) (-944 "POLYCAT.spad" 1558362 1558385 1564826 1564831) (-943 "POLY2UP.spad" 1557810 1557824 1558352 1558357) (-942 "POLY2.spad" 1557405 1557417 1557800 1557805) (-941 "POLUTIL.spad" 1556346 1556375 1557361 1557366) (-940 "POLTOPOL.spad" 1555094 1555109 1556336 1556341) (-939 "POINT.spad" 1553933 1553943 1554020 1554047) (-938 "PNTHEORY.spad" 1550599 1550607 1553923 1553928) (-937 "PMTOOLS.spad" 1549356 1549370 1550589 1550594) (-936 "PMSYM.spad" 1548901 1548911 1549346 1549351) (-935 "PMQFCAT.spad" 1548488 1548502 1548891 1548896) (-934 "PMPRED.spad" 1547957 1547971 1548478 1548483) (-933 "PMPREDFS.spad" 1547401 1547423 1547947 1547952) (-932 "PMPLCAT.spad" 1546471 1546489 1547333 1547338) (-931 "PMLSAGG.spad" 1546052 1546066 1546461 1546466) (-930 "PMKERNEL.spad" 1545619 1545631 1546042 1546047) (-929 "PMINS.spad" 1545195 1545205 1545609 1545614) (-928 "PMFS.spad" 1544768 1544786 1545185 1545190) (-927 "PMDOWN.spad" 1544054 1544068 1544758 1544763) (-926 "PMASS.spad" 1543066 1543074 1544044 1544049) (-925 "PMASSFS.spad" 1542035 1542051 1543056 1543061) (-924 "PLOTTOOL.spad" 1541815 1541823 1542025 1542030) (-923 "PLOT.spad" 1536646 1536654 1541805 1541810) (-922 "PLOT3D.spad" 1533066 1533074 1536636 1536641) (-921 "PLOT1.spad" 1532207 1532217 1533056 1533061) (-920 "PLEQN.spad" 1519423 1519450 1532197 1532202) (-919 "PINTERP.spad" 1519039 1519058 1519413 1519418) (-918 "PINTERPA.spad" 1518821 1518837 1519029 1519034) (-917 "PI.spad" 1518428 1518436 1518795 1518816) (-916 "PID.spad" 1517384 1517392 1518354 1518423) (-915 "PICOERCE.spad" 1517041 1517051 1517374 1517379) (-914 "PGROEB.spad" 1515638 1515652 1517031 1517036) (-913 "PGE.spad" 1506891 1506899 1515628 1515633) (-912 "PGCD.spad" 1505773 1505790 1506881 1506886) (-911 "PFRPAC.spad" 1504916 1504926 1505763 1505768) (-910 "PFR.spad" 1501573 1501583 1504818 1504911) (-909 "PFOTOOLS.spad" 1500831 1500847 1501563 1501568) (-908 "PFOQ.spad" 1500201 1500219 1500821 1500826) (-907 "PFO.spad" 1499620 1499647 1500191 1500196) (-906 "PF.spad" 1499194 1499206 1499425 1499518) (-905 "PFECAT.spad" 1496860 1496868 1499120 1499189) (-904 "PFECAT.spad" 1494554 1494564 1496816 1496821) (-903 "PFBRU.spad" 1492424 1492436 1494544 1494549) (-902 "PFBR.spad" 1489962 1489985 1492414 1492419) (-901 "PERM.spad" 1485643 1485653 1489792 1489807) (-900 "PERMGRP.spad" 1480379 1480389 1485633 1485638) (-899 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1450308 1450313) (-880 "PATAB.spad" 1449166 1449176 1449392 1449397) (-879 "PARTPERM.spad" 1446528 1446536 1449156 1449161) (-878 "PARSURF.spad" 1445956 1445984 1446518 1446523) (-877 "PARSU2.spad" 1445751 1445767 1445946 1445951) (-876 "script-parser.spad" 1445271 1445279 1445741 1445746) (-875 "PARSCURV.spad" 1444699 1444727 1445261 1445266) (-874 "PARSC2.spad" 1444488 1444504 1444689 1444694) (-873 "PARPCURV.spad" 1443946 1443974 1444478 1444483) (-872 "PARPC2.spad" 1443735 1443751 1443936 1443941) (-871 "PAN2EXPR.spad" 1443147 1443155 1443725 1443730) (-870 "PALETTE.spad" 1442117 1442125 1443137 1443142) (-869 "PAIR.spad" 1441100 1441113 1441705 1441710) (-868 "PADICRC.spad" 1438430 1438448 1439605 1439698) (-867 "PADICRAT.spad" 1436445 1436457 1436666 1436759) (-866 "PADIC.spad" 1436140 1436152 1436371 1436440) (-865 "PADICCT.spad" 1434681 1434693 1436066 1436135) (-864 "PADEPAC.spad" 1433360 1433379 1434671 1434676) (-863 "PADE.spad" 1432100 1432116 1433350 1433355) (-862 "OWP.spad" 1431340 1431370 1431958 1432025) (-861 "OVERSET.spad" 1430913 1430921 1431330 1431335) (-860 "OVAR.spad" 1430694 1430717 1430903 1430908) (-859 "OUT.spad" 1429778 1429786 1430684 1430689) (-858 "OUTFORM.spad" 1419074 1419082 1429768 1429773) (-857 "OUTBFILE.spad" 1418492 1418500 1419064 1419069) (-856 "OUTBCON.spad" 1417490 1417498 1418482 1418487) (-855 "OUTBCON.spad" 1416486 1416496 1417480 1417485) (-854 "OSI.spad" 1415961 1415969 1416476 1416481) (-853 "OSGROUP.spad" 1415879 1415887 1415951 1415956) (-852 "ORTHPOL.spad" 1414340 1414350 1415796 1415801) (-851 "OREUP.spad" 1413793 1413821 1414020 1414059) (-850 "ORESUP.spad" 1413092 1413116 1413473 1413512) (-849 "OREPCTO.spad" 1410911 1410923 1413012 1413017) (-848 "OREPCAT.spad" 1404968 1404978 1410867 1410906) (-847 "OREPCAT.spad" 1398915 1398927 1404816 1404821) (-846 "ORDSET.spad" 1398081 1398089 1398905 1398910) (-845 "ORDSET.spad" 1397245 1397255 1398071 1398076) (-844 "ORDRING.spad" 1396635 1396643 1397225 1397240) (-843 "ORDRING.spad" 1396033 1396043 1396625 1396630) (-842 "ORDMON.spad" 1395888 1395896 1396023 1396028) (-841 "ORDFUNS.spad" 1395014 1395030 1395878 1395883) (-840 "ORDFIN.spad" 1394834 1394842 1395004 1395009) (-839 "ORDCOMP.spad" 1393299 1393309 1394381 1394410) (-838 "ORDCOMP2.spad" 1392584 1392596 1393289 1393294) (-837 "OPTPROB.spad" 1391222 1391230 1392574 1392579) (-836 "OPTPACK.spad" 1383607 1383615 1391212 1391217) (-835 "OPTCAT.spad" 1381282 1381290 1383597 1383602) (-834 "OPSIG.spad" 1380934 1380942 1381272 1381277) (-833 "OPQUERY.spad" 1380483 1380491 1380924 1380929) (-832 "OP.spad" 1380225 1380235 1380305 1380372) (-831 "OPERCAT.spad" 1379813 1379823 1380215 1380220) (-830 "OPERCAT.spad" 1379399 1379411 1379803 1379808) (-829 "ONECOMP.spad" 1378144 1378154 1378946 1378975) (-828 "ONECOMP2.spad" 1377562 1377574 1378134 1378139) (-827 "OMSERVER.spad" 1376564 1376572 1377552 1377557) (-826 "OMSAGG.spad" 1376352 1376362 1376520 1376559) (-825 "OMPKG.spad" 1374964 1374972 1376342 1376347) (-824 "OM.spad" 1373929 1373937 1374954 1374959) (-823 "OMLO.spad" 1373354 1373366 1373815 1373854) (-822 "OMEXPR.spad" 1373188 1373198 1373344 1373349) (-821 "OMERR.spad" 1372731 1372739 1373178 1373183) (-820 "OMERRK.spad" 1371765 1371773 1372721 1372726) (-819 "OMENC.spad" 1371109 1371117 1371755 1371760) (-818 "OMDEV.spad" 1365398 1365406 1371099 1371104) (-817 "OMCONN.spad" 1364807 1364815 1365388 1365393) (-816 "OINTDOM.spad" 1364570 1364578 1364733 1364802) (-815 "OFMONOID.spad" 1360757 1360767 1364560 1364565) (-814 "ODVAR.spad" 1360018 1360028 1360747 1360752) (-813 "ODR.spad" 1359662 1359688 1359830 1359979) (-812 "ODPOL.spad" 1357008 1357018 1357348 1357475) (-811 "ODP.spad" 1346855 1346875 1347228 1347359) (-810 "ODETOOLS.spad" 1345438 1345457 1346845 1346850) (-809 "ODESYS.spad" 1343088 1343105 1345428 1345433) (-808 "ODERTRIC.spad" 1339029 1339046 1343045 1343050) (-807 "ODERED.spad" 1338416 1338440 1339019 1339024) (-806 "ODERAT.spad" 1335967 1335984 1338406 1338411) (-805 "ODEPRRIC.spad" 1332858 1332880 1335957 1335962) (-804 "ODEPROB.spad" 1332115 1332123 1332848 1332853) (-803 "ODEPRIM.spad" 1329389 1329411 1332105 1332110) (-802 "ODEPAL.spad" 1328765 1328789 1329379 1329384) (-801 "ODEPACK.spad" 1315367 1315375 1328755 1328760) (-800 "ODEINT.spad" 1314798 1314814 1315357 1315362) (-799 "ODEIFTBL.spad" 1312193 1312201 1314788 1314793) (-798 "ODEEF.spad" 1307560 1307576 1312183 1312188) (-797 "ODECONST.spad" 1307079 1307097 1307550 1307555) (-796 "ODECAT.spad" 1305675 1305683 1307069 1307074) (-795 "OCT.spad" 1303813 1303823 1304529 1304568) (-794 "OCTCT2.spad" 1303457 1303478 1303803 1303808) (-793 "OC.spad" 1301231 1301241 1303413 1303452) (-792 "OC.spad" 1298730 1298742 1300914 1300919) (-791 "OCAMON.spad" 1298578 1298586 1298720 1298725) (-790 "OASGP.spad" 1298393 1298401 1298568 1298573) (-789 "OAMONS.spad" 1297913 1297921 1298383 1298388) (-788 "OAMON.spad" 1297774 1297782 1297903 1297908) (-787 "OAGROUP.spad" 1297636 1297644 1297764 1297769) (-786 "NUMTUBE.spad" 1297223 1297239 1297626 1297631) (-785 "NUMQUAD.spad" 1285085 1285093 1297213 1297218) (-784 "NUMODE.spad" 1276221 1276229 1285075 1285080) (-783 "NUMINT.spad" 1273779 1273787 1276211 1276216) (-782 "NUMFMT.spad" 1272619 1272627 1273769 1273774) (-781 "NUMERIC.spad" 1264691 1264701 1272424 1272429) (-780 "NTSCAT.spad" 1263193 1263209 1264659 1264686) (-779 "NTPOLFN.spad" 1262738 1262748 1263110 1263115) (-778 "NSUP.spad" 1255748 1255758 1260288 1260441) (-777 "NSUP2.spad" 1255140 1255152 1255738 1255743) (-776 "NSMP.spad" 1251335 1251354 1251643 1251770) (-775 "NREP.spad" 1249707 1249721 1251325 1251330) (-774 "NPCOEF.spad" 1248953 1248973 1249697 1249702) (-773 "NORMRETR.spad" 1248551 1248590 1248943 1248948) (-772 "NORMPK.spad" 1246453 1246472 1248541 1248546) (-771 "NORMMA.spad" 1246141 1246167 1246443 1246448) (-770 "NONE.spad" 1245882 1245890 1246131 1246136) (-769 "NONE1.spad" 1245558 1245568 1245872 1245877) (-768 "NODE1.spad" 1245027 1245043 1245548 1245553) (-767 "NNI.spad" 1243914 1243922 1245001 1245022) (-766 "NLINSOL.spad" 1242536 1242546 1243904 1243909) (-765 "NIPROB.spad" 1241077 1241085 1242526 1242531) (-764 "NFINTBAS.spad" 1238537 1238554 1241067 1241072) (-763 "NETCLT.spad" 1238511 1238522 1238527 1238532) (-762 "NCODIV.spad" 1236709 1236725 1238501 1238506) (-761 "NCNTFRAC.spad" 1236351 1236365 1236699 1236704) (-760 "NCEP.spad" 1234511 1234525 1236341 1236346) (-759 "NASRING.spad" 1234107 1234115 1234501 1234506) (-758 "NASRING.spad" 1233701 1233711 1234097 1234102) (-757 "NARNG.spad" 1233045 1233053 1233691 1233696) (-756 "NARNG.spad" 1232387 1232397 1233035 1233040) (-755 "NAGSP.spad" 1231460 1231468 1232377 1232382) (-754 "NAGS.spad" 1220985 1220993 1231450 1231455) (-753 "NAGF07.spad" 1219378 1219386 1220975 1220980) (-752 "NAGF04.spad" 1213610 1213618 1219368 1219373) (-751 "NAGF02.spad" 1207419 1207427 1213600 1213605) (-750 "NAGF01.spad" 1203022 1203030 1207409 1207414) (-749 "NAGE04.spad" 1196482 1196490 1203012 1203017) (-748 "NAGE02.spad" 1186824 1186832 1196472 1196477) (-747 "NAGE01.spad" 1182708 1182716 1186814 1186819) (-746 "NAGD03.spad" 1180628 1180636 1182698 1182703) (-745 "NAGD02.spad" 1173159 1173167 1180618 1180623) (-744 "NAGD01.spad" 1167272 1167280 1173149 1173154) (-743 "NAGC06.spad" 1163059 1163067 1167262 1167267) (-742 "NAGC05.spad" 1161528 1161536 1163049 1163054) (-741 "NAGC02.spad" 1160783 1160791 1161518 1161523) (-740 "NAALG.spad" 1160318 1160328 1160751 1160778) (-739 "NAALG.spad" 1159873 1159885 1160308 1160313) (-738 "MULTSQFR.spad" 1156831 1156848 1159863 1159868) (-737 "MULTFACT.spad" 1156214 1156231 1156821 1156826) (-736 "MTSCAT.spad" 1154248 1154269 1156112 1156209) (-735 "MTHING.spad" 1153905 1153915 1154238 1154243) (-734 "MSYSCMD.spad" 1153339 1153347 1153895 1153900) (-733 "MSET.spad" 1151281 1151291 1153045 1153084) (-732 "MSETAGG.spad" 1151126 1151136 1151249 1151276) (-731 "MRING.spad" 1148097 1148109 1150834 1150901) (-730 "MRF2.spad" 1147665 1147679 1148087 1148092) (-729 "MRATFAC.spad" 1147211 1147228 1147655 1147660) (-728 "MPRFF.spad" 1145241 1145260 1147201 1147206) (-727 "MPOLY.spad" 1142676 1142691 1143035 1143162) (-726 "MPCPF.spad" 1141940 1141959 1142666 1142671) (-725 "MPC3.spad" 1141755 1141795 1141930 1141935) (-724 "MPC2.spad" 1141397 1141430 1141745 1141750) (-723 "MONOTOOL.spad" 1139732 1139749 1141387 1141392) (-722 "MONOID.spad" 1139051 1139059 1139722 1139727) (-721 "MONOID.spad" 1138368 1138378 1139041 1139046) (-720 "MONOGEN.spad" 1137114 1137127 1138228 1138363) (-719 "MONOGEN.spad" 1135882 1135897 1136998 1137003) (-718 "MONADWU.spad" 1133896 1133904 1135872 1135877) (-717 "MONADWU.spad" 1131908 1131918 1133886 1133891) (-716 "MONAD.spad" 1131052 1131060 1131898 1131903) (-715 "MONAD.spad" 1130194 1130204 1131042 1131047) (-714 "MOEBIUS.spad" 1128880 1128894 1130174 1130189) (-713 "MODULE.spad" 1128750 1128760 1128848 1128875) (-712 "MODULE.spad" 1128640 1128652 1128740 1128745) (-711 "MODRING.spad" 1127971 1128010 1128620 1128635) (-710 "MODOP.spad" 1126630 1126642 1127793 1127860) (-709 "MODMONOM.spad" 1126359 1126377 1126620 1126625) (-708 "MODMON.spad" 1123118 1123134 1123837 1123990) (-707 "MODFIELD.spad" 1122476 1122515 1123020 1123113) (-706 "MMLFORM.spad" 1121336 1121344 1122466 1122471) (-705 "MMAP.spad" 1121076 1121110 1121326 1121331) (-704 "MLO.spad" 1119503 1119513 1121032 1121071) (-703 "MLIFT.spad" 1118075 1118092 1119493 1119498) (-702 "MKUCFUNC.spad" 1117608 1117626 1118065 1118070) (-701 "MKRECORD.spad" 1117210 1117223 1117598 1117603) (-700 "MKFUNC.spad" 1116591 1116601 1117200 1117205) (-699 "MKFLCFN.spad" 1115547 1115557 1116581 1116586) (-698 "MKCHSET.spad" 1115412 1115422 1115537 1115542) (-697 "MKBCFUNC.spad" 1114897 1114915 1115402 1115407) (-696 "MINT.spad" 1114336 1114344 1114799 1114892) (-695 "MHROWRED.spad" 1112837 1112847 1114326 1114331) (-694 "MFLOAT.spad" 1111353 1111361 1112727 1112832) (-693 "MFINFACT.spad" 1110753 1110775 1111343 1111348) (-692 "MESH.spad" 1108485 1108493 1110743 1110748) (-691 "MDDFACT.spad" 1106678 1106688 1108475 1108480) (-690 "MDAGG.spad" 1105965 1105975 1106658 1106673) (-689 "MCMPLX.spad" 1101939 1101947 1102553 1102754) (-688 "MCDEN.spad" 1101147 1101159 1101929 1101934) (-687 "MCALCFN.spad" 1098249 1098275 1101137 1101142) (-686 "MAYBE.spad" 1097533 1097544 1098239 1098244) (-685 "MATSTOR.spad" 1094809 1094819 1097523 1097528) (-684 "MATRIX.spad" 1093513 1093523 1093997 1094024) (-683 "MATLIN.spad" 1090839 1090863 1093397 1093402) (-682 "MATCAT.spad" 1082424 1082446 1090807 1090834) (-681 "MATCAT.spad" 1073881 1073905 1082266 1082271) (-680 "MATCAT2.spad" 1073149 1073197 1073871 1073876) (-679 "MAPPKG3.spad" 1072048 1072062 1073139 1073144) (-678 "MAPPKG2.spad" 1071382 1071394 1072038 1072043) (-677 "MAPPKG1.spad" 1070200 1070210 1071372 1071377) (-676 "MAPPAST.spad" 1069513 1069521 1070190 1070195) (-675 "MAPHACK3.spad" 1069321 1069335 1069503 1069508) (-674 "MAPHACK2.spad" 1069086 1069098 1069311 1069316) (-673 "MAPHACK1.spad" 1068716 1068726 1069076 1069081) (-672 "MAGMA.spad" 1066506 1066523 1068706 1068711) (-671 "MACROAST.spad" 1066085 1066093 1066496 1066501) (-670 "M3D.spad" 1063781 1063791 1065463 1065468) (-669 "LZSTAGG.spad" 1061009 1061019 1063771 1063776) (-668 "LZSTAGG.spad" 1058235 1058247 1060999 1061004) (-667 "LWORD.spad" 1054940 1054957 1058225 1058230) (-666 "LSTAST.spad" 1054724 1054732 1054930 1054935) (-665 "LSQM.spad" 1052950 1052964 1053348 1053399) (-664 "LSPP.spad" 1052483 1052500 1052940 1052945) (-663 "LSMP.spad" 1051323 1051351 1052473 1052478) (-662 "LSMP1.spad" 1049127 1049141 1051313 1051318) (-661 "LSAGG.spad" 1048796 1048806 1049095 1049122) (-660 "LSAGG.spad" 1048485 1048497 1048786 1048791) (-659 "LPOLY.spad" 1047439 1047458 1048341 1048410) (-658 "LPEFRAC.spad" 1046696 1046706 1047429 1047434) (-657 "LO.spad" 1046097 1046111 1046630 1046657) (-656 "LOGIC.spad" 1045699 1045707 1046087 1046092) (-655 "LOGIC.spad" 1045299 1045309 1045689 1045694) (-654 "LODOOPS.spad" 1044217 1044229 1045289 1045294) (-653 "LODO.spad" 1043601 1043617 1043897 1043936) (-652 "LODOF.spad" 1042645 1042662 1043558 1043563) (-651 "LODOCAT.spad" 1041303 1041313 1042601 1042640) (-650 "LODOCAT.spad" 1039959 1039971 1041259 1041264) (-649 "LODO2.spad" 1039232 1039244 1039639 1039678) (-648 "LODO1.spad" 1038632 1038642 1038912 1038951) (-647 "LODEEF.spad" 1037404 1037422 1038622 1038627) (-646 "LNAGG.spad" 1033206 1033216 1037394 1037399) (-645 "LNAGG.spad" 1028972 1028984 1033162 1033167) (-644 "LMOPS.spad" 1025708 1025725 1028962 1028967) (-643 "LMODULE.spad" 1025350 1025360 1025698 1025703) (-642 "LMDICT.spad" 1024633 1024643 1024901 1024928) (-641 "LITERAL.spad" 1024539 1024550 1024623 1024628) (-640 "LIST.spad" 1022257 1022267 1023686 1023713) (-639 "LIST3.spad" 1021548 1021562 1022247 1022252) (-638 "LIST2.spad" 1020188 1020200 1021538 1021543) (-637 "LIST2MAP.spad" 1017065 1017077 1020178 1020183) (-636 "LINEXP.spad" 1016497 1016507 1017045 1017060) (-635 "LINDEP.spad" 1015274 1015286 1016409 1016414) (-634 "LIMITRF.spad" 1013188 1013198 1015264 1015269) (-633 "LIMITPS.spad" 1012071 1012084 1013178 1013183) (-632 "LIE.spad" 1010085 1010097 1011361 1011506) (-631 "LIECAT.spad" 1009561 1009571 1010011 1010080) (-630 "LIECAT.spad" 1009065 1009077 1009517 1009522) (-629 "LIB.spad" 1007113 1007121 1007724 1007739) (-628 "LGROBP.spad" 1004466 1004485 1007103 1007108) (-627 "LF.spad" 1003385 1003401 1004456 1004461) (-626 "LFCAT.spad" 1002404 1002412 1003375 1003380) (-625 "LEXTRIPK.spad" 997907 997922 1002394 1002399) (-624 "LEXP.spad" 995910 995937 997887 997902) (-623 "LETAST.spad" 995609 995617 995900 995905) (-622 "LEADCDET.spad" 993993 994010 995599 995604) (-621 "LAZM3PK.spad" 992697 992719 993983 993988) (-620 "LAUPOL.spad" 991386 991399 992290 992359) (-619 "LAPLACE.spad" 990959 990975 991376 991381) (-618 "LA.spad" 990399 990413 990881 990920) (-617 "LALG.spad" 990175 990185 990379 990394) (-616 "LALG.spad" 989959 989971 990165 990170) (-615 "KVTFROM.spad" 989694 989704 989949 989954) (-614 "KTVLOGIC.spad" 989117 989125 989684 989689) (-613 "KRCFROM.spad" 988855 988865 989107 989112) (-612 "KOVACIC.spad" 987568 987585 988845 988850) (-611 "KONVERT.spad" 987290 987300 987558 987563) (-610 "KOERCE.spad" 987027 987037 987280 987285) (-609 "KERNEL.spad" 985562 985572 986811 986816) (-608 "KERNEL2.spad" 985265 985277 985552 985557) (-607 "KDAGG.spad" 984368 984390 985245 985260) (-606 "KDAGG.spad" 983479 983503 984358 984363) (-605 "KAFILE.spad" 982442 982458 982677 982704) (-604 "JORDAN.spad" 980269 980281 981732 981877) (-603 "JOINAST.spad" 979963 979971 980259 980264) (-602 "JAVACODE.spad" 979829 979837 979953 979958) (-601 "IXAGG.spad" 977952 977976 979819 979824) (-600 "IXAGG.spad" 975930 975956 977799 977804) (-599 "IVECTOR.spad" 974701 974716 974856 974883) (-598 "ITUPLE.spad" 973846 973856 974691 974696) (-597 "ITRIGMNP.spad" 972657 972676 973836 973841) (-596 "ITFUN3.spad" 972151 972165 972647 972652) (-595 "ITFUN2.spad" 971881 971893 972141 972146) (-594 "ITAYLOR.spad" 969673 969688 971717 971842) (-593 "ISUPS.spad" 962084 962099 968647 968744) (-592 "ISUMP.spad" 961581 961597 962074 962079) (-591 "ISTRING.spad" 960584 960597 960750 960777) (-590 "ISAST.spad" 960303 960311 960574 960579) (-589 "IRURPK.spad" 959016 959035 960293 960298) (-588 "IRSN.spad" 956976 956984 959006 959011) (-587 "IRRF2F.spad" 955451 955461 956932 956937) (-586 "IRREDFFX.spad" 955052 955063 955441 955446) (-585 "IROOT.spad" 953383 953393 955042 955047) (-584 "IR.spad" 951172 951186 953238 953265) (-583 "IR2.spad" 950192 950208 951162 951167) (-582 "IR2F.spad" 949392 949408 950182 950187) (-581 "IPRNTPK.spad" 949152 949160 949382 949387) (-580 "IPF.spad" 948717 948729 948957 949050) (-579 "IPADIC.spad" 948478 948504 948643 948712) (-578 "IP4ADDR.spad" 948035 948043 948468 948473) (-577 "IOMODE.spad" 947656 947664 948025 948030) (-576 "IOBFILE.spad" 947017 947025 947646 947651) (-575 "IOBCON.spad" 946882 946890 947007 947012) (-574 "INVLAPLA.spad" 946527 946543 946872 946877) (-573 "INTTR.spad" 939773 939790 946517 946522) (-572 "INTTOOLS.spad" 937484 937500 939347 939352) (-571 "INTSLPE.spad" 936790 936798 937474 937479) (-570 "INTRVL.spad" 936356 936366 936704 936785) (-569 "INTRF.spad" 934720 934734 936346 936351) (-568 "INTRET.spad" 934152 934162 934710 934715) (-567 "INTRAT.spad" 932827 932844 934142 934147) (-566 "INTPM.spad" 931190 931206 932470 932475) (-565 "INTPAF.spad" 928958 928976 931122 931127) (-564 "INTPACK.spad" 919268 919276 928948 928953) (-563 "INT.spad" 918629 918637 919122 919263) (-562 "INTHERTR.spad" 917895 917912 918619 918624) (-561 "INTHERAL.spad" 917561 917585 917885 917890) (-560 "INTHEORY.spad" 913974 913982 917551 917556) (-559 "INTG0.spad" 907437 907455 913906 913911) (-558 "INTFTBL.spad" 901466 901474 907427 907432) (-557 "INTFACT.spad" 900525 900535 901456 901461) (-556 "INTEF.spad" 898840 898856 900515 900520) 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"DIAGG.spad" 272198 272210 272550 272555) (-227 "DHMATRIX.spad" 270502 270512 271655 271682) (-226 "DFSFUN.spad" 263910 263918 270492 270497) (-225 "DFLOAT.spad" 260631 260639 263800 263905) (-224 "DFINTTLS.spad" 258840 258856 260621 260626) (-223 "DERHAM.spad" 256750 256782 258820 258835) (-222 "DEQUEUE.spad" 256068 256078 256357 256384) (-221 "DEGRED.spad" 255683 255697 256058 256063) (-220 "DEFINTRF.spad" 253208 253218 255673 255678) (-219 "DEFINTEF.spad" 251704 251720 253198 253203) (-218 "DEFAST.spad" 251072 251080 251694 251699) (-217 "DECIMAL.spad" 249178 249186 249539 249632) (-216 "DDFACT.spad" 246977 246994 249168 249173) (-215 "DBLRESP.spad" 246575 246599 246967 246972) (-214 "DBASE.spad" 245229 245239 246565 246570) (-213 "DATAARY.spad" 244691 244704 245219 245224) (-212 "D03FAFA.spad" 244519 244527 244681 244686) (-211 "D03EEFA.spad" 244339 244347 244509 244514) (-210 "D03AGNT.spad" 243419 243427 244329 244334) (-209 "D02EJFA.spad" 242881 242889 243409 243414) (-208 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"CTRIGMNP.spad" 219718 219734 221218 221223) (-187 "CTOR.spad" 219413 219421 219708 219713) (-186 "CTORKIND.spad" 219016 219024 219403 219408) (-185 "CTORCAT.spad" 218265 218273 219006 219011) (-184 "CTORCAT.spad" 217512 217522 218255 218260) (-183 "CTORCALL.spad" 217092 217100 217502 217507) (-182 "CSTTOOLS.spad" 216335 216348 217082 217087) (-181 "CRFP.spad" 210039 210052 216325 216330) (-180 "CRCEAST.spad" 209759 209767 210029 210034) (-179 "CRAPACK.spad" 208802 208812 209749 209754) (-178 "CPMATCH.spad" 208302 208317 208727 208732) (-177 "CPIMA.spad" 208007 208026 208292 208297) (-176 "COORDSYS.spad" 202900 202910 207997 208002) (-175 "CONTOUR.spad" 202302 202310 202890 202895) (-174 "CONTFRAC.spad" 197914 197924 202204 202297) (-173 "CONDUIT.spad" 197672 197680 197904 197909) (-172 "COMRING.spad" 197346 197354 197610 197667) (-171 "COMPPROP.spad" 196860 196868 197336 197341) (-170 "COMPLPAT.spad" 196627 196642 196850 196855) (-169 "COMPLEX.spad" 190651 190661 190895 191156) (-168 "COMPLEX2.spad" 190364 190376 190641 190646) (-167 "COMPFACT.spad" 189966 189980 190354 190359) (-166 "COMPCAT.spad" 188034 188044 189700 189961) (-165 "COMPCAT.spad" 185795 185807 187463 187468) (-164 "COMMUPC.spad" 185541 185559 185785 185790) (-163 "COMMONOP.spad" 185074 185082 185531 185536) (-162 "COMM.spad" 184883 184891 185064 185069) (-161 "COMMAAST.spad" 184646 184654 184873 184878) (-160 "COMBOPC.spad" 183551 183559 184636 184641) (-159 "COMBINAT.spad" 182296 182306 183541 183546) (-158 "COMBF.spad" 179664 179680 182286 182291) (-157 "COLOR.spad" 178501 178509 179654 179659) (-156 "COLONAST.spad" 178167 178175 178491 178496) (-155 "CMPLXRT.spad" 177876 177893 178157 178162) (-154 "CLLCTAST.spad" 177538 177546 177866 177871) (-153 "CLIP.spad" 173630 173638 177528 177533) (-152 "CLIF.spad" 172269 172285 173586 173625) (-151 "CLAGG.spad" 168754 168764 172259 172264) (-150 "CLAGG.spad" 165110 165122 168617 168622) (-149 "CINTSLPE.spad" 164435 164448 165100 165105) (-148 "CHVAR.spad" 162513 162535 164425 164430) (-147 "CHARZ.spad" 162428 162436 162493 162508) (-146 "CHARPOL.spad" 161936 161946 162418 162423) (-145 "CHARNZ.spad" 161689 161697 161916 161931) (-144 "CHAR.spad" 159557 159565 161679 161684) (-143 "CFCAT.spad" 158873 158881 159547 159552) (-142 "CDEN.spad" 158031 158045 158863 158868) (-141 "CCLASS.spad" 156180 156188 157442 157481) (-140 "CATEGORY.spad" 155270 155278 156170 156175) (-139 "CATCTOR.spad" 155161 155169 155260 155265) (-138 "CATAST.spad" 154788 154796 155151 155156) (-137 "CASEAST.spad" 154502 154510 154778 154783) (-136 "CARTEN.spad" 149605 149629 154492 154497) (-135 "CARTEN2.spad" 148991 149018 149595 149600) (-134 "CARD.spad" 146280 146288 148965 148986) (-133 "CAPSLAST.spad" 146054 146062 146270 146275) (-132 "CACHSET.spad" 145676 145684 146044 146049) (-131 "CABMON.spad" 145229 145237 145666 145671) (-130 "BYTEORD.spad" 144904 144912 145219 145224) (-129 "BYTE.spad" 144325 144333 144894 144899) (-128 "BYTEBUF.spad" 142157 142165 143494 143521) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-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 2282815 2282820 2282825 2282830) (-2 NIL 2282795 2282800 2282805 2282810) (-1 NIL 2282775 2282780 2282785 2282790) (0 NIL 2282755 2282760 2282765 2282770) (-1285 "ZMOD.spad" 2282564 2282577 2282693 2282750) (-1284 "ZLINDEP.spad" 2281608 2281619 2282554 2282559) (-1283 "ZDSOLVE.spad" 2271457 2271479 2281598 2281603) (-1282 "YSTREAM.spad" 2270950 2270961 2271447 2271452) (-1281 "XRPOLY.spad" 2270170 2270190 2270806 2270875) (-1280 "XPR.spad" 2267961 2267974 2269888 2269987) (-1279 "XPOLY.spad" 2267516 2267527 2267817 2267886) (-1278 "XPOLYC.spad" 2266833 2266849 2267442 2267511) (-1277 "XPBWPOLY.spad" 2265270 2265290 2266613 2266682) (-1276 "XF.spad" 2263731 2263746 2265172 2265265) (-1275 "XF.spad" 2262172 2262189 2263615 2263620) (-1274 "XFALG.spad" 2259196 2259212 2262098 2262167) (-1273 "XEXPPKG.spad" 2258447 2258473 2259186 2259191) (-1272 "XDPOLY.spad" 2258061 2258077 2258303 2258372) (-1271 "XALG.spad" 2257721 2257732 2258017 2258056) (-1270 "WUTSET.spad" 2253560 2253577 2257367 2257394) (-1269 "WP.spad" 2252759 2252803 2253418 2253485) (-1268 "WHILEAST.spad" 2252557 2252566 2252749 2252754) (-1267 "WHEREAST.spad" 2252228 2252237 2252547 2252552) (-1266 "WFFINTBS.spad" 2249791 2249813 2252218 2252223) (-1265 "WEIER.spad" 2248005 2248016 2249781 2249786) (-1264 "VSPACE.spad" 2247678 2247689 2247973 2248000) (-1263 "VSPACE.spad" 2247371 2247384 2247668 2247673) (-1262 "VOID.spad" 2247048 2247057 2247361 2247366) (-1261 "VIEW.spad" 2244670 2244679 2247038 2247043) (-1260 "VIEWDEF.spad" 2239867 2239876 2244660 2244665) (-1259 "VIEW3D.spad" 2223702 2223711 2239857 2239862) (-1258 "VIEW2D.spad" 2211439 2211448 2223692 2223697) (-1257 "VECTOR.spad" 2210114 2210125 2210365 2210392) (-1256 "VECTOR2.spad" 2208741 2208754 2210104 2210109) (-1255 "VECTCAT.spad" 2206641 2206652 2208709 2208736) (-1254 "VECTCAT.spad" 2204349 2204362 2206419 2206424) (-1253 "VARIABLE.spad" 2204129 2204144 2204339 2204344) (-1252 "UTYPE.spad" 2203773 2203782 2204119 2204124) (-1251 "UTSODETL.spad" 2203066 2203090 2203729 2203734) (-1250 "UTSODE.spad" 2201254 2201274 2203056 2203061) (-1249 "UTS.spad" 2196043 2196071 2199721 2199818) (-1248 "UTSCAT.spad" 2193494 2193510 2195941 2196038) (-1247 "UTSCAT.spad" 2190589 2190607 2193038 2193043) (-1246 "UTS2.spad" 2190182 2190217 2190579 2190584) (-1245 "URAGG.spad" 2184814 2184825 2190172 2190177) (-1244 "URAGG.spad" 2179410 2179423 2184770 2184775) (-1243 "UPXSSING.spad" 2177053 2177079 2178491 2178624) (-1242 "UPXS.spad" 2174201 2174229 2175185 2175334) (-1241 "UPXSCONS.spad" 2171958 2171978 2172333 2172482) (-1240 "UPXSCCA.spad" 2170523 2170543 2171804 2171953) (-1239 "UPXSCCA.spad" 2169230 2169252 2170513 2170518) (-1238 "UPXSCAT.spad" 2167811 2167827 2169076 2169225) (-1237 "UPXS2.spad" 2167352 2167405 2167801 2167806) (-1236 "UPSQFREE.spad" 2165764 2165778 2167342 2167347) (-1235 "UPSCAT.spad" 2163357 2163381 2165662 2165759) (-1234 "UPSCAT.spad" 2160656 2160682 2162963 2162968) (-1233 "UPOLYC.spad" 2155634 2155645 2160498 2160651) (-1232 "UPOLYC.spad" 2150504 2150517 2155370 2155375) (-1231 "UPOLYC2.spad" 2149973 2149992 2150494 2150499) (-1230 "UP.spad" 2147130 2147145 2147523 2147676) (-1229 "UPMP.spad" 2146020 2146033 2147120 2147125) (-1228 "UPDIVP.spad" 2145583 2145597 2146010 2146015) (-1227 "UPDECOMP.spad" 2143820 2143834 2145573 2145578) (-1226 "UPCDEN.spad" 2143027 2143043 2143810 2143815) (-1225 "UP2.spad" 2142389 2142410 2143017 2143022) (-1224 "UNISEG.spad" 2141742 2141753 2142308 2142313) (-1223 "UNISEG2.spad" 2141235 2141248 2141698 2141703) (-1222 "UNIFACT.spad" 2140336 2140348 2141225 2141230) (-1221 "ULS.spad" 2130888 2130916 2131981 2132410) (-1220 "ULSCONS.spad" 2123282 2123302 2123654 2123803) (-1219 "ULSCCAT.spad" 2121011 2121031 2123128 2123277) (-1218 "ULSCCAT.spad" 2118848 2118870 2120967 2120972) (-1217 "ULSCAT.spad" 2117064 2117080 2118694 2118843) (-1216 "ULS2.spad" 2116576 2116629 2117054 2117059) (-1215 "UINT8.spad" 2116453 2116462 2116566 2116571) (-1214 "UINT32.spad" 2116329 2116338 2116443 2116448) (-1213 "UINT16.spad" 2116205 2116214 2116319 2116324) (-1212 "UFD.spad" 2115270 2115279 2116131 2116200) (-1211 "UFD.spad" 2114397 2114408 2115260 2115265) (-1210 "UDVO.spad" 2113244 2113253 2114387 2114392) (-1209 "UDPO.spad" 2110671 2110682 2113200 2113205) (-1208 "TYPE.spad" 2110603 2110612 2110661 2110666) (-1207 "TYPEAST.spad" 2110522 2110531 2110593 2110598) (-1206 "TWOFACT.spad" 2109172 2109187 2110512 2110517) (-1205 "TUPLE.spad" 2108656 2108667 2109071 2109076) (-1204 "TUBETOOL.spad" 2105493 2105502 2108646 2108651) (-1203 "TUBE.spad" 2104134 2104151 2105483 2105488) (-1202 "TS.spad" 2102723 2102739 2103699 2103796) (-1201 "TSETCAT.spad" 2089850 2089867 2102691 2102718) (-1200 "TSETCAT.spad" 2076963 2076982 2089806 2089811) (-1199 "TRMANIP.spad" 2071329 2071346 2076669 2076674) (-1198 "TRIMAT.spad" 2070288 2070313 2071319 2071324) (-1197 "TRIGMNIP.spad" 2068805 2068822 2070278 2070283) (-1196 "TRIGCAT.spad" 2068317 2068326 2068795 2068800) (-1195 "TRIGCAT.spad" 2067827 2067838 2068307 2068312) (-1194 "TREE.spad" 2066398 2066409 2067434 2067461) (-1193 "TRANFUN.spad" 2066229 2066238 2066388 2066393) (-1192 "TRANFUN.spad" 2066058 2066069 2066219 2066224) (-1191 "TOPSP.spad" 2065732 2065741 2066048 2066053) (-1190 "TOOLSIGN.spad" 2065395 2065406 2065722 2065727) (-1189 "TEXTFILE.spad" 2063952 2063961 2065385 2065390) (-1188 "TEX.spad" 2061084 2061093 2063942 2063947) (-1187 "TEX1.spad" 2060640 2060651 2061074 2061079) (-1186 "TEMUTL.spad" 2060195 2060204 2060630 2060635) (-1185 "TBCMPPK.spad" 2058288 2058311 2060185 2060190) (-1184 "TBAGG.spad" 2057324 2057347 2058268 2058283) (-1183 "TBAGG.spad" 2056368 2056393 2057314 2057319) (-1182 "TANEXP.spad" 2055744 2055755 2056358 2056363) (-1181 "TABLE.spad" 2054155 2054178 2054425 2054452) (-1180 "TABLEAU.spad" 2053636 2053647 2054145 2054150) (-1179 "TABLBUMP.spad" 2050419 2050430 2053626 2053631) (-1178 "SYSTEM.spad" 2049647 2049656 2050409 2050414) (-1177 "SYSSOLP.spad" 2047120 2047131 2049637 2049642) (-1176 "SYSNNI.spad" 2046296 2046307 2047110 2047115) (-1175 "SYSINT.spad" 2045769 2045780 2046286 2046291) (-1174 "SYNTAX.spad" 2042039 2042048 2045759 2045764) (-1173 "SYMTAB.spad" 2040095 2040104 2042029 2042034) (-1172 "SYMS.spad" 2036080 2036089 2040085 2040090) (-1171 "SYMPOLY.spad" 2035087 2035098 2035169 2035296) (-1170 "SYMFUNC.spad" 2034562 2034573 2035077 2035082) (-1169 "SYMBOL.spad" 2031989 2031998 2034552 2034557) (-1168 "SWITCH.spad" 2028746 2028755 2031979 2031984) (-1167 "SUTS.spad" 2025645 2025673 2027213 2027310) (-1166 "SUPXS.spad" 2022780 2022808 2023777 2023926) (-1165 "SUP.spad" 2019549 2019560 2020330 2020483) (-1164 "SUPFRACF.spad" 2018654 2018672 2019539 2019544) (-1163 "SUP2.spad" 2018044 2018057 2018644 2018649) (-1162 "SUMRF.spad" 2017010 2017021 2018034 2018039) (-1161 "SUMFS.spad" 2016643 2016660 2017000 2017005) (-1160 "SULS.spad" 2007182 2007210 2008288 2008717) (-1159 "SUCHTAST.spad" 2006951 2006960 2007172 2007177) (-1158 "SUCH.spad" 2006631 2006646 2006941 2006946) (-1157 "SUBSPACE.spad" 1998638 1998653 2006621 2006626) (-1156 "SUBRESP.spad" 1997798 1997812 1998594 1998599) (-1155 "STTF.spad" 1993897 1993913 1997788 1997793) (-1154 "STTFNC.spad" 1990365 1990381 1993887 1993892) (-1153 "STTAYLOR.spad" 1982763 1982774 1990246 1990251) (-1152 "STRTBL.spad" 1981268 1981285 1981417 1981444) (-1151 "STRING.spad" 1980677 1980686 1980691 1980718) (-1150 "STRICAT.spad" 1980465 1980474 1980645 1980672) (-1149 "STREAM.spad" 1977323 1977334 1979990 1980005) (-1148 "STREAM3.spad" 1976868 1976883 1977313 1977318) (-1147 "STREAM2.spad" 1975936 1975949 1976858 1976863) (-1146 "STREAM1.spad" 1975640 1975651 1975926 1975931) (-1145 "STINPROD.spad" 1974546 1974562 1975630 1975635) (-1144 "STEP.spad" 1973747 1973756 1974536 1974541) (-1143 "STBL.spad" 1972273 1972301 1972440 1972455) (-1142 "STAGG.spad" 1971348 1971359 1972263 1972268) (-1141 "STAGG.spad" 1970421 1970434 1971338 1971343) (-1140 "STACK.spad" 1969772 1969783 1970028 1970055) (-1139 "SREGSET.spad" 1967476 1967493 1969418 1969445) (-1138 "SRDCMPK.spad" 1966021 1966041 1967466 1967471) (-1137 "SRAGG.spad" 1961118 1961127 1965989 1966016) (-1136 "SRAGG.spad" 1956235 1956246 1961108 1961113) (-1135 "SQMATRIX.spad" 1953851 1953869 1954767 1954854) (-1134 "SPLTREE.spad" 1948403 1948416 1953287 1953314) (-1133 "SPLNODE.spad" 1944991 1945004 1948393 1948398) (-1132 "SPFCAT.spad" 1943768 1943777 1944981 1944986) (-1131 "SPECOUT.spad" 1942318 1942327 1943758 1943763) (-1130 "SPADXPT.spad" 1934457 1934466 1942308 1942313) (-1129 "spad-parser.spad" 1933922 1933931 1934447 1934452) (-1128 "SPADAST.spad" 1933623 1933632 1933912 1933917) (-1127 "SPACEC.spad" 1917636 1917647 1933613 1933618) (-1126 "SPACE3.spad" 1917412 1917423 1917626 1917631) (-1125 "SORTPAK.spad" 1916957 1916970 1917368 1917373) (-1124 "SOLVETRA.spad" 1914714 1914725 1916947 1916952) (-1123 "SOLVESER.spad" 1913234 1913245 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"SEGBIND.spad" 1847001 1847012 1847884 1847889) (-1084 "SEGBIND2.spad" 1846697 1846710 1846991 1846996) (-1083 "SEGAST.spad" 1846411 1846420 1846687 1846692) (-1082 "SEG2.spad" 1845836 1845849 1846367 1846372) (-1081 "SDVAR.spad" 1845112 1845123 1845826 1845831) (-1080 "SDPOL.spad" 1842502 1842513 1842793 1842920) (-1079 "SCPKG.spad" 1840581 1840592 1842492 1842497) (-1078 "SCOPE.spad" 1839726 1839735 1840571 1840576) (-1077 "SCACHE.spad" 1838408 1838419 1839716 1839721) (-1076 "SASTCAT.spad" 1838317 1838326 1838398 1838403) (-1075 "SAOS.spad" 1838189 1838198 1838307 1838312) (-1074 "SAERFFC.spad" 1837902 1837922 1838179 1838184) (-1073 "SAE.spad" 1836077 1836093 1836688 1836823) (-1072 "SAEFACT.spad" 1835778 1835798 1836067 1836072) (-1071 "RURPK.spad" 1833419 1833435 1835768 1835773) (-1070 "RULESET.spad" 1832860 1832884 1833409 1833414) (-1069 "RULE.spad" 1831064 1831088 1832850 1832855) (-1068 "RULECOLD.spad" 1830916 1830929 1831054 1831059) (-1067 "RSTRCAST.spad" 1830633 1830642 1830906 1830911) (-1066 "RSETGCD.spad" 1827011 1827031 1830623 1830628) (-1065 "RSETCAT.spad" 1816795 1816812 1826979 1827006) (-1064 "RSETCAT.spad" 1806599 1806618 1816785 1816790) (-1063 "RSDCMPK.spad" 1805051 1805071 1806589 1806594) (-1062 "RRCC.spad" 1803435 1803465 1805041 1805046) (-1061 "RRCC.spad" 1801817 1801849 1803425 1803430) (-1060 "RPTAST.spad" 1801519 1801528 1801807 1801812) (-1059 "RPOLCAT.spad" 1780879 1780894 1801387 1801514) (-1058 "RPOLCAT.spad" 1759953 1759970 1780463 1780468) (-1057 "ROUTINE.spad" 1755816 1755825 1758600 1758627) (-1056 "ROMAN.spad" 1755144 1755153 1755682 1755811) (-1055 "ROIRC.spad" 1754224 1754256 1755134 1755139) (-1054 "RNS.spad" 1753127 1753136 1754126 1754219) (-1053 "RNS.spad" 1752116 1752127 1753117 1753122) (-1052 "RNG.spad" 1751851 1751860 1752106 1752111) (-1051 "RMODULE.spad" 1751489 1751500 1751841 1751846) (-1050 "RMCAT2.spad" 1750897 1750954 1751479 1751484) (-1049 "RMATRIX.spad" 1749721 1749740 1750064 1750103) (-1048 "RMATCAT.spad" 1745254 1745285 1749677 1749716) (-1047 "RMATCAT.spad" 1740677 1740710 1745102 1745107) (-1046 "RINTERP.spad" 1740565 1740585 1740667 1740672) (-1045 "RING.spad" 1740035 1740044 1740545 1740560) (-1044 "RING.spad" 1739513 1739524 1740025 1740030) (-1043 "RIDIST.spad" 1738897 1738906 1739503 1739508) (-1042 "RGCHAIN.spad" 1737476 1737492 1738382 1738409) (-1041 "RGBCSPC.spad" 1737257 1737269 1737466 1737471) (-1040 "RGBCMDL.spad" 1736787 1736799 1737247 1737252) (-1039 "RF.spad" 1734401 1734412 1736777 1736782) (-1038 "RFFACTOR.spad" 1733863 1733874 1734391 1734396) (-1037 "RFFACT.spad" 1733598 1733610 1733853 1733858) (-1036 "RFDIST.spad" 1732586 1732595 1733588 1733593) (-1035 "RETSOL.spad" 1732003 1732016 1732576 1732581) (-1034 "RETRACT.spad" 1731431 1731442 1731993 1731998) (-1033 "RETRACT.spad" 1730857 1730870 1731421 1731426) (-1032 "RETAST.spad" 1730669 1730678 1730847 1730852) (-1031 "RESULT.spad" 1728729 1728738 1729316 1729343) (-1030 "RESRING.spad" 1728076 1728123 1728667 1728724) (-1029 "RESLATC.spad" 1727400 1727411 1728066 1728071) (-1028 "REPSQ.spad" 1727129 1727140 1727390 1727395) (-1027 "REP.spad" 1724681 1724690 1727119 1727124) (-1026 "REPDB.spad" 1724386 1724397 1724671 1724676) (-1025 "REP2.spad" 1713958 1713969 1724228 1724233) (-1024 "REP1.spad" 1707948 1707959 1713908 1713913) (-1023 "REGSET.spad" 1705745 1705762 1707594 1707621) (-1022 "REF.spad" 1705074 1705085 1705700 1705705) (-1021 "REDORDER.spad" 1704250 1704267 1705064 1705069) (-1020 "RECLOS.spad" 1703033 1703053 1703737 1703830) (-1019 "REALSOLV.spad" 1702165 1702174 1703023 1703028) (-1018 "REAL.spad" 1702037 1702046 1702155 1702160) (-1017 "REAL0Q.spad" 1699319 1699334 1702027 1702032) (-1016 "REAL0.spad" 1696147 1696162 1699309 1699314) (-1015 "RDUCEAST.spad" 1695868 1695877 1696137 1696142) (-1014 "RDIV.spad" 1695519 1695544 1695858 1695863) (-1013 "RDIST.spad" 1695082 1695093 1695509 1695514) (-1012 "RDETRS.spad" 1693878 1693896 1695072 1695077) (-1011 "RDETR.spad" 1691985 1692003 1693868 1693873) (-1010 "RDEEFS.spad" 1691058 1691075 1691975 1691980) (-1009 "RDEEF.spad" 1690054 1690071 1691048 1691053) (-1008 "RCFIELD.spad" 1687240 1687249 1689956 1690049) (-1007 "RCFIELD.spad" 1684512 1684523 1687230 1687235) (-1006 "RCAGG.spad" 1682424 1682435 1684502 1684507) (-1005 "RCAGG.spad" 1680263 1680276 1682343 1682348) (-1004 "RATRET.spad" 1679623 1679634 1680253 1680258) (-1003 "RATFACT.spad" 1679315 1679327 1679613 1679618) (-1002 "RANDSRC.spad" 1678634 1678643 1679305 1679310) (-1001 "RADUTIL.spad" 1678388 1678397 1678624 1678629) (-1000 "RADIX.spad" 1675289 1675303 1676855 1676948) (-999 "RADFF.spad" 1673703 1673739 1673821 1673977) (-998 "RADCAT.spad" 1673297 1673305 1673693 1673698) (-997 "RADCAT.spad" 1672889 1672899 1673287 1673292) (-996 "QUEUE.spad" 1672232 1672242 1672496 1672523) (-995 "QUAT.spad" 1670814 1670824 1671156 1671221) (-994 "QUATCT2.spad" 1670433 1670451 1670804 1670809) (-993 "QUATCAT.spad" 1668598 1668608 1670363 1670428) (-992 "QUATCAT.spad" 1666514 1666526 1668281 1668286) (-991 "QUAGG.spad" 1665340 1665350 1666482 1666509) (-990 "QQUTAST.spad" 1665109 1665117 1665330 1665335) (-989 "QFORM.spad" 1664572 1664586 1665099 1665104) (-988 "QFCAT.spad" 1663275 1663285 1664474 1664567) (-987 "QFCAT.spad" 1661569 1661581 1662770 1662775) (-986 "QFCAT2.spad" 1661260 1661276 1661559 1661564) (-985 "QEQUAT.spad" 1660817 1660825 1661250 1661255) (-984 "QCMPACK.spad" 1655564 1655583 1660807 1660812) (-983 "QALGSET.spad" 1651639 1651671 1655478 1655483) (-982 "QALGSET2.spad" 1649635 1649653 1651629 1651634) (-981 "PWFFINTB.spad" 1646945 1646966 1649625 1649630) (-980 "PUSHVAR.spad" 1646274 1646293 1646935 1646940) (-979 "PTRANFN.spad" 1642400 1642410 1646264 1646269) (-978 "PTPACK.spad" 1639488 1639498 1642390 1642395) (-977 "PTFUNC2.spad" 1639309 1639323 1639478 1639483) (-976 "PTCAT.spad" 1638558 1638568 1639277 1639304) (-975 "PSQFR.spad" 1637865 1637889 1638548 1638553) (-974 "PSEUDLIN.spad" 1636723 1636733 1637855 1637860) (-973 "PSETPK.spad" 1622156 1622172 1636601 1636606) (-972 "PSETCAT.spad" 1616076 1616099 1622136 1622151) (-971 "PSETCAT.spad" 1609970 1609995 1616032 1616037) (-970 "PSCURVE.spad" 1608953 1608961 1609960 1609965) (-969 "PSCAT.spad" 1607720 1607749 1608851 1608948) (-968 "PSCAT.spad" 1606577 1606608 1607710 1607715) (-967 "PRTITION.spad" 1605522 1605530 1606567 1606572) (-966 "PRTDAST.spad" 1605241 1605249 1605512 1605517) (-965 "PRS.spad" 1594803 1594820 1605197 1605202) (-964 "PRQAGG.spad" 1594234 1594244 1594771 1594798) (-963 "PROPLOG.spad" 1593637 1593645 1594224 1594229) (-962 "PROPFRML.spad" 1591555 1591566 1593627 1593632) (-961 "PROPERTY.spad" 1591049 1591057 1591545 1591550) (-960 "PRODUCT.spad" 1588729 1588741 1589015 1589070) (-959 "PR.spad" 1587115 1587127 1587820 1587947) (-958 "PRINT.spad" 1586867 1586875 1587105 1587110) (-957 "PRIMES.spad" 1585118 1585128 1586857 1586862) (-956 "PRIMELT.spad" 1583099 1583113 1585108 1585113) (-955 "PRIMCAT.spad" 1582722 1582730 1583089 1583094) (-954 "PRIMARR.spad" 1581727 1581737 1581905 1581932) (-953 "PRIMARR2.spad" 1580450 1580462 1581717 1581722) (-952 "PREASSOC.spad" 1579822 1579834 1580440 1580445) (-951 "PPCURVE.spad" 1578959 1578967 1579812 1579817) (-950 "PORTNUM.spad" 1578734 1578742 1578949 1578954) (-949 "POLYROOT.spad" 1577563 1577585 1578690 1578695) (-948 "POLY.spad" 1574860 1574870 1575377 1575504) (-947 "POLYLIFT.spad" 1574121 1574144 1574850 1574855) (-946 "POLYCATQ.spad" 1572223 1572245 1574111 1574116) (-945 "POLYCAT.spad" 1565629 1565650 1572091 1572218) (-944 "POLYCAT.spad" 1558337 1558360 1564801 1564806) (-943 "POLY2UP.spad" 1557785 1557799 1558327 1558332) (-942 "POLY2.spad" 1557380 1557392 1557775 1557780) (-941 "POLUTIL.spad" 1556321 1556350 1557336 1557341) (-940 "POLTOPOL.spad" 1555069 1555084 1556311 1556316) (-939 "POINT.spad" 1553908 1553918 1553995 1554022) (-938 "PNTHEORY.spad" 1550574 1550582 1553898 1553903) (-937 "PMTOOLS.spad" 1549331 1549345 1550564 1550569) (-936 "PMSYM.spad" 1548876 1548886 1549321 1549326) (-935 "PMQFCAT.spad" 1548463 1548477 1548866 1548871) (-934 "PMPRED.spad" 1547932 1547946 1548453 1548458) (-933 "PMPREDFS.spad" 1547376 1547398 1547922 1547927) (-932 "PMPLCAT.spad" 1546446 1546464 1547308 1547313) (-931 "PMLSAGG.spad" 1546027 1546041 1546436 1546441) (-930 "PMKERNEL.spad" 1545594 1545606 1546017 1546022) (-929 "PMINS.spad" 1545170 1545180 1545584 1545589) (-928 "PMFS.spad" 1544743 1544761 1545160 1545165) (-927 "PMDOWN.spad" 1544029 1544043 1544733 1544738) (-926 "PMASS.spad" 1543041 1543049 1544019 1544024) (-925 "PMASSFS.spad" 1542010 1542026 1543031 1543036) (-924 "PLOTTOOL.spad" 1541790 1541798 1542000 1542005) (-923 "PLOT.spad" 1536621 1536629 1541780 1541785) (-922 "PLOT3D.spad" 1533041 1533049 1536611 1536616) (-921 "PLOT1.spad" 1532182 1532192 1533031 1533036) (-920 "PLEQN.spad" 1519398 1519425 1532172 1532177) (-919 "PINTERP.spad" 1519014 1519033 1519388 1519393) (-918 "PINTERPA.spad" 1518796 1518812 1519004 1519009) (-917 "PI.spad" 1518403 1518411 1518770 1518791) (-916 "PID.spad" 1517359 1517367 1518329 1518398) (-915 "PICOERCE.spad" 1517016 1517026 1517349 1517354) (-914 "PGROEB.spad" 1515613 1515627 1517006 1517011) (-913 "PGE.spad" 1506866 1506874 1515603 1515608) (-912 "PGCD.spad" 1505748 1505765 1506856 1506861) (-911 "PFRPAC.spad" 1504891 1504901 1505738 1505743) (-910 "PFR.spad" 1501548 1501558 1504793 1504886) (-909 "PFOTOOLS.spad" 1500806 1500822 1501538 1501543) (-908 "PFOQ.spad" 1500176 1500194 1500796 1500801) (-907 "PFO.spad" 1499595 1499622 1500166 1500171) (-906 "PF.spad" 1499169 1499181 1499400 1499493) (-905 "PFECAT.spad" 1496835 1496843 1499095 1499164) (-904 "PFECAT.spad" 1494529 1494539 1496791 1496796) (-903 "PFBRU.spad" 1492399 1492411 1494519 1494524) (-902 "PFBR.spad" 1489937 1489960 1492389 1492394) (-901 "PERM.spad" 1485618 1485628 1489767 1489782) (-900 "PERMGRP.spad" 1480354 1480364 1485608 1485613) (-899 "PERMCAT.spad" 1478906 1478916 1480334 1480349) (-898 "PERMAN.spad" 1477438 1477452 1478896 1478901) (-897 "PENDTREE.spad" 1476777 1476787 1477067 1477072) (-896 "PDRING.spad" 1475268 1475278 1476757 1476772) (-895 "PDRING.spad" 1473767 1473779 1475258 1475263) (-894 "PDEPROB.spad" 1472782 1472790 1473757 1473762) (-893 "PDEPACK.spad" 1466784 1466792 1472772 1472777) (-892 "PDECOMP.spad" 1466246 1466263 1466774 1466779) (-891 "PDECAT.spad" 1464600 1464608 1466236 1466241) (-890 "PCOMP.spad" 1464451 1464464 1464590 1464595) (-889 "PBWLB.spad" 1463033 1463050 1464441 1464446) (-888 "PATTERN.spad" 1457464 1457474 1463023 1463028) (-887 "PATTERN2.spad" 1457200 1457212 1457454 1457459) (-886 "PATTERN1.spad" 1455502 1455518 1457190 1457195) (-885 "PATRES.spad" 1453049 1453061 1455492 1455497) (-884 "PATRES2.spad" 1452711 1452725 1453039 1453044) (-883 "PATMATCH.spad" 1450868 1450899 1452419 1452424) (-882 "PATMAB.spad" 1450293 1450303 1450858 1450863) (-881 "PATLRES.spad" 1449377 1449391 1450283 1450288) 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index f7e35655..a55e54a3 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(162091 . 3443021577) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((#0=(-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) #0#) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))))) -((((-563)) . T) (($) -4032 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-555))) (((-407 (-563))) -4032 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-563))))) ((|#1|) . T)) +(162113 . 3443721773) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((#0=(-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) #0#) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))))) +((((-563)) . 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T) (((-407 (-563))) |has| |#2| (-38 (-407 (-563))))) +((($) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) ((|#2|) . T) (((-407 (-563))) |has| |#2| (-38 (-407 (-563))))) (|has| |#1| (-905)) ((((-858)) . T)) ((((-858)) . T)) @@ -24,19 +24,19 @@ ((((-225)) . T) (((-858)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (((|#1|) . T)) -(-4032 (|has| |#1| (-21)) (|has| |#1| (-844))) -((($ $) . T) ((#0=(-407 (-563)) #0#) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -(-4032 (|has| |#1| (-816)) (|has| |#1| (-846))) +(-4034 (|has| |#1| (-21)) (|has| |#1| (-844))) +((($ $) . T) ((#0=(-407 (-563)) #0#) -4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +(-4034 (|has| |#1| (-816)) (|has| |#1| (-846))) ((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) |has| |#1| (-1034 (-563))) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (|has| |#1| (-844)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (((|#1| |#2| |#3|) . T)) ((((-1174)) . T)) ((((-563)) . T) (((-866 |#1|)) . T) (($) . T) (((-407 (-563))) . T)) -((($) . T) (((-407 (-563))) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) . T) (((-407 (-563))) -4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-858)) . T)) ((((-1174)) . T)) (((|#4|) . T)) @@ -46,14 +46,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1174)) . T)) (((|#1|) . T) (((-563)) |has| |#1| (-1034 (-563))) (((-407 (-563))) |has| |#1| (-1034 (-407 (-563))))) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) -(((|#2| (-482 (-3608 |#1|) (-767))) . 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T)) -((((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) . T)) (|has| |#1| (-38 (-407 (-563)))) -((((-388) (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) . T)) +((((-388) (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) . T)) (|has| |#1| (-38 (-407 (-563)))) (|has| |#2| (-1144)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) ((((-858)) . T) (((-1174)) . T)) ((((-858)) . T) (((-1174)) . T)) ((((-858)) . T) (((-1174)) . T)) @@ -786,7 +786,7 @@ ((((-388) (-1151)) . T)) (|has| |#1| (-555)) ((((-563) |#1|) . T)) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((((-563)) . T) (($) . T) (((-407 (-563))) . T)) ((((-563)) . T) (($) . T) (((-407 (-563))) . T)) (((|#2|) . T)) @@ -802,7 +802,7 @@ ((((-640 |#1|)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-611 (-536)))) -(-4032 (|has| |#1| (-846)) (|has| |#1| (-1093))) +(-4034 (|has| |#1| (-846)) (|has| |#1| (-1093))) (((|#2|) |has| |#2| (-309 |#2|))) (((#0=(-563) #0#) . T) ((#1=(-407 (-563)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -812,7 +812,7 @@ (((#0=(-563) #0#) . T) ((#1=(-407 (-563)) #1#) . T) (($ $) . T)) ((($) . T) (((-563)) . T) (((-407 (-563))) . T)) (|has| |#2| (-368)) -(-4032 (|has| |#1| (-846)) (|has| |#1| (-1093))) +(-4034 (|has| |#1| (-846)) (|has| |#1| (-1093))) (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) @@ -826,8 +826,8 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-611 (-536)))) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) -((($) . T) (((-407 (-563))) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((($) . T) (((-407 (-563))) -4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($ $) . T)) ((((-858)) . T)) ((($ $) . T)) @@ -837,12 +837,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) +((($) -4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) ((((-407 (-563))) . T) (((-563)) . T)) ((((-563) (-144)) . T)) ((((-144)) . T)) (((|#1|) . T)) -(-4032 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) +(-4034 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) ((((-112)) . T)) @@ -851,26 +851,26 @@ ((((-858)) . T)) ((((-1174)) . T)) (|has| |#1| (-816)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (|has| |#1| (-846)) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-555))) (|has| |#1| (-555)) ((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) ((|#1|) . T) (((-563)) . T)) (|has| |#1| (-905)) (((|#1|) . T)) (|has| |#1| (-1093)) ((((-858)) . T)) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-555))) ((((-858)) . T)) ((((-858)) . T)) ((((-858)) . T)) (((|#1| (-1257 |#1|) (-1257 |#1|)) . T)) ((((-563) (-144)) . T)) ((($) . T)) -(-4032 (|has| |#4| (-172)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-4032 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-4034 (|has| |#4| (-172)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-4034 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-1174)) . T) (((-858)) . T)) ((((-1174)) . T)) ((((-858)) . T)) @@ -878,14 +878,14 @@ (((|#1| (-967)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-4032 (|has| |#2| (-789)) (|has| |#2| (-844))) -(-4032 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-4034 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-4034 (|has| |#2| (-789)) (|has| |#2| (-844))) (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-4032 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) (((|#1|) . T)) (|has| |#2| (-789)) -(-4032 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-4034 (|has| |#2| (-789)) (|has| |#2| (-844))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (|has| |#2| (-844)) @@ -901,8 +901,8 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-407 (-563))) . T) (($) . T)) -((($) |has| |#1| (-555)) ((|#1|) . T) (((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563))))) (((-563)) . T)) -((($) . T) (((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) ((|#1|) . T)) +((($) |has| |#1| (-555)) ((|#1|) . T) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563))))) (((-563)) . T)) +((($) . T) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-824)) ((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) |has| |#1| (-1034 (-563))) ((|#1|) . T)) (|has| |#1| (-1093)) @@ -913,30 +913,30 @@ (((|#3|) |has| |#3| (-1093))) (|has| |#3| (-368)) (((|#1|) . T) (((-858)) . T)) -((((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($) -4032 (|has| |#1| (-363)) (|has| |#1| (-555))) (((-1249 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +((((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($) -4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (((-1249 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) (((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) (((|#1| |#2|) . T)) (((|#2|) . T)) -(((|#1|) |has| |#1| (-172)) (((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($) -4032 (|has| |#1| (-363)) (|has| |#1| (-555)))) +(((|#1|) |has| |#1| (-172)) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($) -4034 (|has| |#1| (-363)) (|has| |#1| (-555)))) ((($) |has| |#1| (-555)) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) (((|#1| |#1|) |has| |#1| (-172))) (|has| |#2| (-363)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((((-407 (-563))) . T) (((-563)) . T)) -((($ $) -4032 (|has| |#1| (-172)) (|has| |#1| (-555))) ((|#1| |#1|) . T) ((#0=(-407 (-563)) #0#) |has| |#1| (-38 (-407 (-563))))) -((($) -4032 (|has| |#1| (-172)) (|has| |#1| (-555))) ((|#1|) . T) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) +((($ $) -4034 (|has| |#1| (-172)) (|has| |#1| (-555))) ((|#1| |#1|) . T) ((#0=(-407 (-563)) #0#) |has| |#1| (-38 (-407 (-563))))) +((($) -4034 (|has| |#1| (-172)) (|has| |#1| (-555))) ((|#1|) . T) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) ((((-144)) . T)) (((|#1|) . T)) -((($) -4032 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((|#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045)))) +((($) -4034 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((|#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045)))) ((((-144)) . T)) ((((-144)) . T)) ((((-407 (-563))) . #0=(|has| |#2| (-363))) (($) . #0#) ((|#2|) . T) (((-563)) . T)) (((|#1| |#2| |#3|) . T)) -(-4032 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) +(-4034 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) (|has| $ (-147)) (|has| $ (-147)) ((((-1174)) . T)) @@ -944,14 +944,14 @@ ((((-858)) . T)) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-555)) (|has| |#1| (-1045)) (|has| |#1| (-1105))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-555)) (|has| |#1| (-1045)) (|has| |#1| (-1105))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-563))) . T)) (((|#1|) . T)) ((((-1169)) . T)) (|has| |#1| (-555)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (|has| |#1| (-555)) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) @@ -962,7 +962,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-844)) -(((|#2| (-240 (-3608 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-240 (-3610 |#1|) (-767)) (-860 |#1|)) . T)) (|has| |#3| (-844)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -977,20 +977,20 @@ (|has| |#1| (-145)) ((((-407 (-563))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) -(-4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) -(-4032 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) +(-4034 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1135 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1045))) -(((|#2|) . T) (((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) -(-4032 (|has| |#3| (-789)) (|has| |#3| (-844))) -(-4032 (|has| |#3| (-789)) (|has| |#3| (-844))) +(((|#2|) . T) (((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) +(-4034 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-4034 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-694)) . T)) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-555)) (((|#1|) . T)) (((|#1|) . T)) @@ -1014,11 +1014,11 @@ (((|#1| (-407 (-563))) . T)) (((|#3|) . T) (((-609 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) -((((-563)) -4032 (|has| |#2| (-172)) (|has| |#2| (-844)) (-12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) (|has| |#2| (-1045))) ((|#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-1093))) (((-407 (-563))) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093)))) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) +((((-563)) -4034 (|has| |#2| (-172)) (|has| |#2| (-844)) (-12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) (|has| |#2| (-1045))) ((|#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-1093))) (((-407 (-563))) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093)))) (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-563)) . T) (($) . T) (((-407 (-563))) . T)) @@ -1026,8 +1026,8 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) (((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))))) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093))) (((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) |has| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (-309 (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) (((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093))) (((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) |has| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (-309 (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))))) ((((-858)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1038,10 +1038,10 @@ ((($ $) . T) ((#0=(-860 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-824)) (|has| |#1| (-1093)) -(((|#2| |#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) -(((|#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-363)))) -((((-563) (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) +(((|#2| |#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) +(((|#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)))) +((((-563) (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) ((((-1174)) . T)) ((((-767)) . T)) (|has| |#1| (-555)) @@ -1055,31 +1055,31 @@ ((((-116 |#1|)) . T)) (((|#1|) . 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T)) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) (((|#2|) |has| |#2| (-172))) -((($) -4032 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) ((|#2|) |has| |#2| (-172)) (((-407 (-563))) |has| |#2| (-38 (-407 (-563))))) +((($) -4034 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) ((|#2|) |has| |#2| (-172)) (((-407 (-563))) |has| |#2| (-38 (-407 (-563))))) ((((-866 |#1|)) . 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T)) (((|#1|) |has| |#1| (-309 |#1|))) @@ -1129,11 +1129,11 @@ (|has| |#1| (-368)) ((((-1169) $) |has| |#1| (-514 (-1169) $)) (($ $) |has| |#1| (-309 $)) ((|#1| |#1|) |has| |#1| (-309 |#1|)) (((-1169) |#1|) |has| |#1| (-514 (-1169) |#1|))) ((((-1169)) |has| |#1| (-896 (-1169)))) -(-4032 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) +(-4034 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-388) |#1|) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-1093)) (((|#2|) . T) (((-858)) . T)) ((((-858)) . T)) @@ -1141,8 +1141,8 @@ ((((-906 |#1|)) . T)) ((((-858)) . T) (((-1174)) . T)) ((((-1174)) . T)) -((((-407 (-563))) |has| |#2| (-38 (-407 (-563)))) ((|#2|) |has| |#2| (-172)) (($) -4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905)))) -((((-407 (-563))) |has| |#1| (-38 (-407 (-563)))) ((|#1|) |has| |#1| (-172)) (($) -4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905)))) +((((-407 (-563))) |has| |#2| (-38 (-407 (-563)))) ((|#2|) |has| |#2| (-172)) (($) -4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905)))) +((((-407 (-563))) |has| |#1| (-38 (-407 (-563)))) ((|#1|) |has| |#1| (-172)) (($) -4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-563)) . T) (($) . T) (((-407 (-563))) . T)) @@ -1151,16 +1151,16 @@ (((|#1|) . T) (((-407 (-563))) . T) (($) . T) (((-563)) . T)) (((|#1| |#1|) . T)) (((#0=(-866 |#1|)) |has| #0# (-309 #0#))) -((((-563)) . 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T)) (|has| |#1| (-1193)) (((#0=(-563) #0#) . T) ((#1=(-407 (-563)) #1#) . T) (($ $) . T)) ((((-407 (-563))) . T) (($) . T)) @@ -1171,8 +1171,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-563)) #0#) . T)) (|has| |#1| (-363)) ((((-563)) . T) (((-407 (-563))) . T) (($) . T)) -((($ $) . T) ((#0=(-407 (-563)) #0#) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((($ $) . T) ((#0=(-407 (-563)) #0#) -4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) (((|#1|) . T) (($) . T) (((-407 (-563))) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -1187,14 +1187,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) -((($) . T) (((-407 (-563))) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-555))) +((($) . 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T)) +((((-858)) -4034 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-610 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) (((-1257 |#2|)) . T)) (|has| |#1| (-846)) (|has| |#1| (-846)) ((((-1151) (-52)) . T)) @@ -1203,10 +1203,10 @@ ((((-563)) |has| #0=(-407 |#2|) (-636 (-563))) ((#0#) . T)) ((($) . T) (((-563)) . T)) ((((-563) (-144)) . T)) -((((-563) (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T) ((|#1| |#2|) . T)) +((((-563) (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T) ((|#1| |#2|) . T)) ((((-407 (-563))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-858)) . T)) ((((-906 |#1|)) . T)) (|has| |#1| (-363)) @@ -1233,21 +1233,21 @@ ((((-858)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-563) (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T) ((|#1| |#2|) . 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T)) @@ -1255,39 +1255,39 @@ (|has| |#1| (-555)) ((((-1151) |#1|) . T)) (|has| |#1| (-1144)) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-954 |#1|)) . T)) -(((#0=(-407 (-563)) #0#) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($ $) -4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) ((|#1| |#1|) . T)) +(((#0=(-407 (-563)) #0#) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($ $) -4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) ((|#1| |#1|) . T)) ((((-407 (-563))) |has| |#1| (-1034 (-563))) (((-563)) |has| |#1| (-1034 (-563))) (((-1169)) |has| |#1| (-1034 (-1169))) ((|#1|) . T)) ((((-563) |#2|) . T)) ((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) |has| |#1| (-1034 (-563))) ((|#1|) . 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T)) ((($) |has| |#1| (-844))) -((((-563)) -4032 (|has| |#2| (-172)) (|has| |#2| (-844)) (-12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) (|has| |#2| (-1045))) ((|#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-1093))) (((-407 (-563))) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093)))) +((((-563)) -4034 (|has| |#2| (-172)) (|has| |#2| (-844)) (-12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) (|has| |#2| (-1045))) ((|#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-1093))) (((-407 (-563))) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093)))) (((|#1|) . T)) ((((-640 |#4|)) . T) (((-858)) . T)) ((((-536)) |has| |#4| (-611 (-536)))) (((|#1|) . T)) (((|#2|) . T)) ((((-1169)) |has| (-407 |#2|) (-896 (-1169)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((#0=(-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) #0#) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((#0=(-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) #0#) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-858)) -4032 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-610 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1093))) (((-1257 |#3|)) . T)) +((((-858)) -4034 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-610 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1093))) (((-1257 |#3|)) . T)) ((((-563) |#2|) . T)) -(-4032 (|has| |#1| (-846)) (|has| |#1| (-1093))) -(((|#2| |#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) +(-4034 (|has| |#1| (-846)) (|has| |#1| (-1093))) +(((|#2| |#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) (((|#2|) . T) (((-563)) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T) ((|#2|) . T)) ((((-858)) . T)) ((((-858)) . T)) ((((-1151) (-1169) (-563) (-225) (-858)) . T)) @@ -1322,8 +1322,8 @@ (|has| |#1| (-38 (-407 (-563)))) ((((-858)) . T)) ((((-536)) |has| |#1| (-611 (-536)))) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) -(((|#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +(((|#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-407 |#2|)) . T)) ((((-889 |#1|)) . T) ((|#2|) . T) (((-563)) . T) (((-815 |#1|)) . T)) @@ -1335,11 +1335,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1376,7 +1376,7 @@ ((((-995 |#1|)) . T) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-407 (-563))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1165 |#1|)) . T)) ((((-563)) . T) (($) . T) (((-407 (-563))) . T)) @@ -1384,9 +1384,9 @@ (|has| |#1| (-846)) (((|#2|) . T)) ((((-563)) . T) (($) . T) (((-407 (-563))) . T)) -((((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) . T)) ((((-563) |#2|) . T)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) (((|#2|) . T)) ((((-563) |#3|) . T)) (((|#2|) . T)) @@ -1399,7 +1399,7 @@ (|has| |#1| (-1093)) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((#0=(-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) #0#) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((#0=(-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) #0#) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-563)))) (((|#2|) . T)) @@ -1434,19 +1434,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (((|#1| |#2|) . T)) ((((-563) (-144)) . T)) -(((#0=(-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) #0#) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) -((($) -4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) +(((#0=(-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) #0#) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) +((($) -4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) (|has| |#1| (-846)) (((|#2| (-767) (-1075)) . T)) (((|#1| |#2|) . T)) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-555))) (|has| |#1| (-787)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-4032 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-4032 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-4034 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-4034 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1151) |#1|) . T)) @@ -1460,10 +1460,10 @@ (((|#3|) . T)) ((((-1249 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) -(-4032 (|has| |#1| (-846)) (|has| |#1| (-1093))) +(-4034 (|has| |#1| (-846)) (|has| |#1| (-1093))) (((|#1|) . T)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093))) (((-954 |#1|)) . T)) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093))) (((-954 |#1|)) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) @@ -1477,8 +1477,8 @@ ((($) . T)) ((((-388) (-1151)) . T)) ((($) |has| |#1| (-555)) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) -((((-858)) -4032 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-610 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) (((-1257 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2387 (-1151)) (|:| -2557 #0#))) . T)) +((((-858)) -4034 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-610 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) (((-1257 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2387 (-1151)) (|:| -2556 #0#))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) @@ -1486,7 +1486,7 @@ (|has| |#2| (-145)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-4032 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045))) +(-4034 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045))) (|has| |#1| (-363)) ((((-858)) . T)) (|has| |#1| (-38 (-407 (-563)))) @@ -1497,8 +1497,8 @@ (|has| |#1| (-844)) ((((-858)) . T)) (((|#2|) . T)) -((((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($) -4032 (|has| |#1| (-363)) (|has| |#1| (-555))) (((-1249 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($) -4032 (|has| |#1| (-363)) (|has| |#1| (-555)))) +((((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($) -4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (((-1249 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($) -4034 (|has| |#1| (-363)) (|has| |#1| (-555)))) ((($) |has| |#1| (-555)) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) (((|#2|) . T) (((-563)) . T) (((-815 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1507,7 +1507,7 @@ ((((-858)) . T)) ((((-858)) . T)) (|has| |#1| (-1093)) -(((|#2| (-482 (-3608 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-482 (-3610 |#1|) (-767)) (-860 |#1|)) . T)) ((((-407 (-563))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1169)) (-1169)) . T)) (((|#1|) . T)) @@ -1527,16 +1527,16 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) -((((-2 (|:| -2387 (-1169)) (|:| -2557 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) +((((-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))) . T)) ((((-1167 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-1169) (-52)) . T)) ((($ $) . T)) (((|#1| (-563)) . T)) ((((-906 |#1|)) . T)) -(((|#1|) -4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -4032 (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)))) +(((|#1|) -4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -4034 (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)))) (((|#1|) . T) (((-563)) |has| |#1| (-1034 (-563))) (((-407 (-563))) |has| |#1| (-1034 (-407 (-563))))) (|has| |#1| (-846)) (|has| |#1| (-846)) @@ -1554,11 +1554,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1093)))) (|has| |#2| (-846)) (|has| |#1| (-846)) -(((|#3|) -4032 (|has| |#3| (-172)) (|has| |#3| (-363)))) -(-4032 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) +(((|#3|) -4034 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(-4034 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) ((($ $) . T) ((#0=(-407 (-563)) #0#) . T)) ((((-563) |#2|) . T)) -(((|#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)))) (|has| |#1| (-349)) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1093)))) (((|#2|) . T) (((-563)) . T)) @@ -1567,7 +1567,7 @@ (|has| |#1| (-816)) (|has| |#1| (-816)) (((|#1|) . T)) -(-4032 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-844)) (|has| |#1| (-844)) (|has| |#1| (-844)) @@ -1576,13 +1576,13 @@ ((((-563)) . T) (($) . T) (((-407 (-563))) . T)) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-563)))) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-1169)) |has| |#1| (-896 (-1169))) (((-1075)) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((#0=(-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) #0#) |has| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (-309 (-2 (|:| -2387 (-1151)) (|:| -2557 (-52)))))) +(((#0=(-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) #0#) |has| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (-309 (-2 (|:| -2387 (-1151)) (|:| -2556 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (|has| |#1| (-1093)) ((((-858)) . T) (((-1174)) . T)) @@ -1601,11 +1601,11 @@ (((|#1| (-767) (-1075)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) -4032 (|has| |#1| (-844)) (|has| |#1| (-1034 (-563)))) ((|#1|) . T)) +((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) -4034 (|has| |#1| (-844)) (|has| |#1| (-1034 (-563)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) (((|#2|) |has| |#2| (-172))) -(-4032 (|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| (-1093))) +(-4034 (|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| (-1093))) (((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -1628,32 +1628,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) +((((-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))) . T)) ((((-407 |#2|)) . T) (((-407 (-563))) . T) (($) . T)) ((((-667 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1662,7 +1662,7 @@ ((((-858)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) ((((-858)) . T)) -((((-407 (-563))) |has| |#2| (-38 (-407 (-563)))) ((|#2|) |has| |#2| (-172)) (($) -4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905)))) +((((-407 (-563))) |has| |#2| (-38 (-407 (-563)))) ((|#2|) |has| |#2| (-172)) (($) -4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905)))) ((((-1174)) . T)) ((((-407 (-563))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T) (((-563)) . T)) (((|#3|) . T) (((-563)) . T) (((-609 $)) . T)) @@ -1670,12 +1670,12 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#2|) . T)) -(-4032 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1093))) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1093))) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) |has| |#1| (-1034 (-563))) ((|#1|) . T)) (|has| |#1| (-1193)) (|has| |#1| (-1193)) -(-4032 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) +(-4034 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) (|has| |#1| (-1193)) (|has| |#1| (-1193)) (((|#3| |#3|) . T)) @@ -1688,16 +1688,16 @@ (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) ((((-1151) (-52)) . T)) (|has| |#1| (-1093)) -(-4032 (|has| |#2| (-816)) (|has| |#2| (-846))) +(-4034 (|has| |#2| (-816)) (|has| |#2| (-846))) (((|#1|) . T)) (((|#1|) |has| |#1| (-172)) (($) . T)) -((($) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-563))) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -4034 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-563))) -4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($) . T)) ((((-1167 |#1| |#2| |#3|)) -12 (|has| (-1167 |#1| |#2| |#3|) (-309 (-1167 |#1| |#2| |#3|))) (|has| |#1| (-363)))) ((((-858)) . T)) ((((-563)) . T) (($) . T)) ((((-767)) . T)) -(-4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) +(-4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) ((((-858)) . T)) ((($) . T) (((-563)) . T)) @@ -1705,30 +1705,30 @@ (|has| |#2| (-905)) (|has| |#1| (-363)) (((|#2|) |has| |#2| (-1093))) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((((-536)) . T) (((-407 (-1165 (-563)))) . T) (((-225)) . T) (((-379)) . T)) ((((-379)) . T) (((-225)) . T) (((-858)) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) (|has| |#1| (-905)) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-905))) ((($) . T) ((|#2|) . T)) -(-4032 (|has| |#1| (-846)) (|has| |#1| (-1093))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-846)) (|has| |#1| (-1093))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((((-858)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) ((($ $) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((($ $) . T)) ((((-563) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-563)) . T)) ((((-112)) . T)) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) (|has| |#1| (-38 (-407 (-563)))) (((|#1| (-563)) . T)) ((($) . T)) @@ -1750,7 +1750,7 @@ (((|#1| (-1221 |#1| |#2| |#3|)) . T)) (((|#1| (-767)) . T)) (((|#1|) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-858)) . T)) (|has| |#1| (-1093)) ((((-1151) |#1|) . T)) @@ -1770,18 +1770,18 @@ (((|#1|) . T)) ((((-563)) . T)) ((((-858)) . T)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) (((|#3|) . T)) -(-4032 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-4034 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T)) ((((-1242 |#2| |#3| |#4|)) . T) (((-1243 |#1| |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -((((-48)) -12 (|has| |#1| (-555)) (|has| |#1| (-1034 (-563)))) (((-609 $)) . T) ((|#1|) . T) (((-563)) |has| |#1| (-1034 (-563))) (((-407 (-563))) -4032 (-12 (|has| |#1| (-555)) (|has| |#1| (-1034 (-563)))) (|has| |#1| (-1034 (-407 (-563))))) (((-407 (-948 |#1|))) |has| |#1| (-555)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1169)) . T)) +((((-48)) -12 (|has| |#1| (-555)) (|has| |#1| (-1034 (-563)))) (((-609 $)) . T) ((|#1|) . T) (((-563)) |has| |#1| (-1034 (-563))) (((-407 (-563))) -4034 (-12 (|has| |#1| (-555)) (|has| |#1| (-1034 (-563)))) (|has| |#1| (-1034 (-407 (-563))))) (((-407 (-948 |#1|))) |has| |#1| (-555)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1169)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-767)) . T)) -((($) -4032 (|has| |#1| (-363)) (|has| |#1| (-555))) (((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-309 |#1|))) ((((-1243 |#1| |#2| |#3| |#4|)) . T)) ((((-563)) |has| |#1| (-882 (-563))) (((-379)) |has| |#1| (-882 (-379)))) @@ -1789,7 +1789,7 @@ (|has| |#1| (-555)) (((|#1|) . T)) ((((-858)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) (((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) (((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-555)) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) @@ -1797,7 +1797,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1093))) ((((-906 |#1|)) . T) (((-407 (-563))) . T) (($) . T) (((-563)) . T)) -(((|#2|) -4032 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -4034 (|has| |#2| (-172)) (|has| |#2| (-363)))) ((((-1242 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-816)) @@ -1807,8 +1807,8 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| (-563) (-1075)) . T)) -(-4032 (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045))) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +(-4034 (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045))) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (((|#1| (-407 (-563)) (-1075)) . T)) (((|#1| (-767) (-1075)) . T)) (|has| |#1| (-846)) @@ -1821,33 +1821,33 @@ (|has| |#1| (-1093)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-563))) . T)) (|has| |#1| (-1093)) -((((-563)) -4032 (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)))) +((((-563)) -4034 (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)))) (((|#1|) . T)) (|has| |#1| (-1093)) ((((-563)) -12 (|has| |#1| (-363)) (|has| |#2| (-636 (-563)))) ((|#2|) |has| |#1| (-363))) -(-4032 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) -((((-684 (-339 (-1707) (-1707 (QUOTE X) (QUOTE HESS)) (-694)))) . T)) +(-4034 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) +((((-684 (-339 (-1706) (-1706 (QUOTE X) (QUOTE HESS)) (-694)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) -((((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) . T)) ((((-858)) . T)) (|has| |#3| (-844)) ((((-858)) . T)) ((((-1242 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -(((|#1| |#1|) -4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1| |#1|) -4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#1|) . T)) ((((-563)) . T)) ((((-563)) . T)) -(((|#1|) -4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1|) -4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#2|) |has| |#2| (-363))) ((($) . T) ((|#1|) . T) (((-407 (-563))) |has| |#1| (-363))) (|has| |#1| (-846)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2387 (-1169)) (|:| -2557 (-52)))) |has| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (-309 (-2 (|:| -2387 (-1169)) (|:| -2557 (-52)))))) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-905))) +((((-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))) |has| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (-309 (-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-905))) (((|#2|) . T) (((-563)) |has| |#2| (-636 (-563)))) ((((-858)) . T)) ((((-858)) . T)) @@ -1878,25 +1878,25 @@ (|has| |#1| (-145)) ((((-563)) . T) ((|#1|) . T) (($) . T) (((-407 (-563))) . T) (((-1169)) |has| |#1| (-1034 (-1169)))) (((|#1| |#2|) . T)) -((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) -4032 (|has| |#1| (-844)) (|has| |#1| (-1034 (-563)))) ((|#1|) . T)) +((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) -4034 (|has| |#1| (-844)) (|has| |#1| (-1034 (-563)))) ((|#1|) . T)) ((((-144)) . T)) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) (((|#1|) . T)) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1| |#1|) . T) ((#0=(-407 (-563)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-563)) . T)) ((((-858)) . T)) (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| (-407 |#2|) (-233)) ((((-640 |#1|)) . T)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-1045))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) (((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) (((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1923,7 +1923,7 @@ (((|#1| (-407 (-563)) (-1075)) . T)) (((|#1| (-767) (-1075)) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-563)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-563)) -4032 (|has| (-407 (-563)) (-1034 (-563))) (|has| |#1| (-1034 (-563)))) (((-407 (-563))) . T)) +(((|#1|) . T) (((-563)) -4034 (|has| (-407 (-563)) (-1034 (-563))) (|has| |#1| (-1034 (-563)))) (((-407 (-563))) . T)) (((|#1| (-599 |#1| |#3|) (-599 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1944,25 +1944,25 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-844)) ((((-563)) . T) ((|#2|) . T) (((-407 (-563))) |has| |#2| (-1034 (-407 (-563))))) -((((-112)) |has| |#1| (-1093)) (((-858)) -4032 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)) (|has| |#1| (-1105)) (|has| |#1| (-1093)))) +((((-112)) |has| |#1| (-1093)) (((-858)) -4034 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)) (|has| |#1| (-1105)) (|has| |#1| (-1093)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2387 (-1151)) (|:| -2557 (-52)))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 (-52)))) . T)) ((((-858)) . T)) ((((-563) |#1|) . T)) ((((-858)) . T)) ((((-694)) . T) (((-407 (-563))) . T) (((-563)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) (((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) (((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|))))) ((((-379)) . T)) ((((-694)) . T)) ((((-407 (-563))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1|) |has| |#1| (-172))) ((((-407 (-948 |#1|))) . T)) (((|#2| |#2|) . T)) -(-4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-846)) @@ -1973,14 +1973,14 @@ (((|#3|) |has| |#3| (-1045))) ((((-1169)) |has| |#2| (-896 (-1169)))) ((((-858)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-407 (-563))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-363)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-555)) (|has| |#1| (-1045)) (|has| |#1| (-1105))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-555)) (|has| |#1| (-1045)) (|has| |#1| (-1105))) (|has| |#1| (-38 (-407 (-563)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2001,11 +2001,11 @@ (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-846)) -((((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) |has| (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)) (-309 (-2 (|:| -2387 |#1|) (|:| -2556 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2023,11 +2023,11 @@ ((((-536)) |has| |#1| (-611 (-536))) (((-888 (-563))) |has| |#1| (-611 (-888 (-563)))) (((-888 (-379))) |has| |#1| (-611 (-888 (-379)))) (((-379)) . #0=(|has| |#1| (-1018))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-858)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((($ $) . T) (((-609 $) $) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) ((($) . T) (((-1243 |#1| |#2| |#3| |#4|)) . T) (((-407 (-563))) . T)) -((($) -4032 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-555))) +((($) -4034 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-555))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-363)) @@ -2038,11 +2038,11 @@ ((((-379)) . T)) (((|#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1093)))) ((((-858)) . T)) -(-4032 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-4034 (|has| |#2| (-452)) (|has| |#2| (-905))) (((|#1|) . T)) (|has| |#1| (-846)) (|has| |#1| (-846)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) ((((-536)) |has| |#1| (-611 (-536)))) (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) ((((-767)) . T)) @@ -2053,13 +2053,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((((-563)) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (((#0=(-1242 |#2| |#3| |#4|)) . T) (((-407 (-563))) |has| #0# (-38 (-407 (-563)))) (($) . T)) ((((-563)) . T)) (|has| |#1| (-363)) -(-4032 (-12 (|has| (-1249 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-4032 (-12 (|has| (-1249 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-4034 (-12 (|has| (-1249 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-4034 (-12 (|has| (-1249 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-363)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2074,23 +2074,23 @@ (((|#2|) . T)) (|has| |#1| (-1093)) (((|#1| |#2|) . T)) -((((-563)) . T) ((|#1|) . T) (((-407 (-563))) -4032 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-563)))))) +((((-563)) . T) ((|#1|) . T) (((-407 (-563))) -4034 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-563)))))) (((|#1|) . T) (((-563)) |has| |#1| (-636 (-563)))) (((|#3|) |has| |#3| (-172))) -(-4032 (|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| (-1093))) +(-4034 (|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| (-1093))) ((((-858)) . T)) ((((-563)) . T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-407 (-563))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T)) ((((-948 |#1|)) . T) (((-858)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -4032 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-563)) #0#) |has| |#1| (-363))) -((((-2 (|:| -2387 (-1169)) (|:| -2557 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -4034 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-563)) #0#) |has| |#1| (-363))) +((((-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))) . T)) ((((-948 |#1|)) . T)) ((($) . T)) ((((-563) |#1|) . T)) ((((-1169)) |has| (-407 |#2|) (-896 (-1169)))) -(((|#1|) . T) (($) -4032 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-563))) |has| |#1| (-363))) +(((|#1|) . T) (($) -4034 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-563))) |has| |#1| (-363))) ((((-536)) |has| |#2| (-611 (-536)))) ((((-684 |#2|)) . T) (((-858)) . T)) (((|#1|) . T)) @@ -2098,8 +2098,8 @@ (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1093)))) ((((-866 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) -(-4032 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-4032 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-4034 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-4034 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) ((((-858)) . T)) (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1093)))) @@ -2115,17 +2115,17 @@ ((((-407 (-563))) . T) (($) . T)) ((((-407 (-563))) . T) (($) . T)) ((((-407 (-563))) . T) (($) . T)) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-1212))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-1212))) ((($) . T)) ((((-407 (-563))) |has| #0=(-407 |#2|) (-1034 (-407 (-563)))) (((-563)) |has| #0# (-1034 (-563))) ((#0#) . T)) (((|#2|) . T) (((-563)) |has| |#2| (-636 (-563)))) (((|#1| (-767)) . T)) (|has| |#1| (-846)) (((|#1|) . T) (((-563)) |has| |#1| (-636 (-563)))) -((($) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-563))) -4032 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -4034 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-563))) -4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-563)) . T)) (|has| |#1| (-38 (-407 (-563)))) -((((-2 (|:| -2387 (-1151)) (|:| -2557 (-52)))) |has| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (-309 (-2 (|:| -2387 (-1151)) (|:| -2557 (-52)))))) +((((-2 (|:| -2387 (-1151)) (|:| -2556 (-52)))) |has| (-2 (|:| -2387 (-1151)) (|:| -2556 (-52))) (-309 (-2 (|:| -2387 (-1151)) (|:| -2556 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (|has| |#1| (-844)) (|has| |#1| (-38 (-407 (-563)))) @@ -2148,29 +2148,29 @@ (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) ((((-1151)) . T) (((-1169)) . T) (((-225)) . T) (((-563)) . T)) -(((|#2|) . T) (((-563)) . T) (($) -4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (((-1075)) . T) ((|#1|) . T) (((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563)))))) +(((|#2|) . T) (((-563)) . T) (($) -4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (((-1075)) . T) ((|#1|) . T) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563)))))) (((|#1| |#2|) . T)) ((((-144)) . T)) ((((-776 |#1| (-860 |#2|))) . T)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) (|has| |#1| (-1193)) ((((-858)) . T)) (((|#1|) . T)) -(-4032 (|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| (-1093))) +(-4034 (|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| (-1093))) ((((-1169) |#1|) |has| |#1| (-514 (-1169) |#1|))) (((|#2|) . T)) -((($ $) -4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-563)) #0#) |has| |#1| (-38 (-407 (-563))))) +((($ $) -4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-563)) #0#) |has| |#1| (-38 (-407 (-563))))) ((((-906 |#1|)) . T)) ((($) . T)) ((((-407 (-948 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) -((($) -4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) +((($) -4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) ((((-536)) |has| |#4| (-611 (-536)))) ((((-858)) . T) (((-640 |#4|)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093))) (((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) |has| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (-309 (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093))) (((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) |has| (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|)) (-309 (-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))))) (|has| |#1| (-1093)) (|has| |#1| (-363)) (|has| |#1| (-846)) @@ -2179,16 +2179,16 @@ (((|#1|) . T)) ((((-667 |#1|)) . T)) ((($) . T) (((-407 (-563))) . T)) -((($) -4032 (|has| |#1| (-363)) (|has| |#1| (-555))) (((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-4032 (-12 (|has| (-1167 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-4032 (-12 (|has| (-1167 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-4034 (-12 (|has| (-1167 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-4034 (-12 (|has| (-1167 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) ((((-1249 |#1| |#2| |#3|)) |has| |#1| (-363))) (|has| |#1| (-844)) (((|#1| |#2|) . T)) @@ -2212,9 +2212,9 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-611 (-536)))) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-1169) |#1|) |has| |#1| (-514 (-1169) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -4032 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -4034 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) (((|#2|) |has| |#2| (-363))) (((|#2|) . T)) @@ -2236,13 +2236,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-4032 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)) (|has| |#1| (-1105)) (|has| |#1| (-1093))) +(-4034 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)) (|has| |#1| (-1105)) (|has| |#1| (-1093))) (|has| |#1| (-555)) (((|#2|) . T)) ((((-563)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (((|#1|) . T)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-580 |#1|)) . T)) ((($) . T)) @@ -2251,14 +2251,14 @@ ((($) . T)) (((|#1|) . T)) ((((-858)) . T)) -(((|#2|) |has| |#2| (-6 (-4409 "*")))) +(((|#2|) |has| |#2| (-6 (-4410 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#3|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-1242 |#2| |#3| |#4|)) . T) (((-563)) . T) (((-1243 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-407 (-563))) . T)) -((((-48)) -12 (|has| |#1| (-555)) (|has| |#1| (-1034 (-563)))) (((-563)) -4032 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1034 (-563))) (|has| |#1| (-1045))) ((|#1|) . T) (((-609 $)) . T) (($) |has| |#1| (-555)) (((-407 (-563))) -4032 (|has| |#1| (-555)) (|has| |#1| (-1034 (-407 (-563))))) (((-407 (-948 |#1|))) |has| |#1| (-555)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1169)) . T)) +((((-48)) -12 (|has| |#1| (-555)) (|has| |#1| (-1034 (-563)))) (((-563)) -4034 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1034 (-563))) (|has| |#1| (-1045))) ((|#1|) . T) (((-609 $)) . T) (($) |has| |#1| (-555)) (((-407 (-563))) -4034 (|has| |#1| (-555)) (|has| |#1| (-1034 (-407 (-563))))) (((-407 (-948 |#1|))) |has| |#1| (-555)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1169)) . T)) ((((-407 (-563))) |has| |#2| (-1034 (-407 (-563)))) (((-563)) |has| |#2| (-1034 (-563))) ((|#2|) . T) (((-860 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-407 (-563))) . T)) ((((-1118 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-563)) |has| |#1| (-1034 (-563))) (((-407 (-563))) |has| |#1| (-1034 (-407 (-563))))) @@ -2271,12 +2271,12 @@ (((|#1| |#2|) . T)) ((((-1169) |#1|) . T)) (((|#4|) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1169) (-52)) . T)) ((((-1242 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) (((-563)) |has| |#1| (-1034 (-563))) ((|#1|) . T)) ((((-858)) . T)) -(-4032 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) +(-4034 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1093))) (((#0=(-1243 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-563)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-172)) ((#0=(-407 (-563)) #0#) |has| |#1| (-555)) (($ $) |has| |#1| (-555))) (((|#1|) . T) (($) . T) (((-407 (-563))) . T)) @@ -2296,14 +2296,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093)))) (((|#2| |#3|) . T)) -(-4032 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) +(-4034 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) (((|#1| (-531 |#2|)) . T)) (((|#1| (-767)) . T)) (((|#1| (-531 (-1081 (-1169)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-905)) -(-4032 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-4034 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-858)) . T)) ((($ $) . T) ((#0=(-1242 |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-563)) #1#) |has| #0# (-38 (-407 (-563))))) ((((-906 |#1|)) . T)) @@ -2312,14 +2312,14 @@ ((((-858)) . T)) ((($) . T)) ((($) . T)) -(-4032 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-555))) (|has| |#1| (-363)) (|has| |#1| (-363)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1242 |#2| |#3| |#4|)) . T) (((-407 (-563))) |has| #0# (-38 (-407 (-563))))) ((((-1167 |#1| |#2| |#3|)) |has| |#1| (-363))) -(-4032 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) -(-4032 (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045))) +(-4034 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045))) ((((-563)) |has| |#1| (-636 (-563))) ((|#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| (-1093)))) -(((|#2|) -4032 (|has| |#2| (-6 (-4409 "*"))) (|has| |#2| (-172)))) -(-4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(((|#2|) -4034 (|has| |#2| (-6 (-4410 "*"))) (|has| |#2| (-172)))) +(-4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (|has| |#2| (-846)) (|has| |#2| (-905)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-1249 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) ((((-858)) . T)) ((((-536)) . T) (((-563)) . T) (((-888 (-563))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) -((((-2 (|:| -2387 (-1151)) (|:| -2557 (-52)))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 (-52)))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#1| |#2|) . T)) (((|#1| (-407 (-563))) . T)) (((|#1|) . T)) -(-4032 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-4034 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-563))) . T) (($) . T)) (|has| |#1| (-844)) @@ -2388,7 +2388,7 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-187)) . T) (((-858)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2401,7 +2401,7 @@ ((((-858)) . T)) ((((-1151)) . T)) ((((-1169) |#1|) |has| |#1| (-514 (-1169) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) . T)) (|has| |#1| (-846)) ((((-858)) . T)) ((((-536)) |has| |#1| (-611 (-536)))) @@ -2413,16 +2413,16 @@ (((|#2|) . T)) ((((-906 |#1|)) . T) (((-407 (-563))) . T) (($) . T)) ((($) . T) (((-563)) . T) (((-407 (-563))) . T) (((-609 $)) . T)) -(-4032 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-4032 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-4034 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-4034 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-1169) (-52)) . T)) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-4032 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-905)) ((((-906 |#1|)) . T) (((-407 (-563))) . T) (($) . T) (((-563)) . T)) (|has| |#1| (-905)) @@ -2439,12 +2439,12 @@ (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (|has| |#1| (-816)) (((#0=(-906 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-563)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-844)) -((((-1194 |#1|)) . T) (((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-1194 |#1|)) . T) (((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) (((|#1| |#1|) . T) ((#0=(-407 (-563)) #0#) . T) ((#1=(-563) #1#) . T) (($ $) . T)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-563))) . T)) (((|#2|) |has| |#2| (-1045)) (((-563)) -12 (|has| |#2| (-636 (-563))) (|has| |#2| (-1045)))) @@ -2455,11 +2455,11 @@ (((|#2|) . T)) ((((-858)) . T)) ((((-407 (-563))) . T) (((-694)) . T) (($) . T) (((-563)) . T)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -2387 (-1169)) (|:| -2557 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2387 (-1169)) (|:| -2557 #0#))) . T)) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2387 (-1169)) (|:| -2556 #0#))) . T)) (|has| |#1| (-349)) ((((-563)) . T)) ((((-858)) . T)) @@ -2467,15 +2467,15 @@ (((#0=(-1243 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) (((#0=(-1075) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-563)) #0#) . T) ((#1=(-694) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-563))) |has| |#1| (-363))) ((((-858)) . T)) (|has| |#1| (-1093)) (((|#1|) . T)) -(((|#1|) -4032 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -4032 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -4034 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -4034 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-563))) . T) (((-694)) . T) (($) . T)) ((((-578)) . T)) @@ -2498,7 +2498,7 @@ (((|#1|) . T)) ((((-563)) . T)) (((|#2|) . T) (((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) ((|#1|) . T) (($) . T) (((-563)) . T)) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (((|#2|) . T) (((-563)) |has| |#2| (-636 (-563)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2536,7 +2536,7 @@ (|has| |#2| (-1018)) ((($) . T)) (|has| |#1| (-905)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2544,9 +2544,9 @@ ((($) . T)) (|has| |#1| (-363)) ((((-906 |#1|)) . T)) -((($) -4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) +((($) -4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) ((($ $) . T) ((#0=(-407 (-563)) #0#) . T)) -(-4032 (|has| |#1| (-368)) (|has| |#1| (-846))) +(-4034 (|has| |#1| (-368)) (|has| |#1| (-846))) (((|#1|) . T)) ((((-767)) . T)) ((((-858)) . T)) @@ -2557,16 +2557,16 @@ ((((-563)) . T) (($) . T)) ((((-563)) . T) (($) . T)) ((((-767) |#1|) . T)) -(((|#2| (-240 (-3608 |#1|) (-767))) . T)) +(((|#2| (-240 (-3610 |#1|) (-767))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-563))) . T)) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((((-1151)) . T) (((-858)) . T)) -(((#0=(-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) #0#) |has| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (-309 (-2 (|:| -2387 (-1169)) (|:| -2557 (-52)))))) +(((#0=(-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) #0#) |has| (-2 (|:| -2387 (-1169)) (|:| -2556 (-52))) (-309 (-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))))) ((((-1151)) . T)) (|has| |#1| (-905)) (|has| |#2| (-363)) -(-4032 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) (((|#1|) . T)) @@ -2583,11 +2583,11 @@ (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) -(-4032 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-563)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-824))) ((((-858)) . T)) -((((-1169)) -4032 (-12 (|has| |#1| (-15 * (|#1| (-563) |#1|))) (|has| |#1| (-896 (-1169)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1169)))))) +((((-1169)) -4034 (-12 (|has| |#1| (-15 * (|#1| (-563) |#1|))) (|has| |#1| (-896 (-1169)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1169)))))) (|has| |#1| (-363)) ((((-1169)) -12 (|has| |#1| (-15 * (|#1| (-407 (-563)) |#1|))) (|has| |#1| (-896 (-1169))))) (|has| |#1| (-363)) @@ -2598,7 +2598,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-563)) . T) (($) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2623,9 +2623,9 @@ ((((-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-379)))) (((-563)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-563))))) (|has| |#1| (-363)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (|has| |#1| (-363)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) (|has| |#1| (-363)) (|has| |#1| (-555)) (((|#1|) . T)) @@ -2634,22 +2634,22 @@ ((((-1151)) . T) (((-1169)) . T) (((-225)) . T) (((-563)) . T)) (((|#1|) . T)) ((((-407 |#2|)) . T) (((-407 (-563))) . T) (($) . T) (((-563)) . T)) -(-4032 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#2|) . T)) (((|#2|) . T)) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) -((((-2 (|:| -2387 (-1151)) (|:| -2557 |#1|))) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 |#1|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (|has| |#1| (-38 (-407 (-563)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-563)))) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-1151) |#1|) . T)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-580 |#1|)) . T)) ((($) . T)) @@ -2657,7 +2657,7 @@ (|has| |#1| (-555)) (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563)))) -(-4032 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) ((($) . T)) @@ -2684,7 +2684,7 @@ ((((-858)) . T)) ((((-906 |#1|)) . T) (((-407 (-563))) . T) (($) . T) (((-563)) . T)) ((((-536)) |has| |#1| (-611 (-536)))) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1093)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2706,7 +2706,7 @@ ((((-563)) . T)) ((((-858)) . T)) ((((-563)) . T)) -(-4032 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-4034 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2718,9 +2718,9 @@ (((|#1|) . T) (($) . T) (((-407 (-563))) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) -(-4032 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)) (|has| |#1| (-1105)) (|has| |#1| (-1093))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +(-4034 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1169))) (|has| |#1| (-1045)) (|has| |#1| (-1105)) (|has| |#1| (-1093))) (|has| |#1| (-1144)) ((((-563) |#1|) . T)) (((|#1|) . T)) @@ -2740,8 +2740,8 @@ (((|#1|) . T)) (|has| |#1| (-555)) ((((-407 |#2|)) . T) (((-407 (-563))) . T) (($) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2750,7 +2750,7 @@ (|has| |#1| (-555)) (|has| |#1| (-1093)) ((((-776 |#1| (-860 |#2|))) |has| (-776 |#1| (-860 |#2|)) (-309 (-776 |#1| (-860 |#2|))))) -(-4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) +(-4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2762,13 +2762,13 @@ (|has| |#2| (-363)) ((((-580 |#1|)) . T) (((-407 (-563))) . T) (($) . T) (((-563)) . T)) ((((-563)) . T) (((-407 (-563))) . T) (($) . T)) -((((-2 (|:| -2387 (-1151)) (|:| -2557 (-52)))) . T)) +((((-2 (|:| -2387 (-1151)) (|:| -2556 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-563)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) ((((-858)) . T)) ((((-858)) . T)) -(-4032 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-4034 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) ((((-1113)) . T) (((-858)) . T)) ((((-536)) . T) (((-858)) . T)) @@ -2779,12 +2779,12 @@ ((((-563)) . T)) (((|#3|) . T)) ((((-858)) . T)) -(-4032 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) -((((-563)) . T) (((-407 (-563))) -4032 (|has| |#2| (-38 (-407 (-563)))) (|has| |#2| (-1034 (-407 (-563))))) ((|#2|) . T) (($) -4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) (((-860 |#1|)) . T)) -((((-1118 |#1| |#2|)) . T) ((|#2|) . T) (($) -4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563))))) (((-563)) . T)) -((((-1165 |#1|)) . T) (((-563)) . T) (($) -4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (((-1075)) . T) ((|#1|) . 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T)) +((((-1165 |#1|)) . T) (((-563)) . T) (($) -4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) (((-1075)) . T) ((|#1|) . T) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563)))))) +(-4034 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-555)) (|has| |#1| (-1045))) +((((-1118 |#1| (-1169))) . T) (((-563)) . T) (((-1081 (-1169))) . T) (($) -4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563))))) (((-1169)) . T)) (((#0=(-580 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-563)) #1#) . T)) ((($ $) . T) ((#0=(-407 (-563)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -2792,13 +2792,13 @@ ((((-580 |#1|)) . T) (($) . T) (((-407 (-563))) . T)) ((($) . T) (((-407 (-563))) . T)) ((($) . T) (((-407 (-563))) . T)) -(((|#2|) |has| |#2| (-6 (-4409 "*")))) +(((|#2|) |has| |#2| (-6 (-4410 "*")))) (((|#1|) . T)) ((((-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) ((|#1|) . T) (((-563)) . T)) (((|#1|) . T)) ((((-858)) . T)) ((((-294 |#3|)) . T)) -(((#0=(-407 (-563)) #0#) |has| |#2| (-38 (-407 (-563)))) ((|#2| |#2|) . T) (($ $) -4032 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905)))) +(((#0=(-407 (-563)) #0#) |has| |#2| (-38 (-407 (-563)))) ((|#2| |#2|) . T) (($ $) -4034 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-563))) |has| |#2| (-38 (-407 (-563)))) ((|#2|) . T)) @@ -2806,21 +2806,21 @@ (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) (((|#1|) . T) (((-407 (-563))) . T) (($) . T)) -((($ $) -4032 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1| |#1|) . 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T) (((-407 (-563))) -4034 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) ((|#1|) . T)) +(((#0=(-407 (-563)) #0#) |has| |#1| (-38 (-407 (-563)))) ((|#1| |#1|) . T) (($ $) -4034 (|has| |#1| (-172)) (|has| |#1| (-555)))) ((($) . T) (((-407 (-563))) . T)) (((|#1|) . T) (((-407 (-563))) . T) (((-563)) . T) (($) . T)) (((|#2|) |has| |#2| (-1045)) (((-563)) -12 (|has| |#2| (-636 (-563))) (|has| |#2| (-1045)))) -((((-407 (-563))) |has| |#1| (-38 (-407 (-563)))) ((|#1|) . T) (($) -4032 (|has| |#1| (-172)) (|has| |#1| (-555)))) +((((-407 (-563))) |has| |#1| (-38 (-407 (-563)))) ((|#1|) . T) (($) -4034 (|has| |#1| (-172)) (|has| |#1| (-555)))) (|has| |#1| (-555)) (((|#1|) |has| |#1| (-363))) ((((-563)) . T)) @@ -2879,8 +2879,8 @@ ((((-858)) . T)) (|has| |#2| (-816)) (|has| |#2| (-816)) -((((-407 (-563))) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . 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T)) -(-4032 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-4034 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-563)))) ((((-858)) . T)) @@ -3144,19 +3144,19 @@ (((|#1|) |has| |#1| (-172)) (($) |has| |#1| (-555)) (((-407 (-563))) |has| |#1| (-555))) (((|#2|) . T) (((-563)) |has| |#2| (-636 (-563)))) (|has| |#1| (-363)) -(-4032 (|has| |#1| (-15 * (|#1| (-563) |#1|))) (-12 (|has| |#1| (-363)) (|has| |#2| (-233)))) +(-4034 (|has| |#1| (-15 * (|#1| (-563) |#1|))) (-12 (|has| |#1| (-363)) (|has| |#2| (-233)))) (|has| |#1| (-15 * (|#1| (-407 (-563)) |#1|))) (|has| |#1| (-363)) (((|#1|) . T)) -(((#0=(-407 (-563)) #0#) -4032 (|has| |#1| (-38 (-407 (-563)))) (|has| |#1| (-363))) (($ $) -4032 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-555))) ((|#1| |#1|) . 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T)) -(-4032 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-4032 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) +(-4034 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) ((((-1249 |#1| |#2| |#3|)) |has| |#1| (-363))) ((($) . T) (((-866 |#1|)) . T) (((-407 (-563))) . T)) ((((-1249 |#1| |#2| |#3|)) |has| |#1| (-363))) @@ -3217,15 +3217,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-407 |#2|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-407 (-563)) #0#) . T) (($ $) . T)) ((((-563)) . T)) @@ -3255,17 +3255,17 @@ ((((-129)) . T)) ((((-858)) . T)) ((((-1249 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-407 (-563))) |has| |#2| (-38 (-407 (-563)))) ((|#2|) |has| |#2| (-172)) (($) -4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905)))) +((((-407 (-563))) |has| |#2| (-38 (-407 (-563)))) ((|#2|) |has| |#2| (-172)) (($) -4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-407 (-563))) |has| |#2| (-38 (-407 (-563)))) ((|#2|) . T)) (|has| |#1| (-363)) -((($) -4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) +((($) -4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) ((((-1097)) . T)) ((((-858)) . T)) -((($) -4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) +((($) -4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) ((($) . T) (((-407 (-563))) |has| |#1| (-38 (-407 (-563)))) ((|#1|) . T)) ((($) . T)) -((($) -4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) +((($) -4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-563))) |has| |#1| (-38 (-407 (-563))))) ((((-1249 |#1| |#2| |#3|)) . T) (((-1221 |#1| |#2| |#3|)) . T)) ((((-1169)) . T) (((-858)) . T)) (|has| |#2| (-905)) @@ -3275,7 +3275,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-172))) ((((-694)) . T)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) ((((-1174)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1174)) . T)) @@ -3287,13 +3287,13 @@ ((((-1174)) . T)) ((((-1174)) . T)) ((((-1174)) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-349))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1174)) . T)) ((((-1174)) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -(-4032 (|has| |#1| (-172)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-172)) (|has| |#1| (-555))) (((|#1| (-563)) . T)) (((|#1| (-407 (-563))) . T)) (((|#1| (-767)) . T)) @@ -3308,16 +3308,16 @@ ((((-888 (-379))) . T) (((-888 (-563))) . T) (((-1169)) . T) (((-536)) . T)) (((|#1|) . T)) ((((-858)) . T)) -(-4032 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-4032 (-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)))) +(-4034 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (-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)))) ((((-563)) . T)) ((((-563)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-4032 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-4034 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1169)) -12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) -(-4032 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) +(-4034 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3343,7 +3343,7 @@ (((|#1| |#2|) . T)) ((((-563)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-563)) . T)) -(-4032 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-4034 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-563))) . T) (($) . T) (((-563)) . T)) @@ -3355,7 +3355,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-611 (-536)))) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1093)))) ((($) . T) (((-407 (-563))) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) @@ -3366,14 +3366,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-563)) . T)) ((((-1174)) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-555))) -(-4032 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-555))) +(-4034 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#2|) . T)) -(-4032 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-4034 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-858)) -4032 (-12 (|has| |#1| (-610 (-858))) (|has| |#2| (-610 (-858)))) (-12 (|has| |#1| (-1093)) (|has| |#2| (-1093))))) +((((-858)) -4034 (-12 (|has| |#1| (-610 (-858))) (|has| |#2| (-610 (-858)))) (-12 (|has| |#1| (-1093)) (|has| |#2| (-1093))))) ((((-407 |#2|) |#3|) . T)) ((((-407 (-563))) . T) (($) . T)) (|has| |#1| (-38 (-407 (-563)))) @@ -3385,19 +3385,19 @@ (((|#1|) . T) (((-407 (-563))) . T) (((-563)) . T) (($) . T)) (((#0=(-563) #0#) . T)) ((($) . T) (((-407 (-563))) . T)) -(-4032 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-4032 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-4034 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-4034 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T) (((-1174)) . T)) (|has| |#4| (-789)) -(-4032 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-4034 (|has| |#4| (-789)) (|has| |#4| (-844))) (|has| |#4| (-844)) (|has| |#3| (-789)) ((((-1174)) . T)) -(-4032 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-4034 (|has| |#3| (-789)) (|has| |#3| (-844))) (|has| |#3| (-844)) ((((-563)) . T)) (((|#2|) . T)) -((((-1169)) -4032 (-12 (|has| (-1167 |#1| |#2| |#3|) (-896 (-1169))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-563) |#1|))) (|has| |#1| (-896 (-1169)))))) +((((-1169)) -4034 (-12 (|has| (-1167 |#1| |#2| |#3|) (-896 (-1169))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-563) |#1|))) (|has| |#1| (-896 (-1169)))))) ((((-1169)) -12 (|has| |#1| (-15 * (|#1| (-407 (-563)) |#1|))) (|has| |#1| (-896 (-1169))))) ((((-1169)) -12 (|has| |#1| (-15 * (|#1| (-767) |#1|))) (|has| |#1| (-896 (-1169))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3412,11 +3412,11 @@ ((((-1167 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-1133 |#1| |#2|)) . T)) ((((-1167 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) -((((-2 (|:| -2387 (-1169)) (|:| -2557 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) +((((-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1018)) -(((|#2|) . T) (((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) ((((-858)) . T)) ((((-536)) |has| |#2| (-611 (-536))) (((-888 (-563))) |has| |#2| (-611 (-888 (-563)))) (((-888 (-379))) |has| |#2| (-611 (-888 (-379)))) (((-379)) . #0=(|has| |#2| (-1018))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3432,15 +3432,15 @@ ((((-1167 |#1| |#2| |#3|)) . T)) ((((-1167 |#1| |#2| |#3|)) . T) (((-1160 |#1| |#2| |#3|)) . T)) ((((-858)) . T)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) ((((-563) |#1|) . T)) ((((-1167 |#1| |#2| |#3|)) |has| |#1| (-363))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-363)) -(((|#3|) . T) ((|#2|) . T) (($) -4032 (|has| |#4| (-172)) (|has| |#4| (-844)) (|has| |#4| (-1045))) ((|#4|) -4032 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1045)))) -(((|#2|) . T) (($) -4032 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((|#3|) -4032 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045)))) +(((|#3|) . T) ((|#2|) . T) (($) -4034 (|has| |#4| (-172)) (|has| |#4| (-844)) (|has| |#4| (-1045))) ((|#4|) -4034 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1045)))) +(((|#2|) . T) (($) -4034 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((|#3|) -4034 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1045)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-363)) @@ -3455,7 +3455,7 @@ ((((-187)) . T) (((-858)) . T)) ((((-858)) . T)) (((|#1|) . T)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) ((((-129)) . T) (((-858)) . T)) ((((-563) |#1|) . T)) ((((-129)) . T)) @@ -3464,13 +3464,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) -(-4032 (|has| |#1| (-846)) (|has| |#1| (-1093))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-4034 (|has| |#1| (-846)) (|has| |#1| (-1093))) ((((-858)) . T)) ((((-858)) . T)) ((((-858)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -2387 (-1169)) (|:| -2557 (-52)))) . T)) +((((-2 (|:| -2387 (-1169)) (|:| -2556 (-52)))) . T)) ((((-563) (-129)) . T)) (((|#1| (-563)) . T)) (((|#1| (-407 (-563))) . T)) @@ -3484,8 +3484,8 @@ ((((-1174)) . T)) ((((-858)) . T) (((-1174)) . T)) ((((-858)) . T) (((-1174)) . T)) -(-4032 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) -(-4032 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) +(-4034 (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) +(-4034 (|has| |#1| (-452)) (|has| |#1| (-555)) (|has| |#1| (-905))) ((($) . T)) (((|#2| (-531 (-860 |#1|))) . T)) ((((-1174)) . T)) @@ -3500,13 +3500,13 @@ ((((-1174)) . T)) ((((-858)) . T) (((-1174)) . T)) ((((-1174)) . T)) -((((-858)) -4032 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) +((((-858)) -4034 (|has| |#1| (-610 (-858))) (|has| |#1| (-1093)))) (((|#1|) . T)) (((|#2| (-767)) . T)) (((|#1| |#2|) . T)) ((((-1151) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -2387 |#1|) (|:| -2557 |#2|))) . T)) +((((-2 (|:| -2387 |#1|) (|:| -2556 |#2|))) . T)) (|has| |#1| (-555)) (|has| |#1| (-555)) ((($) . T) ((|#2|) . T)) @@ -3515,14 +3515,14 @@ ((((-563)) . T) (($) . T)) (((|#2| $) |has| |#2| (-286 |#2| |#2|))) (((|#1| (-640 |#1|)) |has| |#1| (-844))) -(-4032 (|has| |#1| (-233)) (|has| |#1| (-349))) -(-4032 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-233)) (|has| |#1| (-349))) +(-4034 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1253 |#1|)) . T) (((-563)) . T) ((|#2|) . T) (((-407 (-563))) |has| |#2| (-1034 (-407 (-563))))) (|has| |#1| (-1093)) (((|#1|) . T)) -((((-1253 |#1|)) . T) (((-563)) . T) (($) -4032 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) (((-1075)) . T) ((|#2|) . T) (((-407 (-563))) -4032 (|has| |#2| (-38 (-407 (-563)))) (|has| |#2| (-1034 (-407 (-563)))))) +((((-1253 |#1|)) . T) (((-563)) . T) (($) -4034 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-555)) (|has| |#2| (-905))) (((-1075)) . T) ((|#2|) . T) (((-407 (-563))) -4034 (|has| |#2| (-38 (-407 (-563)))) (|has| |#2| (-1034 (-407 (-563)))))) ((((-407 (-563))) . T) (($) . T)) -((((-995 |#1|)) . T) ((|#1|) . T) (((-563)) -4032 (|has| (-995 |#1|) (-1034 (-563))) (|has| |#1| (-1034 (-563)))) (((-407 (-563))) -4032 (|has| (-995 |#1|) (-1034 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563)))))) +((((-995 |#1|)) . T) ((|#1|) . T) (((-563)) -4034 (|has| (-995 |#1|) (-1034 (-563))) (|has| |#1| (-1034 (-563)))) (((-407 (-563))) -4034 (|has| (-995 |#1|) (-1034 (-407 (-563)))) (|has| |#1| (-1034 (-407 (-563)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1093)))) @@ -3534,10 +3534,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1133 |#1| |#2|) #0#) |has| (-1133 |#1| |#2|) (-309 (-1133 |#1| |#2|)))) (((|#1|) . 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-229) 133360) ((-868 . -905) 133339) ((-126 . -34) T) ((-813 . -131) T) ((-644 . -610) 133321) ((-577 . -102) T) ((-355 . -1276) 133305) ((-352 . -1276) 133289) ((-344 . -1276) 133273) ((-127 . -514) 133206) ((-121 . -514) 133139) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 133077) ((-222 . -102) 133055) ((-689 . -1093) T) ((-694 . -172) T) ((-868 . -643) 133007) ((-65 . -384) T) ((-275 . -610) 132989) ((-65 . -395) T) ((-948 . -377) 132973) ((-866 . -290) T) ((-50 . -610) 132955) ((-995 . -38) 132903) ((-580 . -610) 132885) ((-481 . -377) 132869) ((-580 . -611) 132851) ((-518 . -610) 132833) ((-906 . -1276) 132820) ((-867 . -1208) T) ((-696 . -452) T) ((-495 . -514) 132786) ((-487 . -363) T) ((-355 . -368) 132765) ((-352 . -368) 132744) ((-344 . -368) 132723) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1280 . -1271) 132707) ((-867 . -880) 132684) ((-867 . -882) NIL) ((-960 . -846) 132583) ((-811 . -846) 132534) ((-649 . -651) 132518) ((-1194 . -34) T) ((-171 . -610) 132500) ((-1106 . -21) 132410) ((-1106 . -25) 132261) ((-867 . -1034) 132238) ((-948 . -896) 132219) ((-1230 . -47) 132196) ((-906 . -368) T) ((-59 . -646) 132180) ((-516 . -646) 132164) ((-481 . -896) 132141) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -646) 132125) ((-59 . -373) 132109) ((-620 . -172) T) ((-516 . -373) 132093) ((-496 . -373) 132077) ((-823 . -704) 132061) ((-1165 . -307) 132040) ((-1171 . -131) T) ((-117 . -172) T) ((-1139 . -309) 131978) ((-169 . -1208) T) ((-632 . -740) 131962) ((-604 . -740) 131946) ((-1269 . -131) T) ((-1242 . -916) 131925) ((-1221 . -916) 131904) ((-1221 . -816) NIL) ((-689 . -713) 131854) ((-1220 . -905) 131807) ((-1020 . -1093) T) ((-867 . -377) 131784) ((-867 . -338) 131761) ((-901 . -1105) T) ((-169 . -880) 131745) ((-169 . -882) 131670) ((-487 . -1105) T) ((-354 . -1093) T) ((-217 . -1105) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1034) 131566) ((-319 . -846) T) ((-1257 . -514) 131499) ((-1241 . -643) 131396) 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-713) 129989) ((-169 . -896) 129948) ((-694 . -290) T) ((-689 . -172) T) ((-707 . -111) 129904) ((-1285 . -1052) T) ((-1230 . -377) 129888) ((-418 . -1212) 129866) ((-1111 . -610) 129848) ((-313 . -844) NIL) ((-418 . -555) T) ((-225 . -307) T) ((-1220 . -787) 129801) ((-1220 . -790) 129754) ((-1241 . -722) T) ((-1220 . -722) T) ((-48 . -713) 129719) ((-225 . -1018) T) ((-351 . -1264) 129696) ((-1243 . -411) 129662) ((-714 . -722) T) ((-1230 . -896) 129605) ((-1202 . -613) 129487) ((-112 . -610) 129469) ((-112 . -611) 129451) ((-714 . -473) T) ((-707 . -613) 129401) ((-482 . -21) 129311) ((-127 . -489) 129295) ((-121 . -489) 129279) ((-482 . -25) 129130) ((-620 . -290) T) ((-584 . -1051) 129105) ((-437 . -1093) T) ((-1056 . -307) T) ((-117 . -290) T) ((-1097 . -102) T) ((-999 . -102) T) ((-584 . -111) 129073) ((-1135 . -309) 129011) ((-1202 . -1045) T) ((-1056 . -1018) T) ((-66 . -1208) T) ((-1049 . -25) T) ((-1049 . -21) T) ((-707 . -1045) T) ((-385 . -21) T) ((-385 . -25) T) ((-689 . 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-613) 125544) ((-653 . -1045) T) ((-1285 . -1093) T) ((-454 . -613) 125329) ((-169 . -307) 125260) ((-418 . -23) T) ((-40 . -610) 125242) ((-40 . -611) 125226) ((-108 . -988) 125208) ((-116 . -865) 125192) ((-644 . -613) 125176) ((-48 . -514) 125142) ((-1194 . -1006) 125126) ((-1174 . -610) 125093) ((-1181 . -34) T) ((-950 . -610) 125059) ((-917 . -610) 125041) ((-1106 . -846) 124992) ((-767 . -610) 124974) ((-667 . -610) 124956) ((-1149 . -309) 124894) ((-479 . -34) T) ((-1085 . -1208) T) ((-477 . -452) T) ((-1134 . -34) T) ((-1080 . -1045) T) ((-50 . -613) 124863) ((-778 . -1045) T) ((-776 . -1045) T) ((-642 . -235) 124847) ((-629 . -235) 124793) ((-580 . -613) 124743) ((-518 . -613) 124673) ((-1230 . -307) 124652) ((-1080 . -326) 124613) ((-454 . -1045) T) ((-1171 . -21) T) ((-1080 . -233) 124592) ((-778 . -326) 124569) ((-778 . -233) T) ((-776 . -326) 124541) ((-727 . -1212) 124520) ((-327 . -646) 124504) ((-1171 . -25) T) ((-59 . -34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124483) ((-327 . -373) 124467) ((-497 . -34) T) ((-496 . -34) T) ((-999 . -1144) NIL) ((-727 . -555) 124398) ((-632 . -102) T) ((-604 . -102) T) ((-355 . -722) T) ((-352 . -722) T) ((-344 . -722) T) ((-264 . -722) T) ((-247 . -722) T) ((-1042 . -309) 124306) ((-897 . -1093) 124284) ((-50 . -1045) T) ((-1269 . -21) T) ((-1269 . -25) T) ((-1167 . -555) 124263) ((-1166 . -1212) 124242) ((-580 . -1045) T) ((-518 . -1045) T) ((-1160 . -1212) 124221) ((-361 . -1034) 124205) ((-322 . -1034) 124189) ((-1020 . -290) T) ((-379 . -882) 124171) ((-1166 . -555) 124122) ((-1160 . -555) 124073) ((-999 . -38) 124018) ((-795 . -1105) T) ((-906 . -722) T) ((-580 . -243) T) ((-580 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1119 . -555) 123997) ((-354 . -290) T) ((-642 . -690) 123981) ((-379 . -1034) 123941) ((-1113 . -1052) T) ((-103 . -125) 123925) ((-795 . -23) T) ((-1279 . -1274) 123901) ((-1257 . -286) 123878) ((-407 . -309) 123843) ((-1277 . -1274) 123822) ((-1243 . -1093) T) ((-866 . -610) 123804) ((-832 . -1034) 123773) ((-203 . -783) T) ((-202 . -783) T) ((-201 . -783) T) ((-200 . -783) T) ((-199 . -783) T) ((-198 . -783) T) ((-197 . -783) T) ((-196 . -783) T) ((-195 . -783) T) ((-194 . -783) T) ((-547 . -610) 123755) ((-495 . -998) T) ((-274 . -835) T) ((-273 . -835) T) ((-272 . -835) T) ((-271 . -835) T) ((-48 . -290) T) ((-270 . -835) T) ((-269 . -835) T) ((-268 . -835) T) ((-193 . -783) T) ((-609 . -846) T) ((-649 . -411) 123739) ((-223 . -613) 123701) ((-110 . -846) T) ((-648 . -21) T) ((-648 . -25) T) ((-1280 . -38) 123671) ((-117 . -286) 123622) ((-1257 . -19) 123606) ((-1257 . -601) 123583) ((-1270 . -1093) T) ((-1070 . -1093) T) ((-983 . -1093) T) ((-959 . -131) T) ((-733 . -1093) T) ((-731 . -131) T) ((-711 . -131) T) ((-511 . -789) T) ((-407 . -1144) 123561) ((-453 . -131) T) ((-511 . -790) T) ((-223 . -1045) T) ((-294 . -102) 123343) ((-141 . -1093) T) ((-694 . -998) T) ((-91 . -1208) T) ((-127 . -610) 123275) ((-121 . -610) 123207) ((-1285 . -172) T) ((-1166 . -363) 123186) ((-1160 . -363) 123165) ((-316 . -1093) T) ((-418 . -131) T) ((-313 . -1093) T) ((-407 . -38) 123117) ((-1126 . -102) T) ((-1243 . -713) 123009) ((-649 . -1052) T) ((-1128 . -1252) T) ((-319 . -145) 122988) ((-319 . -147) 122967) ((-139 . -1093) T) ((-136 . -1093) T) ((-114 . -1093) T) ((-854 . -102) T) ((-579 . -610) 122949) ((-563 . -611) 122848) ((-563 . -610) 122830) ((-495 . -610) 122812) ((-495 . -611) 122757) ((-485 . -23) T) ((-482 . -846) 122708) ((-487 . -636) 122690) ((-961 . -610) 122672) ((-217 . -636) 122654) ((-225 . -404) T) ((-657 . -643) 122638) ((-55 . -610) 122620) ((-1165 . -916) 122599) ((-727 . -1105) T) ((-351 . -102) T) ((-1207 . -1076) T) ((-1113 . -840) T) ((-814 . -846) T) ((-727 . -23) T) ((-343 . -1051) 122544) ((-1151 . -1150) T) ((-1140 . -107) 122528) ((-1167 . -1105) T) ((-1166 . -1105) T) ((-515 . -1034) 122512) ((-1160 . -1105) T) ((-1119 . -1105) T) ((-343 . -111) 122441) ((-1000 . -1212) T) ((-126 . -1208) T) ((-910 . -1212) T) ((-689 . -286) NIL) ((-1258 . -610) 122423) ((-1167 . -23) T) ((-1166 . -23) T) ((-1160 . -23) T) ((-1000 . -555) T) ((-1135 . -231) 122407) ((-910 . -555) T) ((-1119 . -23) T) ((-248 . -610) 122389) ((-1068 . -1093) T) ((-795 . -131) T) ((-706 . -610) 122371) ((-316 . -713) 122281) ((-313 . -713) 122210) ((-694 . -610) 122192) ((-694 . -611) 122137) ((-407 . -400) 122121) ((-438 . -1093) T) ((-487 . -25) T) ((-487 . -21) T) ((-1113 . -1093) T) ((-217 . -25) T) ((-217 . -21) T) ((-708 . -411) 122105) ((-710 . -1034) 122074) ((-1257 . -610) 121986) ((-1257 . -611) 121947) ((-1243 . -172) T) ((-245 . -34) T) ((-343 . -613) 121877) ((-394 . -613) 121859) ((-922 . -970) T) ((-1194 . -1208) T) ((-657 . -787) 121838) ((-657 . -790) 121817) ((-398 . -395) T) ((-523 . -102) 121795) ((-1031 . -1093) T) ((-222 . -991) 121779) ((-504 . -102) T) ((-620 . -610) 121761) ((-45 . -846) NIL) ((-620 . -611) 121738) ((-1031 . -607) 121713) ((-897 . -514) 121646) ((-343 . -1045) T) ((-117 . -611) NIL) ((-117 . -610) 121628) ((-868 . -1208) T) ((-665 . -417) 121612) ((-665 . -1116) 121557) ((-500 . -151) 121539) ((-343 . -233) T) ((-343 . -243) T) ((-40 . -1051) 121484) ((-868 . -880) 121468) ((-868 . -882) 121393) ((-708 . -1052) T) ((-689 . -998) NIL) ((-3 . |UnionCategory|) T) ((-1241 . -47) 121363) ((-1220 . -47) 121340) ((-1134 . -1006) 121311) ((-225 . -916) T) ((-40 . -111) 121240) ((-868 . -1034) 121104) ((-1113 . -713) 121091) ((-1098 . -610) 121073) ((-1073 . -147) 121052) ((-1073 . -145) 121003) ((-1000 . -363) T) ((-319 . -1196) 120969) ((-379 . -307) T) ((-319 . -1193) 120935) ((-316 . -172) 120914) ((-313 . -172) T) ((-999 . -231) 120891) ((-910 . -363) T) ((-580 . -1276) 120878) ((-518 . -1276) 120855) ((-359 . -147) 120834) ((-359 . -145) 120785) ((-353 . -147) 120764) ((-353 . -145) 120715) ((-605 . -1184) 120691) ((-345 . -147) 120670) ((-345 . -145) 120621) ((-319 . -35) 120587) ((-475 . -1184) 120566) ((0 . |EnumerationCategory|) T) ((-319 . -95) 120532) ((-379 . -1018) T) ((-108 . -147) T) ((-108 . -145) NIL) ((-45 . -235) 120482) ((-649 . -1093) T) ((-605 . -107) 120429) ((-485 . -131) T) ((-475 . -107) 120379) ((-240 . -1105) 120289) ((-868 . -377) 120273) ((-868 . -338) 120257) ((-240 . -23) 120127) ((-40 . -613) 120057) ((-1056 . -916) T) ((-1056 . -816) T) ((-580 . -368) T) ((-518 . -368) T) ((-351 . -1144) T) ((-327 . -34) T) ((-44 . -417) 120041) ((-1174 . -613) 119976) ((-869 . -1208) T) ((-390 . -740) 119960) ((-1270 . -514) 119893) ((-727 . -131) T) ((-667 . -613) 119877) ((-1249 . -555) 119856) ((-1242 . -1212) 119835) ((-1242 . -555) 119786) ((-1221 . -1212) 119765) ((-311 . -1076) T) ((-1221 . -555) 119716) ((-733 . -514) 119649) ((-1220 . -1208) 119628) ((-1220 . -882) 119501) ((-889 . -1093) T) ((-144 . -840) T) ((-1220 . -880) 119471) ((-686 . -610) 119453) ((-1167 . -131) T) ((-523 . -309) 119391) ((-1166 . -131) T) ((-141 . -514) NIL) ((-1160 . -131) T) ((-1119 . -131) T) ((-1020 . -998) T) ((-1000 . -23) T) ((-351 . -38) 119356) ((-1000 . -1105) T) ((-910 . -1105) T) ((-82 . -610) 119338) ((-40 . -1045) T) ((-866 . -1051) 119325) ((-999 . -349) NIL) ((-868 . -896) 119284) ((-696 . -102) T) ((-967 . -23) T) ((-599 . -1208) T) ((-910 . -23) T) ((-866 . -111) 119269) ((-427 . -1105) T) ((-213 . -1093) T) ((-474 . -47) 119239) ((-134 . -102) T) ((-40 . -233) 119211) ((-40 . -243) T) ((-116 . -102) T) ((-594 . -555) 119190) ((-593 . -555) 119169) ((-689 . -610) 119151) ((-689 . -611) 119059) ((-316 . -514) 119025) ((-313 . -514) 118917) ((-1241 . -1034) 118901) ((-1220 . -1034) 118687) ((-995 . -411) 118671) ((-427 . -23) T) ((-1113 . -172) T) ((-1243 . -290) T) ((-649 . -713) 118641) ((-144 . -1093) T) ((-48 . -998) T) ((-407 . -231) 118625) ((-295 . -235) 118575) ((-867 . -916) T) ((-867 . -816) NIL) ((-866 . -613) 118547) ((-860 . -846) T) ((-1220 . -338) 118517) ((-1220 . -377) 118487) ((-222 . -1114) 118471) ((-1257 . -288) 118448) ((-1202 . -643) 118373) ((-959 . -21) T) ((-959 . -25) T) ((-731 . -21) 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-21) T) ((-40 . -722) T) ((-222 . -514) 108339) ((-593 . -25) T) ((-476 . -151) 108323) ((-463 . -151) 108307) ((-917 . -790) T) ((-917 . -722) T) ((-767 . -789) T) ((-767 . -790) T) ((-506 . -1093) T) ((-502 . -1093) T) ((-767 . -722) T) ((-225 . -363) T) ((-1149 . -1093) 108285) ((-867 . -1212) T) ((-649 . -610) 108267) ((-867 . -555) T) ((-689 . -368) NIL) ((-1285 . -613) 108249) ((-359 . -1264) 108233) ((-665 . -102) T) ((-353 . -1264) 108217) ((-345 . -1264) 108201) ((-1280 . -1093) T) ((-520 . -846) 108180) ((-813 . -452) 108159) ((-1042 . -1093) T) ((-1042 . -1065) 108088) ((-1023 . -972) 108057) ((-815 . -1105) T) ((-999 . -713) 108002) ((-386 . -1105) T) ((-476 . -972) 107971) ((-463 . -972) 107940) ((-110 . -151) 107922) ((-73 . -610) 107904) ((-889 . -610) 107886) ((-1073 . -720) 107865) ((-1285 . -1045) T) ((-812 . -636) 107813) ((-294 . -1052) 107755) ((-169 . -1212) 107660) ((-225 . -1105) T) ((-324 . -23) T) ((-1160 . -988) 107612) ((-839 . -1093) T) ((-1243 . -1051) 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. -309) 100429) ((-570 . -131) T) ((-618 . -844) 100408) ((-1149 . -489) 100392) ((-1143 . -151) 100342) ((-1139 . -610) 100304) ((-1139 . -611) 100265) ((-1020 . -787) T) ((-1020 . -790) T) ((-1020 . -722) T) ((-708 . -1051) 100088) ((-484 . -309) 100026) ((-453 . -417) 99996) ((-351 . -172) T) ((-289 . -38) 99983) ((-274 . -102) T) ((-273 . -102) T) ((-272 . -102) T) ((-271 . -102) T) ((-270 . -102) T) ((-269 . -102) T) ((-343 . -1034) 99960) ((-268 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-207 . -102) T) ((-206 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-194 . -102) T) ((-193 . -102) T) ((-354 . -722) T) ((-708 . -111) 99769) ((-665 . -231) 99753) ((-580 . -307) T) ((-518 . -307) T) ((-294 . -514) 99702) ((-108 . -309) NIL) ((-72 . -395) T) ((-1106 . -102) 99492) ((-829 . -411) 99476) ((-1113 . -791) T) 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. -309) 98159) ((-1119 . -1193) 98125) ((-708 . -1045) T) ((-1056 . -636) 98107) ((-1073 . -38) 97975) ((-948 . -636) 97923) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1105) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97902) ((-708 . -326) 97879) ((-481 . -636) 97827) ((-40 . -1034) 97715) ((-708 . -233) T) ((-696 . -713) 97702) ((-339 . -1093) T) ((-174 . -1093) T) ((-331 . -846) T) ((-418 . -452) 97652) ((-379 . -23) T) ((-359 . -38) 97617) ((-353 . -38) 97582) ((-345 . -38) 97547) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1105) T) ((-108 . -38) 97497) ((-823 . -1105) T) ((-770 . -1093) T) ((-116 . -713) 97484) ((-667 . -1034) 97468) ((-609 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1149 . -286) 97445) ((-1106 . -309) 97383) ((-1095 . -235) 97367) ((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97344) ((-96 . -102) T) ((-648 . -848) 97328) ((-1128 . -1076) T) ((-1056 . -21) T) ((-1056 . -25) T) ((-811 . -231) 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91075) ((-910 . -452) T) ((-65 . -610) 91057) ((-629 . -229) 91003) ((-474 . -23) T) ((-1113 . -790) T) ((-868 . -131) T) ((-1113 . -787) T) ((-1272 . -1274) 90982) ((-1113 . -722) T) ((-649 . -643) 90956) ((-294 . -610) 90697) ((-1135 . -613) 90615) ((-1031 . -34) T) ((-811 . -844) 90594) ((-579 . -307) T) ((-563 . -307) T) ((-495 . -307) T) ((-1281 . -713) 90564) ((-689 . -377) 90546) ((-689 . -338) 90528) ((-477 . -172) T) ((-381 . -713) 90498) ((-862 . -613) 90433) ((-867 . -846) NIL) ((-563 . -1018) T) ((-495 . -1018) T) ((-1126 . -610) 90415) ((-1106 . -238) 90394) ((-214 . -102) T) ((-1143 . -102) T) ((-71 . -610) 90376) ((-1135 . -1045) T) ((-1171 . -38) 90273) ((-854 . -610) 90255) ((-563 . -545) T) ((-665 . -1052) T) ((-727 . -945) 90208) ((-1135 . -233) 90187) ((-1075 . -1093) T) ((-1030 . -25) T) ((-1030 . -21) T) ((-999 . -1051) 90132) ((-901 . -102) T) ((-862 . -1045) T) ((-689 . -896) NIL) ((-355 . -329) 90116) ((-355 . -363) T) ((-352 . -329) 90100) ((-352 . -363) T) 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82456) ((-247 . -636) 82404) ((-696 . -1051) 82391) ((-593 . -1235) 82368) ((-1119 . -284) 82334) ((-319 . -172) 82265) ((-359 . -1093) T) ((-353 . -1093) T) ((-345 . -1093) T) ((-500 . -19) 82247) ((-1113 . -1034) 82229) ((-1095 . -151) 82213) ((-108 . -1093) T) ((-116 . -1051) 82200) ((-707 . -363) T) ((-500 . -601) 82175) ((-696 . -111) 82160) ((-436 . -102) T) ((-45 . -1142) 82110) ((-116 . -111) 82095) ((-632 . -716) T) ((-604 . -716) T) ((-811 . -514) 82028) ((-1031 . -1208) T) ((-939 . -151) 82012) ((-1215 . -610) 81994) ((-1165 . -452) 81925) ((-1159 . -1093) T) ((-1151 . -1093) T) ((-525 . -102) T) ((-520 . -102) 81875) ((-1135 . -643) 81849) ((-1118 . -452) 81800) ((-1080 . -1212) 81779) ((-778 . -1212) 81758) ((-776 . -1212) 81737) ((-62 . -1208) T) ((-477 . -610) 81689) ((-477 . -611) 81611) ((-1080 . -555) 81542) ((-990 . -1093) T) ((-778 . -555) 81453) ((-776 . -555) 81384) ((-482 . -411) 81353) ((-620 . -916) 81332) ((-454 . -1212) 81311) ((-727 . -309) 81298) ((-696 . 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-848) 73124) ((-1171 . -1093) T) ((-103 . -1208) T) ((-948 . -945) 73085) ((-813 . -713) 73027) ((-1221 . -1144) NIL) ((-481 . -945) 72972) ((-1056 . -143) T) ((-60 . -102) 72950) ((-44 . -610) 72932) ((-78 . -610) 72914) ((-351 . -643) 72859) ((-1269 . -1093) T) ((-511 . -846) T) ((-343 . -1105) T) ((-295 . -1093) T) ((-995 . -896) 72818) ((-295 . -607) 72797) ((-1281 . -613) 72746) ((-1249 . -38) 72643) ((-1242 . -38) 72484) ((-1221 . -38) 72280) ((-487 . -1052) T) ((-381 . -613) 72264) ((-217 . -1052) T) ((-343 . -23) T) ((-152 . -610) 72246) ((-829 . -791) 72225) ((-829 . -788) 72204) ((-1207 . -613) 72185) ((-594 . -38) 72158) ((-593 . -38) 72055) ((-866 . -555) T) ((-223 . -131) T) ((-319 . -998) 72021) ((-79 . -610) 72003) ((-708 . -307) 71982) ((-294 . -722) 71884) ((-820 . -102) T) ((-860 . -840) T) ((-294 . -473) 71863) ((-1272 . -102) T) ((-40 . -363) T) ((-868 . -147) 71842) ((-868 . -145) 71821) ((-1151 . -489) 71803) ((-1281 . -1045) T) ((-482 . -514) 71736) ((-1139 . 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. -23) T) ((-767 . -1105) T) ((-563 . -1212) T) ((-495 . -1212) T) ((-319 . -610) 70466) ((-1000 . -231) 70448) ((-169 . -166) 70432) ((-579 . -555) T) ((-563 . -555) T) ((-495 . -555) T) ((-767 . -23) T) ((-1241 . -147) 70411) ((-1152 . -601) 70387) ((-1241 . -145) 70366) ((-1023 . -489) 70350) ((-1220 . -145) 70275) ((-1220 . -147) 70200) ((-1272 . -1278) 70179) ((-476 . -489) 70163) ((-463 . -489) 70147) ((-523 . -34) T) ((-648 . -713) 70117) ((-112 . -963) T) ((-657 . -846) 70096) ((-1171 . -172) 70047) ((-365 . -102) T) ((-240 . -238) 70026) ((-251 . -102) T) ((-250 . -102) T) ((-1230 . -945) 69995) ((-245 . -846) 69974) ((-812 . -38) 69823) ((-45 . -514) 69615) ((-1151 . -286) 69590) ((-214 . -1093) T) ((-1143 . -1093) T) ((-1143 . -607) 69569) ((-584 . -25) T) ((-584 . -21) T) ((-1095 . -309) 69507) ((-959 . -411) 69491) ((-694 . -1212) T) ((-629 . -286) 69466) ((-1080 . -636) 69414) ((-778 . -636) 69362) ((-776 . -636) 69310) ((-343 . -131) T) ((-289 . -610) 69292) ((-901 . 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133593) ((-454 . -610) 133575) ((-454 . -611) 133436) ((-1031 . -229) 133382) ((-868 . -905) 133361) ((-126 . -34) T) ((-813 . -131) T) ((-644 . -610) 133343) ((-577 . -102) T) ((-355 . -1276) 133327) ((-352 . -1276) 133311) ((-344 . -1276) 133295) ((-127 . -514) 133228) ((-121 . -514) 133161) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 133099) ((-222 . -102) 133077) ((-689 . -1093) T) ((-694 . -172) T) ((-868 . -643) 133029) ((-65 . -384) T) ((-275 . -610) 133011) ((-65 . -395) T) ((-948 . -377) 132995) ((-866 . -290) T) ((-50 . -610) 132977) ((-995 . -38) 132925) ((-580 . -610) 132907) ((-481 . -377) 132891) ((-580 . -611) 132873) ((-518 . -610) 132855) ((-906 . -1276) 132842) ((-867 . -1208) T) ((-696 . -452) T) ((-495 . -514) 132808) ((-487 . -363) T) ((-355 . -368) 132787) ((-352 . -368) 132766) ((-344 . -368) 132745) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1280 . -1271) 132729) ((-867 . -880) 132706) ((-867 . -882) NIL) ((-960 . -846) 132605) ((-811 . -846) 132556) ((-649 . -651) 132540) ((-1194 . -34) T) ((-171 . -610) 132522) ((-1106 . -21) 132432) ((-1106 . -25) 132283) ((-867 . -1034) 132260) ((-948 . -896) 132241) ((-1230 . -47) 132218) ((-906 . -368) T) ((-59 . -646) 132202) ((-516 . -646) 132186) ((-481 . -896) 132163) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -646) 132147) ((-59 . -373) 132131) ((-620 . -172) T) ((-516 . -373) 132115) ((-496 . -373) 132099) ((-823 . -704) 132083) ((-1165 . -307) 132062) ((-1171 . -131) T) ((-117 . -172) T) ((-1139 . -309) 132000) ((-169 . -1208) T) ((-632 . -740) 131984) ((-604 . -740) 131968) ((-1269 . -131) T) ((-1242 . -916) 131947) ((-1221 . -916) 131926) ((-1221 . -816) NIL) ((-689 . -713) 131876) ((-1220 . -905) 131829) ((-1020 . -1093) T) ((-867 . -377) 131806) ((-867 . -338) 131783) ((-901 . -1105) T) ((-169 . -880) 131767) ((-169 . -882) 131692) ((-487 . -1105) T) ((-354 . -1093) T) ((-217 . -1105) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1034) 131588) ((-319 . -846) T) ((-1257 . -514) 131521) ((-1241 . -643) 131418) ((-1220 . -643) 131288) ((-868 . -790) 131267) ((-868 . -787) 131246) ((-868 . -722) T) ((-487 . -23) T) ((-223 . -610) 131228) ((-174 . -452) T) ((-222 . -309) 131166) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1281 . -1274) 131145) ((-579 . -290) T) ((-563 . -290) T) ((-672 . -1034) 131129) ((-495 . -290) T) ((-136 . -470) 131084) ((-48 . -1093) T) ((-708 . -231) 131068) ((-867 . -896) NIL) ((-1230 . -882) NIL) ((-885 . -102) T) ((-881 . -102) T) ((-388 . -1093) T) ((-169 . -377) 131052) ((-169 . -338) 131036) ((-1230 . -1034) 130916) ((-851 . -1034) 130812) ((-1135 . -102) T) ((-648 . -131) T) ((-117 . -514) 130720) ((-657 . -788) 130699) ((-657 . -791) 130678) ((-570 . -1034) 130660) ((-294 . -1264) 130630) ((-862 . -102) T) ((-959 . -555) 130609) ((-1202 . -1051) 130492) ((-482 . -636) 130398) ((-900 . -1093) T) ((-1020 . -713) 130335) ((-707 . -1051) 130300) ((-614 . -102) T) ((-599 . -34) T) ((-1140 . -1208) 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-147) T) ((-217 . -145) NIL) ((-1113 . -610) 109140) ((-129 . -102) T) ((-52 . -102) T) ((-1221 . -636) 109092) ((-479 . -107) 109042) ((-989 . -23) T) ((-1281 . -38) 109012) ((-1165 . -1105) T) ((-1118 . -1105) T) ((-1056 . -1212) T) ((-311 . -102) T) ((-850 . -1105) T) ((-948 . -1212) 108991) ((-481 . -1212) 108970) ((-727 . -846) 108949) ((-1056 . -555) T) ((-948 . -555) 108880) ((-1165 . -23) T) ((-1118 . -23) T) ((-850 . -23) T) ((-481 . -555) 108811) ((-1135 . -713) 108743) ((-1139 . -514) 108676) ((-1031 . -611) NIL) ((-1031 . -610) 108658) ((-96 . -1076) T) ((-862 . -713) 108628) ((-1202 . -47) 108597) ((-251 . -131) T) ((-250 . -131) T) ((-1097 . -1093) T) ((-999 . -1093) T) ((-62 . -610) 108579) ((-1160 . -846) NIL) ((-1020 . -788) T) ((-1020 . -791) T) ((-1285 . -1051) 108566) ((-1285 . -111) 108551) ((-866 . -643) 108538) ((-1249 . -25) T) ((-1249 . -21) T) ((-1242 . -21) T) ((-1242 . -25) T) ((-1221 . -21) T) ((-1221 . -25) T) ((-1023 . -151) 108522) ((-868 . -816) 108501) 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T) ((-324 . -23) T) ((-1160 . -988) 107634) ((-839 . -1093) T) ((-1243 . -1051) 107539) ((-1119 . -736) 107518) ((-1241 . -916) 107497) ((-1220 . -916) 107476) ((-866 . -722) T) ((-169 . -555) 107387) ((-579 . -643) 107374) ((-563 . -643) 107361) ((-407 . -1093) T) ((-263 . -1093) T) ((-213 . -610) 107343) ((-495 . -643) 107308) ((-225 . -23) T) ((-1220 . -816) 107261) ((-1279 . -102) T) ((-354 . -1276) 107238) ((-1277 . -102) T) ((-1243 . -111) 107130) ((-144 . -610) 107112) ((-989 . -131) T) ((-44 . -102) T) ((-240 . -846) 107063) ((-1230 . -1212) 107042) ((-103 . -489) 107026) ((-1280 . -713) 106996) ((-1080 . -47) 106957) ((-1056 . -1105) T) ((-948 . -1105) T) ((-127 . -34) T) ((-121 . -34) T) ((-778 . -47) 106934) ((-776 . -47) 106906) ((-1230 . -555) 106817) ((-354 . -368) T) ((-481 . -1105) T) ((-1165 . -131) T) ((-1118 . -131) T) ((-454 . -47) 106796) ((-867 . -363) T) ((-850 . -131) T) ((-152 . -102) T) ((-1056 . -23) T) ((-948 . -23) T) ((-570 . -555) T) ((-812 . -25) T) 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105392) ((-1277 . -1278) 105371) ((-778 . -882) NIL) ((-776 . -882) 105230) ((-1272 . -25) T) ((-1272 . -21) T) ((-1205 . -102) 105208) ((-1099 . -395) T) ((-620 . -643) 105195) ((-454 . -882) NIL) ((-670 . -102) 105173) ((-1080 . -1034) 105000) ((-867 . -23) T) ((-778 . -1034) 104859) ((-776 . -1034) 104716) ((-117 . -643) 104661) ((-454 . -1034) 104537) ((-316 . -613) 104101) ((-313 . -613) 103984) ((-644 . -1034) 103968) ((-624 . -102) T) ((-222 . -489) 103952) ((-1257 . -34) T) ((-136 . -613) 103936) ((-632 . -713) 103920) ((-604 . -713) 103904) ((-665 . -38) 103864) ((-319 . -102) T) ((-85 . -610) 103846) ((-50 . -1034) 103830) ((-1113 . -1051) 103817) ((-1080 . -377) 103801) ((-778 . -377) 103785) ((-694 . -722) T) ((-694 . -790) T) ((-694 . -787) T) ((-580 . -1034) 103772) ((-518 . -1034) 103749) ((-60 . -57) 103711) ((-324 . -131) T) ((-316 . -1045) 103601) ((-313 . -1045) T) ((-169 . -1105) T) ((-776 . -377) 103585) ((-45 . -151) 103535) ((-1000 . -988) 103517) ((-454 . -377) 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-846) NIL) ((-999 . -290) T) ((-251 . -21) T) ((-689 . -643) 102394) ((-351 . -1093) T) ((-251 . -25) T) ((-250 . -21) T) ((-250 . -25) T) ((-152 . -38) 102378) ((-2 . -102) T) ((-906 . -916) T) ((-482 . -1264) 102348) ((-223 . -1034) 102325) ((-1113 . -1045) T) ((-707 . -307) T) ((-294 . -713) 102267) ((-696 . -1052) T) ((-487 . -452) T) ((-407 . -514) 102179) ((-217 . -452) T) ((-1113 . -233) T) ((-295 . -151) 102129) ((-995 . -611) 102090) ((-995 . -610) 102072) ((-985 . -610) 102054) ((-116 . -1052) T) ((-649 . -1051) 102038) ((-225 . -493) T) ((-399 . -610) 102020) ((-399 . -611) 101997) ((-1049 . -1264) 101967) ((-649 . -111) 101946) ((-1135 . -489) 101930) ((-811 . -38) 101900) ((-63 . -441) T) ((-63 . -395) T) ((-1152 . -102) T) ((-867 . -131) T) ((-484 . -102) 101878) ((-1285 . -368) T) ((-1073 . -102) T) ((-1055 . -102) T) ((-351 . -713) 101823) ((-727 . -147) 101802) ((-727 . -145) 101781) ((-649 . -613) 101699) ((-1020 . -643) 101636) ((-523 . -1093) 101614) ((-359 . -102) T) ((-353 . -102) T) ((-345 . -102) T) ((-108 . -102) T) ((-504 . -1093) T) ((-354 . -643) 101559) ((-1165 . -636) 101507) ((-1118 . -636) 101455) ((-385 . -509) 101434) ((-829 . -844) 101413) ((-379 . -1212) T) ((-689 . -722) T) ((-339 . -1052) T) ((-1221 . -988) 101365) ((-174 . -1052) T) ((-103 . -610) 101297) ((-1167 . -145) 101276) ((-1167 . -147) 101255) ((-379 . -555) T) ((-1166 . -147) 101234) ((-1166 . -145) 101213) ((-1160 . -145) 101120) ((-407 . -290) T) ((-1160 . -147) 101027) ((-1119 . -147) 101006) ((-1119 . -145) 100985) ((-319 . -38) 100826) ((-169 . -131) T) ((-313 . -791) NIL) ((-313 . -788) NIL) ((-649 . -1045) T) ((-48 . -643) 100791) ((-889 . -613) 100768) ((-1159 . -102) T) ((-990 . -102) T) ((-989 . -21) T) ((-127 . -1006) 100752) ((-121 . -1006) 100736) ((-989 . -25) T) ((-897 . -119) 100720) ((-1151 . -102) T) ((-812 . -846) 100699) ((-1230 . -131) T) ((-1165 . -25) T) ((-1165 . -21) T) ((-851 . -131) T) ((-1118 . -25) T) ((-1118 . -21) T) ((-850 . -25) T) 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NIL) ((-72 . -395) T) ((-1106 . -102) 99514) ((-829 . -411) 99498) ((-1113 . -791) T) ((-1113 . -788) T) ((-696 . -1093) T) ((-577 . -610) 99480) ((-379 . -363) T) ((-169 . -493) 99458) ((-222 . -610) 99390) ((-134 . -1093) T) ((-116 . -1093) T) ((-48 . -722) T) ((-1042 . -489) 99355) ((-141 . -425) 99337) ((-141 . -368) T) ((-1023 . -102) T) ((-512 . -509) 99316) ((-708 . -613) 99072) ((-476 . -102) T) ((-463 . -102) T) ((-1030 . -1105) T) ((-1174 . -1034) 99007) ((-1167 . -35) 98973) ((-1167 . -95) 98939) ((-1167 . -1196) 98905) ((-1167 . -1193) 98871) ((-1151 . -309) NIL) ((-89 . -396) T) ((-89 . -395) T) ((-1073 . -1144) 98850) ((-1166 . -1193) 98816) ((-1166 . -1196) 98782) ((-1030 . -23) T) ((-1166 . -95) 98748) ((-570 . -493) T) ((-1166 . -35) 98714) ((-1160 . -1193) 98680) ((-1160 . -1196) 98646) ((-1160 . -95) 98612) ((-361 . -1105) T) ((-359 . -1144) 98591) ((-353 . -1144) 98570) ((-345 . -1144) 98549) ((-1160 . -35) 98515) ((-1119 . -35) 98481) ((-1119 . -95) 98447) ((-108 . -1144) T) ((-1119 . -1196) 98413) ((-829 . -1052) 98392) ((-642 . -309) 98330) ((-629 . -309) 98181) ((-1119 . -1193) 98147) ((-708 . -1045) T) ((-1056 . -636) 98129) ((-1073 . -38) 97997) ((-948 . -636) 97945) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1105) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97924) ((-708 . -326) 97901) ((-481 . -636) 97849) ((-40 . -1034) 97737) ((-708 . -233) T) ((-696 . -713) 97724) ((-339 . -1093) T) ((-174 . -1093) T) ((-331 . -846) T) ((-418 . -452) 97674) ((-379 . -23) T) ((-359 . -38) 97639) ((-353 . -38) 97604) ((-345 . -38) 97569) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1105) T) ((-108 . -38) 97519) ((-823 . -1105) T) ((-770 . -1093) T) ((-116 . -713) 97506) ((-667 . -1034) 97490) ((-609 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1149 . -286) 97467) ((-1106 . -309) 97405) ((-1095 . -235) 97389) ((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97366) ((-96 . -102) T) ((-648 . -848) 97350) ((-1128 . -1076) T) ((-1056 . -21) T) ((-1056 . -25) T) ((-811 . -231) 97319) ((-948 . -25) T) ((-948 . -21) T) ((-618 . -1052) T) ((-1113 . -368) T) ((-481 . -25) T) ((-481 . -21) T) ((-1023 . -309) 97257) ((-885 . -610) 97239) ((-881 . -610) 97221) ((-251 . -846) 97172) ((-250 . -846) 97123) ((-523 . -514) 97056) ((-867 . -636) 97033) ((-476 . -309) 96971) ((-463 . -309) 96909) ((-351 . -290) T) ((-1149 . -1245) 96893) ((-1135 . -610) 96855) ((-1135 . -611) 96816) ((-1133 . -102) T) ((-995 . -1051) 96712) ((-40 . -896) 96664) ((-1149 . -601) 96641) ((-1285 . -643) 96628) ((-862 . -490) 96605) ((-1057 . -151) 96551) ((-868 . -1212) T) ((-995 . -111) 96433) ((-339 . -713) 96417) ((-862 . -610) 96379) ((-174 . -713) 96311) ((-407 . -286) 96269) ((-868 . -555) T) ((-108 . -400) 96251) ((-84 . -384) T) ((-84 . -395) T) ((-696 . -172) T) ((-614 . -610) 96233) ((-99 . -722) T) ((-482 . -102) 96023) ((-99 . -473) T) ((-116 . -172) T) ((-1106 . -38) 95993) ((-169 . -636) 95941) 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-147) 95064) ((-593 . -145) 95043) ((-495 . -1034) 94986) ((-1128 . -1130) T) ((-87 . -384) T) ((-87 . -395) T) ((-868 . -363) T) ((-832 . -131) T) ((-823 . -131) T) ((-710 . -23) T) ((-506 . -610) 94952) ((-502 . -610) 94934) ((-1281 . -1052) T) ((-379 . -1054) T) ((-1022 . -1093) 94912) ((-55 . -1034) 94894) ((-897 . -34) T) ((-482 . -309) 94832) ((-590 . -102) T) ((-1149 . -611) 94793) ((-1149 . -610) 94725) ((-1165 . -846) 94704) ((-45 . -102) T) ((-1118 . -846) 94683) ((-813 . -102) T) ((-1230 . -25) T) ((-1230 . -21) T) ((-851 . -25) T) ((-44 . -367) 94667) ((-851 . -21) T) ((-727 . -452) 94618) ((-1280 . -610) 94600) ((-1049 . -309) 94538) ((-666 . -1076) T) ((-603 . -1076) T) ((-390 . -1093) T) ((-570 . -25) T) ((-570 . -21) T) ((-180 . -1076) T) ((-161 . -1076) T) ((-156 . -1076) T) ((-154 . -1076) T) ((-618 . -1093) T) ((-694 . -882) 94520) ((-1257 . -1208) T) ((-227 . -309) 94458) ((-144 . -368) T) ((-1042 . -611) 94400) ((-1042 . -610) 94343) ((-313 . -905) NIL) ((-1215 . -840) T) ((-694 . -1034) 94288) ((-707 . -916) T) ((-474 . -1212) 94267) ((-1166 . -452) 94246) ((-1160 . -452) 94225) ((-330 . -102) T) ((-868 . -1105) T) ((-316 . -643) 94046) ((-313 . -643) 93975) ((-474 . -555) 93926) ((-339 . -514) 93892) ((-549 . -151) 93842) ((-40 . -307) T) ((-839 . -610) 93824) ((-696 . -290) T) ((-868 . -23) T) ((-379 . -493) T) ((-1073 . -231) 93794) ((-512 . -102) T) ((-407 . -611) 93601) ((-407 . -610) 93583) ((-263 . -610) 93565) ((-116 . -290) T) ((-1243 . -722) T) ((-1241 . -363) 93544) ((-1220 . -363) 93523) ((-1270 . -34) T) ((-1215 . -1093) T) ((-117 . -1208) T) ((-108 . -231) 93505) ((-1171 . -102) T) ((-477 . -1093) T) ((-523 . -489) 93489) ((-733 . -34) T) ((-482 . -38) 93459) ((-141 . -34) T) ((-117 . -880) 93436) ((-117 . -882) NIL) ((-620 . -1034) 93319) ((-640 . -846) 93298) ((-1269 . -102) T) ((-295 . -102) T) ((-708 . -368) 93277) ((-117 . -1034) 93254) ((-390 . -713) 93238) ((-618 . -713) 93222) ((-45 . -309) 93026) ((-812 . -145) 93005) 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-329) 90138) ((-355 . -363) T) ((-352 . -329) 90122) ((-352 . -363) T) ((-344 . -329) 90106) ((-344 . -363) T) ((-487 . -102) T) ((-1269 . -38) 90076) ((-546 . -846) T) ((-523 . -682) 90026) ((-217 . -102) T) ((-1020 . -1034) 89906) ((-999 . -111) 89835) ((-1167 . -969) 89804) ((-1166 . -969) 89766) ((-520 . -151) 89750) ((-1073 . -370) 89729) ((-351 . -610) 89711) ((-322 . -21) T) ((-354 . -1034) 89688) ((-322 . -25) T) ((-1160 . -969) 89657) ((-1119 . -969) 89624) ((-76 . -610) 89606) ((-694 . -307) T) ((-169 . -846) 89585) ((-129 . -840) T) ((-906 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-906 . -329) 89572) ((-86 . -610) 89554) ((-694 . -1018) T) ((-672 . -846) T) ((-1241 . -131) T) ((-1220 . -131) T) ((-897 . -1006) 89538) ((-832 . -21) T) ((-48 . -1034) 89481) ((-832 . -25) T) ((-823 . -25) T) ((-823 . -21) T) ((-1279 . -1052) T) ((-548 . -102) T) ((-1277 . -1052) T) ((-649 . -722) T) ((-1097 . -615) 89384) ((-999 . -613) 89314) ((-1280 . -1051) 89298) ((-1230 . -846) 89277) 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-38) 87506) ((-217 . -38) 87456) ((-474 . -493) 87422) ((-1151 . -1137) T) ((-1094 . -102) T) ((-696 . -610) 87404) ((-696 . -611) 87319) ((-710 . -21) T) ((-710 . -25) T) ((-1128 . -102) T) ((-134 . -610) 87301) ((-116 . -610) 87283) ((-157 . -25) T) ((-1279 . -1093) T) ((-868 . -636) 87231) ((-1277 . -1093) T) ((-959 . -102) T) ((-731 . -102) T) ((-711 . -102) T) ((-453 . -102) T) ((-812 . -452) 87182) ((-44 . -1093) T) ((-1081 . -846) T) ((-659 . -131) T) ((-1057 . -309) 87033) ((-665 . -713) 87017) ((-289 . -1052) T) ((-355 . -131) T) ((-352 . -131) T) ((-344 . -131) T) ((-264 . -131) T) ((-247 . -131) T) ((-418 . -102) T) ((-152 . -1093) T) ((-45 . -229) 86967) ((-954 . -846) 86946) ((-995 . -643) 86884) ((-240 . -1264) 86854) ((-1020 . -307) T) ((-294 . -1051) 86775) ((-906 . -131) T) ((-40 . -916) T) ((-487 . -400) 86757) ((-354 . -307) T) ((-217 . -400) 86739) ((-1073 . -411) 86723) ((-294 . -111) 86639) ((-1176 . -846) T) ((-1175 . -846) T) ((-868 . -25) T) ((-868 . -21) T) 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-1052) T) ((-294 . -1045) 85397) ((-1221 . -969) 85366) ((-379 . -846) T) ((-108 . -1052) T) ((-995 . -722) T) ((-866 . -916) T) ((-839 . -791) 85345) ((-839 . -788) 85324) ((-418 . -309) 85263) ((-468 . -102) T) ((-593 . -969) 85232) ((-319 . -1093) T) ((-407 . -791) 85211) ((-407 . -788) 85190) ((-500 . -489) 85172) ((-1243 . -1034) 85138) ((-1241 . -21) T) ((-1241 . -25) T) ((-1220 . -21) T) ((-1220 . -25) T) ((-811 . -713) 85080) ((-351 . -613) 85010) ((-694 . -404) T) ((-1270 . -1208) T) ((-603 . -102) T) ((-1106 . -411) 84979) ((-999 . -368) NIL) ((-666 . -102) T) ((-180 . -102) T) ((-161 . -102) T) ((-156 . -102) T) ((-154 . -102) T) ((-103 . -34) T) ((-733 . -1208) T) ((-44 . -757) T) ((-591 . -102) T) ((-77 . -396) T) ((-77 . -395) T) ((-648 . -651) 84963) ((-141 . -1208) T) ((-867 . -147) T) ((-867 . -145) NIL) ((-1207 . -93) T) ((-351 . -1045) T) ((-70 . -383) T) ((-70 . -395) T) ((-1158 . -102) T) ((-665 . -514) 84896) ((-684 . -309) 84834) ((-959 . -38) 84731) ((-731 . 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83369) ((-81 . -441) T) ((-81 . -395) T) ((-1139 . -34) T) ((-811 . -172) 83348) ((-727 . -102) T) ((-1022 . -610) 83315) ((-500 . -286) 83290) ((-316 . -377) 83259) ((-313 . -377) 83220) ((-313 . -338) 83181) ((-1078 . -610) 83163) ((-812 . -945) 83110) ((-657 . -131) T) ((-1230 . -145) 83089) ((-1230 . -147) 83068) ((-1167 . -102) T) ((-1166 . -102) T) ((-1160 . -102) T) ((-1152 . -1093) T) ((-1119 . -102) T) ((-222 . -34) T) ((-289 . -713) 83055) ((-1152 . -607) 83031) ((-591 . -309) NIL) ((-484 . -1093) 83009) ((-390 . -610) 82991) ((-510 . -846) T) ((-1143 . -229) 82941) ((-1249 . -1248) 82925) ((-1249 . -1235) 82902) ((-1242 . -1240) 82863) ((-1242 . -1235) 82833) ((-1242 . -1238) 82817) ((-1221 . -1219) 82778) ((-1221 . -1235) 82755) ((-618 . -610) 82737) ((-1221 . -1217) 82721) ((-694 . -916) T) ((-1167 . -284) 82687) ((-1166 . -284) 82653) ((-1160 . -284) 82619) ((-1073 . -1093) T) ((-1055 . -1093) T) ((-48 . -302) T) ((-316 . -896) 82585) ((-313 . -896) NIL) ((-1055 . -1062) 82564) ((-1113 . -882) 82546) ((-795 . -38) 82530) ((-264 . -636) 82478) ((-247 . -636) 82426) ((-696 . -1051) 82413) ((-593 . -1235) 82390) ((-1119 . -284) 82356) ((-319 . -172) 82287) ((-359 . -1093) T) ((-353 . -1093) T) ((-345 . -1093) T) ((-500 . -19) 82269) ((-1113 . -1034) 82251) ((-1095 . -151) 82235) ((-108 . -1093) T) ((-116 . -1051) 82222) ((-707 . -363) T) ((-500 . -601) 82197) ((-696 . -111) 82182) ((-436 . -102) T) ((-45 . -1142) 82132) ((-116 . -111) 82117) ((-632 . -716) T) ((-604 . -716) T) ((-811 . -514) 82050) ((-1031 . -1208) T) ((-939 . -151) 82034) ((-1215 . -610) 82016) ((-1165 . -452) 81947) ((-1159 . -1093) T) ((-1151 . -1093) T) ((-525 . -102) T) ((-520 . -102) 81897) ((-1135 . -643) 81871) ((-1118 . -452) 81822) ((-1080 . -1212) 81801) ((-778 . -1212) 81780) ((-776 . -1212) 81759) ((-62 . -1208) T) ((-477 . -610) 81711) ((-477 . -611) 81633) ((-1080 . -555) 81564) ((-990 . -1093) T) ((-778 . -555) 81475) ((-776 . -555) 81406) ((-482 . -411) 81375) ((-620 . -916) 81354) ((-454 . -1212) 81333) ((-727 . -309) 81320) ((-696 . -613) 81292) ((-398 . -610) 81274) ((-670 . -514) 81207) ((-659 . -25) T) ((-659 . -21) T) ((-454 . -555) 81138) ((-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 . -613) 81120) ((-116 . -613) 81092) ((-1259 . -610) 81074) ((-1214 . -846) T) ((-1202 . -1105) T) ((-1202 . -23) T) ((-1160 . -309) 80959) ((-1119 . -309) 80946) ((-1073 . -713) 80814) ((-862 . -643) 80774) ((-939 . -976) 80758) ((-906 . -21) T) ((-289 . -172) T) ((-906 . -25) T) ((-311 . -93) T) ((-868 . -846) 80709) ((-707 . -1105) T) ((-707 . -23) T) ((-696 . -1045) T) ((-642 . -1093) 80687) ((-629 . -1093) T) ((-580 . -1212) T) ((-518 . -1212) T) ((-696 . -233) T) ((-629 . -607) 80662) ((-580 . -555) T) ((-518 . -555) T) ((-359 . -713) 80614) ((-339 . -1051) 80598) ((-353 . -713) 80550) ((-345 . -713) 80502) ((-174 . -1051) 80434) ((-174 . -111) 80345) ((-108 . -713) 80295) ((-339 . -111) 80274) ((-274 . -1093) T) ((-273 . -1093) T) ((-272 . -1093) T) ((-271 . -1093) T) ((-270 . -1093) T) ((-269 . -1093) T) ((-268 . -1093) T) ((-212 . -1093) T) ((-211 . -1093) T) ((-169 . -1196) 80252) ((-169 . -1193) 80230) ((-209 . -1093) T) ((-208 . -1093) T) ((-116 . -1045) T) ((-207 . -1093) T) ((-206 . -1093) T) ((-203 . -1093) T) ((-202 . -1093) T) ((-201 . -1093) T) ((-200 . -1093) T) ((-199 . -1093) T) ((-198 . -1093) T) ((-197 . -1093) T) ((-196 . -1093) T) ((-195 . -1093) T) ((-194 . -1093) T) ((-193 . -1093) T) ((-240 . -102) 80020) ((-169 . -35) 79998) ((-169 . -95) 79976) ((-649 . -1034) 79872) ((-482 . -1052) 79802) ((-1106 . -1093) 79592) ((-1135 . -34) T) ((-665 . -489) 79576) ((-73 . -1208) T) ((-105 . -610) 79558) ((-1281 . -610) 79540) ((-381 . -610) 79522) ((-339 . -613) 79474) ((-174 . -613) 79391) ((-1207 . -490) 79372) ((-727 . -38) 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. -25) T) ((-731 . -1052) T) ((-711 . -1052) T) ((-665 . -1051) 68869) ((-517 . -1076) T) ((-461 . -25) T) ((-117 . -555) T) ((-461 . -21) T) ((-454 . -25) T) ((-454 . -21) T) ((-1279 . -1051) 68853) ((-1135 . -1034) 68749) ((-813 . -290) 68728) ((-1277 . -1051) 68712) ((-819 . -1093) T) ((-1241 . -1193) 68678) ((-962 . -963) T) ((-665 . -111) 68657) ((-295 . -514) 68449) ((-1241 . -1196) 68415) ((-1241 . -95) 68381) ((-1224 . -102) 68359) ((-251 . -309) 68297) ((-250 . -309) 68235) ((-1221 . -231) 68187) ((-1152 . -611) NIL) ((-1152 . -610) 68169) ((-1220 . -1193) 68135) ((-1220 . -1196) 68101) ((-1215 . -368) T) ((-96 . -93) T) ((-1213 . -840) T) ((-1135 . -377) 68085) ((-1113 . -816) T) ((-1113 . -916) T) ((-1106 . -601) 68062) ((-1073 . -611) 68046) ((-484 . -610) 67978) ((-811 . -288) 67955) ((-605 . -151) 67902) ((-418 . -1052) T) ((-487 . -713) 67852) ((-482 . -489) 67836) ((-327 . -846) 67815) ((-339 . -643) 67789) ((-50 . -21) T) ((-50 . -25) T) ((-217 . -713) 67739) ((-169 . 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. -35) NIL) ((-689 . -95) NIL) ((-313 . -988) 25236) ((-183 . -102) T) ((-579 . -452) T) ((-563 . -452) T) ((-495 . -452) T) ((-407 . -363) T) ((-240 . -1045) 25166) ((-1143 . -34) T) ((-477 . -916) T) ((-995 . -636) 25114) ((-251 . -601) 25091) ((-250 . -601) 25068) ((-1073 . -377) 25052) ((-867 . -514) 24960) ((-240 . -233) 24912) ((-1151 . -1208) T) ((-1000 . -613) 24862) ((-910 . -613) 24799) ((-820 . -610) 24781) ((-1280 . -1105) T) ((-1272 . -610) 24763) ((-1230 . -172) 24654) ((-427 . -613) 24623) ((-108 . -377) 24605) ((-108 . -338) 24587) ((-1056 . -290) T) ((-948 . -290) 24518) ((-795 . -368) 24497) ((-642 . -1208) T) ((-629 . -1208) T) ((-481 . -290) 24428) ((-570 . -172) T) ((-327 . -282) 24412) ((-1280 . -23) T) ((-1202 . -102) T) ((-1189 . -1093) T) ((-1081 . -1093) T) ((-1069 . -1093) T) ((-83 . -610) 24394) ((-1176 . -840) T) ((-1175 . -840) T) ((-707 . -102) T) ((-355 . -349) 24373) ((-605 . -1093) T) ((-352 . -349) 24352) ((-344 . -349) 24331) ((-475 . -1093) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index eae6de58..789119cd 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3443021569) -(4410 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3443721765) +(4411 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -477,661 +477,661 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |e04naf| |oddlambert| |listOfMonoms| - |monicRightDivide| |integral?| |processTemplate| - |constantCoefficientRicDE| |factorsOfDegree| |LazardQuotient2| - 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|corrPoly| |basisOfCommutingElements| |finite?| - |conditionP| |elem?| |factorByRecursion| |permutationRepresentation| - |external?| |genericRightTrace| |cAcsch| |simplifyExp| |dequeue| - |getMatch| |f07fdf| |factorSquareFreeByRecursion| - |reducedDiscriminant| |edf2ef| |c02aff| |cSinh| |trapezoidalo| - |condition| |karatsuba| |arity| |direction| |nextLatticePermutation| - |prinshINFO| |regime| |radicalEigenvalues| |associative?| - |approximate| |tubePointsDefault| |graeffe| |e02adf| |level| |comment| - |addBadValue| |const| |totalfract| |basisOfCenter| |complex| |unit| - |rk4a| |and?| |commonDenominator| |OMconnectTCP| |negative?| |eq| - |monicModulo| |alphanumeric?| |discreteLog| |coerceP| |bottom!| - |OMputAtp| |goodPoint| |s14abf| |delay| |open?| |iter| |iiatan| - |symmetricRemainder| |cyclic?| |complexZeros| |matrixConcat3D| - |noLinearFactor?| |someBasis| |clearTheIFTable| |changeVar| |refine| - |close| |pointLists| |rspace| |aLinear| |clearFortranOutputStack| - |Lazard2| |generalPosition| |cyclicEntries| |deleteRoutine!| - |viewSizeDefault| |toseInvertibleSet| |e01sff| |doubleFloatFormat| - |coefChoose| |hasoln| |curveColorPalette| |LyndonWordsList| |remove| - |iicoth| |subMatrix| |nextNormalPrimitivePoly| |display| BY - |expressIdealMember| |setLength!| |extensionDegree| |pmintegrate| - |node?| |explogs2trigs| |lifting1| |halfExtendedResultant2| |f02bjf| - |setClosed| |graphs| |lookup| |nextSublist| |solve1| |int| |mapCoef| - |last| |Si| |roughUnitIdeal?| |createNormalElement| |viewWriteDefault| - |bezoutResultant| |outputArgs| |debug3D| |lfinfieldint| |rightDivide| - |assoc| |cAtan| |iicot| |leftPower| |subtractIfCan| |hex| |readInt32!| - |anticoord| |ParCondList| |stoseInvertible?reg| |cyclicGroup| - |dimensions| |inputBinaryFile| |singularAtInfinity?| |mapSolve| - |solveid| |create| |binaryTournament| |externalList| |lfextlimint| - |leftGcd| |reindex| |plus!| |makeSketch| |rootBound| |function| - |s21bdf| |e02bdf| |SturmHabichtSequence| |input| 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|rightExactQuotient| |rischDEsys| |rootKerSimp| - |complexRoots| |e01saf| |extension| - |removeRoughlyRedundantFactorsInPols| |limitedIntegrate| |magnitude| - |cos| |cSec| |alphanumeric| |c02agf| |stoseIntegralLastSubResultant| - |sturmSequence| |reseed| |contours| |removeSinhSq| |mapBivariate| - |rdHack1| |tan| |fortranLinkerArgs| |parametric?| |oddInfiniteProduct| - |subResultantChain| |split!| |OMputString| |roughSubIdeal?| |cross| - |ip4Address| |difference| |cot| |linearAssociatedLog| |bezoutMatrix| - |mapGen| |cyclicParents| |surface| |ldf2lst| |primeFrobenius| |s17agf| - |removeRoughlyRedundantFactorsInPol| |splitNodeOf!| - |removeRedundantFactorsInContents| |sort| |sec| |derivative| |nthRoot| - |clearTable!| |axesColorDefault| |delta| |generalLambert| |pow| - |f02abf| |lowerCase| |OMputVariable| |exponent| |diophantineSystem| - |csc| |resultantReduitEuclidean| |divergence| |errorInfo| - |complexSolve| |fortranLiteral| |Is| |cardinality| |makeCos| |iroot| - |binding| |asin| |replaceKthElement| |cAcot| |wrregime| |SFunction| - |upDateBranches| |setProperties!| |true| |characteristic| |f02wef| ~= - |lexGroebner| |resultantEuclideannaif| |acos| |basisOfRightNucloid| - |patternMatchTimes| |OMgetAttr| |integralLastSubResultant| |palgint0| - |left| |unary?| |fortranDouble| |currentScope| |completeHensel| - |random| |baseRDE| |coerce| |hash| |atan| |basisOfRightNucleus| - |resultantEuclidean| |elColumn2!| |bat| |f04atf| |right| - |associatedEquations| |bfEntry| |exptMod| |e02gaf| |trivialIdeal?| - |construct| |show| |count| |acot| |noKaratsuba| |knownInfBasis| - |e01bff| |critMonD1| |prindINFO| |factorset| |writeByte!| = - |removeZero| |mkPrim| |subresultantSequence| |asec| - |clipPointsDefault| |iisqrt2| |sequences| |fortranLogical| |d01gaf| - |deriv| |member?| |diagonals| |setMinPoints| |cscIfCan| |trace| |bits| - |acsc| |safeFloor| |branchIfCan| |lambda| |logIfCan| |triangSolve| - |complete| |d02kef| |qualifier| < |coth2trigh| |graphImage| |maxrow| - |sinh| 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- |lintgcd| - |scopes| |var1StepsDefault| |acosh| |evaluateInverse| - |increase| |iiGamma| |rewriteSetWithReduction| |btwFact| - |listRepresentation| |content| / |unitNormalize| |OMgetBind| |atanh| - |normalise| |euclideanNormalForm| |elRow2!| |makeEq| - |topFortranOutputStack| |algebraicSort| |consnewpol| |isPower| - |setelt| |viewport2D| |acoth| |ramified?| |whileLoop| |totalGroebner| - |testModulus| |parents| |sign| |shuffle| |maxRowIndex| |numberOfHues| - |stirling2| |asech| |getZechTable| |accuracyIF| |prinpolINFO| - |rewriteIdealWithHeadRemainder| |lSpaceBasis| |fTable| |sequence| - |complexEigenvectors| |purelyAlgebraic?| |copy| |arg1| |subTriSet?| - |genericLeftNorm| |factorSquareFreePolynomial| |closed?| |ran| |isOp| - |coordinates| |rotatex| |lflimitedint| |multiple| |arg2| |randnum| - |bombieriNorm| |compBound| |zeroDim?| |raisePolynomial| |imagi| - |cCsch| |label| |outputFixed| |cCos| |applyQuote| |mapmult| |element?| - |cExp| |badNum| |nilFactor| |sup| |safetyMargin| |cAsech| - |OMputEndAttr| |autoCoerce| |mapMatrixIfCan| |conditions| |s17ahf| - |leftLcm| |extractTop!| |removeIrreducibleRedundantFactors| |column| - |OMsend| |numberOfComposites| |exponents| |match| |upperCase?| - |supDimElseRittWu?| |sizeLess?| |bothWays| |result| |outputList| - |sinIfCan| |collectQuasiMonic| |symmetricSquare| |constantRight| - |ruleset| |indiceSubResultantEuclidean| |OMserve| |getGraph| |s17acf| - |cubic| |properties| |expint| |deepestTail| |commutative?| |square?| - |replace| |OMreadFile| |colorFunction| |UpTriBddDenomInv| |f04maf| - |Aleph| |translate| |fortranLiteralLine| |unitVector| - |leadingBasisTerm| |subHeight| |rightScalarTimes!| |cycleLength| - |eyeDistance| |cyclicSubmodule| |thetaCoord| |stoseInvertible?| - |algebraicVariables| |s18aff| |red| |rotatey| |suchThat| - |setProperties| |explimitedint| |complementaryBasis| |leftZero| - |e04fdf| |selectOrPolynomials| |completeSmith| |trim| |zeroDimPrime?| - |term?| |bumprow| |innerEigenvectors| |remainder| |systemSizeIF| - |option| |firstDenom| |optAttributes| |coerceListOfPairs| |leftMult| - |symmetricGroup| |nextPrime| |weierstrass| |curryRight| |sdf2lst| - |changeWeightLevel| |nullary?| |fixedPoint| |univariatePolynomial| - |edf2df| |biRank| |infinite?| |stoseSquareFreePart| |nthCoef| |tRange| - |measure| |constDsolve| |symbolTableOf| |nullity| |equality| - |mergeDifference| |asinIfCan| |checkPrecision| |asecIfCan| - |primPartElseUnitCanonical!| |heapSort| |factorSFBRlcUnit| - |monicCompleteDecompose| |showTypeInOutput| |OMopenString| |mapUp!| - |mesh| |basisOfLeftNucloid| |printingInfo?| |minRowIndex| |d01fcf| - |startPolynomial| |computeInt| |perfectSqrt| |possiblyInfinite?| - |cyclotomicDecomposition| |minrank| |lazyPseudoQuotient| |bytes| - |OMputEndBind| |coordinate| |rightTrim| |eq?| |critM| - |evenInfiniteProduct| |interpret| |sinhIfCan| |headReduced?| - |setStatus!| |isList| |expandPower| |iiexp| |leftTrim| |saturate| - |changeName| |addmod| |besselK| |product| |endSubProgram| |signAround| - |qinterval| |semiIndiceSubResultantEuclidean| |factor1| - |jacobiIdentity?| |minimumDegree| |ignore?| |goodnessOfFit| |ParCond| - |contains?| |rCoord| |getCode| |OMputEndBVar| |write!| - |primlimitedint| |retract| |tower| |primitivePart!| |divideIfCan!| - |definingEquations| |computeBasis| |stop| |pToHdmp| |s18acf| - |orthonormalBasis| |extractBottom!| |invertible?| |basisOfLeftNucleus| - |nodes| |expandLog| |s17dgf| |gcdprim| |iiacsch| |realSolve| - |rationalPoints| |normalizeIfCan| |d01amf| |bezoutDiscriminant| - |useEisensteinCriterion| |semiResultantEuclidean1| |quickSort| - |taylorRep| |assign| |euler| |findBinding| |kmax| |perspective| - |hexDigit| |directory| |nthRootIfCan| |leadingExponent| |mix| - |inverseIntegralMatrixAtInfinity| |chiSquare| |decrease| - |countRealRoots| |continue| |iFTable| |lyndonIfCan| - |eisensteinIrreducible?| |att2Result| |diagonalMatrix| |entry?| - |cosIfCan| |getProperties| |complexNumeric| |cAcoth| |pquo| |pastel| - |distdfact| |charpol| |gcdPrimitive| |exteriorDifferential| - |extractClosed| |iiacoth| |hasHi| |clearDenominator| - |mainCoefficients| |musserTrials| |categories| |lyndon?| |f01qcf| - |generalizedEigenvectors| |associates?| |kernels| |alternative?| - |euclideanGroebner| |exprex| |retractIfCan| |setOrder| |rightUnits| - |iteratedInitials| |viewpoint| |jordanAlgebra?| |signatureAst| - |associatorDependence| |univariate| |fixedDivisor| |internal?| - |showTheFTable| |numer| |quasiComponent| |integralRepresents| - |commutator| |meshFun2Var| |divideIfCan| |extendedIntegrate| - |principalAncestors| |central?| |headRemainder| |compdegd| |denom| - |withPredicates| |printTypes| |e01sbf| |move| |sizePascalTriangle| - |null| |mightHaveRoots| |numberOfChildren| |mapExpon| - |possiblyNewVariety?| |log2| |bivariate?| |subscript| |groebnerIdeal| - |prod| |fortranInteger| |cAsin| |f02fjf| |lazyPrem| |factor| |augment| - |not| |generate| SEGMENT |bandedHessian| |pi| |byteBuffer| - |rightAlternative?| |oddintegers| |factorSquareFree| |tubeRadius| - |sqrt| |e02aef| |currentCategoryFrame| |useNagFunctions| |and| - |infinity| |continuedFraction| |rischDE| |leaf?| |cartesian| - |mainMonomial| |nextNormalPoly| |s18def| |leftNorm| |gderiv| - |incrementBy| |or| |semiDegreeSubResultantEuclidean| |showTheIFTable| - |powers| |vconcat| |maxColIndex| |prepareSubResAlgo| |hermite| - |nextPartition| |isAbsolutelyIrreducible?| |xor| |expand| |critT| - |padicallyExpand| |mainSquareFreePart| |finiteBound| |graphState| - |node| |convert| |generalizedInverse| |cCosh| |e02bcf| |ode2| - |filterWhile| |case| |kernel| |leftFactorIfCan| - |linearAssociatedOrder| |randomLC| |localReal?| |genericLeftTrace| - |bag| |e02ahf| |OMsupportsCD?| |sum| |rightGcd| |degreeSubResultant| - |rational?| |map| |Zero| |filterUntil| |draw| |expextendedint| - |hessian| |aspFilename| |irreducible?| |useSingleFactorBound?| - |comparison| |powerAssociative?| |eof?| |f02akf| - |primPartElseUnitCanonical| |One| |removeSinSq| |select| |principal?| - |critB| |members| |badValues| |definingInequation| |infinityNorm| - |OMgetEndAttr| |maxPoints3D| |geometric| |port| |OMputEndApp| - |padicFraction| |power| |mkcomm| |socf2socdf| |inRadical?| |inR?| - |generators| |virtualDegree| |balancedBinaryTree| |lp| |rootSplit| - |stopTableGcd!| |groebnerFactorize| |solveLinearlyOverQ| |bitCoef| - |stiffnessAndStabilityOfODEIF| |leftUnits| |pointColor| |makeObject| - |plenaryPower| |t| |brillhartTrials| |mkAnswer| |fillPascalTriangle| - |maxint| |redPol| |setFieldInfo| |assert| |measure2Result| |ricDsolve| - |totalDifferential| |normalized?| |rightPower| |bumptab1| |iomode| - |lllp| |OMbindTCP| |mainMonomials| |midpoints| |exactQuotient!| - |bracket| |elt| |rst| |coef| |permutations| |purelyTranscendental?| - |hdmpToP| |discriminant| |splitSquarefree| |cup| |iicos| |readable?| - |makeRecord| |tanQ| |kroneckerDelta| LODO2FUN |brillhartIrreducible?| - |monomRDEsys| |rarrow| |genus| |leftTraceMatrix| |romberg| - |setLabelValue| |component| |squareMatrix| |irreducibleFactors| - |nextColeman| |split| |failed?| |compose| |formula| |coerceImages| - |lhs| |list?| |OMgetApp| |LiePolyIfCan| |atoms| |nullSpace| - |systemCommand| |child| |mainDefiningPolynomial| |outputForm| - |Frobenius| |rhs| |smith| |createZechTable| |resultantnaif| - |screenResolution| |lex| |tube| |fill!| |even?| |lowerCase!| - |operator| |palgextint| |radicalRoots| |linearMatrix| - |lazyPseudoDivide| |primitive?| |OMencodingSGML| |row| |s17ajf| - |depth| |capacity| |limitedint| |cCoth| |UP2ifCan| |LyndonCoordinates| - |compiledFunction| |normal| |equation| |multMonom| |imagE| |nrows| - |less?| |style| |ScanArabic| |semiResultantReduitEuclidean| |pushup| - |key| |transcendent?| |OMmakeConn| |lprop| |setPrologue!| - |unaryFunction| |ncols| |polyRicDE| |minGbasis| |quasiRegular| - |c05pbf| |nextsubResultant2| |light| |rightZero| |laurentIfCan| - |symmetricTensors| |iisqrt3| |filename| |po| |f01brf| - |selectMultiDimensionalRoutines| |nextItem| 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- |iiacosh| |predicates| |setMaxPoints| |index| |s15aef| |entry| - |s17dhf| |suffix?| |makingStats?| |seriesSolve| |escape| - |subResultantsChain| |Hausdorff| |complexNumericIfCan| |atanIfCan| - |ranges| |droot| |iiabs| |setScreenResolution| |FormatRoman| - |toseSquareFreePart| |setEpilogue!| |startTableGcd!| |closedCurve?| - |currentEnv| |writeUInt8!| |push| |e02akf| |prefix?| |more?| - |constantOperator| |union| |makeSin| |showIntensityFunctions| |pair| - |parametersOf| |monomial| |OMgetSymbol| |OMputEndError| |inverse| - |monomRDE| |solid?| |readIfCan!| |lists| |multivariate| - |createGenericMatrix| |nothing| |OMputApp| |univariateSolve| - |weighted| |algintegrate| |axes| |leftMinimalPolynomial| - |genericLeftTraceForm| |variables| |crest| |cylindrical| |simplify| - |setOfMinN| |outputFloating| |cyclicEqual?| |digit| |leftFactor| - |outputAsFortran| |cotIfCan| |semicolonSeparate| |shiftLeft| |value| - |stronglyReduced?| |elliptic| |laplace| |outputAsScript| |times!| - |monicDivide| |limit| |integerIfCan| |euclideanSize| |cosh2sech| - |points| |iibinom| |randomR| |pdf2ef| |pointData| |particularSolution| - |top| |infix?| |iiasec| |getRef| |messagePrint| |setright!| |f2df| - |algDsolve| |setprevious!| |supRittWu?| |mask| |innerSolve| - |laplacian| |deepCopy| |zeroSquareMatrix| |rational| |taylor| - |ratDsolve| |chainSubResultants| |quoByVar| |resetAttributeButtons| - |setErrorBound| |getOperator| |parts| |laurent| |oneDimensionalArray| - |setProperty| |initializeGroupForWordProblem| |resetBadValues| - |leftCharacteristicPolynomial| |elements| |multiEuclideanTree| - |drawComplex| |constant| |puiseux| |fi2df| |printInfo| |ratDenom| - |firstSubsetGray| |var2StepsDefault| |sn| |hasPredicate?| |nthFlag| - |lazyPquo| |monomialIntegrate| |palgRDE0| |seed| - |exprHasWeightCosWXorSinWX| |adaptive3D?| |complexForm| - |doubleComplex?| |addPointLast| |inv| |viewZoomDefault| - |rangeIsFinite| |autoReduced?| |mulmod| |s13adf| |OMUnknownCD?| - |tanhIfCan| |ground?| UTS2UP |pdf2df| |primaryDecomp| - |highCommonTerms| |taylorQuoByVar| |radPoly| |cRationalPower| - |inputOutputBinaryFile| |remove!| |ground| |listYoungTableaus| - |generalizedContinuumHypothesisAssumed| |fullPartialFraction| - |fprindINFO| |numerator| |leftScalarTimes!| |outlineRender| |inrootof| - |initiallyReduce| |leadingMonomial| |diagonal?| |numberOfFactors| - |superscript| |generateIrredPoly| |stFuncN| |quoted?| |midpoint| - |realRoots| |extractPoint| |leadingCoefficient| - |factorsOfCyclicGroupSize| |rules| |compound?| |viewPhiDefault| - |simpleBounds?| |algSplitSimple| |status| |indicialEquations| - |changeMeasure| |besselY| |prologue| |tableau| |primitiveMonomials| - |leadingCoefficientRicDE| |selectPolynomials| |resultant| |iicosh| - |HenselLift| |operation| |setLegalFortranSourceExtensions| - |radicalSolve| |solveLinearPolynomialEquation| |cycleTail| - |tubePoints| |reductum| |tableForDiscreteLogarithm| |rootPoly| - |constantKernel| |connectTo| |subspace| |duplicates| - |extendedSubResultantGcd| |size?| |factors| - |semiResultantEuclideannaif| |host| |modularFactor| - |solveLinearPolynomialEquationByFractions| |omError| - |toseLastSubResultant| |squareTop| |nthFactor| |clip| |sort!| - |LazardQuotient| |sylvesterMatrix| |erf| |f01rdf| |cot2trig| - |solveRetract| |slex| |symbolTable| |charthRoot| |mainVariable?| - |deepExpand| |lyndon| |allRootsOf| |weights| |basisOfNucleus| - |var2Steps| |alphabetic?| |pole?| |trailingCoefficient| - |semiLastSubResultantEuclidean| |isConnected?| |monic?| |binomThmExpt| - |localAbs| |makeTerm| |curry| |indicialEquation| |symmetricPower| - |is?| |nonLinearPart| |viewThetaDefault| |zerosOf| |mapExponents| - |s19acf| |hconcat| |roughBasicSet| |fullDisplay| - |numberOfComputedEntries| |d01asf| |readByte!| |setchildren!| - |select!| |powern| |getGoodPrime| |LagrangeInterpolation| |intChoose| - |ptree| |makeViewport2D| |acoshIfCan| |initials| |figureUnits| |front| - |cyclic| |inc| 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|screenResolution3D| |outputAsTex| |cot2tan| |objectOf| |exprToUPS| - |boundOfCauchy| |quadraticForm| |extendIfCan| |exp1| |perfectNthRoot| - |modifyPoint| |reorder| |checkRur| |c06ebf| |normal01| |arrayStack| - |genericRightDiscriminant| |clipBoolean| |quotient| |composites| - |squareFreeLexTriangular| |transpose| |LyndonWordsList1| |property| - |edf2efi| |HermiteIntegrate| |back| |fortranTypeOf| |integralMatrix| - |clearCache| |inconsistent?| |rationalApproximation| |blue| - |setImagSteps| |internalSubQuasiComponent?| |structuralConstants| - |SturmHabichtMultiple| |singleFactorBound| |hMonic| |rowEchelonLocal| - |quadratic?| |lcm| |expPot| |zeroDimensional?| |updatF| - |dihedralGroup| |meshPar2Var| |c06gsf| |setleaves!| |subNodeOf?| - |getMultiplicationTable| |sorted?| |logpart| |Ci| |components| - |relativeApprox| |units| |minset| |quotedOperators| |e01daf| - |integer?| |dimension| |unknownEndian| |stack| |append| |setPoly| - |read!| |d01bbf| |sumOfSquares| |s14aaf| 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|gethi| |nullary| |double| - |halfExtendedSubResultantGcd2| |leftDiscriminant| |eulerPhi| |digits| - |sec2cos| |s13acf| |csch2sinh| |reify| |safeCeiling| - |currentSubProgram| |f01qdf| |rotatez| |explicitlyEmpty?| - |genericLeftDiscriminant| |quartic| |modularGcdPrimitive| |youngGroup| - |basisOfRightAnnihilator| |realEigenvalues| |logical?| |source| - |mapdiv| |subst| |transform| |retractable?| |s19adf| |listOfLists| - |makeFloatFunction| |setStatus| |plus| |space| |c06fqf| |s19aaf| - |OMopenFile| |rootsOf| |simplifyPower| * |separateFactors| |imagk| - |subset?| |nlde| |inverseLaplace| |conditionsForIdempotents| |vspace| - |rightRecip| |separateDegrees| |idealSimplify| |makeFR| |extractIfCan| - |critpOrder| |bivariateSLPEBR| |s17def| |rischNormalize| |f02bbf| - |selectNonFiniteRoutines| |bfKeys| |linearAssociatedExp| |degree| - |getDatabase| |argumentListOf| |usingTable?| |pushuconst| |permanent| - |key?| |outputSpacing| |setColumn!| |maxdeg| |homogeneous?| - |setClipValue| |times| |associatedSystem| |redPo| |physicalLength| - |target| |argumentList!| |declare!| |vark| |isQuotient| - |lowerPolynomial| |prem| |setleft!| |createIrreduciblePoly| |collect| - |gramschmidt| |ceiling| |legendreP| |headAst| |initiallyReduced?| - |e04mbf| |eulerE| |e02agf| |objects| |differentiate| |find| |e01bhf| - |multisect| |quasiMonicPolynomials| |expintfldpoly| |nthExpon| - |lazyIntegrate| |tab1| |base| |realZeros| |drawComplexVectorField| - |setProperty!| |fractionPart| |leastMonomial| |fractRadix| - |integralMatrixAtInfinity| |f01maf| |rightTraceMatrix| - |roughEqualIdeals?| |monom| |unitCanonical| |multiset| |cycles| - |cyclicCopy| |lazyPremWithDefault| |leadingIndex| |tanh2trigh| - |unravel| |categoryFrame| |exprToGenUPS| |blankSeparate| - |mainVariable| |minPoints3D| |height| |unitsColorDefault| - |OMgetEndBind| |sample| |iiasin| |OMgetEndAtp| |OMread| |tanIfCan| - |failed| |removeSquaresIfCan| |ravel| |groebner?| - |ScanFloatIgnoreSpacesIfCan| |countRealRootsMultiple| |listBranches| - |lazyGintegrate| |airyAi| |addPoint2| |common| |zeroMatrix| |reshape| - |recoverAfterFail| |children| |presuper| |segment| |alternating| - |leftDivide| |generic| |scripted?| |hexDigit?| |splitConstant| |tree| - |d02raf| |dmpToP| |userOrdered?| |besselJ| |ipow| |polynomialZeros| - |elseBranch| |OMputSymbol| |clipParametric| |singRicDE| |declare| - |algebraicCoefficients?| |convergents| |generalTwoFactor| - |impliesOperands| |char| |createPrimitiveElement| |clearTheFTable| - |mappingAst| |OMlistSymbols| |setRealSteps| |stopMusserTrials| - |pushdterm| |OMUnknownSymbol?| |e02bef| |qelt| - |numberOfIrreduciblePoly| |tryFunctionalDecomposition| |cycle| - |B1solve| |isMult| |over| |qsetelt| |linearlyDependent?| |tail| - |genericRightTraceForm| |linear?| |character?| |f07aef| |palgLODE| - |prefixRagits| |orbit| |fixPredicate| |swapRows!| |jacobian| |xRange| - |symmetricDifference| |basis| |update| |OMgetFloat| |indices| - |coefficient| |leviCivitaSymbol| |traverse| |exQuo| |positiveSolve| - |yRange| |push!| |LyndonBasis| |setRow!| |slash| |integerBound| - |exprHasAlgebraicWeight| |previous| |setAdaptive| |generator| |zRange| - |squareFreePart| |generalSqFr| |mirror| |sincos| |conjugate| |float| - |callForm?| |internalInfRittWu?| |OMgetObject| |extractProperty| - |map!| |scale| |stoseInvertible?sqfreg| |listLoops| |primeFactor| - |check| |superHeight| |dominantTerm| |f2st| |resultantReduit| - |qsetelt!| |setsubMatrix!| |leftOne| |pushucoef| |largest| |f07adf| - |internalDecompose| |powmod| |limitPlus| |reduceBasisAtInfinity| - |defineProperty| |makeYoungTableau| |match?| |position| - |pseudoRemainder| |just| |log| |unitNormal| |viewport3D| |OMputAttr| - |semiDiscriminantEuclidean| |sylvesterSequence| - |numberOfPrimitivePoly| |swap!| |exponentialOrder| |createNormalPoly| - |rootPower| |reverse| |any?| |e04ucf| |atanhIfCan| |lambert| - |startTable!| |nil| |infinite| |arbitraryExponent| |approximate| - |complex| |shallowMutable| |canonical| |noetherian| |central| + |Record| |Union| |unaryFunction| |lazyPseudoDivide| |zoom| |graeffe| + |integerBound| |bitTruth| |subResultantGcdEuclidean| |triangulate| + |leaf?| |compiledFunction| |lazyPremWithDefault| |rotate| + |pleskenSplit| |contains?| |keys| |semiSubResultantGcdEuclidean2| + |solveInField| |outputForm| |integralMatrixAtInfinity| + |pushFortranOutputStack| |corrPoly| |acsch| |lazyPquo| |drawStyle| + |reciprocalPolynomial| |inf| |semiSubResultantGcdEuclidean1| + |wronskianMatrix| |argscript| |inverseIntegralMatrix| + |popFortranOutputStack| |lifting| |lazyPrem| |outlineRender| + |rootRadius| GE |qinterval| |discriminantEuclidean| + |variationOfParameters| |superscript| |integralMatrix| |lifting1| + |pquo| |next| |diagonals| |schwerpunkt| GT |factors| |subscript| + |reduceBasisAtInfinity| |exprex| |prem| |axes| |setErrorBound| + |genericPosition| LE |redpps| |nthFactor| |scripted?| + |normalizeAtInfinity| |coerceL| |supRittWu?| |controlPanel| + |startPolynomial| |lfunc| LT |B1solve| |nthExpon| |resetNew| + |complementaryBasis| |coerceS| |RittWuCompare| |viewpoint| |cycleElt| + |inHallBasis?| |factorset| |overlap| |symFunc| |integral?| + |basisOfCommutingElements| |nil| |dimensions| |computeCycleLength| + |reorder| |maxrank| |hcrf| |symbolTableOf| |integralAtInfinity?| + |intcompBasis| |setref| |basisOfLeftAnnihilator| |resize| + |computeCycleEntry| |headAst| |minrank| |hclf| |argumentListOf| + |integralBasisAtInfinity| |choosemon| |deref| + |basisOfRightAnnihilator| |move| |findConstructor| |heap| |condition| + |minset| |lexico| |returnTypeOf| |ramified?| |transform| |ref| + |basisOfLeftNucleus| |approximate| |modifyPointData| |dualSignature| + |gcdprim| |nextSublist| |level| |comment| |ramifiedAtInfinity?| + |pack!| |radicalEigenvectors| |basisOfRightNucleus| |complex| + |subspace| |coerceP| |gcdcofact| |overset?| |s17dcf| + |numberOfComponents| |eq| |singular?| |complexLimit| + |radicalEigenvector| |basisOfMiddleNucleus| |makeViewport3D| + |powerSum| |gcdcofactprim| |ParCond| |s17def| |create3Space| |iter| + |singularAtInfinity?| |limit| |radicalEigenvalues| |basisOfNucleus| + |viewport3D| |elementary| |lintgcd| |s17dgf| |redmat| |outputAsScript| + |close| |branchPoint?| |linearlyDependent?| |eigenMatrix| + |basisOfCenter| |alternating| |hex| |regime| |s17dhf| |outputAsTex| + |branchPointAtInfinity?| |linearDependence| |normalise| + |basisOfLeftNucloid| |rightFactorIfCan| |cyclic| |every?| |remove| + |s17dlf| |sqfree| |abs| |display| BY |rationalPoint?| |solveLinear| + |gramschmidt| |basisOfRightNucloid| |leftFactorIfCan| |dihedral| + |any?| |inconsistent?| |s18acf| |Beta| |absolutelyIrreducible?| + |reducedSystem| |orthonormalBasis| |basisOfCentroid| + |monicDecomposeIfCan| |cap| |last| |host| |numFunEvals| |s18adf| + |digamma| |genus| |duplicates?| |antisymmetricTensors| + |radicalOfLeftTraceForm| |monicCompleteDecompose| |assoc| |cup| + |trueEqual| |setAdaptive| |s18aef| |polygamma| |showTypeInOutput| + |getZechTable| |mapGen| |createGenericMatrix| |binding| |divideIfCan| + |wreath| |factorList| |adaptive?| |s18aff| |Gamma| |objectOf| + |createZechTable| |mapExpon| |symmetricTensors| |setProperties| + |noKaratsuba| |SFunction| |listConjugateBases| |input| |/\\| + |function| |setScreenResolution| |s18dcf| |besselJ| |domainOf| + |createMultiplicationTable| |commutativeEquality| |tensorProduct| |id| + |karatsubaOnce| |skewSFunction| |matrixGcd| |library| |\\/| + |screenResolution| |s18def| |besselY| |createMultiplicationMatrix| + |leftMult| |permutationRepresentation| |applyRules| |karatsuba| + |cyclotomicDecomposition| |divideIfCan!| |eval| |setMaxPoints| + |s19aaf| |besselI| |localUnquote| |createLowComplexityTable| + |rightMult| |completeEchelonBasis| |separate| |table| + |cyclotomicFactorization| |leastPower| |output| |compile| |maxPoints| + |s19abf| |besselK| |zeroOf| |arbitrary| + |createLowComplexityNormalBasis| |makeUnit| |createRandomElement| + |pseudoDivide| |new| |rangeIsFinite| |idealiser| |setMinPoints| + |s19acf| |airyAi| |obj| |setColumn!| |representationType| |reverse!| + |cyclicSubmodule| |search| |pseudoQuotient| + |functionIsContinuousAtEndPoints| |idealiserMatrix| |s19adf| + |minPoints| |set| |airyBi| |cache| |dilog| |createPrimitiveElement| + |makeMulti| |standardBasisOfCyclicSubmodule| |setRow!| |composite| + |functionIsOscillatory| |moduleSum| |parametric?| |s20acf| |subNode?| + |sin| |tableForDiscreteLogarithm| |makeTerm| |areEquivalent?| + |oneDimensionalArray| |subResultantGcd| |changeName| |mapUnivariate| + |plotPolar| |s20adf| |infLex?| |cos| |factorsOfCyclicGroupSize| + |listOfMonoms| |isAbsolutelyIrreducible?| |associatedSystem| + |resultant| |exprHasWeightCosWXorSinWX| |mapUnivariateIfCan| |debug3D| + |s21baf| |setEmpty!| |tan| |sizeMultiplication| |symmetricSquare| + |meatAxe| |uncouplingMatrices| |discriminant| |exprHasAlgebraicWeight| + |mapMatrixIfCan| |numFunEvals3D| |s21bbf| |setStatus!| |cot| + |getMultiplicationMatrix| |factor1| |scanOneDimSubspaces| + |associatedEquations| |pseudoRemainder| |knownInfBasis| + |exprHasLogarithmicWeights| |mapBivariate| |s21bcf| |setAdaptive3D| + |sort| |setCondition!| |sec| |arrayStack| |getMultiplicationTable| + |symmetricProduct| |expt| |shiftLeft| |delta| |rootSplit| + |combineFeatureCompatibility| |fullDisplay| |adaptive3D?| |s21bdf| + |setValue!| |csc| |primitive?| |symmetricPower| |showArrayValues| + |setButtonValue| |shiftRight| |sparsityIF| |relationsIdeal| + |setScreenResolution3D| |fortranCompilerName| |empty?| |asin| + |numberOfIrreduciblePoly| |directSum| |showScalarValues| + |setAttributeButtonStep| |karatsubaDivide| + |stiffnessAndStabilityFactor| |saturate| |true| |fortranLinkerArgs| + |screenResolution3D| ~= |splitNodeOf!| |acos| |resetAttributeButtons| + |numberOfPrimitivePoly| |solveLinearPolynomialEquationByFractions| + |solveRetract| |monicDivide| |left| |stiffnessAndStabilityOfODEIF| + |groebner?| |aspFilename| |setMaxPoints3D| |random| |remove!| |coerce| + |hash| |atan| |getButtonValue| |numberOfNormalPoly| |hasSolution?| + |mainVariable| |divideExponents| |right| |systemSizeIF| + |groebnerIdeal| |dimensionsOf| |maxPoints3D| |subNodeOf?| |construct| + |show| |count| |acot| |createIrreduciblePoly| |linSolve| |uniform01| + |decrease| |unmakeSUP| |expenseOfEvaluationIF| |ideal| + |setMinPoints3D| = |restorePrecision| |nodeOf?| |asec| + |createPrimitivePoly| |LyndonWordsList| |normal01| |increase| + |makeSUP| |accuracyIF| |leadingIdeal| |antiCommutator| |minPoints3D| + |trace| |updateStatus!| |morphism| |acsc| |noLinearFactor?| + |createNormalPoly| |LyndonWordsList1| |exponential1| |lambda| + |vectorise| |intermediateResultsIF| |backOldPos| < |tValues| + |commutator| |extractSplittingLeaf| |sinh| |createNormalPrimitivePoly| + |lyndonIfCan| |chiSquare1| |extend| |subscriptedVariables| + |generalPosition| > |tRange| |associator| |squareMatrix| |cosh| + |createPrimitiveNormalPoly| |lyndon| |exponential| |insertRoot!| + |truncate| |central?| |quotient| <= |plot| |complexEigenvalues| + |transpose| |tanh| |nextIrreduciblePoly| |lyndon?| |chiSquare| + |binarySearchTree| |order| |max| |elliptic?| |zeroDim?| >= |pointPlot| + |complexEigenvectors| |trim| |coth| |nextPrimitivePoly| + |numberOfComputedEntries| |factorFraction| |terms| |doubleResultant| + |inRadical?| |calcRanges| |isConnected?| |split| |sech| |showSummary| + |nextNormalPoly| |rst| |componentUpperBound| |squareFreePart| + |distdfact| |cn| |in?| |fixPredicate| |connectTo| |replace| |csch| + |nextNormalPrimitivePoly| |frst| |blue| |BumInSepFFE| + |separateDegrees| |element?| |patternMatch| + |normalizedAssociate| + |upperCase!| |asinh| |nextPrimitiveNormalPoly| |showAttributes| + |lazyEvaluate| |green| |multiplyExponents| |trace2PowMod| + |zeroDimPrime?| |patternMatchTimes| - |normalize| |upperCase| |acosh| + |leastAffineMultiple| |lazy?| |red| |laurentIfCan| |tracePowMod| + |zeroDimPrimary?| |bernoulli| / |outputArgs| |lowerCase!| |atanh| + |reducedQPowers| |explicitlyEmpty?| |whitePoint| |laurentRep| + |irreducible?| |primaryDecomp| |normInvertible?| |chebyshevT| + |lowerCase| |setelt| |acoth| |rootOfIrreduciblePoly| + |explicitEntries?| |uniform| |rationalPower| |parents| |decimal| + |contract| |chebyshevU| |normFactors| |KrullNumber| |asech| |write!| + |matrixDimensions| |binomial| |dominantTerm| |innerint| + |leadingSupport| |npcoef| |cyclotomic| |copy| |numberOfVariables| + |read!| |arg1| |matrixConcat3D| |poisson| |limitPlus| + |exteriorDifferential| |shrinkable| |euler| |listexp| + |algebraicDecompose| |multiple| |iomode| |arg2| |setelt!| |geometric| + |split!| |totalDifferential| |physicalLength!| |label| |fixedDivisor| + |characteristicPolynomial| |transcendentalDecompose| |applyQuote| + |close!| |identityMatrix| |ridHack1| |setlast!| |homogeneous?| + |physicalLength| |realEigenvalues| |laguerre| |internalDecompose| + |autoCoerce| |reopen!| |conditions| |zeroMatrix| |interpolate| + |setrest!| |flexibleArray| |legendre| |realEigenvectors| |decompose| + |rightUnit| |match| |mappingAst| |nullSpace| |mkIntegral| |setfirst!| + |result| |outputList| |elseBranch| |dmpToHdmp| + |halfExtendedResultant2| |upDateBranches| |ruleset| |leftUnit| + |nullary| |nullity| |cycleSplit!| |radPoly| |properties| |thenBranch| + |hdmpToDmp| |halfExtendedResultant1| |preprocess| |mapUp!| + |rightMinimalPolynomial| |fixedPoint| |rowEchelon| |concat!| + |rootPoly| |translate| |generalizedInverse| |pToHdmp| + |extendedResultant| |internalZeroSetSplit| |setleaves!| |recur| + |column| |cycleTail| |goodPoint| |imports| |hdmpToP| + |subResultantsChain| |internalAugment| |mat| |suchThat| |const| |row| + |cycleLength| |chvar| |sequence| |dmpToP| |lazyPseudoQuotient| + |possiblyInfinite?| |neglist| |curry| |maxColIndex| |cycleEntry| + |find| |option| |iterationVar| |pToDmp| |lazyPseudoRemainder| + |explicitlyFinite?| |multiEuclidean| |diag| |minColIndex| + |invmultisect| |clipParametric| |bernoulliB| |nextItem| + |extendedEuclidean| |curryRight| |maxRowIndex| |multisect| + |clipWithRanges| |hMonic| |bivariateSLPEBR| |eulerE| |infiniteProduct| + |euclideanSize| |curryLeft| |minRowIndex| |revert| |numberOfHues| + |updatF| |solveLinearPolynomialEquationByRecursion| |checkPrecision| + |numericIfCan| |evenInfiniteProduct| |sizeLess?| |constantRight| + |antisymmetric?| |generalLambert| |yellow| |sPol| |factorByRecursion| + |complexNumericIfCan| |oddInfiniteProduct| |simplifyPower| + |evenlambert| |binaryTree| |iifact| |updatD| + |factorSquareFreeByRecursion| |FormatArabic| |generalInfiniteProduct| + |number?| |cCos| |radicalSimplify| |rightTrim| |oddlambert| |iibinom| + |minGbasis| |randomR| |interpret| |ScanArabic| |showAll?| + |seriesSolve| |cSin| |denominator| |leftTrim| |lambert| |iiperm| + |lepol| |factorSFBRlcUnit| |FormatRoman| |showAllElements| + |constantToUnaryFunction| |cLog| |numerator| |lagrange| |iipow| + |prinshINFO| |charthRoot| |tubePlot| |cExp| |quadraticForm| + |univariatePolynomial| |iidsum| |prindINFO| |conditionP| |f01bsf| + |subresultantSequence| |retract| |tower| |exponentialOrder| + |cRationalPower| |back| |integrate| |iidprod| |stop| |fprindINFO| + |solveLinearPolynomialEquation| |f01maf| |SturmHabichtSequence| + |completeEval| |cPower| |front| |multiplyCoefficients| |ipow| + |prinpolINFO| |factorSquareFreePolynomial| |f01mcf| + |SturmHabichtCoefficients| |lowerPolynomial| |seriesToOutputForm| + |rotate!| |factorial| |prinb| |factorPolynomial| |f01qcf| + |SturmHabicht| |raisePolynomial| |iCompose| |dequeue!| |extendIfCan| + |multinomial| |directory| |critpOrder| |squareFreePolynomial| |f01qdf| + |countRealRoots| |normalDeriv| |continue| |taylorQuoByVar| |enqueue!| + |algebraicVariables| |permutation| |makeCrit| |gcdPolynomial| |f01qef| + |SturmHabichtMultiple| |ran| |complexNumeric| |iExquo| |quatern| + |zeroSetSplitIntoTriangularSystems| |stirling1| |virtualDegree| + |torsion?| |f01rcf| |countRealRootsMultiple| |highCommonTerms| + |getStream| |imagK| |zeroSetSplit| |stirling2| |categories| + |conditionsForIdempotents| |torsionIfCan| |f01rdf| |signatureAst| + |kernels| |mapCoef| |getRef| |imagJ| |retractIfCan| + |reduceByQuasiMonic| |summation| |genericRightDiscriminant| + |getGoodPrime| |f01ref| |pop!| |nthCoef| |univariate| |makeSeries| + |imagI| |collectQuasiMonic| |factorials| |numer| + |genericRightTraceForm| |badNum| |f02aaf| |push!| |binomThmExpt| GF2FG + |conjugate| |removeZero| |mkcomm| |denom| |genericLeftDiscriminant| + |mix| |f02abf| |minordet| |equality| |pomopo!| FG2F |queue| |null| + |initiallyReduce| |polarCoordinates| |genericLeftTraceForm| + |doubleDisc| |f02adf| |determinant| |nary?| |mapExponents| F2FG + |nthRoot| |factor| |not| |generate| |headReduce| SEGMENT |imaginary| + |pi| |genericRightNorm| |polyred| |f02aef| |diagonalProduct| + |linearAssociatedLog| |sqrt| |explogs2trigs| |fractRadix| |and| + |stronglyReduce| |solid| |infinity| |genericRightTrace| + |padicFraction| |f02aff| |diagonal| |linearAssociatedOrder| + |incrementBy| |trigs2explogs| |wholeRadix| |or| + |rewriteSetWithReduction| |solid?| |genericRightMinimalPolynomial| + |padicallyExpand| |f02agf| |diagonalMatrix| |linearAssociatedExp| + |swap!| |cycleRagits| |xor| |autoReduced?| |expand| |denominators| + |rightRankPolynomial| |numberOfFractionalTerms| |f02ajf| + |scalarMatrix| |node| |convert| |createNormalElement| |fill!| + |prefixRagits| |filterWhile| |case| |initiallyReduced?| |numerators| + |kernel| |genericLeftNorm| |nthFractionalTerm| |f02akf| |hermite| + |bezoutMatrix| |unary?| |setLabelValue| |sum| |minIndex| |fractRagits| + |map| |Zero| |filterUntil| |headReduced?| |convergents| |draw| + |genericLeftTrace| |firstNumer| |f02awf| |completeHermite| + |bezoutResultant| |nullary?| |getCode| |maxIndex| |wholeRagits| |One| + |stronglyReduced?| |select| |approximants| + |genericLeftMinimalPolynomial| |firstDenom| |f02axf| |smith| + |printCode| |entry?| |radix| |reduced?| |reducedForm| |port| + |leftRankPolynomial| |compactFraction| |f02bbf| |completeSmith| + |printStatement| |indices| |randnum| |normalized?| |partialQuotients| + |lp| |generic| |partialFraction| |f02bjf| |diophantineSystem| |block| + |index?| |reseed| |quasiComponent| |partialDenominators| |makeObject| + |t| |rightUnits| |gcdPrimitive| |f02fjf| |csubst| |nor| |returns| + |assert| |entries| |seed| |initials| |partialNumerators| |leftUnits| + |symmetricGroup| |f02wef| |particularSolution| |nand| |goto| |key?| + |rational| |basicSet| |elt| |reducedContinuedFraction| |coef| + |compBound| |alternatingGroup| |f02xef| |mapSolve| |repeatUntilLoop| + |symbolIfCan| |rational?| |makeRecord| |infRittWu?| |push| |tablePow| + |abelianGroup| |f04adf| |quadratic| |whileLoop| |argument| + |rationalIfCan| |getCurve| |bindings| |solveid| |cyclicGroup| |f04arf| + |cubic| |forLoop| |constantKernel| |setvalue!| |formula| |listLoops| + |lhs| |cartesian| |testModulus| |dihedralGroup| |f04asf| |quartic| + |sin?| |systemCommand| |constantIfCan| |setchildren!| |closed?| |rhs| + |polar| |HenselLift| |mathieu11| |f04atf| |aLinear| |zeroVector| + |kovacic| |node?| |open?| |cylindrical| |completeHensel| |mathieu12| + |f04axf| |aQuadratic| |zeroSquareMatrix| |laplace| |child?| + |setClosed| |depth| |spherical| |multMonom| |mathieu22| |f04faf| + |aCubic| |identitySquareMatrix| |normal| |equation| + |trailingCoefficient| |distance| |nrows| |tube| |parabolic| |build| + |f04jgf| |mathieu23| |aQuartic| |key| |lSpaceBasis| |normalizeIfCan| + |nodes| |ncols| |unitVector| |parabolicCylindrical| |leadingIndex| + |mathieu24| |f04maf| |radicalSolve| |finiteBasis| |polCase| |rename| + |cosSinInfo| |ratDenom| |paraboloidal| |filename| |leadingExponent| + |janko2| |f04mbf| |radicalRoots| |code| |principal?| |distFact| + |rename!| |loopPoints| |ratPoly| |ellipticCylindrical| |GospersMethod| + |f04mcf| |rubiksGroup| |not?| |contractSolve| |divisor| + |identification| |mainValue| |generalTwoFactor| |rootPower| + |prolateSpheroidal| |nextSubsetGray| |f04qaf| |youngGroup| + |decomposeFunc| |parse| |useNagFunctions| |lift| |LyndonCoordinates| + |mainDefiningPolynomial| |generalSqFr| |rootProduct| + |oblateSpheroidal| |firstSubsetGray| |lexGroebner| |f07adf| + |unvectorise| |rationalPoints| |reduce| |LyndonBasis| |mainForm| + |twoFactor| |rootSimp| |bipolar| |clipPointsDefault| |totalGroebner| + |f07aef| |bubbleSort!| |nonSingularModel| |zeroDimensional?| |rischDE| + |setOrder| |rootKerSimp| |bipolarCylindrical| |drawToScale| + |expressIdealMember| |f07fdf| |insertionSort!| |loadNativeModule| + |algSplitSimple| |fglmIfCan| |rischDEsys| |derivative| |getOrder| + |leftRank| |toroidal| |adaptive| |expr| |principalIdeal| |f07fef| + |check| |hyperelliptic| |groebner| |monomRDE| |constantOperator| + |less?| |conical| |unknown| |figureUnits| |LagrangeInterpolation| + |s01eaf| |lprop| |real| |elliptic| |lexTriangular| |baseRDE| + |userOrdered?| |modTree| |putColorInfo| |psolve| |s13aaf| |llprop| + |imag| |integralDerivationMatrix| |squareFreeLexTriangular| |polyRDE| + |largest| |multiEuclideanTree| |kind| |appendPoint| |wrregime| + |s13acf| |lllp| |directProduct| |integralRepresents| |leaves| + |belong?| |monomRDEsys| |more?| |component| |op| |variable| |rdregime| + |s13adf| |lllip| |rank| |init| |bezoutDiscriminant| + |integralCoordinates| |Ci| |baseRDEsys| |setVariableOrder| |ranges| + |iterators| |bsolve| |s14aaf| |mesh?| |brace| |bfEntry| |yCoordinates| + |Si| |substring?| |weighted| |getVariableOrder| |setProperty| + |pointLists| |dmp2rfi| |s14abf| |mesh| |destruct| + |inverseIntegralMatrixAtInfinity| |Ei| |rdHack1| |resetVariableOrder| + |deleteProperty!| |makeGraphImage| |index| |se2rfi| |s14baf| + |polygon?| |entry| |linGenPos| |suffix?| |operator| |prime?| + |rightRank| |graphImage| |pr2dmp| |s15adf| |polygon| |setProperties!| + |groebgen| |midpoint| |sample| |doubleRank| |groebSolve| |hasoln| + |s15aef| |closedCurve?| |currentEnv| |getProperties| |totolex| + |prefix?| |midpoints| |rationalFunction| |testDim| |union| |s17acf| + |ParCondList| |pair| |closedCurve| |monomial| |setProperty!| |minPol| + |realZeros| |taylorIfCan| |s17adf| |curve?| |lists| |multivariate| + |getProperty| |computeBasis| |nothing| |mainCharacterization| + |removeZeroes| |fortranLogical| |is?| |s17aef| |curve| |variables| + |scopes| |coord| |algebraicOf| |taylorRep| |fortranInteger| |Is| + |s17aff| |point?| |eigenvalues| |outputAsFortran| |anticoord| + |ReduceOrder| |value| |factorSquareFree| |bfKeys| |fortranDouble| + |addMatchRestricted| |s17agf| |enterPointData| |eigenvector| + |henselFact| |inspect| |fortranReal| |insertMatch| |s17ahf| + |composites| |generalizedEigenvector| |tanintegrate| + |rewriteIdealWithQuasiMonicGenerators| |top| |infix?| |hasHi| + |external?| |addMatch| |s17ajf| |components| |generalizedEigenvectors| + |primextendedint| |squareFreeFactors| |mask| |fmecg| |scalarTypeOf| + |getMatch| |s17akf| |numberOfComposites| |taylor| |eigenvectors| + |expextendedint| |univariatePolynomialsGcds| |commonDenominator| + |fortranCarriageReturn| |failed?| |parts| |laurent| |factorAndSplit| + |primlimitedint| |removeRoughlyRedundantFactorsInContents| + |clearDenominator| |fortranLiteral| |optpair| |d01anf| |member?| + |constant| |puiseux| |rightOne| |printInfo| |explimitedint| + |removeRedundantFactorsInContents| |splitDenominator| + |fortranLiteralLine| |getBadValues| |d01apf| |enumerate| |leftOne| + |primextintfrac| |removeRedundantFactorsInPols| + |monicRightFactorIfCan| |processTemplate| |resetBadValues| |d01aqf| + |setOfMinN| |inv| |rightZero| |primlimintfrac| |irreducibleFactors| + |makeFR| |hasTopPredicate?| |d01asf| |elements| |ground?| |leftZero| + |primintfldpoly| |lazyIrreducibleFactors| |OMReadError?| + |setPrologue!| |musserTrials| |topPredicate| |d01bbf| + |replaceKthElement| |ground| |swap| |expintfldpoly| + |removeIrreducibleRedundantFactors| |OMUnknownSymbol?| |setTex!| + |stopMusserTrials| |setTopPredicate| |d01fcf| |incrementKthElement| + |leadingMonomial| |minPoly| |monomialIntegrate| |normalForm| + |OMUnknownCD?| |setEpilogue!| |numberOfFactors| |patternVariable| + |d01gaf| |float?| |leadingCoefficient| |freeOf?| |rules| + |monomialIntPoly| |changeBase| |OMParseError?| |prologue| + |modularFactor| |status| |withPredicates| |d01gbf| |integer?| + |RemainderList| |primitiveMonomials| |operators| |inverseLaplace| + |companionBlocks| |OMwrite| |epilogue| |operation| + |useSingleFactorBound?| |setPredicates| |d02bbf| |symbol?| |unexpand| + |reductum| |mainKernel| |inputOutputBinaryFile| |xCoord| |po| + |endOfFile?| |useSingleFactorBound| |predicates| |d02bhf| |string?| + |triangSolve| |distribute| |bothWays| |yCoord| |OMread| |readIfCan!| + |useEisensteinCriterion?| |hasPredicate?| |d02cjf| |list?| + |univariateSolve| |functionIsFracPolynomial?| |erf| |bytes| |zCoord| + |OMreadFile| |readLineIfCan!| |useEisensteinCriterion| |symbolTable| + |optional?| |d02ejf| |pair?| |realSolve| |problemPoints| |ip4Address| + |rCoord| |OMreadStr| |readLine!| |eisensteinIrreducible?| |multiple?| + |d02gaf| |atom?| |positiveSolve| |zerosOf| |iprint| |thetaCoord| + |OMlistCDs| |writeLine!| |tryFunctionalDecomposition?| |generic?| + |d02gbf| |null?| |squareFree| |singularitiesOf| |elem?| |phiCoord| + |OMlistSymbols| |sign| |extract!| |tryFunctionalDecomposition| + |quoted?| |d02kef| |startTable!| |linearlyDependentOverZ?| + |polynomialZeros| |notelem| |OMsupportsCD?| |color| |nonQsign| |ptree| + |bag| |btwFact| |inR?| |d02raf| |stopTable!| |weakBiRank| + |linearDependenceOverZ| |inc| |f2df| |logpart| |hue| + |OMsupportsSymbol?| |direction| |beauzamyBound| |isList| |d03edf| + |supDimElseRittWu?| |biRank| |solveLinearlyOverQ| |ef2edf| |ratpart| + |shade| |OMunhandledSymbol| |createThreeSpace| |bombieriNorm| |isOp| + |d03eef| |algebraicSort| |ocf2ocdf| |mkAnswer| |nthRootIfCan| + |OMreceive| |cyclicParents| |rootBound| |d03faf| |satisfy?| + |moreAlgebraic?| |concat| |socf2socdf| |perfectNthPower?| |expIfCan| + |OMsend| |cyclicEqual?| |singleFactorBound| |addBadValue| |e01baf| + |subTriSet?| |df2fi| |perfectNthRoot| |logIfCan| |OMserve| + |cyclicEntries| |quadraticNorm| |badValues| |e01bef| |subPolSet?| + |edf2fi| |approxNthRoot| |sinIfCan| |makeop| |cyclicCopy| + |infinityNorm| |retractable?| |e01bff| |internalSubPolSet?| |edf2df| + |perfectSquare?| |cosIfCan| |opeval| |cyclic?| |scaleRoots| + |ListOfTerms| |e01bgf| |internalInfRittWu?| |expenseOfEvaluation| + |perfectSqrt| |tanIfCan| |evaluateInverse| |complexNormalize| + |shiftRoots| |PDESolve| |e01bhf| |internalSubQuasiComponent?| + |numberOfOperations| |approxSqrt| |cotIfCan| |evaluate| + |complexElementary| |degreePartition| |e01daf| |leftFactor| |optimize| + |subQuasiComponent?| |edf2efi| |generateIrredPoly| |secIfCan| |conjug| + |trigs| |factorOfDegree| |rightFactorCandidate| |e01saf| + |removeSuperfluousQuasiComponents| |signature| |dfRange| + |complexExpand| |cscIfCan| |adjoint| |real?| |factorsOfDegree| + |measure| |e01sbf| |subCase?| |dflist| |complexIntegrate| |asinIfCan| + |arity| |complexForm| |pascalTriangle| |coerceImages| |e01sef| + |removeSuperfluousCases| |eq?| |df2mf| + |dimensionOfIrreducibleRepresentation| |acosIfCan| |getDatabase| + |UpTriBddDenomInv| |rangePascalTriangle| |fixedPoints| |e01sff| + |prepareDecompose| |doublyTransitive?| |ldf2vmf| + |irreducibleRepresentation| |atanIfCan| |numericalOptimization| + |LowTriBddDenomInv| |digit?| |sizePascalTriangle| |odd?| |e02adf| + |branchIfCan| |edf2ef| |checkRur| |acotIfCan| |goodnessOfFit| + |simplify| |delete| |fillPascalTriangle| |even?| |e02aef| + |startTableGcd!| |vedf2vef| |cAcsch| |asecIfCan| |whatInfinity| + |htrigs| |safeCeiling| |numberOfCycles| |e02agf| |stopTableGcd!| + |df2st| |cAsech| |acscIfCan| |infinite?| |simplifyExp| |safeFloor| + |cyclePartition| |e02ahf| |startTableInvSet!| |iroot| |f2st| |cAcoth| + |sinhIfCan| |finite?| |simplifyLog| |setright!| |safetyMargin| + |coerceListOfPairs| |e02ajf| |stopTableInvSet!| |size?| |ldf2lst| + |cAtanh| |coshIfCan| |pureLex| |expandPower| |setleft!| |sumSquares| + |coercePreimagesImages| |e02akf| |stosePrepareSubResAlgo| |exquo| + |sdf2lst| |cAcosh| |tanhIfCan| |totalLex| |expandLog| |point| + |euclideanNormalForm| |listRepresentation| |e02baf| + |stoseInternalLastSubResultant| |getlo| |cAsinh| |cothIfCan| + |reverseLex| |cos2sec| |euclideanGroebner| |permanent| |e02bbf| + |stoseIntegralLastSubResultant| |div| |gethi| |cCsch| |sechIfCan| + |leftLcm| |cosh2sech| |factorGroebnerBasis| |cycles| |e02bcf| + |stoseLastSubResultant| |datalist| |cond| |outputMeasure| |cSech| + |cschIfCan| |rightExtendedGcd| |cot2trig| |series| |groebnerFactorize| + |cycle| |e02bdf| |stoseInvertible?sqfreg| |quo| |measure2Result| + |cCoth| |asinhIfCan| |rightGcd| |coth2trigh| |credPol| + |initializeGroupForWordProblem| |e02bef| |stoseInvertibleSetsqfreg| + |att2Result| |cTanh| |acoshIfCan| |rightExactQuotient| |csc2sin| + |redPol| |movedPoints| |e02daf| |stoseInvertible?reg| |iflist2Result| + |cCosh| |atanhIfCan| |rightRemainder| |csch2sinh| |gbasis| + |wordInGenerators| |e02dcf| |stoseInvertibleSetreg| |pdf2ef| |box| + |cSinh| |acothIfCan| |rightQuotient| |sec2cos| |min| + |brillhartIrreducible?| |critT| |wordInStrongGenerators| |e02ddf| + |stoseInvertible?| |rem| |pdf2df| |cAcsc| |asechIfCan| |rightLcm| + |sech2cosh| |brillhartTrials| |log10| |critM| |orbits| |e02def| + |stoseInvertibleSet| |df2ef| |precision| |cAsec| |acschIfCan| + |leftExtendedGcd| |sin2csc| |critB| |bitand| |li| |orbit| |e02dff| + |stoseSquareFreePart| |fi2df| |cAcot| |pushdown| |leftGcd| |sinh2csch| + |bitior| |critBonD| |permutationGroup| |e02gaf| |coleman| + |balancedBinaryTree| |super| |cAtan| |pushup| |leftExactQuotient| + |tan2trig| |critMTonD1| |wordsForStrongGenerators| |e02zaf| + |inverseColeman| |sylvesterMatrix| |sortConstraints| |cAcos| + |reducedDiscriminant| |leftRemainder| |tanh2trigh| |critMonD1| + |strongGenerators| |e04dgf| |listYoungTableaus| |sumOfSquares| |cAsin| + |idealSimplify| |leftQuotient| |tan2cot| |redPo| |generators| |e04fdf| + |makeYoungTableau| |splitLinear| |cCsc| |definingInequation| + |monicLeftDivide| |tanh2coth| |e04gcf| |nextColeman| |simpleBounds?| + |cSec| |definingEquations| |monicRightDivide| |cot2tan| |polyPart| + |isOpen?| |e04jaf| |nextLatticePermutation| |linearMatrix| Y |cCot| + |setStatus| |leftDivide| |coth2tanh| |fullPartialFraction| + |outputBinaryFile| |e04mbf| |nextPartition| |linearPart| |cTan| + |quasiAlgebraicSet| |rightDivide| |removeCosSq| |primeFrobenius| + |blankSeparate| |e04naf| |numberOfImproperPartitions| |nonLinearPart| + |hermiteH| |removeSinSq| F |discreteLog| |semicolonSeparate| |e04ucf| + |subSet| |quadratic?| |interval| |semiDiscriminantEuclidean| |debug| + |laguerreL| |removeCoshSq| |decreasePrecision| |commaSeparate| + |e04ycf| |unrankImproperPartitions0| |changeNameToObjf| |unit?| + |chainSubResultants| D |legendreP| |removeSinhSq| |zero| + |increasePrecision| |pile| |f01brf| |unrankImproperPartitions1| |test| + |optAttributes| |associates?| |schema| |writeBytes!| + |expandTrigProducts| |bits| |paren| |any| |Nul| |unitCanonical| + |resultantReduit| |writeUInt8!| |fintegrate| |And| |unitNormalize| + |bracket| |frobenius| |mainMonomials| |exponents| |unitNormal| + |resultantReduitEuclidean| |writeInt8!| |coefficient| |unit| |Or| + |computePowers| |prod| |mainCoefficients| |prefix| |iisqrt2| + |lfextendedint| |semiResultantReduitEuclidean| |writeByte!| |coHeight| + |Not| |flagFactor| |overlabel| |pow| |leastMonomial| |iisqrt3| + |lflimitedint| |divide| |sqfrFactor| |overbar| |An| |mainMonomial| + |iiexp| |lfinfieldint| |Lazard| |OMmakeConn| |printHeader| ** + |primeFactor| |prime| |UnVectorise| |quasiMonic?| |iilog| + |lfintegrate| |Lazard2| |OMcloseConn| |returnType!| |nthFlag| |quote| + |Vectorise| |monic?| |balancedFactorisation| |iisin| |lo| + |lfextlimint| |nextsousResultant2| |OMconnInDevice| |argumentList!| + |nthExponent| |supersub| |setPoly| |deepestInitial| |mapDown!| |iicos| + |BasicMethod| |predicate| |incr| EQ |OMconnOutDevice| |resultantnaif| + |endSubProgram| |print| |dim| |irreducibleFactor| |presuper| + |exponent| |iteratedInitials| |viewDeltaYDefault| |iitan| + |PollardSmallFactor| |resolve| |resultantEuclideannaif| |OMconnectTCP| + |currentSubProgram| |nilFactor| |presub| |exQuo| |deepestTail| + |viewDeltaXDefault| |iicot| |showTheFTable| + |semiResultantEuclideannaif| |OMbindTCP| |newSubProgram| + |regularRepresentation| |sub| |moebius| |head| |viewZoomDefault| + |iisec| |clearTheFTable| |pdct| |OMopenFile| |clearTheSymbolTable| + |traceMatrix| |rarrow| |rightRecip| |mdeg| |viewPhiDefault| |iicsc| + |fTable| |powers| |OMopenString| |showTheSymbolTable| |randomLC| + |assign| |name| |leftRecip| |mvar| |viewThetaDefault| |iiasin| + |palgint0| |partition| |OMclose| |printTypes| |minimize| |slash| + |body| |leftPower| |relativeApprox| |pointColorDefault| |iiacos| + |palgextint0| |complete| |OMsetEncoding| |newTypeLists| |exp| + |category| |module| |over| |rightPower| |rootOf| |lineColorDefault| + |iiatan| |palglimint0| |pole?| |OMputApp| |typeLists| ~ |domain| + |rightRegularRepresentation| |zag| |derivationCoordinates| + |allRootsOf| |axesColorDefault| |iiacot| |parameters| |palgRDE0| + |listBranches| |OMputAtp| |externalList| |package| + |leftRegularRepresentation| |insert| |postfix| |one?| + |definingPolynomial| |unitsColorDefault| |iiasec| |palgLODE0| + |triangular?| |OMputAttr| |typeList| |open| |rightTraceMatrix| |infix| + |center| |splitSquarefree| |positive?| |pointSizeDefault| |iiacsc| + |chineseRemainder| |rewriteIdealWithRemainder| |length| |OMputBind| + |parametersOf| |leftTraceMatrix| |vconcat| |fortran| |normalDenom| + |negative?| |viewPosDefault| |iisinh| |divisors| |hi| + |rewriteIdealWithHeadRemainder| |scripts| |OMputBVar| |fortranTypeOf| + |second| |rightDiscriminant| |hconcat| |totalfract| |zero?| + |viewSizeDefault| |iicosh| |eulerPhi| |remainder| |OMputError| |empty| + |third| |leftDiscriminant| |rspace| |pushdterm| |augment| + |viewDefaults| |iitanh| |fibonacci| |headRemainder| |OMputObject| + |compound?| |operations| |represents| |vspace| |pushucoef| + |lastSubResultant| |shift| |viewWriteDefault| |iicoth| |harmonic| + |roughUnitIdeal?| |OMputEndApp| |getOperands| |mergeFactors| |hspace| + |pushuconst| |lastSubResultantElseSplit| |viewWriteAvailable| |iisech| + |jacobi| |roughEqualIdeals?| |OMputEndAtp| |getOperator| |isMult| + |superHeight| |numberOfMonomials| |invertibleSet| |var1StepsDefault| + |iicsch| |moebiusMu| |roughSubIdeal?| |OMputEndAttr| |nil?| + |exprToXXP| |subHeight| |multiset| |invertible?| |var2StepsDefault| + |iiasinh| |numberOfDivisors| |roughBase?| |OMputEndBind| |buildSyntax| + |property| |exprToUPS| |doubleFloatFormat| |mergeDifference| + |invertibleElseSplit?| |tubePointsDefault| |clearCache| |iiacosh| + |sumOfDivisors| |trivialIdeal?| |OMputEndBVar| |solve| |exprToGenUPS| + |messagePrint| |squareFreePrim| |purelyAlgebraicLeadingMonomial?| + |tubeRadiusDefault| |iiatanh| |lcm| |sumOfKthPowerDivisors| + |collectUpper| |OMputEndError| |triangularSystems| |localAbs| + |members| |compdegd| |algebraicCoefficients?| |dimension| |iiacoth| + |HermiteIntegrate| |collect| |OMputEndObject| |nativeModuleExtension| + |units| |universe| |padecf| |univcase| |purelyTranscendental?| |crest| + |stack| |iiasech| |append| |palgint| |collectUnder| |OMputInteger| + |hostByteOrder| |complement| |pade| |consnewpol| |purelyAlgebraic?| + |cfirst| |iiacsch| |gcd| |palgextint| |mainVariable?| |OMputFloat| + |hostPlatform| |cardinality| |comp| |root| |script| |nsqfree| + |prepareSubResAlgo| |sts2stst| |has?| |initial| |specialTrigs| |false| + |palglimint| |mainVariables| |OMputVariable| |rootDirectory| + |internalIntegrate0| |quotientByP| |intChoose| + |internalLastSubResultant| |clikeUniv| |comparison| |localReal?| + |palgRDE| |removeSquaresIfCan| |OMputString| |bumprow| |makeCos| + |moduloP| |coefChoose| |integralLastSubResultant| |weierstrass| + |rischNormalize| |palgLODE| |unprotectedRemoveRedundantFactors| + |OMputSymbol| |bumptab| |makeSin| |modulus| |tex| |myDegree| + |toseLastSubResultant| |qqq| |realElementary| |linear| |splitConstant| + |removeRedundantFactors| |OMgetApp| |bumptab1| |iiGamma| |digits| + |normDeriv2| |toseInvertible?| |integralBasis| |validExponential| |#| + |pmComplexintegrate| |certainlySubVariety?| |OMgetAtp| |untab| |iiabs| + |continuedFraction| |plenaryPower| |toseInvertibleSet| + |localIntegralBasis| |rootNormalize| |polynomial| |pmintegrate| + |possiblyNewVariety?| |OMgetAttr| |bat1| |plusInfinity| |bringDown| + |light| |c02aff| |toseSquareFreePart| |qualifier| |dom| |tanQ| + |infieldint| |probablyZeroDim?| |OMgetBind| |bat| |minusInfinity| + |newReduc| |pastel| |c02agf| |quotedOperators| |mainExpression| + |callForm?| |extendedint| |selectPolynomials| |OMgetBVar| |tab1| + |logical?| |c05adf| |dark| |list| |rur| |changeWeightLevel| + |getIdentifier| |limitedint| |selectOrPolynomials| |OMgetError| |tab| + |character?| |c05nbf| |getSyntaxFormsFromFile| |car| |create| + |characteristicSerie| |getConstant| |integerIfCan| + |selectAndPolynomials| |OMgetObject| |lex| |doubleComplex?| |c05pbf| + |surface| |cdr| |symbol| |enterInCache| |characteristicSet| |select!| + |internalIntegrate| |quasiMonicPolynomials| |OMgetEndApp| |slex| + |complex?| |setDifference| |c06eaf| |coordinate| |expression| + |currentCategoryFrame| |medialSet| |delete!| |infieldIntegrate| + |univariate?| |OMgetEndAtp| |inverse| |title| |double?| + |setIntersection| |c06ebf| |partitions| |options| |currentScope| + |integer| |Hausdorff| |sn| |limitedIntegrate| |univariatePolynomials| + |OMgetEndAttr| |maxrow| |ffactor| |rule| |setUnion| |conjugates| + |c06ecf| |pushNewContour| |Frobenius| |say| |dn| |extendedIntegrate| + |linear?| |OMgetEndBind| |tableau| |type| |qfactor| |c06ekf| |shuffle| + |findBinding| |apply| |transcendenceDegree| |e| |sncndn| |varselect| + |linearPolynomials| |OMgetEndBVar| |listOfLists| |UP2ifCan| + |shufflein| |string| |c06fpf| |contours| |extensionDegree| + |categoryFrame| |kmax| |bivariate?| |OMgetEndError| |tanSum| + |anfactor| |c06fqf| |sequences| |structuralConstants| |size| + |inGroundField?| |ksec| |bivariatePolynomials| |OMgetEndObject| + |tanAn| |fortranCharacter| |permutations| |c06frf| |coordinates| + |leader| |transcendent?| |leadingBasisTerm| |constructor| |vark| + |removeRoughlyRedundantFactorsInPols| |OMgetInteger| |tanNa| + |fortranDoubleComplex| |atoms| |c06fuf| |bounds| |algebraic?| + |ignore?| |removeConstantTerm| |removeRoughlyRedundantFactorsInPol| + |OMgetFloat| |initTable!| |fortranComplex| |c06gbf| |makeResult| + |high| |first| |sh| |computeInt| |void| |reset| |mkPrim| |interReduce| + |OMgetVariable| |printInfo!| |c06gcf| |low| |rest| |mirror| + |checkForZero| |intPatternMatch| |roughBasicSet| |OMgetString| + |startStats!| |binaryTournament| |leftMinimalPolynomial| |substitute| + |c06gqf| |subset?| |monomial?| |logGamma| |numeric| |write| + |primintegrate| |crushedSet| |OMgetSymbol| |printStats!| + |associatorDependence| |removeDuplicates| |c06gsf| + |symmetricDifference| |rquo| |hypergeometric0F1| |save| |radical| + |expintegrate| |rewriteSetByReducingWithParticularGenerators| + |OMgetType| |clearTable!| |lieAlgebra?| |d01ajf| |difference| |lquo| + |rotatez| |OMencodingBinary| |usingTable?| |jordanAlgebra?| |d01akf| + |intersect| |width| |mindegTerm| |rotatey| |call| |readBytes!| + |sylvesterSequence| |OMencodingSGML| |printingInfo?| + |noncommutativeJordanAlgebra?| |d01alf| |part?| |product| |rotatex| + |readUInt32!| |sturmSequence| |OMencodingXML| |makingStats?| + |jordanAdmissible?| |d01amf| |latex| |LiePolyIfCan| |identity| + |readInt32!| |boundOfCauchy| |OMencodingUnknown| |extractIfCan| + |lieAdmissible?| |trunc| |dictionary| |readUInt16!| + |sturmVariationsOf| |omError| |insert!| |jacobiIdentity?| + |constantLeft| |symmetric?| |degree| |dioSolve| |dec| |readInt16!| + |lazyVariations| |unknownEndian| |errorInfo| |interpretString| + |powerAssociative?| |twist| |diagonal?| |quasiRegular| |newLine| + |readUInt8!| |content| |bigEndian| |flatten| |errorKind| + |stripCommentsAndBlanks| |byte| |alternative?| |setsubMatrix!| + |square?| |quasiRegular?| |copies| |readInt8!| |totalDegree| + |littleEndian| |setLength!| |flexible?| |subMatrix| + |rectangularMatrix| |optional| |constant?| |subtractIfCan| |sayLength| + |readByte!| |minimumDegree| |ScanRoman| |delay| |capacity| + |rightAlternative?| |swapColumns!| |characteristic| |mindeg| + |setPosition| |setnext!| |setFieldInfo| |monomials| + |ScanFloatIgnoreSpaces| |findCycle| |byteBuffer| |leftAlternative?| + |swapRows!| |round| |maxdeg| |generalizedContinuumHypothesisAssumed| + |setprevious!| |pol| |isPlus| |ScanFloatIgnoreSpacesIfCan| + |repeating?| |antiAssociative?| |vertConcat| |fractionPart| + |generalizedContinuumHypothesisAssumed?| |shanksDiscLogAlgorithm| |xn| + |isTimes| |numericalIntegration| |repeating| |associative?| + |horizConcat| |wholePart| |quoByVar| |countable?| |reflect| |dAndcExp| + |isExpt| |rk4| |recip| |antiCommutative?| |squareTop| |floor| + |coefficients| |Aleph| |reify| |repSq| |isPower| |pattern| |rk4a| + |integers| |commutative?| |elRow1!| |ceiling| |stFunc1| |unravel| + |separant| |expPot| |rroot| |rk4qc| |oddintegers| + |rightCharacteristicPolynomial| |elRow2!| |norm| |stFunc2| + |leviCivitaSymbol| |isobaric?| |qPot| |qroot| |rk4f| |int| + |outerProduct| |leftCharacteristicPolynomial| |elColumn2!| + |mightHaveRoots| |stFuncN| |kroneckerDelta| |weights| |lookup| |froot| + |aromberg| |mapmult| |varList| |rightNorm| |bright| + |fractionFreeGauss!| |refine| |fixedPointExquo| |reindex| + |differentialVariables| |normal?| |message| |nthr| |asimpson| |deriv| + |leftNorm| |invertIfCan| |middle| |ode1| |principalAncestors| + |extractBottom!| |basis| |firstUncouplingMatrix| |atrapezoidal| + |gderiv| |rightTrace| |copy!| |roman| |ode2| |exportedOperators| + |extractTop!| NOT |normalElement| |integral| |romberg| |compose| + |leftTrace| |plus!| |recoverAfterFail| |ode| |alphanumeric| + |insertBottom!| OR |minimalPolynomial| |primitiveElement| |simpson| + |addiag| |someBasis| |matrix| |minus!| |showTheRoutinesTable| |mpsode| + |alphabetic| |insertTop!| AND |position!| |nextPrime| |trapezoidal| + |lazyIntegrate| |mantissa| |sort!| |leftScalarTimes!| |deleteRoutine!| + UP2UTS |hexDigit| |bottom!| |eof?| |prevPrime| |rombergo| |nlde| + |copyInto!| |rightScalarTimes!| |getExplanations| |cons| UTS2UP + |digit| |top!| |inputBinaryFile| |primes| |simpsono| |powern| + |sorted?| |times!| |getMeasure| LODO2FUN |charClass| |dequeue| |error| + |increment| |selectsecond| |trapezoidalo| |mapdiv| |LiePoly| |power!| + |changeMeasure| RF2UTS |alphanumeric?| |recolor| |charpol| + |selectfirst| |sup| |lazyGintegrate| |arguments| |quickSort| |just| + |changeThreshhold| |magnitude| |lowerCase?| |drawComplex| |solve1| + |makeprod| |imagE| |power| |vector| |mr| |heapSort| |gradient| + |selectMultiDimensionalRoutines| |double| |cross| |upperCase?| + |drawComplexVectorField| |innerEigenvectors| |equivOperands| |imagk| + |sincos| |shellSort| |divergence| |selectNonFiniteRoutines| |dot| + |alphabetic?| |setRealSteps| |parseString| |equiv?| |imagj| |sinhcosh| + |outputSpacing| |laplacian| |selectSumOfSquaresRoutines| |source| + |scan| |hexDigit?| |setImagSteps| |subst| |unparse| |impliesOperands| + |imagi| |subresultantVector| |plus| |outputGeneral| |hessian| + |selectFiniteRoutines| |graphCurves| |escape| |setClipValue| * + |binary| |implies?| |octon| |primitivePart| |outputFixed| + |bandedHessian| |selectODEIVPRoutines| |drawCurves| |ord| |option?| + |packageCall| |orOperands| |ODESolve| |pointData| |outputFloating| + |jacobian| |selectPDERoutines| |scale| |range| |innerSolve1| |or?| + |constDsolve| |parent| |exp1| |bandedJacobian| + |selectOptimizationRoutines| |connect| |colorFunction| |innerSolve| + |andOperands| |showTheIFTable| |extractProperty| |times| |log2| + |duplicates| |selectIntegrationRoutines| |target| |declare!| |region| + |curveColor| |isQuotient| |makeEq| |and?| |clearTheIFTable| + |extractClosed| |rationalApproximation| |removeDuplicates!| |routines| + |points| |pointColor| |modularGcdPrimitive| |iFTable| |notOperand| + |objects| |extractIndex| |differentiate| |relerror| |linears| + |mainSquareFreePart| |getGraph| |clip| |modularGcd| + |showIntensityFunctions| |variable?| |base| |extractPoint| + |complexSolve| |ddFact| |mainPrimitivePart| |putGraph| |clipBoolean| + |reduction| |term| |expint| |traverse| |monom| |complexRoots| + |separateFactors| |mainContent| |graphs| |style| |signAround| |term?| + |diff| |defineProperty| |realRoots| |exptMod| |primitivePart!| + |graphStates| |toScale| |height| |invmod| |equiv| |algDsolve| + |closeComponent| |leadingTerm| |meshPar2Var| |failed| + |nextsubResultant2| |ravel| |graphState| |rootsOf| |pointColorPalette| + |powmod| |implies| |denomLODE| |modifyPoint| |common| |writable?| + |meshFun2Var| |reshape| |LazardQuotient2| |segment| |makeViewport2D| + |makeSketch| |curveColorPalette| |mulmod| |merge!| |indicialEquations| + |addPointLast| |tree| |readable?| |meshPar1Var| |LazardQuotient| + |viewport2D| |inrootof| |var1Steps| |submod| |resultantEuclidean| + |indicialEquation| |addPoint2| |declare| |exists?| |ptFunc| + |subResultantChain| |getPickedPoints| |droot| |char| |var2Steps| + |addmod| |semiResultantEuclidean2| |denomRicDE| |addPoint| |extension| + |minimumExponent| |qelt| |halfExtendedSubResultantGcd2| |colorDef| + |space| |symmetricRemainder| |semiResultantEuclidean1| + |leadingCoefficientRicDE| |merge| |qsetelt| |shallowExpand| |tail| + |maximumExponent| |halfExtendedSubResultantGcd1| |intensity| + |tubePoints| |positiveRemainder| |indiceSubResultant| + |constantCoefficientRicDE| |deepCopy| |deepExpand| |rowEch| |xRange| + |extendedSubResultantGcd| |update| |lighting| |tubeRadius| |bit?| + |indiceSubResultantEuclidean| |changeVar| |shallowCopy| + |clearFortranOutputStack| |rowEchLocal| |yRange| |exactQuotient!| + |clipSurface| |previous| |weight| |algint| + |semiIndiceSubResultantEuclidean| |ratDsolve| |numberOfChildren| + |generator| |showFortranOutputStack| |rowEchelonLocal| |zRange| + |exactQuotient| |showClipRegion| |makeVariable| |float| |algintegrate| + |degreeSubResultant| |indicialEquationAtInfinity| |children| + |topFortranOutputStack| |map!| |normalizedDivide| + |primPartElseUnitCanonical!| |showRegion| |finiteBound| + |palgintegrate| |degreeSubResultantEuclidean| |reduceLODE| |child| + |qsetelt!| |setFormula!| |maxint| |primPartElseUnitCanonical| + |hitherPlane| |palginfieldint| |semiDegreeSubResultantEuclidean| + |singRicDE| |birth| |linkToFortran| |binaryFunction| + |lazyResidueClass| |match?| |position| |eyeDistance| |complexZeros| + |log| |bitLength| |lastSubResultantEuclidean| |polyRicDE| |internal?| + |setLegalFortranSourceExtensions| |makeFloatFunction| |monicModulo| + |perspective| |divisorCascade| |constantOpIfCan| |reverse| |bitCoef| + |semiLastSubResultantEuclidean| |ricDsolve| |root?| |fracPart| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index fb759cd3..95c377f3 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,349 +1,349 @@ -(3195384 . 3443021592) -((-3523 (((-112) (-1 (-112) |#2| |#2|) $) 63) (((-112) $) NIL)) (-2770 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-1849 ((|#2| $ (-563) |#2|) NIL) ((|#2| $ (-1224 (-563)) |#2|) 34)) (-2907 (($ $) 59)) (-2444 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-4368 (((-563) (-1 (-112) |#2|) $) 22) (((-563) |#2| $) NIL) (((-563) 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T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -4032 (|has| |#2| (-1093)) (|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|) -4032 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -4032 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-613 #0=(-407 (-563))) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093))) ((-613 (-563)) -4032 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-613 |#2|) -4032 (|has| |#2| (-1093)) (|has| |#2| (-172))) ((-610 (-858)) -4032 (|has| |#2| (-1093)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-610 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-610 (-1257 |#2|)) . 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T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((-643 |#2|) -4032 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-643 $) -4032 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-636 (-563)) -12 (|has| |#2| (-636 (-563))) (|has| |#2| (-1045))) ((-636 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -4032 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -4032 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -4032 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -4032 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -4032 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -4032 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1169)) -12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093))) ((-1034 (-563)) -12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) ((-1034 |#2|) |has| |#2| (-1093)) ((-1051 |#2|) -4032 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -4032 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -4032 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1105) -4032 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1093) -4032 (|has| |#2| (-1093)) (|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))) ((-1208) . T) ((-1264 |#2|) |has| |#2| (-363))) -((-1567 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2444 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2240 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -1567 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2444 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2240 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1208) (-1208)) (T -239)) -((-2240 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1208)) (-4 *7 (-1208)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2444 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1208)) (-4 *2 (-1208)) (-5 *1 (-239 *5 *6 *2)))) (-1567 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1208)) (-4 *5 (-1208)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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|#2| (-1093)))) (((-407 (-563)) $) NIL (-12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093)))) ((|#2| $) 27 (|has| |#2| (-1093)))) (-2950 (((-684 (-563)) (-684 $)) NIL (-12 (|has| |#2| (-636 (-563))) (|has| |#2| (-1045)))) (((-2 (|:| -2835 (-684 (-563))) (|:| |vec| (-1257 (-563)))) (-684 $) (-1257 $)) NIL (-12 (|has| |#2| (-636 (-563))) (|has| |#2| (-1045)))) (((-2 (|:| -2835 (-684 |#2|)) (|:| |vec| (-1257 |#2|))) (-684 $) (-1257 $)) NIL (|has| |#2| (-1045))) (((-684 |#2|) (-684 $)) NIL (|has| |#2| (-1045)))) (-3400 (((-3 $ "failed") $) 53 (|has| |#2| (-722)))) (-1691 (($) NIL (|has| |#2| (-368)))) (-4355 ((|#2| $ (-563) |#2|) NIL (|has| $ (-6 -4408)))) (-4293 ((|#2| $ (-563)) 51)) (-3101 (((-112) $) NIL (|has| |#2| (-844)))) (-2659 (((-640 |#2|) $) 15 (|has| $ (-6 -4407)))) (-3827 (((-112) $) NIL (|has| |#2| (-722)))) (-1419 (((-112) $) NIL (|has| |#2| (-844)))) (-2581 (((-112) $ (-767)) NIL)) (-2411 (((-563) $) 20 (|has| (-563) (-846)))) (-3084 (($ $ $) NIL (-4032 (|has| |#2| 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|#2| (-309 |#2|)) (|has| |#2| (-1093)))) (($ $ (-640 |#2|) (-640 |#2|)) NIL (-12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))))) (-2026 (((-112) $ $) NIL)) (-2105 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4407)) (|has| |#2| (-1093))))) (-2836 (((-640 |#2|) $) NIL)) (-3756 (((-112) $) NIL)) (-3135 (($) NIL)) (-2309 ((|#2| $ (-563) |#2|) NIL) ((|#2| $ (-563)) 21)) (-4092 ((|#2| $ $) NIL (|has| |#2| (-1045)))) (-2510 (($ (-1257 |#2|)) 18)) (-3533 (((-134)) NIL (|has| |#2| (-363)))) (-4202 (($ $) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1045)))) (($ $ (-767)) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1045)))) (($ $ (-1169)) NIL (-12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) (($ $ (-640 (-1169))) NIL (-12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) (($ $ (-1169) (-767)) NIL (-12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) (($ $ (-640 (-1169)) (-640 (-767))) NIL (-12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) (($ $ (-1 |#2| |#2|) (-767)) NIL (|has| |#2| (-1045))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1045)))) (-1709 (((-767) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4407))) (((-767) |#2| $) NIL (-12 (|has| $ (-6 -4407)) (|has| |#2| (-1093))))) (-1872 (($ $) NIL)) (-1693 (((-1257 |#2|) $) 10) (($ (-563)) NIL (-4032 (-12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) (|has| |#2| (-1045)))) (($ (-407 (-563))) NIL (-12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093)))) (($ |#2|) 13 (|has| |#2| (-1093))) (((-858) $) NIL (|has| |#2| (-610 (-858))))) (-1675 (((-767)) NIL (|has| |#2| (-1045)))) (-4383 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4407)))) (-2509 (($ $) NIL (|has| |#2| (-844)))) (-2241 (($) 35 (|has| |#2| (-131)) CONST)) (-2254 (($) 38 (|has| |#2| (-722)) CONST)) (-3209 (($ $) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1045)))) (($ $ (-767)) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1045)))) (($ $ (-1169)) NIL (-12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) (($ $ (-640 (-1169))) NIL (-12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) (($ $ (-1169) (-767)) NIL (-12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) (($ $ (-640 (-1169)) (-640 (-767))) NIL (-12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045)))) (($ $ (-1 |#2| |#2|) (-767)) NIL (|has| |#2| (-1045))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1045)))) (-1778 (((-112) $ $) NIL (-4032 (|has| |#2| (-789)) (|has| |#2| (-844))))) (-1756 (((-112) $ $) NIL (-4032 (|has| |#2| (-789)) (|has| |#2| (-844))))) (-1718 (((-112) $ $) 26 (|has| |#2| (-1093)))) (-1768 (((-112) $ $) NIL (-4032 (|has| |#2| (-789)) (|has| |#2| (-844))))) (-1744 (((-112) $ $) 58 (-4032 (|has| |#2| (-789)) (|has| |#2| (-844))))) (-1837 (($ $ |#2|) NIL (|has| |#2| (-363)))) (-1826 (($ $ $) NIL (|has| |#2| (-1045))) (($ $) NIL (|has| |#2| (-1045)))) (-1814 (($ $ $) 33 (|has| |#2| (-25)))) (** (($ $ (-767)) NIL (|has| |#2| (-722))) (($ $ (-917)) NIL (|has| |#2| (-722)))) (* (($ (-563) $) NIL (|has| |#2| (-1045))) (($ $ $) 44 (|has| |#2| (-722))) (($ $ |#2|) 42 (|has| |#2| (-722))) (($ |#2| $) 43 (|has| |#2| (-722))) (($ (-767) $) NIL (|has| |#2| (-131))) (($ (-917) $) NIL (|has| |#2| (-25)))) (-3608 (((-767) $) NIL (|has| $ (-6 -4407))))) +((-2509 (*1 *1 *2) (-12 (-5 *2 (-1257 *4)) (-4 *4 (-1208)) (-4 *1 (-238 *3 *4)))) (-2392 (*1 *1 *2) (-12 (-5 *2 (-917)) (-4 *1 (-238 *3 *4)) (-4 *4 (-1045)) (-4 *4 (-1208)))) (-4121 (*1 *2 *1 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1208)) (-4 *2 (-1045)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1208)) (-4 *2 (-722)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1208)) (-4 *2 (-722))))) +(-13 (-601 (-563) |t#2|) (-610 (-1257 |t#2|)) (-10 -8 (-6 -4408) (-15 -2509 ($ (-1257 |t#2|))) (IF (|has| |t#2| (-1093)) (-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 -2392 ($ (-917))) (-15 -4121 (|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 -4405)) (-6 -4405) |%noBranch|) (IF (|has| |t#2| (-844)) (-6 (-844)) |%noBranch|) (IF (|has| |t#2| (-789)) (-6 (-789)) |%noBranch|) (IF (|has| |t#2| (-363)) (-6 (-1264 |t#2|)) |%noBranch|))) +(((-21) -4034 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-23) -4034 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -4034 (|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) -4034 (|has| |#2| (-1093)) (|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|) -4034 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -4034 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-613 #0=(-407 (-563))) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093))) ((-613 (-563)) -4034 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-613 |#2|) -4034 (|has| |#2| (-1093)) (|has| |#2| (-172))) ((-610 (-858)) -4034 (|has| |#2| (-1093)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-610 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-610 (-1257 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-563) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1093)) ((-489 |#2|) . T) ((-601 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((-643 |#2|) -4034 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-643 $) -4034 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-636 (-563)) -12 (|has| |#2| (-636 (-563))) (|has| |#2| (-1045))) ((-636 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -4034 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -4034 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -4034 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -4034 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -4034 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -4034 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1169)) -12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093))) ((-1034 (-563)) -12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) ((-1034 |#2|) |has| |#2| (-1093)) ((-1051 |#2|) -4034 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -4034 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -4034 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1105) -4034 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1093) -4034 (|has| |#2| (-1093)) (|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))) ((-1208) . T) ((-1264 |#2|) |has| |#2| (-363))) +((-4132 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2444 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2238 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -4132 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2444 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2238 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1208) (-1208)) (T -239)) +((-2238 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1208)) (-4 *7 (-1208)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2444 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1208)) (-4 *2 (-1208)) (-5 *1 (-239 *5 *6 *2)))) (-4132 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1208)) (-4 *5 (-1208)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-407 (-563))) |has| |#1| (-38 (-407 (-563)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-563)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-613 #0#) -4034 (|has| |#1| (-1034 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563))))) ((-613 (-563)) . T) ((-613 |#1|) . T) ((-613 |#2|) . T) ((-613 |#3|) . T) ((-613 $) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452))) ((-610 (-858)) . 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T) ((-23) . T) ((-47 |#1| #0=(-563)) . T) ((-25) . T) ((-38 #1=(-407 (-563))) -4032 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-563))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 |#2|) |has| |#1| (-363)) ((-38 $) -4032 (|has| |#1| (-555)) (|has| |#1| (-363))) ((-35) |has| |#1| (-38 (-407 (-563)))) ((-95) |has| |#1| (-38 (-407 (-563)))) ((-102) . T) ((-111 #1# #1#) -4032 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-563))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-363)) ((-111 $ $) -4032 (|has| |#1| (-555)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) -4032 (-12 (|has| |#1| (-363)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -4032 (-12 (|has| |#1| (-363)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-613 #1#) -4032 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-563))))) ((-613 (-563)) . T) ((-613 #2=(-1169)) -12 (|has| |#1| (-363)) (|has| |#2| (-1034 (-1169)))) ((-613 |#1|) |has| |#1| (-172)) ((-613 |#2|) . 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T) ((-172) -4032 (|has| |#1| (-555)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-611 (-225)) -12 (|has| |#1| (-363)) (|has| |#2| (-1018))) ((-611 (-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-1018))) ((-611 (-536)) -12 (|has| |#1| (-363)) (|has| |#2| (-611 (-536)))) ((-611 (-888 (-379))) -12 (|has| |#1| (-363)) (|has| |#2| (-611 (-888 (-379))))) ((-611 (-888 (-563))) -12 (|has| |#1| (-363)) (|has| |#2| (-611 (-888 (-563))))) ((-231 |#2|) |has| |#1| (-363)) ((-233) -4032 (-12 (|has| |#1| (-363)) (|has| |#2| (-233))) (|has| |#1| (-15 * (|#1| (-563) |#1|)))) ((-243) |has| |#1| (-363)) ((-284) |has| |#1| (-38 (-407 (-563)))) ((-286 |#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) ((-286 $ $) |has| (-563) (-1105)) ((-290) -4032 (|has| |#1| (-555)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-309 |#2|))) ((-363) |has| |#1| (-363)) ((-338 |#2|) |has| |#1| (-363)) ((-377 |#2|) |has| |#1| (-363)) ((-400 |#2|) |has| |#1| (-363)) ((-452) |has| |#1| (-363)) ((-493) |has| |#1| (-38 (-407 (-563)))) ((-514 (-1169) |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-514 (-1169) |#2|))) ((-514 |#2| |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-309 |#2|))) ((-555) -4032 (|has| |#1| (-555)) (|has| |#1| (-363))) ((-643 #1#) -4032 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-563))))) ((-643 |#1|) . T) ((-643 |#2|) |has| |#1| (-363)) ((-643 $) . T) ((-636 (-563)) -12 (|has| |#1| (-363)) (|has| |#2| (-636 (-563)))) ((-636 |#2|) |has| |#1| (-363)) ((-713 #1#) -4032 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-563))))) ((-713 |#1|) |has| |#1| (-172)) ((-713 |#2|) |has| |#1| (-363)) ((-713 $) -4032 (|has| |#1| (-555)) (|has| |#1| (-363))) ((-722) . T) ((-787) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-788) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-790) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-791) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-816) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-844) -12 (|has| |#1| (-363)) (|has| |#2| (-816))) ((-846) -4032 (-12 (|has| |#1| (-363)) (|has| |#2| (-846))) (-12 (|has| |#1| (-363)) (|has| |#2| (-816)))) ((-896 (-1169)) -4032 (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1169)))) (-12 (|has| |#1| (-15 * (|#1| (-563) |#1|))) (|has| |#1| (-896 (-1169))))) ((-882 (-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-379)))) ((-882 (-563)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-563)))) ((-880 |#2|) |has| |#1| (-363)) ((-905) -12 (|has| |#1| (-363)) (|has| |#2| (-905))) ((-969 |#1| #0# (-1075)) . T) ((-916) |has| |#1| (-363)) ((-988 |#2|) |has| |#1| (-363)) ((-998) |has| |#1| (-38 (-407 (-563)))) ((-1018) -12 (|has| |#1| (-363)) (|has| |#2| (-1018))) ((-1034 (-407 (-563))) -12 (|has| |#1| (-363)) (|has| |#2| (-1034 (-563)))) ((-1034 (-563)) -12 (|has| |#1| (-363)) (|has| |#2| (-1034 (-563)))) ((-1034 #2#) -12 (|has| |#1| (-363)) (|has| |#2| (-1034 (-1169)))) ((-1034 |#2|) . T) ((-1051 #1#) -4032 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-563))))) ((-1051 |#1|) . T) ((-1051 |#2|) |has| |#1| (-363)) ((-1051 $) -4032 (|has| |#1| (-555)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1045) . T) ((-1052) . T) ((-1105) . T) ((-1093) . T) ((-1144) -12 (|has| |#1| (-363)) (|has| |#2| (-1144))) ((-1193) |has| |#1| (-38 (-407 (-563)))) ((-1196) |has| |#1| (-38 (-407 (-563)))) ((-1208) |has| |#1| (-363)) ((-1212) |has| |#1| (-363)) ((-1217 |#1|) . T) ((-1235 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-767)) . T) ((-25) . T) ((-38 #1=(-407 (-563))) |has| |#1| (-38 (-407 (-563)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-407 (-563)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-613 #1#) -4034 (|has| |#1| (-1034 (-407 (-563)))) (|has| |#1| (-38 (-407 (-563))))) ((-613 (-563)) . T) ((-613 #2=(-1075)) . T) ((-613 |#1|) . T) ((-613 $) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-610 (-858)) . T) ((-172) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-611 (-536)) -12 (|has| (-1075) (-611 (-536))) (|has| |#1| (-611 (-536)))) ((-611 (-888 (-379))) -12 (|has| (-1075) (-611 (-888 (-379)))) (|has| |#1| (-611 (-888 (-379))))) ((-611 (-888 (-563))) -12 (|has| (-1075) (-611 (-888 (-563)))) (|has| |#1| (-611 (-888 (-563))))) ((-231 |#1|) . T) ((-233) . T) ((-286 (-407 $) (-407 $)) |has| |#1| (-555)) ((-286 |#1| |#1|) . T) ((-286 $ $) . T) ((-290) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 $) . T) ((-326 |#1| #0#) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -4034 (|has| |#1| (-905)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-514 #2# |#1|) . T) ((-514 #2# $) . T) ((-514 $ $) . T) ((-555) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-643 #1#) |has| |#1| (-38 (-407 (-563)))) ((-643 |#1|) . T) ((-643 $) . T) ((-636 (-563)) |has| |#1| (-636 (-563))) ((-636 |#1|) . T) ((-713 #1#) |has| |#1| (-38 (-407 (-563)))) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-722) . T) ((-846) |has| |#1| (-846)) ((-896 #2#) . T) ((-896 (-1169)) |has| |#1| (-896 (-1169))) ((-882 (-379)) -12 (|has| (-1075) (-882 (-379))) (|has| |#1| (-882 (-379)))) ((-882 (-563)) -12 (|has| (-1075) (-882 (-563))) (|has| |#1| (-882 (-563)))) ((-945 |#1| #0# #2#) . T) ((-905) |has| |#1| (-905)) ((-916) |has| |#1| (-363)) ((-1034 (-407 (-563))) |has| |#1| (-1034 (-407 (-563)))) ((-1034 (-563)) |has| |#1| (-1034 (-563))) ((-1034 #2#) . T) ((-1034 |#1|) . T) ((-1051 #1#) |has| |#1| (-38 (-407 (-563)))) ((-1051 |#1|) . T) ((-1051 $) -4034 (|has| |#1| (-905)) (|has| |#1| (-555)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1045) . T) ((-1052) . T) ((-1105) . T) ((-1093) . T) ((-1144) |has| |#1| (-1144)) ((-1212) |has| |#1| (-905))) +((-2605 (((-640 (-1075)) $) 28)) (-2750 (($ $) 25)) (-2587 (($ |#2| |#3|) NIL) (($ $ (-1075) |#3|) 22) (($ $ (-640 (-1075)) (-640 |#3|)) 21)) (-2715 (($ $) 14)) (-2725 ((|#2| $) 12)) (-3871 ((|#3| $) 10))) +(((-1234 |#1| |#2| |#3|) (-10 -8 (-15 -2605 ((-640 (-1075)) |#1|)) (-15 -2587 (|#1| |#1| (-640 (-1075)) (-640 |#3|))) (-15 -2587 (|#1| |#1| (-1075) |#3|)) (-15 -2750 (|#1| |#1|)) (-15 -2587 (|#1| |#2| |#3|)) (-15 -3871 (|#3| |#1|)) (-15 -2715 (|#1| |#1|)) (-15 -2725 (|#2| |#1|))) (-1235 |#2| |#3|) (-1045) (-788)) (T -1234)) +NIL +(-10 -8 (-15 -2605 ((-640 (-1075)) |#1|)) (-15 -2587 (|#1| |#1| (-640 (-1075)) (-640 |#3|))) (-15 -2587 (|#1| |#1| (-1075) |#3|)) (-15 -2750 (|#1| |#1|)) (-15 -2587 (|#1| |#2| |#3|)) (-15 -3871 (|#3| |#1|)) (-15 -2715 (|#1| |#1|)) (-15 -2725 (|#2| |#1|))) +((-1677 (((-112) $ $) 7)) (-3439 (((-112) $) 16)) (-2605 (((-640 (-1075)) $) 77)) (-2517 (((-1169) $) 106)) (-3241 (((-2 (|:| -3245 $) (|:| 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3195369 3195374 3195379 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3195354 3195359 3195364 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3195339 3195344 3195349 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3195324 3195329 3195334 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1285 3194500 3195199 3195276 "ZMOD" 3195281 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1284 3193610 3193774 3193983 "ZLINDEP" 3194332 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1283 3182914 3184678 3186650 "ZDSOLVE" 3191740 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1282 3182160 3182301 3182490 "YSTREAM" 3182760 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1281 3179971 3181461 3181665 "XRPOLY" 3182003 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1280 3176559 3177842 3178417 "XPR" 3179443 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1279 3174315 3175890 3176094 "XPOLY" 3176390 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1278 3172106 3173440 3173495 "XPOLYC" 3173783 NIL XPOLYC (NIL T T) -9 NIL 3173896 NIL) (-1277 3168524 3170623 3171011 "XPBWPOLY" 3171764 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1276 3164435 3166687 3166729 "XF" 3167350 NIL XF (NIL T) -9 NIL 3167750 NIL) (-1275 3164056 3164144 3164313 "XF-" 3164318 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1274 3159390 3160645 3160700 "XFALG" 3162872 NIL XFALG (NIL T T) -9 NIL 3163661 NIL) (-1273 3158523 3158627 3158832 "XEXPPKG" 3159282 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1272 3156667 3158373 3158469 "XDPOLY" 3158474 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1271 3155612 3156178 3156221 "XALG" 3156226 NIL XALG (NIL T) -9 NIL 3156337 NIL) (-1270 3149081 3153589 3154083 "WUTSET" 3155204 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1269 3147372 3148133 3148456 "WP" 3148892 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1268 3147001 3147194 3147264 "WHILEAST" 3147324 T WHILEAST (NIL) -8 NIL NIL NIL) (-1267 3146500 3146718 3146812 "WHEREAST" 3146929 T WHEREAST (NIL) -8 NIL NIL NIL) (-1266 3145386 3145584 3145879 "WFFINTBS" 3146297 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1265 3143290 3143717 3144179 "WEIER" 3144958 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1264 3142437 3142861 3142903 "VSPACE" 3143039 NIL VSPACE (NIL T) -9 NIL 3143113 NIL) (-1263 3142275 3142302 3142393 "VSPACE-" 3142398 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1262 3142083 3142126 3142194 "VOID" 3142229 T VOID (NIL) -8 NIL NIL NIL) (-1261 3140219 3140578 3140984 "VIEW" 3141699 T VIEW (NIL) -7 NIL NIL NIL) (-1260 3136644 3137282 3138019 "VIEWDEF" 3139504 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1259 3125980 3128192 3130365 "VIEW3D" 3134493 T VIEW3D (NIL) -8 NIL NIL NIL) (-1258 3118262 3119891 3121470 "VIEW2D" 3124423 T VIEW2D (NIL) -8 NIL NIL NIL) (-1257 3113666 3118032 3118124 "VECTOR" 3118205 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1256 3112243 3112502 3112820 "VECTOR2" 3113396 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1255 3105770 3110027 3110070 "VECTCAT" 3111063 NIL VECTCAT (NIL T) -9 NIL 3111649 NIL) (-1254 3104784 3105038 3105428 "VECTCAT-" 3105433 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1253 3104265 3104435 3104555 "VARIABLE" 3104699 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1252 3104198 3104203 3104233 "UTYPE" 3104238 T UTYPE (NIL) -9 NIL NIL NIL) (-1251 3103028 3103182 3103444 "UTSODETL" 3104024 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1250 3100468 3100928 3101452 "UTSODE" 3102569 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1249 3092344 3098094 3098583 "UTS" 3100037 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3083587 3088911 3088954 "UTSCAT" 3090066 NIL UTSCAT (NIL T) -9 NIL 3090823 NIL) (-1247 3080942 3081657 3082646 "UTSCAT-" 3082651 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1246 3080569 3080612 3080745 "UTS2" 3080893 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1245 3074842 3077407 3077450 "URAGG" 3079520 NIL URAGG (NIL T) -9 NIL 3080243 NIL) (-1244 3071781 3072644 3073767 "URAGG-" 3073772 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1243 3067505 3070395 3070867 "UPXSSING" 3071445 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1242 3059607 3066752 3067025 "UPXS" 3067290 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1241 3052720 3059511 3059583 "UPXSCONS" 3059588 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1240 3042965 3049715 3049777 "UPXSCCA" 3050351 NIL UPXSCCA (NIL T T) -9 NIL 3050584 NIL) (-1239 3042603 3042688 3042862 "UPXSCCA-" 3042867 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1238 3032701 3039224 3039267 "UPXSCAT" 3039915 NIL UPXSCAT (NIL T) -9 NIL 3040523 NIL) (-1237 3032131 3032210 3032389 "UPXS2" 3032616 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1236 3030785 3031038 3031389 "UPSQFREE" 3031874 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1235 3024573 3027587 3027642 "UPSCAT" 3028803 NIL UPSCAT (NIL T T) -9 NIL 3029577 NIL) (-1234 3023777 3023984 3024311 "UPSCAT-" 3024316 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1233 3009627 3017625 3017668 "UPOLYC" 3019769 NIL UPOLYC (NIL T) -9 NIL 3020990 NIL) (-1232 3000956 3003381 3006528 "UPOLYC-" 3006533 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1231 3000583 3000626 3000759 "UPOLYC2" 3000907 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1230 2992157 3000266 3000395 "UP" 3000502 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1229 2991496 2991603 2991767 "UPMP" 2992046 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1228 2991049 2991130 2991269 "UPDIVP" 2991409 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1227 2989617 2989866 2990182 "UPDECOMP" 2990798 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1226 2988852 2988964 2989149 "UPCDEN" 2989501 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1225 2988371 2988440 2988589 "UP2" 2988777 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1224 2986888 2987575 2987852 "UNISEG" 2988129 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1223 2986103 2986230 2986435 "UNISEG2" 2986731 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1222 2985163 2985343 2985569 "UNIFACT" 2985919 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1221 2969130 2984340 2984591 "ULS" 2984970 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1220 2957170 2969034 2969106 "ULSCONS" 2969111 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1219 2939786 2951728 2951790 "ULSCCAT" 2952428 NIL ULSCCAT (NIL T T) -9 NIL 2952716 NIL) (-1218 2938836 2939081 2939469 "ULSCCAT-" 2939474 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1217 2928711 2935148 2935191 "ULSCAT" 2936054 NIL ULSCAT (NIL T) -9 NIL 2936784 NIL) (-1216 2928141 2928220 2928399 "ULS2" 2928626 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1215 2927278 2927753 2927854 "UINT8" 2927965 T UINT8 (NIL) -8 NIL NIL 2928044) (-1214 2926414 2926889 2926990 "UINT32" 2927101 T UINT32 (NIL) -8 NIL NIL 2927180) (-1213 2925550 2926025 2926126 "UINT16" 2926237 T UINT16 (NIL) -8 NIL NIL 2926316) (-1212 2923953 2924876 2924906 "UFD" 2925118 T UFD (NIL) -9 NIL 2925232 NIL) (-1211 2923747 2923793 2923888 "UFD-" 2923893 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1210 2922829 2923012 2923228 "UDVO" 2923553 T UDVO (NIL) -7 NIL NIL NIL) (-1209 2920645 2921054 2921525 "UDPO" 2922393 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1208 2920578 2920583 2920613 "TYPE" 2920618 T TYPE (NIL) -9 NIL NIL NIL) (-1207 2920365 2920533 2920564 "TYPEAST" 2920569 T TYPEAST (NIL) -8 NIL NIL NIL) (-1206 2919336 2919538 2919778 "TWOFACT" 2920159 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1205 2918408 2918745 2918980 "TUPLE" 2919136 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1204 2916099 2916618 2917157 "TUBETOOL" 2917891 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1203 2914948 2915153 2915394 "TUBE" 2915892 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1202 2909712 2913920 2914203 "TS" 2914700 NIL TS (NIL T) -8 NIL NIL NIL) (-1201 2898379 2902471 2902568 "TSETCAT" 2907837 NIL TSETCAT (NIL T T T T) -9 NIL 2909368 NIL) (-1200 2893114 2894711 2896602 "TSETCAT-" 2896607 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1199 2887377 2888223 2889165 "TRMANIP" 2892250 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1198 2886818 2886881 2887044 "TRIMAT" 2887309 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1197 2884614 2884851 2885215 "TRIGMNIP" 2886567 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1196 2884134 2884247 2884277 "TRIGCAT" 2884490 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1195 2883803 2883882 2884023 "TRIGCAT-" 2884028 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1194 2880700 2882661 2882942 "TREE" 2883557 NIL TREE (NIL T) -8 NIL NIL NIL) (-1193 2879974 2880502 2880532 "TRANFUN" 2880567 T TRANFUN (NIL) -9 NIL 2880633 NIL) (-1192 2879253 2879444 2879724 "TRANFUN-" 2879729 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1191 2879057 2879089 2879150 "TOPSP" 2879214 T TOPSP (NIL) -7 NIL NIL NIL) (-1190 2878405 2878520 2878674 "TOOLSIGN" 2878938 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1189 2877066 2877582 2877821 "TEXTFILE" 2878188 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1188 2875005 2875519 2875948 "TEX" 2876659 T TEX (NIL) -8 NIL NIL NIL) (-1187 2874786 2874817 2874889 "TEX1" 2874968 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1186 2874434 2874497 2874587 "TEMUTL" 2874718 T TEMUTL (NIL) -7 NIL NIL NIL) (-1185 2872588 2872868 2873193 "TBCMPPK" 2874157 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1184 2864476 2870748 2870804 "TBAGG" 2871204 NIL TBAGG (NIL T T) -9 NIL 2871415 NIL) (-1183 2859546 2861034 2862788 "TBAGG-" 2862793 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1182 2858930 2859037 2859182 "TANEXP" 2859435 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1181 2852431 2858787 2858880 "TABLE" 2858885 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1180 2851843 2851942 2852080 "TABLEAU" 2852328 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1179 2846451 2847671 2848919 "TABLBUMP" 2850629 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1178 2845879 2845979 2846107 "SYSTEM" 2846345 T SYSTEM (NIL) -7 NIL NIL NIL) (-1177 2842342 2843037 2843820 "SYSSOLP" 2845130 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1176 2841399 2841866 2841979 "SYSNNI" 2842165 NIL SYSNNI (NIL NIL) -8 NIL NIL 2842244) (-1175 2840852 2841257 2841299 "SYSINT" 2841304 NIL SYSINT (NIL NIL) -8 NIL NIL 2841312) (-1174 2837186 2838113 2838829 "SYNTAX" 2840158 T SYNTAX (NIL) -8 NIL NIL NIL) (-1173 2834344 2834946 2835578 "SYMTAB" 2836576 T SYMTAB (NIL) -8 NIL NIL NIL) (-1172 2829593 2830495 2831478 "SYMS" 2833383 T SYMS (NIL) -8 NIL NIL NIL) (-1171 2826865 2829051 2829281 "SYMPOLY" 2829398 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1170 2826382 2826457 2826580 "SYMFUNC" 2826777 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1169 2822434 2823694 2824507 "SYMBOL" 2825591 T SYMBOL (NIL) -8 NIL NIL NIL) (-1168 2815973 2817662 2819382 "SWITCH" 2820736 T SWITCH (NIL) -8 NIL NIL NIL) (-1167 2809243 2814794 2815097 "SUTS" 2815728 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2801344 2808490 2808763 "SUPXS" 2809028 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2792874 2800962 2801088 "SUP" 2801253 NIL SUP (NIL T) -8 NIL NIL NIL) (-1164 2792033 2792160 2792377 "SUPFRACF" 2792742 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1163 2791654 2791713 2791826 "SUP2" 2791968 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1162 2790067 2790341 2790704 "SUMRF" 2791353 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1161 2789381 2789447 2789646 "SUMFS" 2789988 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1160 2773388 2788558 2788809 "SULS" 2789188 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2773017 2773210 2773280 "SUCHTAST" 2773340 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1158 2772339 2772542 2772682 "SUCH" 2772925 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1157 2766233 2767245 2768204 "SUBSPACE" 2771427 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1156 2765663 2765753 2765917 "SUBRESP" 2766121 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1155 2759032 2760328 2761639 "STTF" 2764399 NIL STTF (NIL T) -7 NIL NIL NIL) (-1154 2753205 2754325 2755472 "STTFNC" 2757932 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1153 2744520 2746387 2748181 "STTAYLOR" 2751446 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1152 2737764 2744384 2744467 "STRTBL" 2744472 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1151 2733155 2737719 2737750 "STRING" 2737755 T STRING (NIL) -8 NIL NIL NIL) (-1150 2728043 2732528 2732558 "STRICAT" 2732617 T STRICAT (NIL) -9 NIL 2732679 NIL) (-1149 2720853 2725662 2726273 "STREAM" 2727467 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1148 2720363 2720440 2720584 "STREAM3" 2720770 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1147 2719345 2719528 2719763 "STREAM2" 2720176 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1146 2719033 2719085 2719178 "STREAM1" 2719287 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1145 2718049 2718230 2718461 "STINPROD" 2718849 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1144 2717627 2717811 2717841 "STEP" 2717921 T STEP (NIL) -9 NIL 2717999 NIL) (-1143 2711170 2717526 2717603 "STBL" 2717608 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1142 2706344 2710391 2710434 "STAGG" 2710587 NIL STAGG (NIL T) -9 NIL 2710676 NIL) (-1141 2704046 2704648 2705520 "STAGG-" 2705525 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1140 2702241 2703816 2703908 "STACK" 2703989 NIL STACK (NIL T) -8 NIL NIL NIL) (-1139 2694966 2700382 2700838 "SREGSET" 2701871 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1138 2687392 2688760 2690273 "SRDCMPK" 2693572 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2680359 2684832 2684862 "SRAGG" 2686165 T SRAGG (NIL) -9 NIL 2686773 NIL) (-1136 2679376 2679631 2680010 "SRAGG-" 2680015 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1135 2673871 2678323 2678744 "SQMATRIX" 2679002 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1134 2667620 2670589 2671316 "SPLTREE" 2673216 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1133 2663610 2664276 2664922 "SPLNODE" 2667046 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1132 2662657 2662890 2662920 "SPFCAT" 2663364 T SPFCAT (NIL) -9 NIL NIL NIL) (-1131 2661394 2661604 2661868 "SPECOUT" 2662415 T SPECOUT (NIL) -7 NIL NIL NIL) (-1130 2653046 2654790 2654820 "SPADXPT" 2659212 T SPADXPT (NIL) -9 NIL 2661246 NIL) (-1129 2652807 2652847 2652916 "SPADPRSR" 2652999 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1128 2650990 2652762 2652793 "SPADAST" 2652798 T SPADAST (NIL) -8 NIL NIL NIL) (-1127 2642961 2644708 2644751 "SPACEC" 2649124 NIL SPACEC (NIL T) -9 NIL 2650940 NIL) (-1126 2641132 2642893 2642942 "SPACE3" 2642947 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1125 2639884 2640055 2640346 "SORTPAK" 2640937 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1124 2637934 2638237 2638656 "SOLVETRA" 2639548 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1123 2636945 2637167 2637441 "SOLVESER" 2637707 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1122 2632165 2633046 2634048 "SOLVERAD" 2635997 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1121 2627980 2628589 2629318 "SOLVEFOR" 2631532 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1120 2622277 2627329 2627426 "SNTSCAT" 2627431 NIL SNTSCAT (NIL T T T T) -9 NIL 2627501 NIL) (-1119 2616420 2620600 2620991 "SMTS" 2621967 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1118 2610871 2616308 2616385 "SMP" 2616390 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1117 2609030 2609331 2609729 "SMITH" 2610568 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1116 2601925 2606081 2606184 "SMATCAT" 2607535 NIL SMATCAT (NIL NIL T T T) -9 NIL 2608085 NIL) (-1115 2598865 2599688 2600866 "SMATCAT-" 2600871 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1114 2596578 2598101 2598144 "SKAGG" 2598405 NIL SKAGG (NIL T) -9 NIL 2598540 NIL) (-1113 2592920 2595994 2596189 "SINT" 2596376 T SINT (NIL) -8 NIL NIL 2596549) (-1112 2592692 2592730 2592796 "SIMPAN" 2592876 T SIMPAN (NIL) -7 NIL NIL NIL) (-1111 2591999 2592227 2592367 "SIG" 2592574 T SIG (NIL) -8 NIL NIL NIL) (-1110 2590837 2591058 2591333 "SIGNRF" 2591758 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1109 2589642 2589793 2590084 "SIGNEF" 2590666 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1108 2588975 2589225 2589349 "SIGAST" 2589540 T SIGAST (NIL) -8 NIL NIL NIL) (-1107 2586665 2587119 2587625 "SHP" 2588516 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1106 2580571 2586566 2586642 "SHDP" 2586647 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1105 2580170 2580336 2580366 "SGROUP" 2580459 T SGROUP (NIL) -9 NIL 2580521 NIL) (-1104 2580028 2580054 2580127 "SGROUP-" 2580132 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1103 2576864 2577561 2578284 "SGCF" 2579327 T SGCF (NIL) -7 NIL NIL NIL) (-1102 2571259 2576311 2576408 "SFRTCAT" 2576413 NIL SFRTCAT (NIL T T T T) -9 NIL 2576452 NIL) (-1101 2564683 2565698 2566834 "SFRGCD" 2570242 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1100 2557811 2558882 2560068 "SFQCMPK" 2563616 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2557433 2557522 2557632 "SFORT" 2557752 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1098 2556578 2557273 2557394 "SEXOF" 2557399 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1097 2555712 2556459 2556527 "SEX" 2556532 T SEX (NIL) -8 NIL NIL NIL) (-1096 2551251 2551940 2552035 "SEXCAT" 2554972 NIL SEXCAT (NIL T T T T T) -9 NIL 2555550 NIL) (-1095 2548431 2551185 2551233 "SET" 2551238 NIL SET (NIL T) -8 NIL NIL NIL) (-1094 2546682 2547144 2547449 "SETMN" 2548172 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1093 2546288 2546414 2546444 "SETCAT" 2546561 T SETCAT (NIL) -9 NIL 2546646 NIL) (-1092 2546068 2546120 2546219 "SETCAT-" 2546224 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1091 2542455 2544529 2544572 "SETAGG" 2545442 NIL SETAGG (NIL T) -9 NIL 2545782 NIL) (-1090 2541913 2542029 2542266 "SETAGG-" 2542271 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1089 2541383 2541609 2541710 "SEQAST" 2541834 T SEQAST (NIL) -8 NIL NIL NIL) (-1088 2540582 2540876 2540937 "SEGXCAT" 2541223 NIL SEGXCAT (NIL T T) -9 NIL 2541343 NIL) (-1087 2539638 2540248 2540430 "SEG" 2540435 NIL SEG (NIL T) -8 NIL NIL NIL) (-1086 2538617 2538831 2538874 "SEGCAT" 2539396 NIL SEGCAT (NIL T) -9 NIL 2539617 NIL) (-1085 2537666 2537996 2538196 "SEGBIND" 2538452 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1084 2537287 2537346 2537459 "SEGBIND2" 2537601 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1083 2536888 2537088 2537165 "SEGAST" 2537232 T SEGAST (NIL) -8 NIL NIL NIL) (-1082 2536107 2536233 2536437 "SEG2" 2536732 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1081 2535544 2536042 2536089 "SDVAR" 2536094 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1080 2527834 2535314 2535444 "SDPOL" 2535449 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1079 2526427 2526693 2527012 "SCPKG" 2527549 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1078 2525563 2525743 2525943 "SCOPE" 2526249 T SCOPE (NIL) -8 NIL NIL NIL) (-1077 2524784 2524917 2525096 "SCACHE" 2525418 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1076 2524456 2524616 2524646 "SASTCAT" 2524651 T SASTCAT (NIL) -9 NIL 2524664 NIL) (-1075 2523970 2524291 2524367 "SAOS" 2524402 T SAOS (NIL) -8 NIL NIL NIL) (-1074 2523535 2523570 2523743 "SAERFFC" 2523929 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1073 2517509 2523432 2523512 "SAE" 2523517 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1072 2517102 2517137 2517296 "SAEFACT" 2517468 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1071 2515423 2515737 2516138 "RURPK" 2516768 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1070 2514059 2514338 2514650 "RULESET" 2515257 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1069 2511246 2511749 2512214 "RULE" 2513740 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1068 2510885 2511040 2511123 "RULECOLD" 2511198 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1067 2510383 2510602 2510696 "RSTRCAST" 2510813 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2505232 2506026 2506946 "RSETGCD" 2509582 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2494489 2499541 2499638 "RSETCAT" 2503757 NIL RSETCAT (NIL T T T T) -9 NIL 2504854 NIL) (-1064 2492416 2492955 2493779 "RSETCAT-" 2493784 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2484803 2486178 2487698 "RSDCMPK" 2491015 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2482808 2483249 2483323 "RRCC" 2484409 NIL RRCC (NIL T T) -9 NIL 2484753 NIL) (-1061 2482159 2482333 2482612 "RRCC-" 2482617 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2481629 2481855 2481956 "RPTAST" 2482080 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2455635 2465222 2465289 "RPOLCAT" 2475953 NIL RPOLCAT (NIL T T T) -9 NIL 2479112 NIL) (-1058 2447135 2449473 2452595 "RPOLCAT-" 2452600 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2438182 2445346 2445828 "ROUTINE" 2446675 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2435015 2437808 2437948 "ROMAN" 2438064 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2433290 2433875 2434135 "ROIRC" 2434820 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2429683 2431926 2431956 "RNS" 2432260 T RNS (NIL) -9 NIL 2432533 NIL) (-1053 2428192 2428575 2429109 "RNS-" 2429184 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2427641 2428023 2428053 "RNG" 2428058 T RNG (NIL) -9 NIL 2428079 NIL) (-1051 2427033 2427395 2427438 "RMODULE" 2427500 NIL RMODULE (NIL T) -9 NIL 2427542 NIL) (-1050 2425869 2425963 2426299 "RMCAT2" 2426934 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2422746 2425215 2425512 "RMATRIX" 2425631 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2415688 2417922 2418037 "RMATCAT" 2421396 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2422378 NIL) (-1047 2415063 2415210 2415517 "RMATCAT-" 2415522 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2414630 2414705 2414833 "RINTERP" 2414982 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2413763 2414283 2414313 "RING" 2414369 T RING (NIL) -9 NIL 2414455 NIL) (-1044 2413555 2413599 2413696 "RING-" 2413701 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2412396 2412633 2412891 "RIDIST" 2413319 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2403712 2411864 2412070 "RGCHAIN" 2412244 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2403088 2403468 2403509 "RGBCSPC" 2403567 NIL RGBCSPC (NIL T) -9 NIL 2403619 NIL) (-1040 2402272 2402627 2402668 "RGBCMDL" 2402900 NIL RGBCMDL (NIL T) -9 NIL 2403014 NIL) (-1039 2399266 2399880 2400550 "RF" 2401636 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2398912 2398975 2399078 "RFFACTOR" 2399197 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2398637 2398672 2398769 "RFFACT" 2398871 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2396754 2397118 2397500 "RFDIST" 2398277 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2396207 2396299 2396462 "RETSOL" 2396656 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2395843 2395923 2395966 "RETRACT" 2396099 NIL RETRACT (NIL T) -9 NIL 2396186 NIL) (-1033 2395692 2395717 2395804 "RETRACT-" 2395809 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2395321 2395514 2395584 "RETAST" 2395644 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2388175 2394974 2395101 "RESULT" 2395216 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2386801 2387444 2387643 "RESRING" 2388078 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2386437 2386486 2386584 "RESLATC" 2386738 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2386143 2386177 2386284 "REPSQ" 2386396 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2383565 2384145 2384747 "REP" 2385563 T REP (NIL) -7 NIL NIL NIL) (-1026 2383263 2383297 2383408 "REPDB" 2383524 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2377173 2378552 2379775 "REP2" 2382075 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2373550 2374231 2375039 "REP1" 2376400 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2366276 2371691 2372147 "REGSET" 2373180 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2365089 2365424 2365674 "REF" 2366061 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2364466 2364569 2364736 "REDORDER" 2364973 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2360471 2363679 2363906 "RECLOS" 2364294 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2359523 2359704 2359919 "REALSOLV" 2360278 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2359369 2359410 2359440 "REAL" 2359445 T REAL (NIL) -9 NIL 2359480 NIL) (-1017 2355852 2356654 2357538 "REAL0Q" 2358534 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2351453 2352441 2353502 "REAL0" 2354833 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2350951 2351170 2351264 "RDUCEAST" 2351381 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2350356 2350428 2350635 "RDIV" 2350873 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2349424 2349598 2349811 "RDIST" 2350178 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2348021 2348308 2348680 "RDETRS" 2349132 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2345833 2346287 2346825 "RDETR" 2347563 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2344444 2344722 2345126 "RDEEFS" 2345549 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2342939 2343245 2343677 "RDEEF" 2344132 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2337200 2340075 2340105 "RCFIELD" 2341400 T RCFIELD (NIL) -9 NIL 2342130 NIL) (-1007 2335264 2335768 2336464 "RCFIELD-" 2336539 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2331580 2333365 2333408 "RCAGG" 2334492 NIL RCAGG (NIL T) -9 NIL 2334957 NIL) (-1005 2331208 2331302 2331465 "RCAGG-" 2331470 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2330543 2330655 2330820 "RATRET" 2331092 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2330096 2330163 2330284 "RATFACT" 2330471 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2329404 2329524 2329676 "RANDSRC" 2329966 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2329138 2329182 2329255 "RADUTIL" 2329353 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2322291 2327971 2328281 "RADIX" 2328862 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2313948 2322135 2322263 "RADFF" 2322268 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2313600 2313675 2313703 "RADCAT" 2313860 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2313385 2313433 2313530 "RADCAT-" 2313535 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2311536 2313160 2313249 "QUEUE" 2313329 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2308112 2311473 2311518 "QUAT" 2311523 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2307750 2307793 2307920 "QUATCT2" 2308063 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2301497 2304799 2304839 "QUATCAT" 2305619 NIL QUATCAT (NIL T) -9 NIL 2306385 NIL) (-992 2297641 2298678 2300065 "QUATCAT-" 2300159 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2295161 2296725 2296766 "QUAGG" 2297141 NIL QUAGG (NIL T) -9 NIL 2297316 NIL) (-990 2294793 2294986 2295054 "QQUTAST" 2295113 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2293718 2294191 2294363 "QFORM" 2294665 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2284930 2290135 2290175 "QFCAT" 2290833 NIL QFCAT (NIL T) -9 NIL 2291834 NIL) (-987 2280502 2281703 2283294 "QFCAT-" 2283388 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2280140 2280183 2280310 "QFCAT2" 2280453 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2279600 2279710 2279840 "QEQUAT" 2280030 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2272748 2273819 2275003 "QCMPACK" 2278533 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2270324 2270745 2271173 "QALGSET" 2272403 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2269569 2269743 2269975 "QALGSET2" 2270144 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2268260 2268483 2268800 "PWFFINTB" 2269342 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2266442 2266610 2266964 "PUSHVAR" 2268074 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2262360 2263414 2263455 "PTRANFN" 2265339 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2260762 2261053 2261375 "PTPACK" 2262071 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2260394 2260451 2260560 "PTFUNC2" 2260699 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2254921 2259266 2259307 "PTCAT" 2259603 NIL PTCAT (NIL T) -9 NIL 2259756 NIL) (-975 2254579 2254614 2254738 "PSQFR" 2254880 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2253174 2253472 2253806 "PSEUDLIN" 2254277 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2239944 2242308 2244632 "PSETPK" 2250934 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2232988 2235702 2235798 "PSETCAT" 2238819 NIL PSETCAT (NIL T T T T) -9 NIL 2239633 NIL) (-971 2230824 2231458 2232279 "PSETCAT-" 2232284 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2230173 2230338 2230366 "PSCURVE" 2230634 T PSCURVE (NIL) -9 NIL 2230801 NIL) (-969 2226529 2228011 2228076 "PSCAT" 2228920 NIL PSCAT (NIL T T T) -9 NIL 2229160 NIL) (-968 2225592 2225808 2226208 "PSCAT-" 2226213 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2224324 2224957 2225162 "PRTITION" 2225407 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2223826 2224045 2224137 "PRTDAST" 2224252 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2212924 2215130 2217318 "PRS" 2221688 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2210782 2212274 2212314 "PRQAGG" 2212497 NIL PRQAGG (NIL T) -9 NIL 2212599 NIL) (-963 2210168 2210397 2210425 "PROPLOG" 2210610 T PROPLOG (NIL) -9 NIL 2210732 NIL) (-962 2207338 2207982 2208446 "PROPFRML" 2209736 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2206798 2206908 2207038 "PROPERTY" 2207228 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2200883 2204964 2205784 "PRODUCT" 2206024 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2198196 2200341 2200575 "PR" 2200694 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2197992 2198024 2198083 "PRINT" 2198157 T PRINT (NIL) -7 NIL NIL NIL) (-957 2197332 2197449 2197601 "PRIMES" 2197872 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2195397 2195798 2196264 "PRIMELT" 2196911 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2195126 2195175 2195203 "PRIMCAT" 2195327 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2191287 2195064 2195109 "PRIMARR" 2195114 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2190294 2190472 2190700 "PRIMARR2" 2191105 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2189937 2189993 2190104 "PREASSOC" 2190232 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2189412 2189545 2189573 "PPCURVE" 2189778 T PPCURVE (NIL) -9 NIL 2189914 NIL) (-950 2189034 2189207 2189290 "PORTNUM" 2189349 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2186393 2186792 2187384 "POLYROOT" 2188615 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2180338 2185997 2186157 "POLY" 2186266 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2179721 2179779 2180013 "POLYLIFT" 2180274 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2175996 2176445 2177074 "POLYCATQ" 2179266 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2162813 2168171 2168236 "POLYCAT" 2171750 NIL POLYCAT (NIL T T T) -9 NIL 2173678 NIL) (-944 2156263 2158124 2160508 "POLYCAT-" 2160513 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2155850 2155918 2156038 "POLY2UP" 2156189 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2155482 2155539 2155648 "POLY2" 2155787 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2154167 2154406 2154682 "POLUTIL" 2155256 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2152522 2152799 2153130 "POLTOPOL" 2153889 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2148040 2152458 2152504 "POINT" 2152509 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2146227 2146584 2146959 "PNTHEORY" 2147685 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2144646 2144943 2145355 "PMTOOLS" 2145925 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2144239 2144317 2144434 "PMSYM" 2144562 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2143749 2143818 2143992 "PMQFCAT" 2144164 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2143104 2143214 2143370 "PMPRED" 2143626 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2142500 2142586 2142747 "PMPREDFS" 2143005 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2141143 2141351 2141736 "PMPLCAT" 2142262 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2140675 2140754 2140906 "PMLSAGG" 2141058 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2140150 2140226 2140407 "PMKERNEL" 2140593 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2139767 2139842 2139955 "PMINS" 2140069 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2139195 2139264 2139480 "PMFS" 2139692 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2138423 2138541 2138746 "PMDOWN" 2139072 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2137586 2137745 2137927 "PMASS" 2138261 T PMASS (NIL) -7 NIL NIL NIL) (-925 2136860 2136971 2137134 "PMASSFS" 2137472 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2136515 2136583 2136677 "PLOTTOOL" 2136786 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2131137 2132326 2133474 "PLOT" 2135387 T PLOT (NIL) -8 NIL NIL NIL) (-922 2126951 2127985 2128906 "PLOT3D" 2130236 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2125863 2126040 2126275 "PLOT1" 2126755 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2101257 2105929 2110780 "PLEQN" 2121129 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2100575 2100697 2100877 "PINTERP" 2101122 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2100268 2100315 2100418 "PINTERPA" 2100522 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2099516 2100037 2100124 "PI" 2100164 T PI (NIL) -8 NIL NIL 2100231) (-916 2097913 2098854 2098882 "PID" 2099064 T PID (NIL) -9 NIL 2099198 NIL) (-915 2097638 2097675 2097763 "PICOERCE" 2097870 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2096958 2097097 2097273 "PGROEB" 2097494 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2092545 2093359 2094264 "PGE" 2096073 T PGE (NIL) -7 NIL NIL NIL) (-912 2090669 2090915 2091281 "PGCD" 2092262 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2090007 2090110 2090271 "PFRPAC" 2090553 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2086687 2088555 2088908 "PFR" 2089686 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2085076 2085320 2085645 "PFOTOOLS" 2086434 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2083609 2083848 2084199 "PFOQ" 2084833 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2082082 2082294 2082657 "PFO" 2083393 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2078670 2081971 2082040 "PF" 2082045 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2076104 2077341 2077369 "PFECAT" 2077954 T PFECAT (NIL) -9 NIL 2078338 NIL) (-904 2075549 2075703 2075917 "PFECAT-" 2075922 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2074153 2074404 2074705 "PFBRU" 2075298 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2072020 2072371 2072803 "PFBR" 2073804 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2067936 2069396 2070072 "PERM" 2071377 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2063202 2064143 2065013 "PERMGRP" 2067099 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2061334 2062265 2062306 "PERMCAT" 2062752 NIL PERMCAT (NIL T) -9 NIL 2063057 NIL) (-898 2060987 2061028 2061152 "PERMAN" 2061287 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2058523 2060652 2060774 "PENDTREE" 2060898 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2056616 2057350 2057391 "PDRING" 2058048 NIL PDRING (NIL T) -9 NIL 2058334 NIL) (-895 2055719 2055937 2056299 "PDRING-" 2056304 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2052961 2053712 2054380 "PDEPROB" 2055071 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2050508 2051010 2051565 "PDEPACK" 2052426 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2049420 2049610 2049861 "PDECOMP" 2050307 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2047025 2047842 2047870 "PDECAT" 2048657 T PDECAT (NIL) -9 NIL 2049370 NIL) (-890 2046776 2046809 2046899 "PCOMP" 2046986 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2044981 2045577 2045874 "PBWLB" 2046505 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2037486 2039054 2040392 "PATTERN" 2043664 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2037118 2037175 2037284 "PATTERN2" 2037423 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2034875 2035263 2035720 "PATTERN1" 2036707 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2032270 2032824 2033305 "PATRES" 2034440 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2031834 2031901 2032033 "PATRES2" 2032197 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2029717 2030122 2030529 "PATMATCH" 2031501 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2029253 2029436 2029477 "PATMAB" 2029584 NIL PATMAB (NIL T) -9 NIL 2029667 NIL) (-881 2027798 2028107 2028365 "PATLRES" 2029058 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2027344 2027467 2027508 "PATAB" 2027513 NIL PATAB (NIL T) -9 NIL 2027685 NIL) (-879 2024825 2025357 2025930 "PARTPERM" 2026791 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2024446 2024509 2024611 "PARSURF" 2024756 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2024078 2024135 2024244 "PARSU2" 2024383 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2023842 2023882 2023949 "PARSER" 2024031 T PARSER (NIL) -7 NIL NIL NIL) (-875 2023463 2023526 2023628 "PARSCURV" 2023773 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2023095 2023152 2023261 "PARSC2" 2023400 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2022734 2022792 2022889 "PARPCURV" 2023031 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2022366 2022423 2022532 "PARPC2" 2022671 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2021886 2021972 2022091 "PAN2EXPR" 2022267 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2020692 2021007 2021235 "PALETTE" 2021678 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2019160 2019697 2020057 "PAIR" 2020378 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2013066 2018419 2018613 "PADICRC" 2019015 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2006330 2012412 2012596 "PADICRAT" 2012914 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2004680 2006267 2006312 "PADIC" 2006317 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2001890 2003420 2003460 "PADICCT" 2004041 NIL PADICCT (NIL NIL) -9 NIL 2004323 NIL) (-864 2000847 2001047 2001315 "PADEPAC" 2001677 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2000059 2000192 2000398 "PADE" 2000709 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 1998481 1999267 1999547 "OWP" 1999863 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 1998001 1998187 1998284 "OVERSET" 1998404 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1997074 1997606 1997778 "OVAR" 1997869 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1996338 1996459 1996620 "OUT" 1996933 T OUT (NIL) -7 NIL NIL NIL) (-858 1985245 1987447 1989647 "OUTFORM" 1994158 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1984581 1984842 1984969 "OUTBFILE" 1985138 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1983888 1984053 1984081 "OUTBCON" 1984399 T OUTBCON (NIL) -9 NIL 1984565 NIL) (-855 1983489 1983601 1983758 "OUTBCON-" 1983763 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1982897 1983218 1983307 "OSI" 1983420 T OSI (NIL) -8 NIL NIL NIL) (-853 1982453 1982765 1982793 "OSGROUP" 1982798 T OSGROUP (NIL) -9 NIL 1982820 NIL) (-852 1981198 1981425 1981710 "ORTHPOL" 1982200 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1978784 1981033 1981154 "OREUP" 1981159 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976222 1978475 1978602 "ORESUP" 1978726 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1973750 1974250 1974811 "OREPCTO" 1975711 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1967574 1969741 1969782 "OREPCAT" 1972130 NIL OREPCAT (NIL T) -9 NIL 1973234 NIL) (-847 1964721 1965503 1966561 "OREPCAT-" 1966566 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1963898 1964170 1964198 "ORDSET" 1964507 T ORDSET (NIL) -9 NIL 1964671 NIL) (-845 1963417 1963539 1963732 "ORDSET-" 1963737 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1962051 1962808 1962836 "ORDRING" 1963038 T ORDRING (NIL) -9 NIL 1963163 NIL) (-843 1961696 1961790 1961934 "ORDRING-" 1961939 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1961102 1961539 1961567 "ORDMON" 1961572 T ORDMON (NIL) -9 NIL 1961593 NIL) (-841 1960264 1960411 1960606 "ORDFUNS" 1960951 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1959628 1960021 1960049 "ORDFIN" 1960114 T ORDFIN (NIL) -9 NIL 1960188 NIL) (-839 1956220 1958214 1958623 "ORDCOMP" 1959252 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1955486 1955613 1955799 "ORDCOMP2" 1956080 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1952094 1952977 1953791 "OPTPROB" 1954692 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1948896 1949535 1950239 "OPTPACK" 1951410 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1946609 1947349 1947377 "OPTCAT" 1948196 T OPTCAT (NIL) -9 NIL 1948846 NIL) (-834 1946052 1946286 1946391 "OPSIG" 1946524 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1945820 1945859 1945925 "OPQUERY" 1946006 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1942986 1944131 1944635 "OP" 1945349 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1942521 1942692 1942733 "OPERCAT" 1942868 NIL OPERCAT (NIL T) -9 NIL 1942936 NIL) (-830 1942367 1942394 1942480 "OPERCAT-" 1942485 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1939212 1941164 1941533 "ONECOMP" 1942031 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1938517 1938632 1938806 "ONECOMP2" 1939084 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1937936 1938042 1938172 "OMSERVER" 1938407 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1934824 1937376 1937416 "OMSAGG" 1937477 NIL OMSAGG (NIL T) -9 NIL 1937541 NIL) (-825 1933447 1933710 1933992 "OMPKG" 1934562 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1932877 1932980 1933008 "OM" 1933307 T OM (NIL) -9 NIL NIL NIL) (-823 1931459 1932426 1932595 "OMLO" 1932758 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1930384 1930531 1930758 "OMEXPR" 1931285 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1929702 1929930 1930066 "OMERR" 1930268 T OMERR (NIL) -8 NIL NIL NIL) (-820 1928880 1929123 1929283 "OMERRK" 1929562 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1928358 1928557 1928665 "OMENC" 1928792 T OMENC (NIL) -8 NIL NIL NIL) (-818 1922253 1923438 1924609 "OMDEV" 1927207 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1921322 1921493 1921687 "OMCONN" 1922079 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1919943 1920885 1920913 "OINTDOM" 1920918 T OINTDOM (NIL) -9 NIL 1920939 NIL) (-815 1915749 1916933 1917649 "OFMONOID" 1919259 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1915187 1915686 1915731 "ODVAR" 1915736 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1912645 1914932 1915087 "ODR" 1915092 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1904989 1912421 1912547 "ODPOL" 1912552 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1898865 1904861 1904966 "ODP" 1904971 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1897631 1897846 1898121 "ODETOOLS" 1898639 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1894600 1895256 1895972 "ODESYS" 1896964 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1889482 1890390 1891415 "ODERTRIC" 1893675 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1888908 1888990 1889184 "ODERED" 1889394 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1885796 1886344 1887021 "ODERAT" 1888331 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1882756 1883220 1883817 "ODEPRRIC" 1885325 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1880726 1881295 1881781 "ODEPROB" 1882290 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1877248 1877731 1878378 "ODEPRIM" 1880205 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1876497 1876599 1876859 "ODEPAL" 1877140 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1872659 1873450 1874314 "ODEPACK" 1875653 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1871692 1871799 1872028 "ODEINT" 1872548 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1865793 1867218 1868665 "ODEIFTBL" 1870265 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1861128 1861914 1862873 "ODEEF" 1864952 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1860463 1860552 1860782 "ODECONST" 1861033 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1858614 1859249 1859277 "ODECAT" 1859882 T ODECAT (NIL) -9 NIL 1860413 NIL) (-795 1855521 1858326 1858445 "OCT" 1858527 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1855159 1855202 1855329 "OCTCT2" 1855472 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1849933 1852333 1852373 "OC" 1853470 NIL OC (NIL T) -9 NIL 1854328 NIL) (-792 1847160 1847908 1848898 "OC-" 1848992 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1846538 1846980 1847008 "OCAMON" 1847013 T OCAMON (NIL) -9 NIL 1847034 NIL) (-790 1846095 1846410 1846438 "OASGP" 1846443 T OASGP (NIL) -9 NIL 1846463 NIL) (-789 1845382 1845845 1845873 "OAMONS" 1845913 T OAMONS (NIL) -9 NIL 1845956 NIL) (-788 1844822 1845229 1845257 "OAMON" 1845262 T OAMON (NIL) -9 NIL 1845282 NIL) (-787 1844126 1844618 1844646 "OAGROUP" 1844651 T OAGROUP (NIL) -9 NIL 1844671 NIL) (-786 1843816 1843866 1843954 "NUMTUBE" 1844070 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1837389 1838907 1840443 "NUMQUAD" 1842300 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1833145 1834133 1835158 "NUMODE" 1836384 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1830526 1831380 1831408 "NUMINT" 1832331 T NUMINT (NIL) -9 NIL 1833095 NIL) (-782 1829474 1829671 1829889 "NUMFMT" 1830328 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1815833 1818778 1821310 "NUMERIC" 1826981 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1810230 1815282 1815377 "NTSCAT" 1815382 NIL NTSCAT (NIL T T T T) -9 NIL 1815421 NIL) (-779 1809424 1809589 1809782 "NTPOLFN" 1810069 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1797264 1806249 1807061 "NSUP" 1808645 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1796896 1796953 1797062 "NSUP2" 1797201 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1786893 1796670 1796803 "NSMP" 1796808 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1785325 1785626 1785983 "NREP" 1786581 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1783916 1784168 1784526 "NPCOEF" 1785068 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1782982 1783097 1783313 "NORMRETR" 1783797 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1781023 1781313 1781722 "NORMPK" 1782690 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1780708 1780736 1780860 "NORMMA" 1780989 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1780535 1780665 1780694 "NONE" 1780699 T NONE (NIL) -8 NIL NIL NIL) (-769 1780324 1780353 1780422 "NONE1" 1780499 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1779807 1779869 1780055 "NODE1" 1780256 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1778078 1778901 1779156 "NNI" 1779503 T NNI (NIL) -8 NIL NIL 1779738) (-766 1776498 1776811 1777175 "NLINSOL" 1777746 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1772766 1773734 1774633 "NIPROB" 1775619 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1771523 1771757 1772059 "NFINTBAS" 1772528 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1770697 1771173 1771214 "NETCLT" 1771386 NIL NETCLT (NIL T) -9 NIL 1771468 NIL) (-762 1769405 1769636 1769917 "NCODIV" 1770465 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1769167 1769204 1769279 "NCNTFRAC" 1769362 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1767347 1767711 1768131 "NCEP" 1768792 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1766258 1766997 1767025 "NASRING" 1767135 T NASRING (NIL) -9 NIL 1767209 NIL) (-758 1766053 1766097 1766191 "NASRING-" 1766196 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1765206 1765705 1765733 "NARNG" 1765850 T NARNG (NIL) -9 NIL 1765941 NIL) (-756 1764898 1764965 1765099 "NARNG-" 1765104 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1763777 1763984 1764219 "NAGSP" 1764683 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1755049 1756733 1758406 "NAGS" 1762124 T NAGS (NIL) -7 NIL NIL NIL) (-753 1753597 1753905 1754236 "NAGF07" 1754738 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1748135 1749426 1750733 "NAGF04" 1752310 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1741103 1742717 1744350 "NAGF02" 1746522 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1736327 1737427 1738544 "NAGF01" 1740006 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1729955 1731521 1733106 "NAGE04" 1734762 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1721124 1723245 1725375 "NAGE02" 1727845 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1717077 1718024 1718988 "NAGE01" 1720180 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1714872 1715406 1715964 "NAGD03" 1716539 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1706622 1708550 1710504 "NAGD02" 1712938 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1700433 1701858 1703298 "NAGD01" 1705202 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1696642 1697464 1698301 "NAGC06" 1699616 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1695107 1695439 1695795 "NAGC05" 1696306 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1694483 1694602 1694746 "NAGC02" 1694983 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1693543 1694100 1694140 "NAALG" 1694219 NIL NAALG (NIL T) -9 NIL 1694280 NIL) (-739 1693378 1693407 1693497 "NAALG-" 1693502 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1687328 1688436 1689623 "MULTSQFR" 1692274 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1686647 1686722 1686906 "MULTFACT" 1687240 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1679740 1683610 1683663 "MTSCAT" 1684733 NIL MTSCAT (NIL T T) -9 NIL 1685247 NIL) (-735 1679452 1679506 1679598 "MTHING" 1679680 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1679244 1679277 1679337 "MSYSCMD" 1679412 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1675356 1677999 1678319 "MSET" 1678957 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1672451 1674917 1674958 "MSETAGG" 1674963 NIL MSETAGG (NIL T) -9 NIL 1674997 NIL) (-731 1668334 1669830 1670575 "MRING" 1671751 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1667900 1667967 1668098 "MRF2" 1668261 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1667518 1667553 1667697 "MRATFAC" 1667859 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1665130 1665425 1665856 "MPRFF" 1667223 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1659190 1664984 1665081 "MPOLY" 1665086 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1658680 1658715 1658923 "MPCPF" 1659149 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1658194 1658237 1658421 "MPC3" 1658631 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1657389 1657470 1657691 "MPC2" 1658109 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1655690 1656027 1656417 "MONOTOOL" 1657049 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1654941 1655232 1655260 "MONOID" 1655479 T MONOID (NIL) -9 NIL 1655626 NIL) (-721 1654487 1654606 1654787 "MONOID-" 1654792 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1645346 1651254 1651313 "MONOGEN" 1651987 NIL MONOGEN (NIL T T) -9 NIL 1652443 NIL) (-719 1642564 1643299 1644299 "MONOGEN-" 1644418 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1641423 1641843 1641871 "MONADWU" 1642263 T MONADWU (NIL) -9 NIL 1642501 NIL) (-717 1640795 1640954 1641202 "MONADWU-" 1641207 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1640180 1640398 1640426 "MONAD" 1640633 T MONAD (NIL) -9 NIL 1640745 NIL) (-715 1639865 1639943 1640075 "MONAD-" 1640080 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1638181 1638778 1639057 "MOEBIUS" 1639618 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1637573 1637951 1637991 "MODULE" 1637996 NIL MODULE (NIL T) -9 NIL 1638022 NIL) (-712 1637141 1637237 1637427 "MODULE-" 1637432 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1634856 1635505 1635832 "MODRING" 1636965 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1631842 1632961 1633482 "MODOP" 1634385 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1630457 1630909 1631186 "MODMONOM" 1631705 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1620264 1628748 1629162 "MODMON" 1630094 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1617455 1619108 1619384 "MODFIELD" 1620139 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1616459 1616736 1616926 "MMLFORM" 1617285 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1615985 1616028 1616207 "MMAP" 1616410 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1614202 1614935 1614976 "MLO" 1615399 NIL MLO (NIL T) -9 NIL 1615641 NIL) (-703 1611569 1612084 1612686 "MLIFT" 1613683 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1610960 1611044 1611198 "MKUCFUNC" 1611480 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1610559 1610629 1610752 "MKRECORD" 1610883 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1609607 1609768 1609996 "MKFUNC" 1610370 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1608995 1609099 1609255 "MKFLCFN" 1609490 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1608538 1608905 1608964 "MKCHSET" 1608969 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-697 1607815 1607917 1608102 "MKBCFUNC" 1608431 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-696 1604557 1607369 1607505 "MINT" 1607699 T MINT (NIL) -8 NIL NIL NIL) (-695 1603369 1603612 1603889 "MHROWRED" 1604312 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-694 1598795 1601904 1602309 "MFLOAT" 1602984 T MFLOAT (NIL) -8 NIL NIL NIL) (-693 1598152 1598228 1598399 "MFINFACT" 1598707 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-692 1594467 1595315 1596199 "MESH" 1597288 T MESH (NIL) -7 NIL NIL NIL) (-691 1592857 1593169 1593522 "MDDFACT" 1594154 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-690 1589699 1592016 1592057 "MDAGG" 1592312 NIL MDAGG (NIL T) -9 NIL 1592455 NIL) (-689 1579477 1588992 1589199 "MCMPLX" 1589512 T MCMPLX (NIL) -8 NIL NIL NIL) (-688 1578618 1578764 1578964 "MCDEN" 1579326 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-687 1576508 1576778 1577158 "MCALCFN" 1578348 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-686 1575433 1575673 1575906 "MAYBE" 1576314 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-685 1573045 1573568 1574130 "MATSTOR" 1574904 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-684 1569051 1572417 1572665 "MATRIX" 1572830 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-683 1564820 1565524 1566260 "MATLIN" 1568408 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-682 1554974 1558112 1558189 "MATCAT" 1563069 NIL MATCAT (NIL T T T) -9 NIL 1564486 NIL) (-681 1551338 1552351 1553707 "MATCAT-" 1553712 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-680 1549932 1550085 1550418 "MATCAT2" 1551173 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-679 1548044 1548368 1548752 "MAPPKG3" 1549607 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-678 1547025 1547198 1547420 "MAPPKG2" 1547868 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-677 1545524 1545808 1546135 "MAPPKG1" 1546731 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-676 1544630 1544930 1545107 "MAPPAST" 1545367 T MAPPAST (NIL) -8 NIL NIL NIL) (-675 1544241 1544299 1544422 "MAPHACK3" 1544566 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-674 1543833 1543894 1544008 "MAPHACK2" 1544173 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-673 1543271 1543374 1543516 "MAPHACK1" 1543724 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-672 1541377 1541971 1542275 "MAGMA" 1542999 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-671 1540883 1541101 1541192 "MACROAST" 1541306 T MACROAST (NIL) -8 NIL NIL NIL) (-670 1537350 1539122 1539583 "M3D" 1540455 NIL M3D (NIL T) -8 NIL NIL NIL) (-669 1531504 1535719 1535760 "LZSTAGG" 1536542 NIL LZSTAGG (NIL T) -9 NIL 1536837 NIL) (-668 1527478 1528635 1530092 "LZSTAGG-" 1530097 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-667 1524592 1525369 1525856 "LWORD" 1527023 NIL LWORD (NIL T) -8 NIL NIL NIL) (-666 1524195 1524396 1524471 "LSTAST" 1524537 T LSTAST (NIL) -8 NIL NIL NIL) (-665 1517396 1523966 1524100 "LSQM" 1524105 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-664 1516620 1516759 1516987 "LSPP" 1517251 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-663 1514432 1514733 1515189 "LSMP" 1516309 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-662 1511211 1511885 1512615 "LSMP1" 1513734 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-661 1505136 1510378 1510419 "LSAGG" 1510481 NIL LSAGG (NIL T) -9 NIL 1510559 NIL) (-660 1501831 1502755 1503968 "LSAGG-" 1503973 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-659 1499457 1500975 1501224 "LPOLY" 1501626 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-658 1499039 1499124 1499247 "LPEFRAC" 1499366 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-657 1497386 1498133 1498386 "LO" 1498871 NIL LO (NIL T T T) -8 NIL NIL NIL) (-656 1497038 1497150 1497178 "LOGIC" 1497289 T LOGIC (NIL) -9 NIL 1497370 NIL) (-655 1496900 1496923 1496994 "LOGIC-" 1496999 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-654 1496093 1496233 1496426 "LODOOPS" 1496756 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-653 1493551 1496009 1496075 "LODO" 1496080 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-652 1492089 1492324 1492677 "LODOF" 1493298 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-651 1488445 1490842 1490883 "LODOCAT" 1491321 NIL LODOCAT (NIL T) -9 NIL 1491532 NIL) (-650 1488178 1488236 1488363 "LODOCAT-" 1488368 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-649 1485533 1488019 1488137 "LODO2" 1488142 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-648 1483003 1485470 1485515 "LODO1" 1485520 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-647 1481863 1482028 1482340 "LODEEF" 1482826 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-646 1477149 1479993 1480034 "LNAGG" 1480981 NIL LNAGG (NIL T) -9 NIL 1481425 NIL) (-645 1476296 1476510 1476852 "LNAGG-" 1476857 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-644 1472459 1473221 1473860 "LMOPS" 1475711 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-643 1471854 1472216 1472257 "LMODULE" 1472318 NIL LMODULE (NIL T) -9 NIL 1472360 NIL) (-642 1469100 1471499 1471622 "LMDICT" 1471764 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-641 1468826 1469008 1469068 "LITERAL" 1469073 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-640 1462053 1467772 1468070 "LIST" 1468561 NIL LIST (NIL T) -8 NIL NIL NIL) (-639 1461578 1461652 1461791 "LIST3" 1461973 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-638 1460585 1460763 1460991 "LIST2" 1461396 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-637 1458719 1459031 1459430 "LIST2MAP" 1460232 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-636 1457449 1458085 1458126 "LINEXP" 1458381 NIL LINEXP (NIL T) -9 NIL 1458530 NIL) (-635 1456096 1456356 1456653 "LINDEP" 1457201 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-634 1452863 1453582 1454359 "LIMITRF" 1455351 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-633 1451139 1451434 1451850 "LIMITPS" 1452558 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-632 1445594 1450650 1450878 "LIE" 1450960 NIL LIE (NIL T T) -8 NIL NIL NIL) (-631 1444643 1445086 1445126 "LIECAT" 1445266 NIL LIECAT (NIL T) -9 NIL 1445417 NIL) (-630 1444484 1444511 1444599 "LIECAT-" 1444604 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-629 1437096 1443933 1444098 "LIB" 1444339 T LIB (NIL) -8 NIL NIL NIL) (-628 1432733 1433614 1434549 "LGROBP" 1436213 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-627 1430599 1430873 1431235 "LF" 1432454 NIL LF (NIL T T) -7 NIL NIL NIL) (-626 1429439 1430131 1430159 "LFCAT" 1430366 T LFCAT (NIL) -9 NIL 1430505 NIL) (-625 1426343 1426971 1427659 "LEXTRIPK" 1428803 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-624 1423114 1423913 1424416 "LEXP" 1425923 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-623 1422617 1422835 1422927 "LETAST" 1423042 T LETAST (NIL) -8 NIL NIL NIL) (-622 1421015 1421328 1421729 "LEADCDET" 1422299 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-621 1420205 1420279 1420508 "LAZM3PK" 1420936 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-620 1415160 1418282 1418820 "LAUPOL" 1419717 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-619 1414725 1414769 1414937 "LAPLACE" 1415110 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-618 1412699 1413826 1414077 "LA" 1414558 NIL LA (NIL T T T) -8 NIL NIL NIL) (-617 1411780 1412330 1412371 "LALG" 1412433 NIL LALG (NIL T) -9 NIL 1412492 NIL) (-616 1411494 1411553 1411689 "LALG-" 1411694 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-615 1411329 1411353 1411394 "KVTFROM" 1411456 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-614 1410132 1410546 1410775 "KTVLOGIC" 1411120 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-613 1409967 1409991 1410032 "KRCFROM" 1410094 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-612 1408871 1409058 1409357 "KOVACIC" 1409767 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-611 1408706 1408730 1408771 "KONVERT" 1408833 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-610 1408541 1408565 1408606 "KOERCE" 1408668 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-609 1406275 1407035 1407428 "KERNEL" 1408180 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-608 1405777 1405858 1405988 "KERNEL2" 1406189 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-607 1399628 1404316 1404370 "KDAGG" 1404747 NIL KDAGG (NIL T T) -9 NIL 1404953 NIL) (-606 1399157 1399281 1399486 "KDAGG-" 1399491 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-605 1392332 1398818 1398973 "KAFILE" 1399035 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-604 1386787 1391843 1392071 "JORDAN" 1392153 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-603 1386193 1386436 1386557 "JOINAST" 1386686 T JOINAST (NIL) -8 NIL NIL NIL) (-602 1386039 1386098 1386153 "JAVACODE" 1386158 T JAVACODE (NIL) -8 NIL NIL NIL) (-601 1382338 1384244 1384298 "IXAGG" 1385227 NIL IXAGG (NIL T T) -9 NIL 1385686 NIL) (-600 1381257 1381563 1381982 "IXAGG-" 1381987 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-599 1376837 1381179 1381238 "IVECTOR" 1381243 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-598 1375603 1375840 1376106 "ITUPLE" 1376604 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-597 1374039 1374216 1374522 "ITRIGMNP" 1375425 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-596 1372784 1372988 1373271 "ITFUN3" 1373815 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-595 1372416 1372473 1372582 "ITFUN2" 1372721 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-594 1370253 1371278 1371577 "ITAYLOR" 1372150 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-593 1359236 1364390 1365553 "ISUPS" 1369123 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-592 1358340 1358480 1358716 "ISUMP" 1359083 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-591 1353604 1358141 1358220 "ISTRING" 1358293 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-590 1353107 1353325 1353417 "ISAST" 1353532 T ISAST (NIL) -8 NIL NIL NIL) (-589 1352317 1352398 1352614 "IRURPK" 1353021 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-588 1351253 1351454 1351694 "IRSN" 1352097 T IRSN (NIL) -7 NIL NIL NIL) (-587 1349282 1349637 1350073 "IRRF2F" 1350891 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-586 1349029 1349067 1349143 "IRREDFFX" 1349238 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-585 1347644 1347903 1348202 "IROOT" 1348762 NIL IROOT (NIL T) -7 NIL NIL NIL) (-584 1344276 1345328 1346020 "IR" 1346984 NIL IR (NIL T) -8 NIL NIL NIL) (-583 1341889 1342384 1342950 "IR2" 1343754 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-582 1340961 1341074 1341295 "IR2F" 1341772 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-581 1340752 1340786 1340846 "IPRNTPK" 1340921 T IPRNTPK (NIL) -7 NIL NIL NIL) (-580 1337371 1340641 1340710 "IPF" 1340715 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-579 1335734 1337296 1337353 "IPADIC" 1337358 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-578 1335074 1335294 1335424 "IP4ADDR" 1335624 T IP4ADDR (NIL) -8 NIL NIL NIL) (-577 1334574 1334778 1334888 "IOMODE" 1334984 T IOMODE (NIL) -8 NIL NIL NIL) (-576 1333647 1334171 1334298 "IOBFILE" 1334467 T IOBFILE (NIL) -8 NIL NIL NIL) (-575 1333135 1333551 1333579 "IOBCON" 1333584 T IOBCON (NIL) -9 NIL 1333605 NIL) (-574 1332632 1332690 1332880 "INVLAPLA" 1333071 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-573 1322281 1324634 1327020 "INTTR" 1330296 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-572 1318625 1319367 1320231 "INTTOOLS" 1321466 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-571 1318211 1318302 1318419 "INTSLPE" 1318528 T INTSLPE (NIL) -7 NIL NIL NIL) (-570 1316206 1318134 1318193 "INTRVL" 1318198 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-569 1313808 1314320 1314895 "INTRF" 1315691 NIL INTRF (NIL T) -7 NIL NIL NIL) (-568 1313219 1313316 1313458 "INTRET" 1313706 NIL INTRET (NIL T) -7 NIL NIL NIL) (-567 1311216 1311605 1312075 "INTRAT" 1312827 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-566 1308444 1309027 1309653 "INTPM" 1310701 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-565 1305147 1305746 1306491 "INTPAF" 1307830 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-564 1300326 1301288 1302339 "INTPACK" 1304116 T INTPACK (NIL) -7 NIL NIL NIL) (-563 1297238 1300055 1300182 "INT" 1300219 T INT (NIL) -8 NIL NIL NIL) (-562 1296490 1296642 1296850 "INTHERTR" 1297080 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-561 1295929 1296009 1296197 "INTHERAL" 1296404 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-560 1293775 1294218 1294675 "INTHEORY" 1295492 T INTHEORY (NIL) -7 NIL NIL NIL) (-559 1285083 1286704 1288483 "INTG0" 1292127 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-558 1265656 1270446 1275256 "INTFTBL" 1280293 T INTFTBL (NIL) -8 NIL NIL NIL) (-557 1264905 1265043 1265216 "INTFACT" 1265515 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-556 1262290 1262736 1263300 "INTEF" 1264459 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-555 1260757 1261462 1261490 "INTDOM" 1261791 T INTDOM (NIL) -9 NIL 1261998 NIL) (-554 1260126 1260300 1260542 "INTDOM-" 1260547 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-553 1256621 1258510 1258564 "INTCAT" 1259363 NIL INTCAT (NIL T) -9 NIL 1259683 NIL) (-552 1256094 1256196 1256324 "INTBIT" 1256513 T INTBIT (NIL) -7 NIL NIL NIL) (-551 1254765 1254919 1255233 "INTALG" 1255939 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-550 1254222 1254312 1254482 "INTAF" 1254669 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-549 1247676 1254032 1254172 "INTABL" 1254177 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-548 1247136 1247549 1247577 "INT8" 1247582 T INT8 (NIL) -8 NIL NIL 1247590) (-547 1246595 1247008 1247036 "INT32" 1247041 T INT32 (NIL) -8 NIL NIL 1247049) (-546 1246054 1246467 1246495 "INT16" 1246500 T INT16 (NIL) -8 NIL NIL 1246508) (-545 1241069 1243743 1243771 "INS" 1244705 T INS (NIL) -9 NIL 1245370 NIL) (-544 1238309 1239080 1240054 "INS-" 1240127 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237084 1237311 1237609 "INPSIGN" 1238062 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1236202 1236319 1236516 "INPRODPF" 1236964 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1235096 1235213 1235450 "INPRODFF" 1236082 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1234096 1234248 1234508 "INNMFACT" 1234932 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1233293 1233390 1233578 "INMODGCD" 1233995 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1231802 1232046 1232370 "INFSP" 1233038 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1230986 1231103 1231286 "INFPROD0" 1231682 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1227868 1229051 1229566 "INFORM" 1230479 T INFORM (NIL) -8 NIL NIL NIL) (-535 1227478 1227538 1227636 "INFORM1" 1227803 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227001 1227090 1227204 "INFINITY" 1227384 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1226177 1226721 1226822 "INETCLTS" 1226920 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1224794 1225043 1225364 "INEP" 1225925 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224070 1224691 1224756 "INDE" 1224761 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1223634 1223702 1223819 "INCRMAPS" 1223997 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1222452 1222903 1223109 "INBFILE" 1223448 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1217763 1218688 1219632 "INBFF" 1221540 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1216671 1216940 1216968 "INBCON" 1217481 T INBCON (NIL) -9 NIL 1217747 NIL) (-526 1215923 1216146 1216422 "INBCON-" 1216427 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1215425 1215644 1215736 "INAST" 1215851 T INAST (NIL) -8 NIL NIL NIL) (-524 1214879 1215104 1215210 "IMPTAST" 1215339 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1211373 1214723 1214827 "IMATRIX" 1214832 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210085 1210208 1210523 "IMATQF" 1211229 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1208305 1208532 1208869 "IMATLIN" 1209841 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1202931 1208229 1208287 "ILIST" 1208292 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1200884 1202791 1202904 "IIARRAY2" 1202909 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1196317 1200795 1200859 "IFF" 1200864 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1195691 1195934 1196050 "IFAST" 1196221 T IFAST (NIL) -8 NIL NIL NIL) (-516 1190734 1194983 1195171 "IFARRAY" 1195548 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1189941 1190638 1190711 "IFAMON" 1190716 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1189525 1189590 1189644 "IEVALAB" 1189851 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1189200 1189268 1189428 "IEVALAB-" 1189433 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1188858 1189114 1189177 "IDPO" 1189182 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1188135 1188747 1188822 "IDPOAMS" 1188827 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1187469 1188024 1188099 "IDPOAM" 1188104 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1186554 1186804 1186857 "IDPC" 1187270 NIL IDPC (NIL T T) -9 NIL 1187419 NIL) (-508 1186050 1186446 1186519 "IDPAM" 1186524 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1185453 1185942 1186015 "IDPAG" 1186020 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1185221 1185368 1185418 "IDENT" 1185423 T IDENT (NIL) -8 NIL NIL NIL) (-505 1181476 1182324 1183219 "IDECOMP" 1184378 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1174350 1175399 1176446 "IDEAL" 1180512 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1173514 1173626 1173825 "ICDEN" 1174234 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1172613 1172994 1173141 "ICARD" 1173387 T ICARD (NIL) -8 NIL NIL NIL) (-501 1170673 1170986 1171391 "IBPTOOLS" 1172290 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1166307 1170293 1170406 "IBITS" 1170592 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163030 1163606 1164301 "IBATOOL" 1165724 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1160810 1161271 1161804 "IBACHIN" 1162565 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1158687 1160656 1160759 "IARRAY2" 1160764 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1154840 1158613 1158670 "IARRAY1" 1158675 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1148834 1153252 1153733 "IAN" 1154379 T IAN (NIL) -8 NIL NIL NIL) (-494 1148345 1148402 1148575 "IALGFACT" 1148771 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1147873 1147986 1148014 "HYPCAT" 1148221 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1147411 1147528 1147714 "HYPCAT-" 1147719 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147033 1147206 1147289 "HOSTNAME" 1147348 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1146878 1146915 1146956 "HOMOTOP" 1146961 NIL HOMOTOP (NIL T) -9 NIL 1146994 NIL) (-489 1143557 1144888 1144929 "HOAGG" 1145910 NIL HOAGG (NIL T) -9 NIL 1146589 NIL) (-488 1142151 1142550 1143076 "HOAGG-" 1143081 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136190 1141746 1141895 "HEXADEC" 1142022 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1134938 1135160 1135423 "HEUGCD" 1135967 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134041 1134775 1134905 "HELLFDIV" 1134910 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1132269 1133818 1133906 "HEAP" 1133985 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1131560 1131821 1131955 "HEADAST" 1132155 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1125480 1131475 1131537 "HDP" 1131542 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1119231 1125115 1125267 "HDMP" 1125381 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1118556 1118695 1118859 "HB" 1119087 T HB (NIL) -7 NIL NIL NIL) (-479 1112053 1118402 1118506 "HASHTBL" 1118511 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1111556 1111774 1111866 "HASAST" 1111981 T HASAST (NIL) -8 NIL NIL NIL) (-477 1109369 1111178 1111360 "HACKPI" 1111394 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105064 1109222 1109335 "GTSET" 1109340 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1098590 1104942 1105040 "GSTBL" 1105045 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1090903 1097621 1097886 "GSERIES" 1098381 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090070 1090461 1090489 "GROUP" 1090692 T GROUP (NIL) -9 NIL 1090826 NIL) (-472 1089436 1089595 1089846 "GROUP-" 1089851 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1087805 1088124 1088511 "GROEBSOL" 1089113 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1086745 1087007 1087058 "GRMOD" 1087587 NIL GRMOD (NIL T T) -9 NIL 1087755 NIL) (-469 1086513 1086549 1086677 "GRMOD-" 1086682 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1081839 1082867 1083867 "GRIMAGE" 1085533 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1080306 1080566 1080890 "GRDEF" 1081535 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1079750 1079866 1080007 "GRAY" 1080185 T GRAY (NIL) -7 NIL NIL NIL) (-465 1078963 1079343 1079394 "GRALG" 1079547 NIL GRALG (NIL T T) -9 NIL 1079640 NIL) (-464 1078624 1078697 1078860 "GRALG-" 1078865 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1075428 1078209 1078387 "GPOLSET" 1078531 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1074782 1074839 1075097 "GOSPER" 1075365 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1070541 1071220 1071746 "GMODPOL" 1074481 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1069546 1069730 1069968 "GHENSEL" 1070353 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1063597 1064440 1065467 "GENUPS" 1068630 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1063294 1063345 1063434 "GENUFACT" 1063540 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1062706 1062783 1062948 "GENPGCD" 1063212 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062180 1062215 1062428 "GENMFACT" 1062665 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1060748 1061003 1061310 "GENEEZ" 1061923 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1054661 1060359 1060521 "GDMP" 1060671 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044038 1048432 1049538 "GCNAALG" 1053644 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1042465 1043293 1043321 "GCDDOM" 1043576 T GCDDOM (NIL) -9 NIL 1043733 NIL) (-451 1041935 1042062 1042277 "GCDDOM-" 1042282 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1040607 1040792 1041096 "GB" 1041714 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029227 1031553 1033945 "GBINTERN" 1038298 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027064 1027356 1027777 "GBF" 1028902 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1025845 1026010 1026277 "GBEUCLID" 1026880 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025194 1025319 1025468 "GAUSSFAC" 1025716 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1023561 1023863 1024177 "GALUTIL" 1024913 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1021869 1022143 1022467 "GALPOLYU" 1023288 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019234 1019524 1019931 "GALFACTU" 1021566 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011040 1012539 1014147 "GALFACT" 1017666 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1008428 1009086 1009114 "FVFUN" 1010270 T FVFUN (NIL) -9 NIL 1010990 NIL) (-440 1007694 1007876 1007904 "FVC" 1008195 T FVC (NIL) -9 NIL 1008378 NIL) (-439 1007364 1007519 1007587 "FUNDESC" 1007646 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007006 1007161 1007242 "FUNCTION" 1007316 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1004777 1005328 1005794 "FT" 1006560 T FT (NIL) -8 NIL NIL NIL) (-436 1003595 1004078 1004281 "FTEM" 1004594 T FTEM (NIL) -8 NIL NIL NIL) (-435 1001851 1002140 1002544 "FSUPFACT" 1003286 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000248 1000537 1000869 "FST" 1001539 T FST (NIL) -8 NIL NIL NIL) (-433 999419 999525 999720 "FSRED" 1000130 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998098 998353 998707 "FSPRMELT" 999134 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995183 995621 996120 "FSPECF" 997661 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977243 985686 985726 "FS" 989574 NIL FS (NIL T) -9 NIL 991863 NIL) (-429 965893 968883 972939 "FS-" 973236 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 965407 965461 965638 "FSINT" 965834 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 963734 964400 964703 "FSERIES" 965186 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 962748 962864 963095 "FSCINT" 963614 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 958982 961692 961733 "FSAGG" 962103 NIL FSAGG (NIL T) -9 NIL 962362 NIL) (-424 956744 957345 958141 "FSAGG-" 958236 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 955786 955929 956156 "FSAGG2" 956597 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 953441 953720 954274 "FS2UPS" 955504 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953023 953066 953221 "FS2" 953392 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 951880 952051 952360 "FS2EXPXP" 952848 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 951306 951421 951573 "FRUTIL" 951760 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 942761 946801 948159 "FR" 949980 NIL FR (NIL T) -8 NIL NIL NIL) (-417 937836 940479 940519 "FRNAALG" 941915 NIL FRNAALG (NIL T) -9 NIL 942522 NIL) (-416 933514 934585 935860 "FRNAALG-" 936610 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933152 933195 933322 "FRNAAF2" 933465 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 931559 932006 932301 "FRMOD" 932964 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 929338 929942 930259 "FRIDEAL" 931350 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 928533 928620 928909 "FRIDEAL2" 929245 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 927666 928080 928121 "FRETRCT" 928126 NIL FRETRCT (NIL T) -9 NIL 928302 NIL) (-410 926778 927009 927360 "FRETRCT-" 927365 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 923990 925166 925225 "FRAMALG" 926107 NIL FRAMALG (NIL T T) -9 NIL 926399 NIL) (-408 922124 922579 923209 "FRAMALG-" 923432 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916082 921599 921875 "FRAC" 921880 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 915718 915775 915882 "FRAC2" 916019 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 915354 915411 915518 "FR2" 915655 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910027 912879 912907 "FPS" 914026 T FPS (NIL) -9 NIL 914583 NIL) (-403 909476 909585 909749 "FPS-" 909895 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 906930 908565 908593 "FPC" 908818 T FPC (NIL) -9 NIL 908960 NIL) (-401 906723 906763 906860 "FPC-" 906865 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 905601 906211 906252 "FPATMAB" 906257 NIL FPATMAB (NIL T) -9 NIL 906409 NIL) (-399 903301 903777 904203 "FPARFRAC" 905238 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 898695 899193 899875 "FORTRAN" 902733 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 896411 896911 897450 "FORT" 898176 T FORT (NIL) -7 NIL NIL NIL) (-396 894087 894649 894677 "FORTFN" 895737 T FORTFN (NIL) -9 NIL 896361 NIL) (-395 893851 893901 893929 "FORTCAT" 893988 T FORTCAT (NIL) -9 NIL 894050 NIL) (-394 891984 892467 892857 "FORMULA" 893481 T FORMULA (NIL) -8 NIL NIL NIL) (-393 891772 891802 891871 "FORMULA1" 891948 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891295 891347 891520 "FORDER" 891714 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 890391 890555 890748 "FOP" 891122 T FOP (NIL) -7 NIL NIL NIL) (-390 888999 889671 889845 "FNLA" 890273 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 887754 888143 888171 "FNCAT" 888631 T FNCAT (NIL) -9 NIL 888891 NIL) (-388 887320 887713 887741 "FNAME" 887746 T FNAME (NIL) -8 NIL NIL NIL) (-387 885983 886912 886940 "FMTC" 886945 T FMTC (NIL) -9 NIL 886981 NIL) (-386 882345 883506 884135 "FMONOID" 885387 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 881564 882087 882236 "FM" 882241 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 878988 879634 879662 "FMFUN" 880806 T FMFUN (NIL) -9 NIL 881514 NIL) (-383 878257 878438 878466 "FMC" 878756 T FMC (NIL) -9 NIL 878938 NIL) (-382 875451 876285 876339 "FMCAT" 877534 NIL FMCAT (NIL T T) -9 NIL 878029 NIL) (-381 874344 875217 875317 "FM1" 875396 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872118 872534 873028 "FLOATRP" 873895 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 865742 869847 870468 "FLOAT" 871517 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863180 863680 864258 "FLOATCP" 865209 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 861989 862793 862834 "FLINEXP" 862839 NIL FLINEXP (NIL T) -9 NIL 862932 NIL) (-376 861143 861378 861706 "FLINEXP-" 861711 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860219 860363 860587 "FLASORT" 860995 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 857436 858278 858330 "FLALG" 859557 NIL FLALG (NIL T T) -9 NIL 860024 NIL) (-373 851220 854922 854963 "FLAGG" 856225 NIL FLAGG (NIL T) -9 NIL 856877 NIL) (-372 849946 850285 850775 "FLAGG-" 850780 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 848988 849131 849358 "FLAGG2" 849799 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 845963 846937 846996 "FINRALG" 848124 NIL FINRALG (NIL T T) -9 NIL 848632 NIL) (-369 845123 845352 845691 "FINRALG-" 845696 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 844529 844742 844770 "FINITE" 844966 T FINITE (NIL) -9 NIL 845073 NIL) (-367 836987 839148 839188 "FINAALG" 842855 NIL FINAALG (NIL T) -9 NIL 844308 NIL) (-366 832328 833369 834513 "FINAALG-" 835892 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 831723 832083 832186 "FILE" 832258 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830407 830719 830773 "FILECAT" 831457 NIL FILECAT (NIL T T) -9 NIL 831673 NIL) (-363 828275 829769 829797 "FIELD" 829837 T FIELD (NIL) -9 NIL 829917 NIL) (-362 826895 827280 827791 "FIELD-" 827796 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 824773 825530 825877 "FGROUP" 826581 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 823863 824027 824247 "FGLMICPK" 824605 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 819730 823788 823845 "FFX" 823850 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819331 819392 819527 "FFSLPE" 819663 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815324 816103 816899 "FFPOLY" 818567 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 814828 814864 815073 "FFPOLY2" 815282 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 810714 814747 814810 "FFP" 814815 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806147 810625 810689 "FF" 810694 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801308 805490 805680 "FFNBX" 806001 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796282 800443 800701 "FFNBP" 801162 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 790950 795566 795777 "FFNB" 796115 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 789782 789980 790295 "FFINTBAS" 790747 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786010 788189 788217 "FFIELDC" 788837 T FFIELDC (NIL) -9 NIL 789213 NIL) (-348 784673 785043 785540 "FFIELDC-" 785545 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784243 784288 784412 "FFHOM" 784615 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 781941 782425 782942 "FFF" 783758 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 777594 781683 781784 "FFCGX" 781884 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773261 777326 777433 "FFCGP" 777537 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768479 772988 773096 "FFCG" 773197 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750312 759350 759436 "FFCAT" 764601 NIL FFCAT (NIL T T T) -9 NIL 766052 NIL) (-341 745510 746557 747871 "FFCAT-" 749101 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 744921 744964 745199 "FFCAT2" 745461 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734133 737893 739113 "FEXPR" 743773 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733133 733568 733609 "FEVALAB" 733693 NIL FEVALAB (NIL T) -9 NIL 733954 NIL) (-337 732292 732502 732840 "FEVALAB-" 732845 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 730885 731675 731878 "FDIV" 732191 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 727951 728666 728781 "FDIVCAT" 730349 NIL FDIVCAT (NIL T T T T) -9 NIL 730786 NIL) (-334 727713 727740 727910 "FDIVCAT-" 727915 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 726933 727020 727297 "FDIV2" 727620 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 725619 725878 726167 "FCPAK1" 726664 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 724747 725119 725260 "FCOMP" 725510 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708484 711897 715435 "FC" 721229 T FC (NIL) -8 NIL NIL NIL) (-329 701063 705048 705088 "FAXF" 706890 NIL FAXF (NIL T) -9 NIL 707582 NIL) (-328 698342 698997 699822 "FAXF-" 700287 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693442 697718 697894 "FARRAY" 698199 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 688695 690727 690780 "FAMR" 691803 NIL FAMR (NIL T T) -9 NIL 692263 NIL) (-325 687585 687887 688322 "FAMR-" 688327 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 686781 687507 687560 "FAMONOID" 687565 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 684593 685277 685330 "FAMONC" 686271 NIL FAMONC (NIL T T) -9 NIL 686657 NIL) (-322 683285 684347 684484 "FAGROUP" 684489 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681080 681399 681802 "FACUTIL" 682966 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680179 680364 680586 "FACTFUNC" 680890 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672584 679430 679642 "EXPUPXS" 680035 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670067 670607 671193 "EXPRTUBE" 672018 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666261 666853 667590 "EXPRODE" 669406 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 651635 664916 665344 "EXPR" 665865 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646042 646629 647442 "EXPR2UPS" 650933 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 645678 645735 645842 "EXPR2" 645979 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637083 644810 645107 "EXPEXPAN" 645515 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 636910 637040 637069 "EXIT" 637074 T EXIT (NIL) -8 NIL NIL NIL) (-311 636417 636634 636725 "EXITAST" 636839 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636044 636106 636219 "EVALCYC" 636349 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635585 635703 635744 "EVALAB" 635914 NIL EVALAB (NIL T) -9 NIL 636018 NIL) (-308 635066 635188 635409 "EVALAB-" 635414 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632534 633802 633830 "EUCDOM" 634385 T EUCDOM (NIL) -9 NIL 634735 NIL) (-306 630939 631381 631971 "EUCDOM-" 631976 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618479 621237 623987 "ESTOOLS" 628209 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618111 618168 618277 "ESTOOLS2" 618416 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 617862 617904 617984 "ESTOOLS1" 618063 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 611767 613495 613523 "ES" 616291 T ES (NIL) -9 NIL 617700 NIL) (-301 606715 608001 609818 "ES-" 609982 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603090 603850 604630 "ESCONT" 605955 T ESCONT (NIL) -7 NIL NIL NIL) (-299 602835 602867 602949 "ESCONT1" 603052 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602510 602560 602660 "ES2" 602779 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602140 602198 602307 "ES1" 602446 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601356 601485 601661 "ERROR" 601984 T ERROR (NIL) -7 NIL NIL NIL) (-295 594859 601215 601306 "EQTBL" 601311 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587416 590173 591622 "EQ" 593443 NIL -3299 (NIL T) -8 NIL NIL NIL) (-293 587048 587105 587214 "EQ2" 587353 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582340 583386 584479 "EP" 585987 NIL EP (NIL T) -7 NIL NIL NIL) (-291 580922 581223 581540 "ENV" 582043 T ENV (NIL) -8 NIL NIL NIL) (-290 580101 580621 580649 "ENTIRER" 580654 T ENTIRER (NIL) -9 NIL 580700 NIL) (-289 576603 578056 578426 "EMR" 579900 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 575747 575932 575986 "ELTAGG" 576366 NIL ELTAGG (NIL T T) -9 NIL 576577 NIL) (-287 575466 575528 575669 "ELTAGG-" 575674 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575255 575284 575338 "ELTAB" 575422 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574381 574527 574726 "ELFUTS" 575106 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574123 574179 574207 "ELEMFUN" 574312 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 573993 574014 574082 "ELEMFUN-" 574087 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 568884 572093 572134 "ELAGG" 573074 NIL ELAGG (NIL T) -9 NIL 573537 NIL) (-281 567169 567603 568266 "ELAGG-" 568271 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 565826 566106 566401 "ELABEXPR" 566894 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 558692 560493 561320 "EFUPXS" 565102 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552142 553943 554753 "EFULS" 557968 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549564 549922 550401 "EFSTRUC" 551774 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538636 540201 541761 "EF" 548079 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 537737 538121 538270 "EAB" 538507 T EAB (NIL) -8 NIL NIL NIL) (-274 536946 537696 537724 "E04UCFA" 537729 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536155 536905 536933 "E04NAFA" 536938 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535364 536114 536142 "E04MBFA" 536147 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534573 535323 535351 "E04JAFA" 535356 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 533784 534532 534560 "E04GCFA" 534565 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 532995 533743 533771 "E04FDFA" 533776 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532204 532954 532982 "E04DGFA" 532987 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526382 527729 529093 "E04AGNT" 530860 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525088 525568 525608 "DVARCAT" 526083 NIL DVARCAT (NIL T) -9 NIL 526282 NIL) (-265 524292 524504 524818 "DVARCAT-" 524823 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517192 524091 524220 "DSMP" 524225 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512002 513137 514205 "DROPT" 516144 T DROPT (NIL) -8 NIL NIL NIL) (-262 511667 511726 511824 "DROPT1" 511937 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 506782 507908 509045 "DROPT0" 510550 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505127 505452 505838 "DRAWPT" 506416 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 499714 500637 501716 "DRAW" 504101 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499347 499400 499518 "DRAWHACK" 499655 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498078 498347 498638 "DRAWCX" 499076 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497594 497662 497813 "DRAWCURV" 498004 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488065 490024 492139 "DRAWCFUN" 495499 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 484878 486760 486801 "DQAGG" 487430 NIL DQAGG (NIL T) -9 NIL 487703 NIL) (-253 473157 479856 479939 "DPOLCAT" 481791 NIL DPOLCAT (NIL T T T T) -9 NIL 482336 NIL) (-252 467996 469342 471300 "DPOLCAT-" 471305 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461151 467857 467955 "DPMO" 467960 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454209 460931 461098 "DPMM" 461103 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 453841 454128 454176 "DOMCTOR" 454181 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453136 453363 453500 "DOMAIN" 453724 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 446887 452771 452923 "DMP" 453037 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446487 446543 446687 "DLP" 446825 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440357 445814 446004 "DLIST" 446329 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437201 439210 439251 "DLAGG" 439801 NIL DLAGG (NIL T) -9 NIL 440031 NIL) (-243 436014 436644 436672 "DIVRING" 436764 T DIVRING (NIL) -9 NIL 436847 NIL) (-242 435251 435441 435741 "DIVRING-" 435746 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433353 433710 434116 "DISPLAY" 434865 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427295 433267 433330 "DIRPROD" 433335 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426143 426346 426611 "DIRPROD2" 427088 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415406 421358 421411 "DIRPCAT" 421821 NIL DIRPCAT (NIL NIL T) -9 NIL 422661 NIL) (-237 412732 413374 414255 "DIRPCAT-" 414592 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412019 412179 412365 "DIOSP" 412566 T DIOSP (NIL) -7 NIL NIL NIL) (-235 408721 410931 410972 "DIOPS" 411406 NIL DIOPS (NIL T) -9 NIL 411635 NIL) (-234 408270 408384 408575 "DIOPS-" 408580 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407162 407756 407784 "DIFRING" 407971 T DIFRING (NIL) -9 NIL 408081 NIL) (-232 406808 406885 407037 "DIFRING-" 407042 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404613 405851 405892 "DIFEXT" 406255 NIL DIFEXT (NIL T) -9 NIL 406549 NIL) (-230 402898 403326 403992 "DIFEXT-" 403997 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400220 402430 402471 "DIAGG" 402476 NIL DIAGG (NIL T) -9 NIL 402496 NIL) (-228 399604 399761 400013 "DIAGG-" 400018 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395069 398563 398840 "DHMATRIX" 399373 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390681 391590 392600 "DFSFUN" 394079 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 385797 389612 389924 "DFLOAT" 390389 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384025 384306 384702 "DFINTTLS" 385505 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381090 382046 382446 "DERHAM" 383691 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 378939 380865 380954 "DEQUEUE" 381034 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378154 378287 378483 "DEGRED" 378801 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374549 375294 376147 "DEFINTRF" 377382 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372076 372545 373144 "DEFINTEF" 374068 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371453 371696 371811 "DEFAST" 371981 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365492 371048 371197 "DECIMAL" 371324 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363004 363462 363968 "DDFACT" 365036 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362600 362643 362794 "DBLRESP" 362955 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360499 360833 361193 "DBASE" 362367 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359768 359979 360125 "DATAARY" 360398 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 358901 359727 359755 "D03FAFA" 359760 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358035 358860 358888 "D03EEFA" 358893 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 355985 356451 356940 "D03AGNT" 357566 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355301 355944 355972 "D02EJFA" 355977 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354617 355260 355288 "D02CJFA" 355293 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 353933 354576 354604 "D02BHFA" 354609 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353249 353892 353920 "D02BBFA" 353925 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346447 348035 349641 "D02AGNT" 351663 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344216 344738 345284 "D01WGTS" 345921 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343311 344175 344203 "D01TRNS" 344208 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342406 343270 343298 "D01GBFA" 343303 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341501 342365 342393 "D01FCFA" 342398 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340596 341460 341488 "D01ASFA" 341493 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339691 340555 340583 "D01AQFA" 340588 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338786 339650 339678 "D01APFA" 339683 T D01APFA (NIL) -8 NIL NIL NIL) (-197 337881 338745 338773 "D01ANFA" 338778 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 336976 337840 337868 "D01AMFA" 337873 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336071 336935 336963 "D01ALFA" 336968 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335166 336030 336058 "D01AKFA" 336063 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334261 335125 335153 "D01AJFA" 335158 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327558 329109 330670 "D01AGNT" 332720 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 326895 327023 327175 "CYCLOTOM" 327426 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323630 324343 325070 "CYCLES" 326188 T CYCLES (NIL) -7 NIL NIL NIL) (-189 322942 323076 323247 "CVMP" 323491 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320713 320971 321347 "CTRIGMNP" 322670 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320204 320504 320578 "CTOR" 320659 T CTOR (NIL) -8 NIL NIL NIL) (-186 319740 319935 320036 "CTORKIND" 320123 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319088 319347 319375 "CTORCAT" 319557 T CTORCAT (NIL) -9 NIL 319670 NIL) (-184 318686 318797 318956 "CTORCAT-" 318961 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318202 318389 318487 "CTORCALL" 318608 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317576 317675 317828 "CSTTOOLS" 318099 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 313375 314032 314790 "CRFP" 316888 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 312877 313096 313188 "CRCEAST" 313303 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 311924 312109 312337 "CRAPACK" 312681 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311308 311409 311613 "CPMATCH" 311800 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311033 311061 311167 "CPIMA" 311274 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 307397 308069 308787 "COORDSYS" 310368 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 306781 306910 307060 "CONTOUR" 307267 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302707 304784 305276 "CONTFRAC" 306321 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 302587 302608 302636 "CONDUIT" 302673 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301760 302280 302308 "COMRING" 302313 T COMRING (NIL) -9 NIL 302365 NIL) (-171 300841 301118 301302 "COMPPROP" 301596 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 300502 300537 300665 "COMPLPAT" 300800 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 290559 300311 300420 "COMPLEX" 300425 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 290195 290252 290359 "COMPLEX2" 290496 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 289913 289948 290046 "COMPFACT" 290154 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274075 284295 284335 "COMPCAT" 285339 NIL COMPCAT (NIL T) -9 NIL 286735 NIL) (-165 263591 266514 270141 "COMPCAT-" 270497 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 263320 263348 263451 "COMMUPC" 263557 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263115 263148 263207 "COMMONOP" 263281 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 262698 262866 262953 "COMM" 263048 T COMM (NIL) -8 NIL NIL NIL) (-161 262302 262502 262577 "COMMAAST" 262643 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 261551 261745 261773 "COMBOPC" 262111 T COMBOPC (NIL) -9 NIL 262286 NIL) (-159 260447 260657 260899 "COMBINAT" 261341 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 256645 257218 257858 "COMBF" 259869 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 255431 255761 255996 "COLOR" 256430 T COLOR (NIL) -8 NIL NIL NIL) (-156 254934 255152 255244 "COLONAST" 255359 T COLONAST (NIL) -8 NIL NIL NIL) (-155 254574 254621 254746 "CMPLXRT" 254881 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254049 254274 254373 "CLLCTAST" 254495 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 249551 250579 251659 "CLIP" 252989 T CLIP (NIL) -7 NIL NIL NIL) (-152 247933 248657 248896 "CLIF" 249378 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244155 246079 246120 "CLAGG" 247049 NIL CLAGG (NIL T) -9 NIL 247585 NIL) (-150 242577 243034 243617 "CLAGG-" 243622 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242121 242206 242346 "CINTSLPE" 242486 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239622 240093 240641 "CHVAR" 241649 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 238865 239385 239413 "CHARZ" 239418 T CHARZ (NIL) -9 NIL 239433 NIL) (-146 238619 238659 238737 "CHARPOL" 238819 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237746 238299 238327 "CHARNZ" 238374 T CHARNZ (NIL) -9 NIL 238430 NIL) (-144 235735 236436 236771 "CHAR" 237431 T CHAR (NIL) -8 NIL NIL NIL) (-143 235461 235522 235550 "CFCAT" 235661 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234706 234817 234999 "CDEN" 235345 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230698 233859 234139 "CCLASS" 234446 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230005 230148 230311 "CATEGORY" 230555 T -10 (NIL) -8 NIL NIL NIL) (-139 229637 229924 229972 "CATCTOR" 229977 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229111 229337 229436 "CATAST" 229558 T CATAST (NIL) -8 NIL NIL NIL) (-137 228614 228832 228924 "CASEAST" 229039 T CASEAST (NIL) -8 NIL NIL NIL) (-136 223666 224643 225396 "CARTEN" 227917 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 222774 222922 223143 "CARTEN2" 223513 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221116 221924 222181 "CARD" 222537 T CARD (NIL) -8 NIL NIL NIL) (-133 220719 220920 220995 "CAPSLAST" 221061 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220091 220419 220447 "CACHSET" 220579 T CACHSET (NIL) -9 NIL 220656 NIL) (-131 219587 219883 219911 "CABMON" 219961 T CABMON (NIL) -9 NIL 220017 NIL) (-130 219087 219291 219401 "BYTEORD" 219497 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218110 218633 218769 "BYTE" 218932 T BYTE (NIL) -8 NIL NIL 219048) (-128 213519 217578 217741 "BYTEBUF" 217967 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211076 213211 213318 "BTREE" 213445 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208574 210724 210846 "BTOURN" 210986 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205991 208044 208085 "BTCAT" 208153 NIL BTCAT (NIL T) -9 NIL 208230 NIL) (-124 205658 205738 205887 "BTCAT-" 205892 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200950 204801 204829 "BTAGG" 205051 T BTAGG (NIL) -9 NIL 205212 NIL) (-122 200440 200565 200771 "BTAGG-" 200776 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197484 199718 199933 "BSTREE" 200257 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196622 196748 196932 "BRILL" 197340 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193321 195348 195389 "BRAGG" 196038 NIL BRAGG (NIL T) -9 NIL 196296 NIL) (-118 191850 192256 192811 "BRAGG-" 192816 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185114 191196 191380 "BPADICRT" 191698 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183464 185051 185096 "BPADIC" 185101 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183162 183192 183306 "BOUNDZRO" 183428 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178677 179768 180635 "BOP" 182315 T BOP (NIL) -8 NIL NIL NIL) (-113 176298 176742 177262 "BOP1" 178190 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175000 175722 175915 "BOOLEAN" 176125 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174362 174740 174794 "BMODULE" 174799 NIL BMODULE (NIL T T) -9 NIL 174864 NIL) (-110 170192 174160 174233 "BITS" 174309 T BITS (NIL) -8 NIL NIL NIL) (-109 169604 169726 169868 "BINDING" 170070 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169201 169349 "BINARY" 169476 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127098 127712 127823 "ASP24" 127934 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126175 126900 127012 "ASP20" 127017 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125263 125876 125986 "ASP1" 126096 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124207 124937 125056 "ASP19" 125175 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 123944 124011 124087 "ASP12" 124162 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122796 123543 123687 "ASP10" 123831 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120695 122640 122731 "ARRAY2" 122736 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116511 120343 120457 "ARRAY1" 120612 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115543 115716 115937 "ARRAY12" 116334 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109902 111773 111848 "ARR2CAT" 114478 NIL ARR2CAT (NIL T T T) -9 NIL 115236 NIL) (-56 107336 108080 109034 "ARR2CAT-" 109039 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106930 107163 107242 "ARITY" 107275 T ARITY (NIL) -8 NIL NIL NIL) (-54 105678 105830 106136 "APPRULE" 106766 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105329 105377 105496 "APPLYORE" 105624 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104303 104594 104789 "ANY" 105152 T ANY (NIL) -8 NIL NIL NIL) (-51 103581 103704 103861 "ANY1" 104177 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101146 102018 102345 "ANTISYM" 103305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100661 100850 100947 "ANON" 101067 T ANON (NIL) -8 NIL NIL NIL) (-48 94793 99200 99654 "AN" 100225 T AN (NIL) -8 NIL NIL NIL) (-47 91049 92403 92454 "AMR" 93202 NIL AMR (NIL T T) -9 NIL 93802 NIL) (-46 90161 90382 90745 "AMR-" 90750 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74711 90078 90139 "ALIST" 90144 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71548 74305 74474 "ALGSC" 74629 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68104 68658 69265 "ALGPKG" 70988 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67381 67482 67666 "ALGMFACT" 67990 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63120 63805 64460 "ALGMANIP" 66904 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437 NIL) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856 NIL) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283 NIL) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332 NIL) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908 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 3195589 3195594 3195599 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3195574 3195579 3195584 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3195559 3195564 3195569 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3195544 3195549 3195554 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1285 3194721 3195419 3195496 "ZMOD" 3195501 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1284 3193831 3193995 3194204 "ZLINDEP" 3194553 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1283 3183135 3184899 3186871 "ZDSOLVE" 3191961 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1282 3182381 3182522 3182711 "YSTREAM" 3182981 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1281 3180192 3181682 3181886 "XRPOLY" 3182224 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1280 3176780 3178063 3178638 "XPR" 3179664 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1279 3174536 3176111 3176315 "XPOLY" 3176611 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1278 3172327 3173661 3173716 "XPOLYC" 3174004 NIL XPOLYC (NIL T T) -9 NIL 3174117 NIL) (-1277 3168745 3170844 3171232 "XPBWPOLY" 3171985 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1276 3164656 3166908 3166950 "XF" 3167571 NIL XF (NIL T) -9 NIL 3167971 NIL) (-1275 3164277 3164365 3164534 "XF-" 3164539 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1274 3159611 3160866 3160921 "XFALG" 3163093 NIL XFALG (NIL T T) -9 NIL 3163882 NIL) (-1273 3158744 3158848 3159053 "XEXPPKG" 3159503 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1272 3156888 3158594 3158690 "XDPOLY" 3158695 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1271 3155833 3156399 3156442 "XALG" 3156447 NIL XALG (NIL T) -9 NIL 3156558 NIL) (-1270 3149302 3153810 3154304 "WUTSET" 3155425 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1269 3147593 3148354 3148677 "WP" 3149113 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1268 3147222 3147415 3147485 "WHILEAST" 3147545 T WHILEAST (NIL) -8 NIL NIL NIL) (-1267 3146721 3146939 3147033 "WHEREAST" 3147150 T WHEREAST (NIL) -8 NIL NIL NIL) (-1266 3145607 3145805 3146100 "WFFINTBS" 3146518 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1265 3143511 3143938 3144400 "WEIER" 3145179 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1264 3142658 3143082 3143124 "VSPACE" 3143260 NIL VSPACE (NIL T) -9 NIL 3143334 NIL) (-1263 3142496 3142523 3142614 "VSPACE-" 3142619 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1262 3142304 3142347 3142415 "VOID" 3142450 T VOID (NIL) -8 NIL NIL NIL) (-1261 3140440 3140799 3141205 "VIEW" 3141920 T VIEW (NIL) -7 NIL NIL NIL) (-1260 3136865 3137503 3138240 "VIEWDEF" 3139725 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1259 3126201 3128413 3130586 "VIEW3D" 3134714 T VIEW3D (NIL) -8 NIL NIL NIL) (-1258 3118483 3120112 3121691 "VIEW2D" 3124644 T VIEW2D (NIL) -8 NIL NIL NIL) (-1257 3113887 3118253 3118345 "VECTOR" 3118426 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1256 3112464 3112723 3113041 "VECTOR2" 3113617 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1255 3105991 3110248 3110291 "VECTCAT" 3111284 NIL VECTCAT (NIL T) -9 NIL 3111870 NIL) (-1254 3105005 3105259 3105649 "VECTCAT-" 3105654 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1253 3104486 3104656 3104776 "VARIABLE" 3104920 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1252 3104419 3104424 3104454 "UTYPE" 3104459 T UTYPE (NIL) -9 NIL NIL NIL) (-1251 3103249 3103403 3103665 "UTSODETL" 3104245 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1250 3100689 3101149 3101673 "UTSODE" 3102790 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1249 3092565 3098315 3098804 "UTS" 3100258 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3083808 3089132 3089175 "UTSCAT" 3090287 NIL UTSCAT (NIL T) -9 NIL 3091044 NIL) (-1247 3081163 3081878 3082867 "UTSCAT-" 3082872 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1246 3080790 3080833 3080966 "UTS2" 3081114 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1245 3075063 3077628 3077671 "URAGG" 3079741 NIL URAGG (NIL T) -9 NIL 3080464 NIL) (-1244 3072002 3072865 3073988 "URAGG-" 3073993 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1243 3067726 3070616 3071088 "UPXSSING" 3071666 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1242 3059828 3066973 3067246 "UPXS" 3067511 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1241 3052941 3059732 3059804 "UPXSCONS" 3059809 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1240 3043186 3049936 3049998 "UPXSCCA" 3050572 NIL UPXSCCA (NIL T T) -9 NIL 3050805 NIL) (-1239 3042824 3042909 3043083 "UPXSCCA-" 3043088 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1238 3032922 3039445 3039488 "UPXSCAT" 3040136 NIL UPXSCAT (NIL T) -9 NIL 3040744 NIL) (-1237 3032352 3032431 3032610 "UPXS2" 3032837 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1236 3031006 3031259 3031610 "UPSQFREE" 3032095 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1235 3024794 3027808 3027863 "UPSCAT" 3029024 NIL UPSCAT (NIL T T) -9 NIL 3029798 NIL) (-1234 3023998 3024205 3024532 "UPSCAT-" 3024537 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1233 3009848 3017846 3017889 "UPOLYC" 3019990 NIL UPOLYC (NIL T) -9 NIL 3021211 NIL) (-1232 3001177 3003602 3006749 "UPOLYC-" 3006754 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1231 3000804 3000847 3000980 "UPOLYC2" 3001128 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1230 2992378 3000487 3000616 "UP" 3000723 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1229 2991717 2991824 2991988 "UPMP" 2992267 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1228 2991270 2991351 2991490 "UPDIVP" 2991630 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1227 2989838 2990087 2990403 "UPDECOMP" 2991019 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1226 2989073 2989185 2989370 "UPCDEN" 2989722 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1225 2988592 2988661 2988810 "UP2" 2988998 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1224 2987109 2987796 2988073 "UNISEG" 2988350 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1223 2986324 2986451 2986656 "UNISEG2" 2986952 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1222 2985384 2985564 2985790 "UNIFACT" 2986140 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1221 2969351 2984561 2984812 "ULS" 2985191 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1220 2957391 2969255 2969327 "ULSCONS" 2969332 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1219 2940007 2951949 2952011 "ULSCCAT" 2952649 NIL ULSCCAT (NIL T T) -9 NIL 2952937 NIL) (-1218 2939057 2939302 2939690 "ULSCCAT-" 2939695 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1217 2928932 2935369 2935412 "ULSCAT" 2936275 NIL ULSCAT (NIL T) -9 NIL 2937005 NIL) (-1216 2928362 2928441 2928620 "ULS2" 2928847 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1215 2927499 2927974 2928075 "UINT8" 2928186 T UINT8 (NIL) -8 NIL NIL 2928265) (-1214 2926635 2927110 2927211 "UINT32" 2927322 T UINT32 (NIL) -8 NIL NIL 2927401) (-1213 2925771 2926246 2926347 "UINT16" 2926458 T UINT16 (NIL) -8 NIL NIL 2926537) (-1212 2924174 2925097 2925127 "UFD" 2925339 T UFD (NIL) -9 NIL 2925453 NIL) (-1211 2923968 2924014 2924109 "UFD-" 2924114 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1210 2923050 2923233 2923449 "UDVO" 2923774 T UDVO (NIL) -7 NIL NIL NIL) (-1209 2920866 2921275 2921746 "UDPO" 2922614 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1208 2920799 2920804 2920834 "TYPE" 2920839 T TYPE (NIL) -9 NIL NIL NIL) (-1207 2920586 2920754 2920785 "TYPEAST" 2920790 T TYPEAST (NIL) -8 NIL NIL NIL) (-1206 2919557 2919759 2919999 "TWOFACT" 2920380 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1205 2918629 2918966 2919201 "TUPLE" 2919357 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1204 2916320 2916839 2917378 "TUBETOOL" 2918112 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1203 2915169 2915374 2915615 "TUBE" 2916113 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1202 2909933 2914141 2914424 "TS" 2914921 NIL TS (NIL T) -8 NIL NIL NIL) (-1201 2898600 2902692 2902789 "TSETCAT" 2908058 NIL TSETCAT (NIL T T T T) -9 NIL 2909589 NIL) (-1200 2893335 2894932 2896823 "TSETCAT-" 2896828 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1199 2887598 2888444 2889386 "TRMANIP" 2892471 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1198 2887039 2887102 2887265 "TRIMAT" 2887530 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1197 2884835 2885072 2885436 "TRIGMNIP" 2886788 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1196 2884355 2884468 2884498 "TRIGCAT" 2884711 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1195 2884024 2884103 2884244 "TRIGCAT-" 2884249 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1194 2880921 2882882 2883163 "TREE" 2883778 NIL TREE (NIL T) -8 NIL NIL NIL) (-1193 2880195 2880723 2880753 "TRANFUN" 2880788 T TRANFUN (NIL) -9 NIL 2880854 NIL) (-1192 2879474 2879665 2879945 "TRANFUN-" 2879950 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1191 2879278 2879310 2879371 "TOPSP" 2879435 T TOPSP (NIL) -7 NIL NIL NIL) (-1190 2878626 2878741 2878895 "TOOLSIGN" 2879159 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1189 2877287 2877803 2878042 "TEXTFILE" 2878409 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1188 2875226 2875740 2876169 "TEX" 2876880 T TEX (NIL) -8 NIL NIL NIL) (-1187 2875007 2875038 2875110 "TEX1" 2875189 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1186 2874655 2874718 2874808 "TEMUTL" 2874939 T TEMUTL (NIL) -7 NIL NIL NIL) (-1185 2872809 2873089 2873414 "TBCMPPK" 2874378 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1184 2864697 2870969 2871025 "TBAGG" 2871425 NIL TBAGG (NIL T T) -9 NIL 2871636 NIL) (-1183 2859767 2861255 2863009 "TBAGG-" 2863014 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1182 2859151 2859258 2859403 "TANEXP" 2859656 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1181 2852652 2859008 2859101 "TABLE" 2859106 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1180 2852064 2852163 2852301 "TABLEAU" 2852549 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1179 2846672 2847892 2849140 "TABLBUMP" 2850850 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1178 2845894 2846041 2846222 "SYSTEM" 2846513 T SYSTEM (NIL) -8 NIL NIL NIL) (-1177 2842357 2843052 2843835 "SYSSOLP" 2845145 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1176 2841414 2841881 2841994 "SYSNNI" 2842180 NIL SYSNNI (NIL NIL) -8 NIL NIL 2842259) (-1175 2840867 2841272 2841314 "SYSINT" 2841319 NIL SYSINT (NIL NIL) -8 NIL NIL 2841327) (-1174 2837201 2838128 2838844 "SYNTAX" 2840173 T SYNTAX (NIL) -8 NIL NIL NIL) (-1173 2834359 2834961 2835593 "SYMTAB" 2836591 T SYMTAB (NIL) -8 NIL NIL NIL) (-1172 2829608 2830510 2831493 "SYMS" 2833398 T SYMS (NIL) -8 NIL NIL NIL) (-1171 2826879 2829066 2829296 "SYMPOLY" 2829413 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1170 2826396 2826471 2826594 "SYMFUNC" 2826791 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1169 2822448 2823708 2824521 "SYMBOL" 2825605 T SYMBOL (NIL) -8 NIL NIL NIL) (-1168 2815987 2817676 2819396 "SWITCH" 2820750 T SWITCH (NIL) -8 NIL NIL NIL) (-1167 2809257 2814808 2815111 "SUTS" 2815742 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2801358 2808504 2808777 "SUPXS" 2809042 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2792888 2800976 2801102 "SUP" 2801267 NIL SUP (NIL T) -8 NIL NIL NIL) (-1164 2792047 2792174 2792391 "SUPFRACF" 2792756 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1163 2791668 2791727 2791840 "SUP2" 2791982 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1162 2790081 2790355 2790718 "SUMRF" 2791367 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1161 2789395 2789461 2789660 "SUMFS" 2790002 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1160 2773402 2788572 2788823 "SULS" 2789202 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2773031 2773224 2773294 "SUCHTAST" 2773354 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1158 2772353 2772556 2772696 "SUCH" 2772939 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1157 2766247 2767259 2768218 "SUBSPACE" 2771441 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1156 2765677 2765767 2765931 "SUBRESP" 2766135 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1155 2759046 2760342 2761653 "STTF" 2764413 NIL STTF (NIL T) -7 NIL NIL NIL) (-1154 2753219 2754339 2755486 "STTFNC" 2757946 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1153 2744534 2746401 2748195 "STTAYLOR" 2751460 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1152 2737778 2744398 2744481 "STRTBL" 2744486 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1151 2733169 2737733 2737764 "STRING" 2737769 T STRING (NIL) -8 NIL NIL NIL) (-1150 2728057 2732542 2732572 "STRICAT" 2732631 T STRICAT (NIL) -9 NIL 2732693 NIL) (-1149 2720867 2725676 2726287 "STREAM" 2727481 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1148 2720377 2720454 2720598 "STREAM3" 2720784 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1147 2719359 2719542 2719777 "STREAM2" 2720190 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1146 2719047 2719099 2719192 "STREAM1" 2719301 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1145 2718063 2718244 2718475 "STINPROD" 2718863 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1144 2717641 2717825 2717855 "STEP" 2717935 T STEP (NIL) -9 NIL 2718013 NIL) (-1143 2711184 2717540 2717617 "STBL" 2717622 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1142 2706358 2710405 2710448 "STAGG" 2710601 NIL STAGG (NIL T) -9 NIL 2710690 NIL) (-1141 2704060 2704662 2705534 "STAGG-" 2705539 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1140 2702255 2703830 2703922 "STACK" 2704003 NIL STACK (NIL T) -8 NIL NIL NIL) (-1139 2694980 2700396 2700852 "SREGSET" 2701885 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1138 2687406 2688774 2690287 "SRDCMPK" 2693586 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2680373 2684846 2684876 "SRAGG" 2686179 T SRAGG (NIL) -9 NIL 2686787 NIL) (-1136 2679390 2679645 2680024 "SRAGG-" 2680029 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1135 2673885 2678337 2678758 "SQMATRIX" 2679016 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1134 2667634 2670603 2671330 "SPLTREE" 2673230 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1133 2663624 2664290 2664936 "SPLNODE" 2667060 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1132 2662671 2662904 2662934 "SPFCAT" 2663378 T SPFCAT (NIL) -9 NIL NIL NIL) (-1131 2661408 2661618 2661882 "SPECOUT" 2662429 T SPECOUT (NIL) -7 NIL NIL NIL) (-1130 2653060 2654804 2654834 "SPADXPT" 2659226 T SPADXPT (NIL) -9 NIL 2661260 NIL) (-1129 2652821 2652861 2652930 "SPADPRSR" 2653013 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1128 2651004 2652776 2652807 "SPADAST" 2652812 T SPADAST (NIL) -8 NIL NIL NIL) (-1127 2642975 2644722 2644765 "SPACEC" 2649138 NIL SPACEC (NIL T) -9 NIL 2650954 NIL) (-1126 2641146 2642907 2642956 "SPACE3" 2642961 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1125 2639898 2640069 2640360 "SORTPAK" 2640951 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1124 2637948 2638251 2638670 "SOLVETRA" 2639562 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1123 2636959 2637181 2637455 "SOLVESER" 2637721 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1122 2632179 2633060 2634062 "SOLVERAD" 2636011 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1121 2627994 2628603 2629332 "SOLVEFOR" 2631546 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1120 2622291 2627343 2627440 "SNTSCAT" 2627445 NIL SNTSCAT (NIL T T T T) -9 NIL 2627515 NIL) (-1119 2616434 2620614 2621005 "SMTS" 2621981 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1118 2610884 2616322 2616399 "SMP" 2616404 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1117 2609043 2609344 2609742 "SMITH" 2610581 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1116 2601938 2606094 2606197 "SMATCAT" 2607548 NIL SMATCAT (NIL NIL T T T) -9 NIL 2608098 NIL) (-1115 2598878 2599701 2600879 "SMATCAT-" 2600884 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1114 2596591 2598114 2598157 "SKAGG" 2598418 NIL SKAGG (NIL T) -9 NIL 2598553 NIL) (-1113 2592933 2596007 2596202 "SINT" 2596389 T SINT (NIL) -8 NIL NIL 2596562) (-1112 2592705 2592743 2592809 "SIMPAN" 2592889 T SIMPAN (NIL) -7 NIL NIL NIL) (-1111 2592012 2592240 2592380 "SIG" 2592587 T SIG (NIL) -8 NIL NIL NIL) (-1110 2590850 2591071 2591346 "SIGNRF" 2591771 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1109 2589655 2589806 2590097 "SIGNEF" 2590679 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1108 2588988 2589238 2589362 "SIGAST" 2589553 T SIGAST (NIL) -8 NIL NIL NIL) (-1107 2586678 2587132 2587638 "SHP" 2588529 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1106 2580584 2586579 2586655 "SHDP" 2586660 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1105 2580183 2580349 2580379 "SGROUP" 2580472 T SGROUP (NIL) -9 NIL 2580534 NIL) (-1104 2580041 2580067 2580140 "SGROUP-" 2580145 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1103 2576877 2577574 2578297 "SGCF" 2579340 T SGCF (NIL) -7 NIL NIL NIL) (-1102 2571272 2576324 2576421 "SFRTCAT" 2576426 NIL SFRTCAT (NIL T T T T) -9 NIL 2576465 NIL) (-1101 2564696 2565711 2566847 "SFRGCD" 2570255 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1100 2557824 2558895 2560081 "SFQCMPK" 2563629 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2557446 2557535 2557645 "SFORT" 2557765 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1098 2556591 2557286 2557407 "SEXOF" 2557412 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1097 2555725 2556472 2556540 "SEX" 2556545 T SEX (NIL) -8 NIL NIL NIL) (-1096 2551264 2551953 2552048 "SEXCAT" 2554985 NIL SEXCAT (NIL T T T T T) -9 NIL 2555563 NIL) (-1095 2548444 2551198 2551246 "SET" 2551251 NIL SET (NIL T) -8 NIL NIL NIL) (-1094 2546695 2547157 2547462 "SETMN" 2548185 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1093 2546301 2546427 2546457 "SETCAT" 2546574 T SETCAT (NIL) -9 NIL 2546659 NIL) (-1092 2546081 2546133 2546232 "SETCAT-" 2546237 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1091 2542468 2544542 2544585 "SETAGG" 2545455 NIL SETAGG (NIL T) -9 NIL 2545795 NIL) (-1090 2541926 2542042 2542279 "SETAGG-" 2542284 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1089 2541396 2541622 2541723 "SEQAST" 2541847 T SEQAST (NIL) -8 NIL NIL NIL) (-1088 2540595 2540889 2540950 "SEGXCAT" 2541236 NIL SEGXCAT (NIL T T) -9 NIL 2541356 NIL) (-1087 2539651 2540261 2540443 "SEG" 2540448 NIL SEG (NIL T) -8 NIL NIL NIL) (-1086 2538630 2538844 2538887 "SEGCAT" 2539409 NIL SEGCAT (NIL T) -9 NIL 2539630 NIL) (-1085 2537679 2538009 2538209 "SEGBIND" 2538465 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1084 2537300 2537359 2537472 "SEGBIND2" 2537614 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1083 2536901 2537101 2537178 "SEGAST" 2537245 T SEGAST (NIL) -8 NIL NIL NIL) (-1082 2536120 2536246 2536450 "SEG2" 2536745 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1081 2535557 2536055 2536102 "SDVAR" 2536107 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1080 2527847 2535327 2535457 "SDPOL" 2535462 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1079 2526440 2526706 2527025 "SCPKG" 2527562 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1078 2525576 2525756 2525956 "SCOPE" 2526262 T SCOPE (NIL) -8 NIL NIL NIL) (-1077 2524797 2524930 2525109 "SCACHE" 2525431 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1076 2524469 2524629 2524659 "SASTCAT" 2524664 T SASTCAT (NIL) -9 NIL 2524677 NIL) (-1075 2523983 2524304 2524380 "SAOS" 2524415 T SAOS (NIL) -8 NIL NIL NIL) (-1074 2523548 2523583 2523756 "SAERFFC" 2523942 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1073 2517522 2523445 2523525 "SAE" 2523530 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1072 2517115 2517150 2517309 "SAEFACT" 2517481 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1071 2515436 2515750 2516151 "RURPK" 2516781 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1070 2514072 2514351 2514663 "RULESET" 2515270 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1069 2511259 2511762 2512227 "RULE" 2513753 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1068 2510898 2511053 2511136 "RULECOLD" 2511211 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1067 2510396 2510615 2510709 "RSTRCAST" 2510826 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2505245 2506039 2506959 "RSETGCD" 2509595 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2494502 2499554 2499651 "RSETCAT" 2503770 NIL RSETCAT (NIL T T T T) -9 NIL 2504867 NIL) (-1064 2492429 2492968 2493792 "RSETCAT-" 2493797 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2484816 2486191 2487711 "RSDCMPK" 2491028 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2482821 2483262 2483336 "RRCC" 2484422 NIL RRCC (NIL T T) -9 NIL 2484766 NIL) (-1061 2482172 2482346 2482625 "RRCC-" 2482630 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2481642 2481868 2481969 "RPTAST" 2482093 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2455648 2465235 2465302 "RPOLCAT" 2475966 NIL RPOLCAT (NIL T T T) -9 NIL 2479125 NIL) (-1058 2447149 2449486 2452608 "RPOLCAT-" 2452613 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2438196 2445360 2445842 "ROUTINE" 2446689 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2435029 2437822 2437962 "ROMAN" 2438078 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2433304 2433889 2434149 "ROIRC" 2434834 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2429697 2431940 2431970 "RNS" 2432274 T RNS (NIL) -9 NIL 2432547 NIL) (-1053 2428206 2428589 2429123 "RNS-" 2429198 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2427655 2428037 2428067 "RNG" 2428072 T RNG (NIL) -9 NIL 2428093 NIL) (-1051 2427047 2427409 2427452 "RMODULE" 2427514 NIL RMODULE (NIL T) -9 NIL 2427556 NIL) (-1050 2425883 2425977 2426313 "RMCAT2" 2426948 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2422760 2425229 2425526 "RMATRIX" 2425645 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2415702 2417936 2418051 "RMATCAT" 2421410 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2422392 NIL) (-1047 2415077 2415224 2415531 "RMATCAT-" 2415536 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2414644 2414719 2414847 "RINTERP" 2414996 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2413777 2414297 2414327 "RING" 2414383 T RING (NIL) -9 NIL 2414469 NIL) (-1044 2413569 2413613 2413710 "RING-" 2413715 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2412410 2412647 2412905 "RIDIST" 2413333 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2403726 2411878 2412084 "RGCHAIN" 2412258 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2403102 2403482 2403523 "RGBCSPC" 2403581 NIL RGBCSPC (NIL T) -9 NIL 2403633 NIL) (-1040 2402286 2402641 2402682 "RGBCMDL" 2402914 NIL RGBCMDL (NIL T) -9 NIL 2403028 NIL) (-1039 2399280 2399894 2400564 "RF" 2401650 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2398926 2398989 2399092 "RFFACTOR" 2399211 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2398651 2398686 2398783 "RFFACT" 2398885 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2396768 2397132 2397514 "RFDIST" 2398291 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2396221 2396313 2396476 "RETSOL" 2396670 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2395857 2395937 2395980 "RETRACT" 2396113 NIL RETRACT (NIL T) -9 NIL 2396200 NIL) (-1033 2395706 2395731 2395818 "RETRACT-" 2395823 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2395335 2395528 2395598 "RETAST" 2395658 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2388189 2394988 2395115 "RESULT" 2395230 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2386815 2387458 2387657 "RESRING" 2388092 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2386451 2386500 2386598 "RESLATC" 2386752 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2386157 2386191 2386298 "REPSQ" 2386410 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2383579 2384159 2384761 "REP" 2385577 T REP (NIL) -7 NIL NIL NIL) (-1026 2383277 2383311 2383422 "REPDB" 2383538 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2377187 2378566 2379789 "REP2" 2382089 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2373564 2374245 2375053 "REP1" 2376414 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2366290 2371705 2372161 "REGSET" 2373194 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2365103 2365438 2365688 "REF" 2366075 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2364480 2364583 2364750 "REDORDER" 2364987 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2360485 2363693 2363920 "RECLOS" 2364308 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2359537 2359718 2359933 "REALSOLV" 2360292 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2359383 2359424 2359454 "REAL" 2359459 T REAL (NIL) -9 NIL 2359494 NIL) (-1017 2355866 2356668 2357552 "REAL0Q" 2358548 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2351467 2352455 2353516 "REAL0" 2354847 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2350965 2351184 2351278 "RDUCEAST" 2351395 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2350370 2350442 2350649 "RDIV" 2350887 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2349438 2349612 2349825 "RDIST" 2350192 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2348035 2348322 2348694 "RDETRS" 2349146 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2345847 2346301 2346839 "RDETR" 2347577 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2344458 2344736 2345140 "RDEEFS" 2345563 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2342953 2343259 2343691 "RDEEF" 2344146 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2337214 2340089 2340119 "RCFIELD" 2341414 T RCFIELD (NIL) -9 NIL 2342144 NIL) (-1007 2335278 2335782 2336478 "RCFIELD-" 2336553 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2331594 2333379 2333422 "RCAGG" 2334506 NIL RCAGG (NIL T) -9 NIL 2334971 NIL) (-1005 2331222 2331316 2331479 "RCAGG-" 2331484 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2330557 2330669 2330834 "RATRET" 2331106 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2330110 2330177 2330298 "RATFACT" 2330485 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2329418 2329538 2329690 "RANDSRC" 2329980 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2329152 2329196 2329269 "RADUTIL" 2329367 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2322305 2327985 2328295 "RADIX" 2328876 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2313962 2322149 2322277 "RADFF" 2322282 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2313614 2313689 2313717 "RADCAT" 2313874 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2313399 2313447 2313544 "RADCAT-" 2313549 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2311550 2313174 2313263 "QUEUE" 2313343 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2308126 2311487 2311532 "QUAT" 2311537 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2307764 2307807 2307934 "QUATCT2" 2308077 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2301511 2304813 2304853 "QUATCAT" 2305633 NIL QUATCAT (NIL T) -9 NIL 2306399 NIL) (-992 2297655 2298692 2300079 "QUATCAT-" 2300173 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2295175 2296739 2296780 "QUAGG" 2297155 NIL QUAGG (NIL T) -9 NIL 2297330 NIL) (-990 2294807 2295000 2295068 "QQUTAST" 2295127 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2293732 2294205 2294377 "QFORM" 2294679 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2284944 2290149 2290189 "QFCAT" 2290847 NIL QFCAT (NIL T) -9 NIL 2291848 NIL) (-987 2280516 2281717 2283308 "QFCAT-" 2283402 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2280154 2280197 2280324 "QFCAT2" 2280467 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2279614 2279724 2279854 "QEQUAT" 2280044 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2272762 2273833 2275017 "QCMPACK" 2278547 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2270338 2270759 2271187 "QALGSET" 2272417 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2269583 2269757 2269989 "QALGSET2" 2270158 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2268274 2268497 2268814 "PWFFINTB" 2269356 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2266456 2266624 2266978 "PUSHVAR" 2268088 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2262374 2263428 2263469 "PTRANFN" 2265353 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2260776 2261067 2261389 "PTPACK" 2262085 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2260408 2260465 2260574 "PTFUNC2" 2260713 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2254935 2259280 2259321 "PTCAT" 2259617 NIL PTCAT (NIL T) -9 NIL 2259770 NIL) (-975 2254593 2254628 2254752 "PSQFR" 2254894 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2253188 2253486 2253820 "PSEUDLIN" 2254291 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2239958 2242322 2244646 "PSETPK" 2250948 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2233002 2235716 2235812 "PSETCAT" 2238833 NIL PSETCAT (NIL T T T T) -9 NIL 2239647 NIL) (-971 2230838 2231472 2232293 "PSETCAT-" 2232298 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2230187 2230352 2230380 "PSCURVE" 2230648 T PSCURVE (NIL) -9 NIL 2230815 NIL) (-969 2226543 2228025 2228090 "PSCAT" 2228934 NIL PSCAT (NIL T T T) -9 NIL 2229174 NIL) (-968 2225606 2225822 2226222 "PSCAT-" 2226227 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2224338 2224971 2225176 "PRTITION" 2225421 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2223840 2224059 2224151 "PRTDAST" 2224266 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2212938 2215144 2217332 "PRS" 2221702 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2210796 2212288 2212328 "PRQAGG" 2212511 NIL PRQAGG (NIL T) -9 NIL 2212613 NIL) (-963 2210182 2210411 2210439 "PROPLOG" 2210624 T PROPLOG (NIL) -9 NIL 2210746 NIL) (-962 2207352 2207996 2208460 "PROPFRML" 2209750 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2206812 2206922 2207052 "PROPERTY" 2207242 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2200897 2204978 2205798 "PRODUCT" 2206038 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2198210 2200355 2200589 "PR" 2200708 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2198006 2198038 2198097 "PRINT" 2198171 T PRINT (NIL) -7 NIL NIL NIL) (-957 2197346 2197463 2197615 "PRIMES" 2197886 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2195411 2195812 2196278 "PRIMELT" 2196925 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2195140 2195189 2195217 "PRIMCAT" 2195341 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2191301 2195078 2195123 "PRIMARR" 2195128 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2190308 2190486 2190714 "PRIMARR2" 2191119 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2189951 2190007 2190118 "PREASSOC" 2190246 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2189426 2189559 2189587 "PPCURVE" 2189792 T PPCURVE (NIL) -9 NIL 2189928 NIL) (-950 2189048 2189221 2189304 "PORTNUM" 2189363 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2186407 2186806 2187398 "POLYROOT" 2188629 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2180352 2186011 2186171 "POLY" 2186280 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2179735 2179793 2180027 "POLYLIFT" 2180288 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2176010 2176459 2177088 "POLYCATQ" 2179280 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2162827 2168185 2168250 "POLYCAT" 2171764 NIL POLYCAT (NIL T T T) -9 NIL 2173692 NIL) (-944 2156277 2158138 2160522 "POLYCAT-" 2160527 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2155864 2155932 2156052 "POLY2UP" 2156203 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2155496 2155553 2155662 "POLY2" 2155801 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2154181 2154420 2154696 "POLUTIL" 2155270 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2152536 2152813 2153144 "POLTOPOL" 2153903 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2148054 2152472 2152518 "POINT" 2152523 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2146241 2146598 2146973 "PNTHEORY" 2147699 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2144660 2144957 2145369 "PMTOOLS" 2145939 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2144253 2144331 2144448 "PMSYM" 2144576 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2143763 2143832 2144006 "PMQFCAT" 2144178 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2143118 2143228 2143384 "PMPRED" 2143640 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2142514 2142600 2142761 "PMPREDFS" 2143019 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2141157 2141365 2141750 "PMPLCAT" 2142276 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2140689 2140768 2140920 "PMLSAGG" 2141072 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2140164 2140240 2140421 "PMKERNEL" 2140607 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2139781 2139856 2139969 "PMINS" 2140083 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2139209 2139278 2139494 "PMFS" 2139706 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2138437 2138555 2138760 "PMDOWN" 2139086 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2137600 2137759 2137941 "PMASS" 2138275 T PMASS (NIL) -7 NIL NIL NIL) (-925 2136874 2136985 2137148 "PMASSFS" 2137486 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2136529 2136597 2136691 "PLOTTOOL" 2136800 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2131151 2132340 2133488 "PLOT" 2135401 T PLOT (NIL) -8 NIL NIL NIL) (-922 2126965 2127999 2128920 "PLOT3D" 2130250 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2125877 2126054 2126289 "PLOT1" 2126769 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2101271 2105943 2110794 "PLEQN" 2121143 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2100589 2100711 2100891 "PINTERP" 2101136 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2100282 2100329 2100432 "PINTERPA" 2100536 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2099530 2100051 2100138 "PI" 2100178 T PI (NIL) -8 NIL NIL 2100245) (-916 2097927 2098868 2098896 "PID" 2099078 T PID (NIL) -9 NIL 2099212 NIL) (-915 2097652 2097689 2097777 "PICOERCE" 2097884 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2096972 2097111 2097287 "PGROEB" 2097508 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2092559 2093373 2094278 "PGE" 2096087 T PGE (NIL) -7 NIL NIL NIL) (-912 2090683 2090929 2091295 "PGCD" 2092276 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2090021 2090124 2090285 "PFRPAC" 2090567 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2086701 2088569 2088922 "PFR" 2089700 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2085090 2085334 2085659 "PFOTOOLS" 2086448 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2083623 2083862 2084213 "PFOQ" 2084847 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2082096 2082308 2082671 "PFO" 2083407 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2078684 2081985 2082054 "PF" 2082059 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2076118 2077355 2077383 "PFECAT" 2077968 T PFECAT (NIL) -9 NIL 2078352 NIL) (-904 2075563 2075717 2075931 "PFECAT-" 2075936 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2074167 2074418 2074719 "PFBRU" 2075312 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2072034 2072385 2072817 "PFBR" 2073818 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2067950 2069410 2070086 "PERM" 2071391 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2063216 2064157 2065027 "PERMGRP" 2067113 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2061348 2062279 2062320 "PERMCAT" 2062766 NIL PERMCAT (NIL T) -9 NIL 2063071 NIL) (-898 2061001 2061042 2061166 "PERMAN" 2061301 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2058537 2060666 2060788 "PENDTREE" 2060912 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2056630 2057364 2057405 "PDRING" 2058062 NIL PDRING (NIL T) -9 NIL 2058348 NIL) (-895 2055733 2055951 2056313 "PDRING-" 2056318 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2052975 2053726 2054394 "PDEPROB" 2055085 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2050522 2051024 2051579 "PDEPACK" 2052440 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2049434 2049624 2049875 "PDECOMP" 2050321 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2047039 2047856 2047884 "PDECAT" 2048671 T PDECAT (NIL) -9 NIL 2049384 NIL) (-890 2046790 2046823 2046913 "PCOMP" 2047000 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2044995 2045591 2045888 "PBWLB" 2046519 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2037500 2039068 2040406 "PATTERN" 2043678 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2037132 2037189 2037298 "PATTERN2" 2037437 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2034889 2035277 2035734 "PATTERN1" 2036721 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2032284 2032838 2033319 "PATRES" 2034454 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2031848 2031915 2032047 "PATRES2" 2032211 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2029731 2030136 2030543 "PATMATCH" 2031515 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2029267 2029450 2029491 "PATMAB" 2029598 NIL PATMAB (NIL T) -9 NIL 2029681 NIL) (-881 2027812 2028121 2028379 "PATLRES" 2029072 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2027358 2027481 2027522 "PATAB" 2027527 NIL PATAB (NIL T) -9 NIL 2027699 NIL) (-879 2024839 2025371 2025944 "PARTPERM" 2026805 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2024460 2024523 2024625 "PARSURF" 2024770 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2024092 2024149 2024258 "PARSU2" 2024397 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2023856 2023896 2023963 "PARSER" 2024045 T PARSER (NIL) -7 NIL NIL NIL) (-875 2023477 2023540 2023642 "PARSCURV" 2023787 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2023109 2023166 2023275 "PARSC2" 2023414 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2022748 2022806 2022903 "PARPCURV" 2023045 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2022380 2022437 2022546 "PARPC2" 2022685 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2021900 2021986 2022105 "PAN2EXPR" 2022281 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2020706 2021021 2021249 "PALETTE" 2021692 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2019174 2019711 2020071 "PAIR" 2020392 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2013080 2018433 2018627 "PADICRC" 2019029 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2006344 2012426 2012610 "PADICRAT" 2012928 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2004694 2006281 2006326 "PADIC" 2006331 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2001904 2003434 2003474 "PADICCT" 2004055 NIL PADICCT (NIL NIL) -9 NIL 2004337 NIL) (-864 2000861 2001061 2001329 "PADEPAC" 2001691 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2000073 2000206 2000412 "PADE" 2000723 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 1998495 1999281 1999561 "OWP" 1999877 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 1998015 1998201 1998298 "OVERSET" 1998418 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1997088 1997620 1997792 "OVAR" 1997883 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1996352 1996473 1996634 "OUT" 1996947 T OUT (NIL) -7 NIL NIL NIL) (-858 1985259 1987461 1989661 "OUTFORM" 1994172 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1984595 1984856 1984983 "OUTBFILE" 1985152 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1983902 1984067 1984095 "OUTBCON" 1984413 T OUTBCON (NIL) -9 NIL 1984579 NIL) (-855 1983503 1983615 1983772 "OUTBCON-" 1983777 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1982911 1983232 1983321 "OSI" 1983434 T OSI (NIL) -8 NIL NIL NIL) (-853 1982467 1982779 1982807 "OSGROUP" 1982812 T OSGROUP (NIL) -9 NIL 1982834 NIL) (-852 1981212 1981439 1981724 "ORTHPOL" 1982214 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1978798 1981047 1981168 "OREUP" 1981173 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976236 1978489 1978616 "ORESUP" 1978740 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1973764 1974264 1974825 "OREPCTO" 1975725 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1967588 1969755 1969796 "OREPCAT" 1972144 NIL OREPCAT (NIL T) -9 NIL 1973248 NIL) (-847 1964735 1965517 1966575 "OREPCAT-" 1966580 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1963912 1964184 1964212 "ORDSET" 1964521 T ORDSET (NIL) -9 NIL 1964685 NIL) (-845 1963431 1963553 1963746 "ORDSET-" 1963751 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1962065 1962822 1962850 "ORDRING" 1963052 T ORDRING (NIL) -9 NIL 1963177 NIL) (-843 1961710 1961804 1961948 "ORDRING-" 1961953 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1961116 1961553 1961581 "ORDMON" 1961586 T ORDMON (NIL) -9 NIL 1961607 NIL) (-841 1960278 1960425 1960620 "ORDFUNS" 1960965 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1959642 1960035 1960063 "ORDFIN" 1960128 T ORDFIN (NIL) -9 NIL 1960202 NIL) (-839 1956234 1958228 1958637 "ORDCOMP" 1959266 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1955500 1955627 1955813 "ORDCOMP2" 1956094 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1952108 1952991 1953805 "OPTPROB" 1954706 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1948910 1949549 1950253 "OPTPACK" 1951424 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1946623 1947363 1947391 "OPTCAT" 1948210 T OPTCAT (NIL) -9 NIL 1948860 NIL) (-834 1946066 1946300 1946405 "OPSIG" 1946538 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1945834 1945873 1945939 "OPQUERY" 1946020 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1943000 1944145 1944649 "OP" 1945363 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1942535 1942706 1942747 "OPERCAT" 1942882 NIL OPERCAT (NIL T) -9 NIL 1942950 NIL) (-830 1942381 1942408 1942494 "OPERCAT-" 1942499 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1939226 1941178 1941547 "ONECOMP" 1942045 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1938531 1938646 1938820 "ONECOMP2" 1939098 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1937950 1938056 1938186 "OMSERVER" 1938421 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1934838 1937390 1937430 "OMSAGG" 1937491 NIL OMSAGG (NIL T) -9 NIL 1937555 NIL) (-825 1933461 1933724 1934006 "OMPKG" 1934576 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1932891 1932994 1933022 "OM" 1933321 T OM (NIL) -9 NIL NIL NIL) (-823 1931473 1932440 1932609 "OMLO" 1932772 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1930398 1930545 1930772 "OMEXPR" 1931299 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1929716 1929944 1930080 "OMERR" 1930282 T OMERR (NIL) -8 NIL NIL NIL) (-820 1928894 1929137 1929297 "OMERRK" 1929576 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1928372 1928571 1928679 "OMENC" 1928806 T OMENC (NIL) -8 NIL NIL NIL) (-818 1922267 1923452 1924623 "OMDEV" 1927221 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1921336 1921507 1921701 "OMCONN" 1922093 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1919957 1920899 1920927 "OINTDOM" 1920932 T OINTDOM (NIL) -9 NIL 1920953 NIL) (-815 1915763 1916947 1917663 "OFMONOID" 1919273 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1915201 1915700 1915745 "ODVAR" 1915750 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1912659 1914946 1915101 "ODR" 1915106 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1905003 1912435 1912561 "ODPOL" 1912566 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1898879 1904875 1904980 "ODP" 1904985 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1897645 1897860 1898135 "ODETOOLS" 1898653 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1894614 1895270 1895986 "ODESYS" 1896978 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1889496 1890404 1891429 "ODERTRIC" 1893689 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1888922 1889004 1889198 "ODERED" 1889408 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1885810 1886358 1887035 "ODERAT" 1888345 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1882770 1883234 1883831 "ODEPRRIC" 1885339 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1880740 1881309 1881795 "ODEPROB" 1882304 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1877262 1877745 1878392 "ODEPRIM" 1880219 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1876511 1876613 1876873 "ODEPAL" 1877154 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1872673 1873464 1874328 "ODEPACK" 1875667 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1871706 1871813 1872042 "ODEINT" 1872562 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1865807 1867232 1868679 "ODEIFTBL" 1870279 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1861142 1861928 1862887 "ODEEF" 1864966 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1860477 1860566 1860796 "ODECONST" 1861047 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1858628 1859263 1859291 "ODECAT" 1859896 T ODECAT (NIL) -9 NIL 1860427 NIL) (-795 1855535 1858340 1858459 "OCT" 1858541 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1855173 1855216 1855343 "OCTCT2" 1855486 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1849947 1852347 1852387 "OC" 1853484 NIL OC (NIL T) -9 NIL 1854342 NIL) (-792 1847174 1847922 1848912 "OC-" 1849006 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1846552 1846994 1847022 "OCAMON" 1847027 T OCAMON (NIL) -9 NIL 1847048 NIL) (-790 1846109 1846424 1846452 "OASGP" 1846457 T OASGP (NIL) -9 NIL 1846477 NIL) (-789 1845396 1845859 1845887 "OAMONS" 1845927 T OAMONS (NIL) -9 NIL 1845970 NIL) (-788 1844836 1845243 1845271 "OAMON" 1845276 T OAMON (NIL) -9 NIL 1845296 NIL) (-787 1844140 1844632 1844660 "OAGROUP" 1844665 T OAGROUP (NIL) -9 NIL 1844685 NIL) (-786 1843830 1843880 1843968 "NUMTUBE" 1844084 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1837403 1838921 1840457 "NUMQUAD" 1842314 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1833159 1834147 1835172 "NUMODE" 1836398 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1830540 1831394 1831422 "NUMINT" 1832345 T NUMINT (NIL) -9 NIL 1833109 NIL) (-782 1829488 1829685 1829903 "NUMFMT" 1830342 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1815847 1818792 1821324 "NUMERIC" 1826995 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1810244 1815296 1815391 "NTSCAT" 1815396 NIL NTSCAT (NIL T T T T) -9 NIL 1815435 NIL) (-779 1809438 1809603 1809796 "NTPOLFN" 1810083 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1797278 1806263 1807075 "NSUP" 1808659 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1796910 1796967 1797076 "NSUP2" 1797215 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1786907 1796684 1796817 "NSMP" 1796822 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1785339 1785640 1785997 "NREP" 1786595 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1783930 1784182 1784540 "NPCOEF" 1785082 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1782996 1783111 1783327 "NORMRETR" 1783811 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1781037 1781327 1781736 "NORMPK" 1782704 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1780722 1780750 1780874 "NORMMA" 1781003 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1780549 1780679 1780708 "NONE" 1780713 T NONE (NIL) -8 NIL NIL NIL) (-769 1780338 1780367 1780436 "NONE1" 1780513 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1779821 1779883 1780069 "NODE1" 1780270 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1778092 1778915 1779170 "NNI" 1779517 T NNI (NIL) -8 NIL NIL 1779752) (-766 1776512 1776825 1777189 "NLINSOL" 1777760 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1772780 1773748 1774647 "NIPROB" 1775633 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1771537 1771771 1772073 "NFINTBAS" 1772542 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1770711 1771187 1771228 "NETCLT" 1771400 NIL NETCLT (NIL T) -9 NIL 1771482 NIL) (-762 1769419 1769650 1769931 "NCODIV" 1770479 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1769181 1769218 1769293 "NCNTFRAC" 1769376 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1767361 1767725 1768145 "NCEP" 1768806 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1766272 1767011 1767039 "NASRING" 1767149 T NASRING (NIL) -9 NIL 1767223 NIL) (-758 1766067 1766111 1766205 "NASRING-" 1766210 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1765220 1765719 1765747 "NARNG" 1765864 T NARNG (NIL) -9 NIL 1765955 NIL) (-756 1764912 1764979 1765113 "NARNG-" 1765118 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1763791 1763998 1764233 "NAGSP" 1764697 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1755063 1756747 1758420 "NAGS" 1762138 T NAGS (NIL) -7 NIL NIL NIL) (-753 1753611 1753919 1754250 "NAGF07" 1754752 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1748149 1749440 1750747 "NAGF04" 1752324 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1741117 1742731 1744364 "NAGF02" 1746536 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1736341 1737441 1738558 "NAGF01" 1740020 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1729969 1731535 1733120 "NAGE04" 1734776 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1721138 1723259 1725389 "NAGE02" 1727859 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1717091 1718038 1719002 "NAGE01" 1720194 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1714886 1715420 1715978 "NAGD03" 1716553 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1706636 1708564 1710518 "NAGD02" 1712952 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1700447 1701872 1703312 "NAGD01" 1705216 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1696656 1697478 1698315 "NAGC06" 1699630 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1695121 1695453 1695809 "NAGC05" 1696320 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1694497 1694616 1694760 "NAGC02" 1694997 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1693557 1694114 1694154 "NAALG" 1694233 NIL NAALG (NIL T) -9 NIL 1694294 NIL) (-739 1693392 1693421 1693511 "NAALG-" 1693516 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1687342 1688450 1689637 "MULTSQFR" 1692288 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1686661 1686736 1686920 "MULTFACT" 1687254 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1679754 1683624 1683677 "MTSCAT" 1684747 NIL MTSCAT (NIL T T) -9 NIL 1685261 NIL) (-735 1679466 1679520 1679612 "MTHING" 1679694 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1679258 1679291 1679351 "MSYSCMD" 1679426 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1675370 1678013 1678333 "MSET" 1678971 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1672465 1674931 1674972 "MSETAGG" 1674977 NIL MSETAGG (NIL T) -9 NIL 1675011 NIL) (-731 1668348 1669844 1670589 "MRING" 1671765 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1667914 1667981 1668112 "MRF2" 1668275 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1667532 1667567 1667711 "MRATFAC" 1667873 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1665144 1665439 1665870 "MPRFF" 1667237 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1659204 1664998 1665095 "MPOLY" 1665100 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1658694 1658729 1658937 "MPCPF" 1659163 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1658208 1658251 1658435 "MPC3" 1658645 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1657403 1657484 1657705 "MPC2" 1658123 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1655704 1656041 1656431 "MONOTOOL" 1657063 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1654955 1655246 1655274 "MONOID" 1655493 T MONOID (NIL) -9 NIL 1655640 NIL) (-721 1654501 1654620 1654801 "MONOID-" 1654806 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1645360 1651268 1651327 "MONOGEN" 1652001 NIL MONOGEN (NIL T T) -9 NIL 1652457 NIL) (-719 1642578 1643313 1644313 "MONOGEN-" 1644432 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1641437 1641857 1641885 "MONADWU" 1642277 T MONADWU (NIL) -9 NIL 1642515 NIL) (-717 1640809 1640968 1641216 "MONADWU-" 1641221 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1640194 1640412 1640440 "MONAD" 1640647 T MONAD (NIL) -9 NIL 1640759 NIL) (-715 1639879 1639957 1640089 "MONAD-" 1640094 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1638195 1638792 1639071 "MOEBIUS" 1639632 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1637587 1637965 1638005 "MODULE" 1638010 NIL MODULE (NIL T) -9 NIL 1638036 NIL) (-712 1637155 1637251 1637441 "MODULE-" 1637446 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1634870 1635519 1635846 "MODRING" 1636979 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1631856 1632975 1633496 "MODOP" 1634399 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1630471 1630923 1631200 "MODMONOM" 1631719 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1620278 1628762 1629176 "MODMON" 1630108 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1617469 1619122 1619398 "MODFIELD" 1620153 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1616473 1616750 1616940 "MMLFORM" 1617299 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1615999 1616042 1616221 "MMAP" 1616424 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1614216 1614949 1614990 "MLO" 1615413 NIL MLO (NIL T) -9 NIL 1615655 NIL) (-703 1611583 1612098 1612700 "MLIFT" 1613697 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1610974 1611058 1611212 "MKUCFUNC" 1611494 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1610573 1610643 1610766 "MKRECORD" 1610897 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1609621 1609782 1610010 "MKFUNC" 1610384 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1609009 1609113 1609269 "MKFLCFN" 1609504 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1608552 1608919 1608978 "MKCHSET" 1608983 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-697 1607829 1607931 1608116 "MKBCFUNC" 1608445 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-696 1604571 1607383 1607519 "MINT" 1607713 T MINT (NIL) -8 NIL NIL NIL) (-695 1603383 1603626 1603903 "MHROWRED" 1604326 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-694 1598809 1601918 1602323 "MFLOAT" 1602998 T MFLOAT (NIL) -8 NIL NIL NIL) (-693 1598166 1598242 1598413 "MFINFACT" 1598721 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-692 1594481 1595329 1596213 "MESH" 1597302 T MESH (NIL) -7 NIL NIL NIL) (-691 1592871 1593183 1593536 "MDDFACT" 1594168 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-690 1589713 1592030 1592071 "MDAGG" 1592326 NIL MDAGG (NIL T) -9 NIL 1592469 NIL) (-689 1579491 1589006 1589213 "MCMPLX" 1589526 T MCMPLX (NIL) -8 NIL NIL NIL) (-688 1578632 1578778 1578978 "MCDEN" 1579340 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-687 1576522 1576792 1577172 "MCALCFN" 1578362 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-686 1575447 1575687 1575920 "MAYBE" 1576328 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-685 1573059 1573582 1574144 "MATSTOR" 1574918 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-684 1569065 1572431 1572679 "MATRIX" 1572844 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-683 1564834 1565538 1566274 "MATLIN" 1568422 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-682 1554988 1558126 1558203 "MATCAT" 1563083 NIL MATCAT (NIL T T T) -9 NIL 1564500 NIL) (-681 1551352 1552365 1553721 "MATCAT-" 1553726 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-680 1549946 1550099 1550432 "MATCAT2" 1551187 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-679 1548058 1548382 1548766 "MAPPKG3" 1549621 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-678 1547039 1547212 1547434 "MAPPKG2" 1547882 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-677 1545538 1545822 1546149 "MAPPKG1" 1546745 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-676 1544644 1544944 1545121 "MAPPAST" 1545381 T MAPPAST (NIL) -8 NIL NIL NIL) (-675 1544255 1544313 1544436 "MAPHACK3" 1544580 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-674 1543847 1543908 1544022 "MAPHACK2" 1544187 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-673 1543285 1543388 1543530 "MAPHACK1" 1543738 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-672 1541391 1541985 1542289 "MAGMA" 1543013 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-671 1540897 1541115 1541206 "MACROAST" 1541320 T MACROAST (NIL) -8 NIL NIL NIL) (-670 1537364 1539136 1539597 "M3D" 1540469 NIL M3D (NIL T) -8 NIL NIL NIL) (-669 1531518 1535733 1535774 "LZSTAGG" 1536556 NIL LZSTAGG (NIL T) -9 NIL 1536851 NIL) (-668 1527492 1528649 1530106 "LZSTAGG-" 1530111 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-667 1524606 1525383 1525870 "LWORD" 1527037 NIL LWORD (NIL T) -8 NIL NIL NIL) (-666 1524209 1524410 1524485 "LSTAST" 1524551 T LSTAST (NIL) -8 NIL NIL NIL) (-665 1517410 1523980 1524114 "LSQM" 1524119 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-664 1516634 1516773 1517001 "LSPP" 1517265 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-663 1514446 1514747 1515203 "LSMP" 1516323 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-662 1511225 1511899 1512629 "LSMP1" 1513748 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-661 1505150 1510392 1510433 "LSAGG" 1510495 NIL LSAGG (NIL T) -9 NIL 1510573 NIL) (-660 1501845 1502769 1503982 "LSAGG-" 1503987 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-659 1499471 1500989 1501238 "LPOLY" 1501640 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-658 1499053 1499138 1499261 "LPEFRAC" 1499380 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-657 1497400 1498147 1498400 "LO" 1498885 NIL LO (NIL T T T) -8 NIL NIL NIL) (-656 1497052 1497164 1497192 "LOGIC" 1497303 T LOGIC (NIL) -9 NIL 1497384 NIL) (-655 1496914 1496937 1497008 "LOGIC-" 1497013 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-654 1496107 1496247 1496440 "LODOOPS" 1496770 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-653 1493565 1496023 1496089 "LODO" 1496094 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-652 1492103 1492338 1492691 "LODOF" 1493312 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-651 1488459 1490856 1490897 "LODOCAT" 1491335 NIL LODOCAT (NIL T) -9 NIL 1491546 NIL) (-650 1488192 1488250 1488377 "LODOCAT-" 1488382 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-649 1485547 1488033 1488151 "LODO2" 1488156 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-648 1483017 1485484 1485529 "LODO1" 1485534 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-647 1481877 1482042 1482354 "LODEEF" 1482840 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-646 1477163 1480007 1480048 "LNAGG" 1480995 NIL LNAGG (NIL T) -9 NIL 1481439 NIL) (-645 1476310 1476524 1476866 "LNAGG-" 1476871 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-644 1472473 1473235 1473874 "LMOPS" 1475725 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-643 1471868 1472230 1472271 "LMODULE" 1472332 NIL LMODULE (NIL T) -9 NIL 1472374 NIL) (-642 1469114 1471513 1471636 "LMDICT" 1471778 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-641 1468840 1469022 1469082 "LITERAL" 1469087 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-640 1462067 1467786 1468084 "LIST" 1468575 NIL LIST (NIL T) -8 NIL NIL NIL) (-639 1461592 1461666 1461805 "LIST3" 1461987 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-638 1460599 1460777 1461005 "LIST2" 1461410 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-637 1458733 1459045 1459444 "LIST2MAP" 1460246 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-636 1457463 1458099 1458140 "LINEXP" 1458395 NIL LINEXP (NIL T) -9 NIL 1458544 NIL) (-635 1456110 1456370 1456667 "LINDEP" 1457215 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-634 1452877 1453596 1454373 "LIMITRF" 1455365 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-633 1451153 1451448 1451864 "LIMITPS" 1452572 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-632 1445608 1450664 1450892 "LIE" 1450974 NIL LIE (NIL T T) -8 NIL NIL NIL) (-631 1444657 1445100 1445140 "LIECAT" 1445280 NIL LIECAT (NIL T) -9 NIL 1445431 NIL) (-630 1444498 1444525 1444613 "LIECAT-" 1444618 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-629 1437110 1443947 1444112 "LIB" 1444353 T LIB (NIL) -8 NIL NIL NIL) (-628 1432747 1433628 1434563 "LGROBP" 1436227 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-627 1430613 1430887 1431249 "LF" 1432468 NIL LF (NIL T T) -7 NIL NIL NIL) (-626 1429453 1430145 1430173 "LFCAT" 1430380 T LFCAT (NIL) -9 NIL 1430519 NIL) (-625 1426357 1426985 1427673 "LEXTRIPK" 1428817 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-624 1423128 1423927 1424430 "LEXP" 1425937 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-623 1422631 1422849 1422941 "LETAST" 1423056 T LETAST (NIL) -8 NIL NIL NIL) (-622 1421029 1421342 1421743 "LEADCDET" 1422313 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-621 1420219 1420293 1420522 "LAZM3PK" 1420950 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-620 1415173 1418296 1418834 "LAUPOL" 1419731 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-619 1414738 1414782 1414950 "LAPLACE" 1415123 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-618 1412712 1413839 1414090 "LA" 1414571 NIL LA (NIL T T T) -8 NIL NIL NIL) (-617 1411793 1412343 1412384 "LALG" 1412446 NIL LALG (NIL T) -9 NIL 1412505 NIL) (-616 1411507 1411566 1411702 "LALG-" 1411707 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-615 1411342 1411366 1411407 "KVTFROM" 1411469 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-614 1410145 1410559 1410788 "KTVLOGIC" 1411133 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-613 1409980 1410004 1410045 "KRCFROM" 1410107 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-612 1408884 1409071 1409370 "KOVACIC" 1409780 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-611 1408719 1408743 1408784 "KONVERT" 1408846 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-610 1408554 1408578 1408619 "KOERCE" 1408681 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-609 1406288 1407048 1407441 "KERNEL" 1408193 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-608 1405790 1405871 1406001 "KERNEL2" 1406202 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-607 1399641 1404329 1404383 "KDAGG" 1404760 NIL KDAGG (NIL T T) -9 NIL 1404966 NIL) (-606 1399170 1399294 1399499 "KDAGG-" 1399504 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-605 1392345 1398831 1398986 "KAFILE" 1399048 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-604 1386800 1391856 1392084 "JORDAN" 1392166 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-603 1386206 1386449 1386570 "JOINAST" 1386699 T JOINAST (NIL) -8 NIL NIL NIL) (-602 1386052 1386111 1386166 "JAVACODE" 1386171 T JAVACODE (NIL) -8 NIL NIL NIL) (-601 1382351 1384257 1384311 "IXAGG" 1385240 NIL IXAGG (NIL T T) -9 NIL 1385699 NIL) (-600 1381270 1381576 1381995 "IXAGG-" 1382000 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-599 1376850 1381192 1381251 "IVECTOR" 1381256 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-598 1375616 1375853 1376119 "ITUPLE" 1376617 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-597 1374052 1374229 1374535 "ITRIGMNP" 1375438 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-596 1372797 1373001 1373284 "ITFUN3" 1373828 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-595 1372429 1372486 1372595 "ITFUN2" 1372734 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-594 1370266 1371291 1371590 "ITAYLOR" 1372163 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-593 1359249 1364403 1365566 "ISUPS" 1369136 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-592 1358353 1358493 1358729 "ISUMP" 1359096 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-591 1353617 1358154 1358233 "ISTRING" 1358306 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-590 1353120 1353338 1353430 "ISAST" 1353545 T ISAST (NIL) -8 NIL NIL NIL) (-589 1352330 1352411 1352627 "IRURPK" 1353034 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-588 1351266 1351467 1351707 "IRSN" 1352110 T IRSN (NIL) -7 NIL NIL NIL) (-587 1349295 1349650 1350086 "IRRF2F" 1350904 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-586 1349042 1349080 1349156 "IRREDFFX" 1349251 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-585 1347657 1347916 1348215 "IROOT" 1348775 NIL IROOT (NIL T) -7 NIL NIL NIL) (-584 1344289 1345341 1346033 "IR" 1346997 NIL IR (NIL T) -8 NIL NIL NIL) (-583 1341902 1342397 1342963 "IR2" 1343767 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-582 1340974 1341087 1341308 "IR2F" 1341785 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-581 1340765 1340799 1340859 "IPRNTPK" 1340934 T IPRNTPK (NIL) -7 NIL NIL NIL) (-580 1337384 1340654 1340723 "IPF" 1340728 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-579 1335747 1337309 1337366 "IPADIC" 1337371 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-578 1335087 1335307 1335437 "IP4ADDR" 1335637 T IP4ADDR (NIL) -8 NIL NIL NIL) (-577 1334587 1334791 1334901 "IOMODE" 1334997 T IOMODE (NIL) -8 NIL NIL NIL) (-576 1333660 1334184 1334311 "IOBFILE" 1334480 T IOBFILE (NIL) -8 NIL NIL NIL) (-575 1333148 1333564 1333592 "IOBCON" 1333597 T IOBCON (NIL) -9 NIL 1333618 NIL) (-574 1332645 1332703 1332893 "INVLAPLA" 1333084 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-573 1322294 1324647 1327033 "INTTR" 1330309 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-572 1318638 1319380 1320244 "INTTOOLS" 1321479 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-571 1318224 1318315 1318432 "INTSLPE" 1318541 T INTSLPE (NIL) -7 NIL NIL NIL) (-570 1316219 1318147 1318206 "INTRVL" 1318211 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-569 1313821 1314333 1314908 "INTRF" 1315704 NIL INTRF (NIL T) -7 NIL NIL NIL) (-568 1313232 1313329 1313471 "INTRET" 1313719 NIL INTRET (NIL T) -7 NIL NIL NIL) (-567 1311229 1311618 1312088 "INTRAT" 1312840 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-566 1308457 1309040 1309666 "INTPM" 1310714 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-565 1305160 1305759 1306504 "INTPAF" 1307843 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-564 1300339 1301301 1302352 "INTPACK" 1304129 T INTPACK (NIL) -7 NIL NIL NIL) (-563 1297250 1300068 1300195 "INT" 1300232 T INT (NIL) -8 NIL NIL NIL) (-562 1296502 1296654 1296862 "INTHERTR" 1297092 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-561 1295941 1296021 1296209 "INTHERAL" 1296416 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-560 1293787 1294230 1294687 "INTHEORY" 1295504 T INTHEORY (NIL) -7 NIL NIL NIL) (-559 1285095 1286716 1288495 "INTG0" 1292139 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-558 1265668 1270458 1275268 "INTFTBL" 1280305 T INTFTBL (NIL) -8 NIL NIL NIL) (-557 1264917 1265055 1265228 "INTFACT" 1265527 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-556 1262302 1262748 1263312 "INTEF" 1264471 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-555 1260769 1261474 1261502 "INTDOM" 1261803 T INTDOM (NIL) -9 NIL 1262010 NIL) (-554 1260138 1260312 1260554 "INTDOM-" 1260559 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-553 1256633 1258522 1258576 "INTCAT" 1259375 NIL INTCAT (NIL T) -9 NIL 1259695 NIL) (-552 1256106 1256208 1256336 "INTBIT" 1256525 T INTBIT (NIL) -7 NIL NIL NIL) (-551 1254777 1254931 1255245 "INTALG" 1255951 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-550 1254234 1254324 1254494 "INTAF" 1254681 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-549 1247688 1254044 1254184 "INTABL" 1254189 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-548 1247148 1247561 1247589 "INT8" 1247594 T INT8 (NIL) -8 NIL NIL 1247602) (-547 1246607 1247020 1247048 "INT32" 1247053 T INT32 (NIL) -8 NIL NIL 1247061) (-546 1246066 1246479 1246507 "INT16" 1246512 T INT16 (NIL) -8 NIL NIL 1246520) (-545 1241081 1243755 1243783 "INS" 1244717 T INS (NIL) -9 NIL 1245382 NIL) (-544 1238321 1239092 1240066 "INS-" 1240139 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237096 1237323 1237621 "INPSIGN" 1238074 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1236214 1236331 1236528 "INPRODPF" 1236976 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1235108 1235225 1235462 "INPRODFF" 1236094 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1234108 1234260 1234520 "INNMFACT" 1234944 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1233305 1233402 1233590 "INMODGCD" 1234007 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1231814 1232058 1232382 "INFSP" 1233050 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1230998 1231115 1231298 "INFPROD0" 1231694 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1227880 1229063 1229578 "INFORM" 1230491 T INFORM (NIL) -8 NIL NIL NIL) (-535 1227490 1227550 1227648 "INFORM1" 1227815 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227013 1227102 1227216 "INFINITY" 1227396 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1226189 1226733 1226834 "INETCLTS" 1226932 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1224806 1225055 1225376 "INEP" 1225937 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224082 1224703 1224768 "INDE" 1224773 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1223646 1223714 1223831 "INCRMAPS" 1224009 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1222464 1222915 1223121 "INBFILE" 1223460 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1217775 1218700 1219644 "INBFF" 1221552 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1216683 1216952 1216980 "INBCON" 1217493 T INBCON (NIL) -9 NIL 1217759 NIL) (-526 1215935 1216158 1216434 "INBCON-" 1216439 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1215437 1215656 1215748 "INAST" 1215863 T INAST (NIL) -8 NIL NIL NIL) (-524 1214891 1215116 1215222 "IMPTAST" 1215351 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1211385 1214735 1214839 "IMATRIX" 1214844 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210097 1210220 1210535 "IMATQF" 1211241 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1208317 1208544 1208881 "IMATLIN" 1209853 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1202943 1208241 1208299 "ILIST" 1208304 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1200896 1202803 1202916 "IIARRAY2" 1202921 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1196329 1200807 1200871 "IFF" 1200876 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1195703 1195946 1196062 "IFAST" 1196233 T IFAST (NIL) -8 NIL NIL NIL) (-516 1190746 1194995 1195183 "IFARRAY" 1195560 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1189953 1190650 1190723 "IFAMON" 1190728 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1189537 1189602 1189656 "IEVALAB" 1189863 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1189212 1189280 1189440 "IEVALAB-" 1189445 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1188870 1189126 1189189 "IDPO" 1189194 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1188147 1188759 1188834 "IDPOAMS" 1188839 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1187481 1188036 1188111 "IDPOAM" 1188116 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1186566 1186816 1186869 "IDPC" 1187282 NIL IDPC (NIL T T) -9 NIL 1187431 NIL) (-508 1186062 1186458 1186531 "IDPAM" 1186536 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1185465 1185954 1186027 "IDPAG" 1186032 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1185233 1185380 1185430 "IDENT" 1185435 T IDENT (NIL) -8 NIL NIL NIL) (-505 1181488 1182336 1183231 "IDECOMP" 1184390 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1174362 1175411 1176458 "IDEAL" 1180524 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1173526 1173638 1173837 "ICDEN" 1174246 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1172625 1173006 1173153 "ICARD" 1173399 T ICARD (NIL) -8 NIL NIL NIL) (-501 1170685 1170998 1171403 "IBPTOOLS" 1172302 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1166319 1170305 1170418 "IBITS" 1170604 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163042 1163618 1164313 "IBATOOL" 1165736 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1160822 1161283 1161816 "IBACHIN" 1162577 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1158699 1160668 1160771 "IARRAY2" 1160776 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1154852 1158625 1158682 "IARRAY1" 1158687 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1148846 1153264 1153745 "IAN" 1154391 T IAN (NIL) -8 NIL NIL NIL) (-494 1148357 1148414 1148587 "IALGFACT" 1148783 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1147885 1147998 1148026 "HYPCAT" 1148233 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1147423 1147540 1147726 "HYPCAT-" 1147731 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147045 1147218 1147301 "HOSTNAME" 1147360 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1146890 1146927 1146968 "HOMOTOP" 1146973 NIL HOMOTOP (NIL T) -9 NIL 1147006 NIL) (-489 1143569 1144900 1144941 "HOAGG" 1145922 NIL HOAGG (NIL T) -9 NIL 1146601 NIL) (-488 1142163 1142562 1143088 "HOAGG-" 1143093 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136202 1141758 1141907 "HEXADEC" 1142034 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1134950 1135172 1135435 "HEUGCD" 1135979 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134053 1134787 1134917 "HELLFDIV" 1134922 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1132281 1133830 1133918 "HEAP" 1133997 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1131572 1131833 1131967 "HEADAST" 1132167 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1125492 1131487 1131549 "HDP" 1131554 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1119243 1125127 1125279 "HDMP" 1125393 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1118568 1118707 1118871 "HB" 1119099 T HB (NIL) -7 NIL NIL NIL) (-479 1112065 1118414 1118518 "HASHTBL" 1118523 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1111568 1111786 1111878 "HASAST" 1111993 T HASAST (NIL) -8 NIL NIL NIL) (-477 1109381 1111190 1111372 "HACKPI" 1111406 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105076 1109234 1109347 "GTSET" 1109352 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1098602 1104954 1105052 "GSTBL" 1105057 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1090915 1097633 1097898 "GSERIES" 1098393 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090082 1090473 1090501 "GROUP" 1090704 T GROUP (NIL) -9 NIL 1090838 NIL) (-472 1089448 1089607 1089858 "GROUP-" 1089863 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1087817 1088136 1088523 "GROEBSOL" 1089125 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1086757 1087019 1087070 "GRMOD" 1087599 NIL GRMOD (NIL T T) -9 NIL 1087767 NIL) (-469 1086525 1086561 1086689 "GRMOD-" 1086694 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1081851 1082879 1083879 "GRIMAGE" 1085545 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1080318 1080578 1080902 "GRDEF" 1081547 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1079762 1079878 1080019 "GRAY" 1080197 T GRAY (NIL) -7 NIL NIL NIL) (-465 1078975 1079355 1079406 "GRALG" 1079559 NIL GRALG (NIL T T) -9 NIL 1079652 NIL) (-464 1078636 1078709 1078872 "GRALG-" 1078877 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1075440 1078221 1078399 "GPOLSET" 1078543 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1074794 1074851 1075109 "GOSPER" 1075377 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1070553 1071232 1071758 "GMODPOL" 1074493 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1069558 1069742 1069980 "GHENSEL" 1070365 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1063609 1064452 1065479 "GENUPS" 1068642 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1063306 1063357 1063446 "GENUFACT" 1063552 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1062718 1062795 1062960 "GENPGCD" 1063224 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062192 1062227 1062440 "GENMFACT" 1062677 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1060760 1061015 1061322 "GENEEZ" 1061935 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1054673 1060371 1060533 "GDMP" 1060683 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044050 1048444 1049550 "GCNAALG" 1053656 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1042477 1043305 1043333 "GCDDOM" 1043588 T GCDDOM (NIL) -9 NIL 1043745 NIL) (-451 1041947 1042074 1042289 "GCDDOM-" 1042294 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1040619 1040804 1041108 "GB" 1041726 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029239 1031565 1033957 "GBINTERN" 1038310 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027076 1027368 1027789 "GBF" 1028914 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1025857 1026022 1026289 "GBEUCLID" 1026892 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025206 1025331 1025480 "GAUSSFAC" 1025728 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1023573 1023875 1024189 "GALUTIL" 1024925 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1021881 1022155 1022479 "GALPOLYU" 1023300 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019246 1019536 1019943 "GALFACTU" 1021578 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011052 1012551 1014159 "GALFACT" 1017678 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1008440 1009098 1009126 "FVFUN" 1010282 T FVFUN (NIL) -9 NIL 1011002 NIL) (-440 1007706 1007888 1007916 "FVC" 1008207 T FVC (NIL) -9 NIL 1008390 NIL) (-439 1007376 1007531 1007599 "FUNDESC" 1007658 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007018 1007173 1007254 "FUNCTION" 1007328 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1004789 1005340 1005806 "FT" 1006572 T FT (NIL) -8 NIL NIL NIL) (-436 1003607 1004090 1004293 "FTEM" 1004606 T FTEM (NIL) -8 NIL NIL NIL) (-435 1001863 1002152 1002556 "FSUPFACT" 1003298 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000260 1000549 1000881 "FST" 1001551 T FST (NIL) -8 NIL NIL NIL) (-433 999431 999537 999732 "FSRED" 1000142 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998110 998365 998719 "FSPRMELT" 999146 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995195 995633 996132 "FSPECF" 997673 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977255 985698 985738 "FS" 989586 NIL FS (NIL T) -9 NIL 991875 NIL) (-429 965905 968895 972951 "FS-" 973248 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 965419 965473 965650 "FSINT" 965846 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 963746 964412 964715 "FSERIES" 965198 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 962760 962876 963107 "FSCINT" 963626 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 958994 961704 961745 "FSAGG" 962115 NIL FSAGG (NIL T) -9 NIL 962374 NIL) (-424 956756 957357 958153 "FSAGG-" 958248 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 955798 955941 956168 "FSAGG2" 956609 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 953453 953732 954286 "FS2UPS" 955516 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953035 953078 953233 "FS2" 953404 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 951892 952063 952372 "FS2EXPXP" 952860 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 951318 951433 951585 "FRUTIL" 951772 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 942772 946813 948171 "FR" 949992 NIL FR (NIL T) -8 NIL NIL NIL) (-417 937847 940490 940530 "FRNAALG" 941926 NIL FRNAALG (NIL T) -9 NIL 942533 NIL) (-416 933525 934596 935871 "FRNAALG-" 936621 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933163 933206 933333 "FRNAAF2" 933476 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 931570 932017 932312 "FRMOD" 932975 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 929349 929953 930270 "FRIDEAL" 931361 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 928544 928631 928920 "FRIDEAL2" 929256 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 927677 928091 928132 "FRETRCT" 928137 NIL FRETRCT (NIL T) -9 NIL 928313 NIL) (-410 926789 927020 927371 "FRETRCT-" 927376 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 924001 925177 925236 "FRAMALG" 926118 NIL FRAMALG (NIL T T) -9 NIL 926410 NIL) (-408 922135 922590 923220 "FRAMALG-" 923443 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916092 921610 921886 "FRAC" 921891 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 915728 915785 915892 "FRAC2" 916029 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 915364 915421 915528 "FR2" 915665 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910037 912889 912917 "FPS" 914036 T FPS (NIL) -9 NIL 914593 NIL) (-403 909486 909595 909759 "FPS-" 909905 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 906940 908575 908603 "FPC" 908828 T FPC (NIL) -9 NIL 908970 NIL) (-401 906733 906773 906870 "FPC-" 906875 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 905611 906221 906262 "FPATMAB" 906267 NIL FPATMAB (NIL T) -9 NIL 906419 NIL) (-399 903311 903787 904213 "FPARFRAC" 905248 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 898705 899203 899885 "FORTRAN" 902743 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 896421 896921 897460 "FORT" 898186 T FORT (NIL) -7 NIL NIL NIL) (-396 894097 894659 894687 "FORTFN" 895747 T FORTFN (NIL) -9 NIL 896371 NIL) (-395 893861 893911 893939 "FORTCAT" 893998 T FORTCAT (NIL) -9 NIL 894060 NIL) (-394 891994 892477 892867 "FORMULA" 893491 T FORMULA (NIL) -8 NIL NIL NIL) (-393 891782 891812 891881 "FORMULA1" 891958 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891305 891357 891530 "FORDER" 891724 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 890401 890565 890758 "FOP" 891132 T FOP (NIL) -7 NIL NIL NIL) (-390 889009 889681 889855 "FNLA" 890283 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 887764 888153 888181 "FNCAT" 888641 T FNCAT (NIL) -9 NIL 888901 NIL) (-388 887330 887723 887751 "FNAME" 887756 T FNAME (NIL) -8 NIL NIL NIL) (-387 885993 886922 886950 "FMTC" 886955 T FMTC (NIL) -9 NIL 886991 NIL) (-386 882354 883516 884145 "FMONOID" 885397 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 881573 882096 882245 "FM" 882250 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 878997 879643 879671 "FMFUN" 880815 T FMFUN (NIL) -9 NIL 881523 NIL) (-383 878266 878447 878475 "FMC" 878765 T FMC (NIL) -9 NIL 878947 NIL) (-382 875460 876294 876348 "FMCAT" 877543 NIL FMCAT (NIL T T) -9 NIL 878038 NIL) (-381 874353 875226 875326 "FM1" 875405 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872127 872543 873037 "FLOATRP" 873904 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 865751 869856 870477 "FLOAT" 871526 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863189 863689 864267 "FLOATCP" 865218 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 861998 862802 862843 "FLINEXP" 862848 NIL FLINEXP (NIL T) -9 NIL 862941 NIL) (-376 861152 861387 861715 "FLINEXP-" 861720 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860228 860372 860596 "FLASORT" 861004 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 857445 858287 858339 "FLALG" 859566 NIL FLALG (NIL T T) -9 NIL 860033 NIL) (-373 851229 854931 854972 "FLAGG" 856234 NIL FLAGG (NIL T) -9 NIL 856886 NIL) (-372 849955 850294 850784 "FLAGG-" 850789 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 848997 849140 849367 "FLAGG2" 849808 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 845972 846946 847005 "FINRALG" 848133 NIL FINRALG (NIL T T) -9 NIL 848641 NIL) (-369 845132 845361 845700 "FINRALG-" 845705 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 844538 844751 844779 "FINITE" 844975 T FINITE (NIL) -9 NIL 845082 NIL) (-367 836996 839157 839197 "FINAALG" 842864 NIL FINAALG (NIL T) -9 NIL 844317 NIL) (-366 832337 833378 834522 "FINAALG-" 835901 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 831732 832092 832195 "FILE" 832267 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830416 830728 830782 "FILECAT" 831466 NIL FILECAT (NIL T T) -9 NIL 831682 NIL) (-363 828284 829778 829806 "FIELD" 829846 T FIELD (NIL) -9 NIL 829926 NIL) (-362 826904 827289 827800 "FIELD-" 827805 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 824782 825539 825886 "FGROUP" 826590 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 823872 824036 824256 "FGLMICPK" 824614 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 819739 823797 823854 "FFX" 823859 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819340 819401 819536 "FFSLPE" 819672 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815333 816112 816908 "FFPOLY" 818576 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 814837 814873 815082 "FFPOLY2" 815291 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 810723 814756 814819 "FFP" 814824 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806156 810634 810698 "FF" 810703 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801317 805499 805689 "FFNBX" 806010 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796291 800452 800710 "FFNBP" 801171 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 790959 795575 795786 "FFNB" 796124 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 789791 789989 790304 "FFINTBAS" 790756 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786019 788198 788226 "FFIELDC" 788846 T FFIELDC (NIL) -9 NIL 789222 NIL) (-348 784682 785052 785549 "FFIELDC-" 785554 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784252 784297 784421 "FFHOM" 784624 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 781950 782434 782951 "FFF" 783767 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 777603 781692 781793 "FFCGX" 781893 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773271 777335 777442 "FFCGP" 777546 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768489 772998 773106 "FFCG" 773207 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750322 759360 759446 "FFCAT" 764611 NIL FFCAT (NIL T T T) -9 NIL 766062 NIL) (-341 745520 746567 747881 "FFCAT-" 749111 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 744931 744974 745209 "FFCAT2" 745471 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734142 737903 739123 "FEXPR" 743783 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733142 733577 733618 "FEVALAB" 733702 NIL FEVALAB (NIL T) -9 NIL 733963 NIL) (-337 732301 732511 732849 "FEVALAB-" 732854 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 730894 731684 731887 "FDIV" 732200 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 727960 728675 728790 "FDIVCAT" 730358 NIL FDIVCAT (NIL T T T T) -9 NIL 730795 NIL) (-334 727722 727749 727919 "FDIVCAT-" 727924 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 726942 727029 727306 "FDIV2" 727629 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 725628 725887 726176 "FCPAK1" 726673 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 724756 725128 725269 "FCOMP" 725519 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708493 711906 715444 "FC" 721238 T FC (NIL) -8 NIL NIL NIL) (-329 701072 705057 705097 "FAXF" 706899 NIL FAXF (NIL T) -9 NIL 707591 NIL) (-328 698351 699006 699831 "FAXF-" 700296 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693451 697727 697903 "FARRAY" 698208 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 688704 690736 690789 "FAMR" 691812 NIL FAMR (NIL T T) -9 NIL 692272 NIL) (-325 687594 687896 688331 "FAMR-" 688336 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 686790 687516 687569 "FAMONOID" 687574 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 684602 685286 685339 "FAMONC" 686280 NIL FAMONC (NIL T T) -9 NIL 686666 NIL) (-322 683294 684356 684493 "FAGROUP" 684498 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681089 681408 681811 "FACUTIL" 682975 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680188 680373 680595 "FACTFUNC" 680899 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672593 679439 679651 "EXPUPXS" 680044 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670076 670616 671202 "EXPRTUBE" 672027 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666270 666862 667599 "EXPRODE" 669415 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 651644 664925 665353 "EXPR" 665874 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646051 646638 647451 "EXPR2UPS" 650942 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 645687 645744 645851 "EXPR2" 645988 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637092 644819 645116 "EXPEXPAN" 645524 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 636919 637049 637078 "EXIT" 637083 T EXIT (NIL) -8 NIL NIL NIL) (-311 636426 636643 636734 "EXITAST" 636848 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636053 636115 636228 "EVALCYC" 636358 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635594 635712 635753 "EVALAB" 635923 NIL EVALAB (NIL T) -9 NIL 636027 NIL) (-308 635075 635197 635418 "EVALAB-" 635423 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632543 633811 633839 "EUCDOM" 634394 T EUCDOM (NIL) -9 NIL 634744 NIL) (-306 630948 631390 631980 "EUCDOM-" 631985 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618488 621246 623996 "ESTOOLS" 628218 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618120 618177 618286 "ESTOOLS2" 618425 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 617871 617913 617993 "ESTOOLS1" 618072 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 611776 613504 613532 "ES" 616300 T ES (NIL) -9 NIL 617709 NIL) (-301 606724 608010 609827 "ES-" 609991 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603099 603859 604639 "ESCONT" 605964 T ESCONT (NIL) -7 NIL NIL NIL) (-299 602844 602876 602958 "ESCONT1" 603061 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602519 602569 602669 "ES2" 602788 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602149 602207 602316 "ES1" 602455 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601365 601494 601670 "ERROR" 601993 T ERROR (NIL) -7 NIL NIL NIL) (-295 594868 601224 601315 "EQTBL" 601320 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587425 590182 591631 "EQ" 593452 NIL -3303 (NIL T) -8 NIL NIL NIL) (-293 587057 587114 587223 "EQ2" 587362 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582349 583395 584488 "EP" 585996 NIL EP (NIL T) -7 NIL NIL NIL) (-291 580931 581232 581549 "ENV" 582052 T ENV (NIL) -8 NIL NIL NIL) (-290 580110 580630 580658 "ENTIRER" 580663 T ENTIRER (NIL) -9 NIL 580709 NIL) (-289 576612 578065 578435 "EMR" 579909 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 575756 575941 575995 "ELTAGG" 576375 NIL ELTAGG (NIL T T) -9 NIL 576586 NIL) (-287 575475 575537 575678 "ELTAGG-" 575683 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575264 575293 575347 "ELTAB" 575431 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574390 574536 574735 "ELFUTS" 575115 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574132 574188 574216 "ELEMFUN" 574321 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574002 574023 574091 "ELEMFUN-" 574096 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 568893 572102 572143 "ELAGG" 573083 NIL ELAGG (NIL T) -9 NIL 573546 NIL) (-281 567178 567612 568275 "ELAGG-" 568280 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 565835 566115 566410 "ELABEXPR" 566903 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 558701 560502 561329 "EFUPXS" 565111 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552151 553952 554762 "EFULS" 557977 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549573 549931 550410 "EFSTRUC" 551783 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538645 540210 541770 "EF" 548088 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 537746 538130 538279 "EAB" 538516 T EAB (NIL) -8 NIL NIL NIL) (-274 536955 537705 537733 "E04UCFA" 537738 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536164 536914 536942 "E04NAFA" 536947 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535373 536123 536151 "E04MBFA" 536156 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534582 535332 535360 "E04JAFA" 535365 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 533793 534541 534569 "E04GCFA" 534574 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533004 533752 533780 "E04FDFA" 533785 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532213 532963 532991 "E04DGFA" 532996 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526391 527738 529102 "E04AGNT" 530869 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525097 525577 525617 "DVARCAT" 526092 NIL DVARCAT (NIL T) -9 NIL 526291 NIL) (-265 524301 524513 524827 "DVARCAT-" 524832 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517201 524100 524229 "DSMP" 524234 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512011 513146 514214 "DROPT" 516153 T DROPT (NIL) -8 NIL NIL NIL) (-262 511676 511735 511833 "DROPT1" 511946 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 506791 507917 509054 "DROPT0" 510559 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505136 505461 505847 "DRAWPT" 506425 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 499723 500646 501725 "DRAW" 504110 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499356 499409 499527 "DRAWHACK" 499664 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498087 498356 498647 "DRAWCX" 499085 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497603 497671 497822 "DRAWCURV" 498013 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488074 490033 492148 "DRAWCFUN" 495508 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 484887 486769 486810 "DQAGG" 487439 NIL DQAGG (NIL T) -9 NIL 487712 NIL) (-253 473166 479865 479948 "DPOLCAT" 481800 NIL DPOLCAT (NIL T T T T) -9 NIL 482345 NIL) (-252 468005 469351 471309 "DPOLCAT-" 471314 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461160 467866 467964 "DPMO" 467969 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454218 460940 461107 "DPMM" 461112 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 453850 454137 454185 "DOMCTOR" 454190 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453145 453372 453509 "DOMAIN" 453733 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 446896 452780 452932 "DMP" 453046 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446496 446552 446696 "DLP" 446834 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440366 445823 446013 "DLIST" 446338 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437210 439219 439260 "DLAGG" 439810 NIL DLAGG (NIL T) -9 NIL 440040 NIL) (-243 436023 436653 436681 "DIVRING" 436773 T DIVRING (NIL) -9 NIL 436856 NIL) (-242 435260 435450 435750 "DIVRING-" 435755 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433362 433719 434125 "DISPLAY" 434874 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427304 433276 433339 "DIRPROD" 433344 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426152 426355 426620 "DIRPROD2" 427097 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415415 421367 421420 "DIRPCAT" 421830 NIL DIRPCAT (NIL NIL T) -9 NIL 422670 NIL) (-237 412741 413383 414264 "DIRPCAT-" 414601 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412028 412188 412374 "DIOSP" 412575 T DIOSP (NIL) -7 NIL NIL NIL) (-235 408730 410940 410981 "DIOPS" 411415 NIL DIOPS (NIL T) -9 NIL 411644 NIL) (-234 408279 408393 408584 "DIOPS-" 408589 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407171 407765 407793 "DIFRING" 407980 T DIFRING (NIL) -9 NIL 408090 NIL) (-232 406817 406894 407046 "DIFRING-" 407051 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404622 405860 405901 "DIFEXT" 406264 NIL DIFEXT (NIL T) -9 NIL 406558 NIL) (-230 402907 403335 404001 "DIFEXT-" 404006 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400229 402439 402480 "DIAGG" 402485 NIL DIAGG (NIL T) -9 NIL 402505 NIL) (-228 399613 399770 400022 "DIAGG-" 400027 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395078 398572 398849 "DHMATRIX" 399382 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390690 391599 392609 "DFSFUN" 394088 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 385806 389621 389933 "DFLOAT" 390398 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384034 384315 384711 "DFINTTLS" 385514 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381098 382055 382455 "DERHAM" 383700 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 378947 380873 380962 "DEQUEUE" 381042 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378162 378295 378491 "DEGRED" 378809 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374557 375302 376155 "DEFINTRF" 377390 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372084 372553 373152 "DEFINTEF" 374076 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371461 371704 371819 "DEFAST" 371989 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365500 371056 371205 "DECIMAL" 371332 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363012 363470 363976 "DDFACT" 365044 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362608 362651 362802 "DBLRESP" 362963 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360507 360841 361201 "DBASE" 362375 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359776 359987 360133 "DATAARY" 360406 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 358909 359735 359763 "D03FAFA" 359768 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358043 358868 358896 "D03EEFA" 358901 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 355993 356459 356948 "D03AGNT" 357574 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355309 355952 355980 "D02EJFA" 355985 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354625 355268 355296 "D02CJFA" 355301 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 353941 354584 354612 "D02BHFA" 354617 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353257 353900 353928 "D02BBFA" 353933 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346455 348043 349649 "D02AGNT" 351671 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344224 344746 345292 "D01WGTS" 345929 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343319 344183 344211 "D01TRNS" 344216 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342414 343278 343306 "D01GBFA" 343311 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341509 342373 342401 "D01FCFA" 342406 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340604 341468 341496 "D01ASFA" 341501 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339699 340563 340591 "D01AQFA" 340596 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338794 339658 339686 "D01APFA" 339691 T D01APFA (NIL) -8 NIL NIL NIL) (-197 337889 338753 338781 "D01ANFA" 338786 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 336984 337848 337876 "D01AMFA" 337881 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336079 336943 336971 "D01ALFA" 336976 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335174 336038 336066 "D01AKFA" 336071 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334269 335133 335161 "D01AJFA" 335166 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327566 329117 330678 "D01AGNT" 332728 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 326903 327031 327183 "CYCLOTOM" 327434 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323638 324351 325078 "CYCLES" 326196 T CYCLES (NIL) -7 NIL NIL NIL) (-189 322950 323084 323255 "CVMP" 323499 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320721 320979 321355 "CTRIGMNP" 322678 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320212 320512 320586 "CTOR" 320667 T CTOR (NIL) -8 NIL NIL NIL) (-186 319748 319943 320044 "CTORKIND" 320131 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319096 319355 319383 "CTORCAT" 319565 T CTORCAT (NIL) -9 NIL 319678 NIL) (-184 318694 318805 318964 "CTORCAT-" 318969 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318210 318397 318495 "CTORCALL" 318616 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317584 317683 317836 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256004 "COLOR" 256438 T COLOR (NIL) -8 NIL NIL NIL) (-156 254942 255160 255252 "COLONAST" 255367 T COLONAST (NIL) -8 NIL NIL NIL) (-155 254582 254629 254754 "CMPLXRT" 254889 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254057 254282 254381 "CLLCTAST" 254503 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 249559 250587 251667 "CLIP" 252997 T CLIP (NIL) -7 NIL NIL NIL) (-152 247941 248665 248904 "CLIF" 249386 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244163 246087 246128 "CLAGG" 247057 NIL CLAGG (NIL T) -9 NIL 247593 NIL) (-150 242585 243042 243625 "CLAGG-" 243630 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242129 242214 242354 "CINTSLPE" 242494 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239630 240101 240649 "CHVAR" 241657 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 238873 239393 239421 "CHARZ" 239426 T CHARZ (NIL) -9 NIL 239441 NIL) (-146 238627 238667 238745 "CHARPOL" 238827 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237754 238307 238335 "CHARNZ" 238382 T CHARNZ (NIL) -9 NIL 238438 NIL) (-144 235743 236444 236779 "CHAR" 237439 T CHAR (NIL) -8 NIL NIL NIL) (-143 235469 235530 235558 "CFCAT" 235669 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234714 234825 235007 "CDEN" 235353 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230706 233867 234147 "CCLASS" 234454 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230013 230156 230319 "CATEGORY" 230563 T -10 (NIL) -8 NIL NIL NIL) (-139 229645 229932 229980 "CATCTOR" 229985 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229119 229345 229444 "CATAST" 229566 T CATAST (NIL) -8 NIL NIL NIL) (-137 228622 228840 228932 "CASEAST" 229047 T CASEAST (NIL) -8 NIL NIL NIL) (-136 223674 224651 225404 "CARTEN" 227925 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 222782 222930 223151 "CARTEN2" 223521 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221124 221932 222189 "CARD" 222545 T CARD (NIL) -8 NIL NIL NIL) (-133 220727 220928 221003 "CAPSLAST" 221069 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220099 220427 220455 "CACHSET" 220587 T CACHSET (NIL) -9 NIL 220664 NIL) (-131 219595 219891 219919 "CABMON" 219969 T CABMON (NIL) -9 NIL 220025 NIL) (-130 219095 219299 219409 "BYTEORD" 219505 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218118 218641 218777 "BYTE" 218940 T BYTE (NIL) -8 NIL NIL 219056) (-128 213519 217623 217795 "BYTEBUF" 217966 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211076 213211 213318 "BTREE" 213445 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208574 210724 210846 "BTOURN" 210986 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205991 208044 208085 "BTCAT" 208153 NIL BTCAT (NIL T) -9 NIL 208230 NIL) (-124 205658 205738 205887 "BTCAT-" 205892 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200950 204801 204829 "BTAGG" 205051 T BTAGG (NIL) -9 NIL 205212 NIL) (-122 200440 200565 200771 "BTAGG-" 200776 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197484 199718 199933 "BSTREE" 200257 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196622 196748 196932 "BRILL" 197340 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193321 195348 195389 "BRAGG" 196038 NIL BRAGG (NIL T) -9 NIL 196296 NIL) (-118 191850 192256 192811 "BRAGG-" 192816 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185114 191196 191380 "BPADICRT" 191698 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183464 185051 185096 "BPADIC" 185101 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183162 183192 183306 "BOUNDZRO" 183428 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178677 179768 180635 "BOP" 182315 T BOP (NIL) -8 NIL NIL NIL) (-113 176298 176742 177262 "BOP1" 178190 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175000 175722 175915 "BOOLEAN" 176125 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174362 174740 174794 "BMODULE" 174799 NIL BMODULE (NIL T T) -9 NIL 174864 NIL) (-110 170192 174160 174233 "BITS" 174309 T BITS (NIL) -8 NIL NIL NIL) (-109 169604 169726 169868 "BINDING" 170070 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169201 169349 "BINARY" 169476 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL 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ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437 NIL) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856 NIL) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283 NIL) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332 NIL) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908 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 diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index c3fec088..2e62d387 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,65 +1,103 @@ -(735720 . 3443021573) -(((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1151)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)) (-5 *2 (-1262)) - (-5 *1 (-984 *4 *5 *6 *7 *8)) (-4 *8 (-1065 *4 *5 *6 *7)))) - ((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1151)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)) (-5 *2 (-1262)) - (-5 *1 (-1100 *4 *5 *6 *7 *8)) (-4 *8 (-1065 *4 *5 *6 *7))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1149 *3)) (-4 *3 (-1045)) (-5 *1 (-1153 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1249 *2 *3 *4)) (-4 *2 (-1045)) (-14 *3 (-1169)) - (-14 *4 *2)))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1193))))) -(((*1 *2 *3 *3 *3 *3 *3 *3 *4 *4 *4 *3 *3 *5 *6 *3 *6 *6 *5 *6 *6 *6 *6 - *5 *3 *3 *3 *3 *3 *6 *6 *6 *3 *3 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(-640 (-2 (|:| |poly| *6) (|:| -1420 (-649 *6 (-407 *6)))))) + (-5 *1 (-808 *5 *6)) (-5 *3 (-649 *6 (-407 *6)))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-363)) (-5 *2 (-640 *3)) (-5 *1 (-941 *4 *3)) - (-4 *3 (-1233 *4))))) -(((*1 *2 *3) - (-12 (-4 *4 (-555)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -2315 *4))) + (-12 (-4 *4 (-555)) + (-5 *2 + (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) (-5 *1 (-965 *4 *3)) (-4 *3 (-1233 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-1262)) (-5 *1 (-818))))) -(((*1 *1) (-5 *1 (-1259)))) -(((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -1414 *1) (|:| -4394 *1) (|:| |associate| *1))) - (-4 *1 (-555))))) +(((*1 *2 *2) (-12 (-5 *2 (-563)) (-5 *1 (-552))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -72,7 +110,7 @@ ((*1 *1 *1) (-4 *1 (-284))) ((*1 *2 *3) (-12 (-5 *3 (-418 *4)) (-4 *4 (-555)) - (-5 *2 (-640 (-2 (|:| -2311 (-767)) (|:| |logand| *4)))) + (-5 *2 (-640 (-2 (|:| -2310 (-767)) (|:| |logand| *4)))) (-5 *1 (-320 *4)))) ((*1 *1 *1) (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-640 (-1169))) @@ -92,8 +130,16 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-767)) (-5 *1 (-1277 *3 *4)) (-4 *4 (-713 (-407 (-563)))) (-4 *3 (-846)) (-4 *4 (-172))))) -(((*1 *1 *2) (-12 (-5 *1 (-686 *2)) (-4 *2 (-610 (-858)))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-1233 *2)) (-4 *2 (-1045))))) +(((*1 *2 *3 *4) + (-12 (-5 *2 (-640 (-169 *4))) (-5 *1 (-155 *3 *4)) + (-4 *3 (-1233 (-169 (-563)))) (-4 *4 (-13 (-363) (-844))))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-363) (-844))) (-5 *2 (-640 (-169 *4))) + (-5 *1 (-181 *4 *3)) (-4 *3 (-1233 (-169 *4))))) + ((*1 *2 *3 *4) + (-12 (-4 *4 (-13 (-363) (-844))) (-5 *2 (-640 (-169 *4))) + (-5 *1 (-181 *4 *3)) (-4 *3 (-1233 (-169 *4)))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-379)) (-5 *2 (-1262)) (-5 *1 (-1259))))) (((*1 *2 *1) (-12 (-4 *1 (-132)) (-5 *2 (-767)))) ((*1 *2 *3 *1 *2) (-12 (-5 *2 (-563)) (-4 *1 (-373 *3)) (-4 *3 (-1208)) @@ -108,190 +154,152 @@ ((*1 *2 *3 *1 *2) (-12 (-4 *1 (-1137)) (-5 *2 (-563)) (-5 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(-555))) (-5 *2 (-1165 *5)) (-5 *1 (-32 *4 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-609 *1)) (-4 *1 (-1045)) (-4 *1 (-302)) + (-5 *2 (-1165 *1))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-788)))) ((*1 *2 *1) (-12 (-4 *1 (-382 *3 *2)) (-4 *3 (-1045)) (-4 *2 (-1093)))) ((*1 *2 *1) (-12 (-14 *3 (-640 (-1169))) (-4 *4 (-172)) - (-4 *6 (-238 (-3608 *3) (-767))) + (-4 *6 (-238 (-3610 *3) (-767))) (-14 *7 - (-1 (-112) (-2 (|:| -2555 *5) (|:| -1654 *6)) - (-2 (|:| -2555 *5) (|:| -1654 *6)))) + (-1 (-112) (-2 (|:| -2552 *5) (|:| -3311 *6)) + (-2 (|:| -2552 *5) (|:| -3311 *6)))) (-5 *2 (-709 *5 *6 *7)) (-5 *1 (-461 *3 *4 *5 *6 *7 *8)) (-4 *5 (-846)) (-4 *8 (-945 *4 *6 (-860 *3))))) ((*1 *2 *1) @@ -8262,110 +7827,102 @@ ((*1 *1 *1) (-12 (-4 *1 (-969 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-788)) (-4 *4 (-846))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) - (-4 *4 (-846)))) - ((*1 *2 *2 *1) - (-12 (-4 *1 (-1201 *3 *4 *5 *2)) (-4 *3 (-555)) (-4 *4 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(-4 *2 (-1233 *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 (-1212)) - (-4 *4 (-1233 (-407 *2))) (-4 *2 (-1233 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1201 *3 *4 *5 *6)) (-4 *3 (-555)) (-4 *4 (-789)) - (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1201 *4 *5 *6 *3)) (-4 *4 (-555)) (-4 *5 (-789)) - (-4 *6 (-846)) (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-112))))) + (-12 (-5 *2 (-418 *3)) (-5 *1 (-1003 *3)) + (-4 *3 (-1233 (-407 (-563)))))) + ((*1 *2 *3) + (-12 (-5 *2 (-418 *3)) (-5 *1 (-1222 *3)) (-4 *3 (-1233 (-563)))))) (((*1 *2 *1) (-12 (-5 *2 (-563)) (-5 *1 (-854)))) ((*1 *2 *1) (-12 (-5 *2 (-1097)) (-5 *1 (-961)))) ((*1 *2 *1) (-12 (-5 *2 (-1151)) (-5 *1 (-985)))) @@ -8832,10 +8393,14 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-1093) (-34))) (-5 *1 (-1133 *2 *3)) (-4 *3 (-13 (-1093) (-34)))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-767)) (-4 *1 (-1233 *3)) (-4 *3 (-1045))))) -(((*1 *1 *2) 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(-1165 (-1020 *4)))) (-5 *3 (-858)) + (-5 *1 (-1020 *4)) (-4 *4 (-13 (-844) (-363) (-1018)))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1 (-939 (-225)) (-939 (-225)))) (-5 *3 (-640 (-263))) + (-5 *1 (-261)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1 (-939 (-225)) (-939 (-225)))) (-5 *1 (-263)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-640 (-481 *5 *6))) (-5 *3 (-481 *5 *6)) + (-14 *5 (-640 (-1169))) (-4 *6 (-452)) (-5 *2 (-1257 *6)) + (-5 *1 (-628 *5 *6))))) +(((*1 *2 *1) (-12 (-5 *2 (-640 (-1078))) (-5 *1 (-291))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-640 (-316 (-225)))) (|:| -2523 (-640 (-225))))) + (-2 (|:| |lfn| (-640 (-316 (-225)))) (|:| -2522 (-640 (-225))))) (-5 *2 (-640 (-1169))) (-5 *1 (-267)))) ((*1 *2 *3) (-12 (-5 *3 (-1165 *7)) (-4 *7 (-945 *6 *4 *5)) (-4 *4 (-789)) @@ -8895,7 +8474,7 @@ (-5 *1 (-946 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-363) - (-10 -8 (-15 -1693 ($ *7)) (-15 -2143 (*7 $)) (-15 -2154 (*7 $))))))) + (-10 -8 (-15 -1692 ($ *7)) (-15 -2143 (*7 $)) (-15 -2153 (*7 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1095 (-1169))) (-5 *1 (-962 *3)) (-4 *3 (-963)))) ((*1 *2 *1) @@ -8907,62 +8486,55 @@ ((*1 *2 *3) (-12 (-5 *3 (-407 (-948 *4))) (-4 *4 (-555)) (-5 *2 (-640 (-1169))) (-5 *1 (-1039 *4))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-407 (-948 *3))) (-5 *1 (-453 *3 *4 *5 *6)) - (-4 *3 (-555)) (-4 *3 (-172)) (-14 *4 (-917)) - (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 *3)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-4 *3 (-555)) - (-5 *2 (-1165 *3))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-917)) (-5 *4 (-870)) (-5 *2 (-1262)) (-5 *1 (-1258)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-917)) (-5 *4 (-1151)) (-5 *2 (-1262)) (-5 *1 (-1258)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-1262)) (-5 *1 (-1259))))) +(((*1 *1 *2 *2) (-12 (-5 *1 (-873 *2)) (-4 *2 (-1208)))) + ((*1 *1 *2 *2 *2) (-12 (-5 *1 (-875 *2)) (-4 *2 (-1208)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1127 *3)) (-4 *3 (-1045)) (-5 *2 (-640 (-939 *3))))) + ((*1 *1 *2) + (-12 (-5 *2 (-640 (-939 *3))) (-4 *3 (-1045)) (-4 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(-14 *2 (-563)) (-5 *1 (-868 *2 *3)) (-4 *3 (-865 *2)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-563)) (-4 *1 (-1219 *3 *4)) (-4 *3 (-1045)) + (-4 *4 (-1248 *3)))) + ((*1 *1 *1) + (-12 (-4 *1 (-1219 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-1248 *2))))) +(((*1 *2 *1) + (|partial| -12 (-5 *2 (-1055 (-1020 *3) (-1165 (-1020 *3)))) + (-5 *1 (-1020 *3)) (-4 *3 (-13 (-844) (-363) (-1018)))))) (((*1 *1) (-12 (-5 *1 (-686 *2)) (-4 *2 (-610 (-858)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-684 (-948 *4))) (-5 *1 (-1024 *4)) - (-4 *4 (-1045))))) +(((*1 *2 *2) + (-12 (-5 *2 (-640 (-481 *3 *4))) (-14 *3 (-640 (-1169))) + (-4 *4 (-452)) (-5 *1 (-628 *3 *4))))) +(((*1 *2 *3 *3 *1) + (|partial| -12 (-5 *3 (-1169)) (-5 *2 (-1097)) (-5 *1 (-291))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1165 (-407 (-1165 *2)))) (-5 *4 (-609 *2)) (-4 *2 (-13 (-430 *5) (-27) (-1193))) @@ -8979,7 +8551,7 @@ (-4 *6 (-1045)) (-4 *2 (-13 (-363) - (-10 -8 (-15 -1693 ($ *7)) (-15 -2143 (*7 $)) (-15 -2154 (*7 $))))) + (-10 -8 (-15 -1692 ($ 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@@ (-4 *2 (-363)) (-14 *5 (-989 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-709 *5 *6 *7)) (-4 *5 (-846)) - (-4 *6 (-238 (-3608 *4) (-767))) + (-4 *6 (-238 (-3610 *4) (-767))) (-14 *7 - (-1 (-112) (-2 (|:| -2555 *5) (|:| -1654 *6)) - (-2 (|:| -2555 *5) (|:| -1654 *6)))) + (-1 (-112) (-2 (|:| -2552 *5) (|:| -3311 *6)) + (-2 (|:| -2552 *5) (|:| -3311 *6)))) (-14 *4 (-640 (-1169))) (-4 *2 (-172)) (-5 *1 (-461 *4 *2 *5 *6 *7 *8)) (-4 *8 (-945 *2 *6 (-860 *4))))) ((*1 *1 *2 *3) @@ -9062,24 +8654,31 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-969 *4 *3 *2)) (-4 *4 (-1045)) (-4 *3 (-788)) (-4 *2 (-846))))) -(((*1 *2 *1) (-12 (-5 *2 (-640 (-1169))) (-5 *1 (-1173))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1127 *3)) (-4 *3 (-1045)) (-5 *2 (-640 (-939 *3))))) + ((*1 *1 *2) + (-12 (-5 *2 (-640 (-939 *3))) (-4 *3 (-1045)) (-4 *1 (-1127 *3)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-640 (-640 *3))) (-4 *1 (-1127 *3)) (-4 *3 (-1045)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-640 (-939 *3))) (-4 *1 (-1127 *3)) (-4 *3 (-1045))))) (((*1 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(-563)) - (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *3) + (-12 (-5 *3 (-640 (-481 *4 *5))) (-14 *4 (-640 (-1169))) + (-4 *5 (-452)) + (-5 *2 + (-2 (|:| |gblist| (-640 (-247 *4 *5))) + (|:| |gvlist| (-640 (-563))))) + (-5 *1 (-628 *4 *5))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225))) - (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -4166 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-2 @@ -9250,7 +8828,7 @@ (-3 (|:| |str| (-1149 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2516 + (|:| -4166 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -9258,8 +8836,14 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-558))))) -(((*1 *2 *3 *4) +(((*1 *2 *1) (-12 (-4 *1 (-1127 *3)) (-4 *3 (-1045)) (-5 *2 (-112))))) +(((*1 *2 *3 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(-5 *2 (-316 (-225))) (-5 *1 (-305))))) -(((*1 *2 *3 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) - (-5 *1 (-751))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-563)) (-5 *1 (-691 *2)) (-4 *2 (-1233 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *2 *2)) (-4 *2 (-1248 *4)) (-5 *1 (-1250 *4 *2)) - (-4 *4 (-38 (-407 (-563))))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-563)) (-5 *2 (-112)) (-5 *1 (-552))))) + (-12 (|has| *2 (-6 (-4410 "*"))) (-4 *5 (-373 *2)) (-4 *6 (-373 *2)) + (-4 *2 (-1045)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1233 *2)) + (-4 *4 (-682 *2 *5 *6))))) (((*1 *1 *1) (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) (-4 *4 (-846)))) @@ -9397,8 +9013,8 @@ (-12 (-5 *3 (-684 *5)) (-5 *4 (-1257 *5)) (-4 *5 (-363)) (-5 *2 (-767)) (-5 *1 (-662 *5)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-363)) (-4 *6 (-13 (-373 *5) (-10 -7 (-6 -4408)))) - (-4 *4 (-13 (-373 *5) (-10 -7 (-6 -4408)))) (-5 *2 (-767)) + (-12 (-4 *5 (-363)) (-4 *6 (-13 (-373 *5) (-10 -7 (-6 -4409)))) + (-4 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(-1002))))) +(((*1 *2 *1) (-12 - (-5 *3 - (-2 (|:| -1994 (-379)) (|:| -3348 (-1151)) - (|:| |explanations| (-640 (-1151))) (|:| |extra| (-1031)))) - (-5 *2 (-1031)) (-5 *1 (-305))))) + (-5 *2 + (-640 + (-2 + (|:| -2387 + (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225))) + (|:| -4166 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (|:| -2556 + (-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| (-1149 (-225))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4166 + (-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 (-558)))) + ((*1 *2 *1) + (-12 (-4 *1 (-601 *3 *4)) (-4 *3 (-1093)) (-4 *4 (-1208)) + (-5 *2 (-640 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-114)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-1151)) (-4 *4 (-846)) (-5 *1 (-925 *4 *2)) @@ -10696,29 +10489,50 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-1169)) (-5 *4 (-1151)) (-5 *2 (-316 (-563))) (-5 *1 (-926))))) +(((*1 *1 *2) (-12 (-5 *2 (-316 (-169 (-379)))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-563))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-379))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-689))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-696))) (-5 *1 (-330)))) + ((*1 *1 *2) (-12 (-5 *2 (-316 (-694))) (-5 *1 (-330)))) + ((*1 *1) (-5 *1 (-330)))) +(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-123)))) (((*1 *2 *3 *4) - 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(|:| |particular| *1) (|:| -4013 (-640 *1)))) + (-4 *1 (-367 *3)))) + ((*1 *2) + (|partial| -12 + (-5 *2 + (-2 (|:| |particular| (-453 *3 *4 *5 *6)) + (|:| -4013 (-640 (-453 *3 *4 *5 *6))))) + (-5 *1 (-453 *3 *4 *5 *6)) (-4 *3 (-172)) (-14 *4 (-917)) + (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 *3)))))) (((*1 *2 *3) (-12 (-5 *3 (-767)) (-5 *2 (-1 (-379))) (-5 *1 (-1036))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-917)) (-4 *1 (-740 *3)) (-4 *3 (-172))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-875 (-1 (-225) (-225)))) (-5 *4 (-1087 (-379))) (-5 *5 (-640 (-263))) (-5 *2 (-1126 (-225))) (-5 *1 (-255)))) @@ -10772,117 +10586,128 @@ (-12 (-5 *3 (-878 *5)) (-5 *4 (-1085 (-379))) (-4 *5 (-13 (-611 (-536)) (-1093))) (-5 *2 (-1126 (-225))) (-5 *1 (-259 *5))))) -(((*1 *1 *2) (-12 (-5 *2 (-870)) (-5 *1 (-263)))) - ((*1 *1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-263))))) -(((*1 *2) - (|partial| -12 (-4 *3 (-555)) (-4 *3 (-172)) - (-5 *2 (-2 (|:| |particular| *1) (|:| -4315 (-640 *1)))) - (-4 *1 (-367 *3)))) - ((*1 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*3 *4 *5 *6)) + (-4 *3 (-555)) (-4 *3 (-172)) (-14 *4 (-917)) + (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 *3)))))) (((*1 *2 *1) - (-12 (-4 *1 (-335 *3 *4 *5 *6)) (-4 *3 (-363)) (-4 *4 (-1233 *3)) - (-4 *5 (-1233 (-407 *4))) (-4 *6 (-342 *3 *4 *5)) (-5 *2 (-112))))) + (-12 (-5 *2 (-1149 (-407 *3))) (-5 *1 (-174 *3)) (-4 *3 (-307))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4407)) (-4 *1 (-151 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4408)) (-4 *1 (-151 *3)) (-4 *3 (-1208)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1208)) (-5 *1 (-598 *3)))) @@ -10893,43 +10718,40 @@ (-4 *5 (-789)) (-4 *3 (-846)) (-4 *2 (-1059 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-767)) (-5 *1 (-1205 *2)) (-4 *2 (-1208))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-452))) (-5 *1 (-1199 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1193)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1201 *3 *4 *5 *6)) (-4 *3 (-555)) (-4 *4 (-789)) + (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 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*3) + (-12 (-4 *4 (-307)) (-4 *5 (-373 *4)) (-4 *6 (-373 *4)) + (-5 *2 (-2 (|:| |Hermite| *3) (|:| |eqMat| *3))) + (-5 *1 (-1117 *4 *5 *6 *3)) (-4 *3 (-682 *4 *5 *6))))) +(((*1 *2 *3 *3 *3 *4 *4 *3) (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) (-5 *1 (-751))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-529))))) -(((*1 *2) (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-5 *2 (-112))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-114) (-114))) (-5 *1 (-114))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-442 *3)) (-4 *3 (-1233 (-563)))))) -(((*1 *2 *3) - (-12 (-4 *4 (-349)) (-5 *2 (-112)) (-5 *1 (-216 *4 *3)) - (-4 *3 (-1233 *4))))) -(((*1 *2 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-755))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1093)) (-4 *3 (-896 *5)) (-5 *2 (-684 *3)) - (-5 *1 (-687 *5 *3 *6 *4)) (-4 *6 (-373 *3)) - (-4 *4 (-13 (-373 *5) (-10 -7 (-6 -4407))))))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -1701 *6) (|:| |sol?| (-112))) (-563) - *6)) - (-4 *6 (-363)) (-4 *7 (-1233 *6)) - (-5 *2 - (-3 (-2 (|:| |answer| (-407 *7)) (|:| |a0| *6)) - (-2 (|:| -3646 (-407 *7)) (|:| |coeff| (-407 *7))) "failed")) - (-5 *1 (-573 *6 *7)) (-5 *3 (-407 *7))))) +(((*1 *2 *1) (-12 (-5 *1 (-910 *2)) (-4 *2 (-307))))) +(((*1 *2 *1) + (-12 (-5 *2 (-407 (-948 *3))) (-5 *1 (-453 *3 *4 *5 *6)) + (-4 *3 (-555)) (-4 *3 (-172)) (-14 *4 (-917)) + (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 *3)))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 (-225) (-225))) (-5 *4 (-1087 (-379))) (-5 *5 (-640 (-263))) (-5 *2 (-1258)) (-5 *1 (-255)))) @@ -11027,6 +10849,20 @@ ((*1 *2 *3 *3 *3 *4) (-12 (-5 *3 (-640 (-225))) (-5 *4 (-640 (-263))) (-5 *2 (-1259)) (-5 *1 (-260))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1149 (-407 *3))) (-5 *1 (-174 *3)) (-4 *3 (-307))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-640 *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 *1) + (-12 (-4 *1 (-1201 *3 *4 *5 *6)) (-4 *3 (-555)) (-4 *4 (-789)) + (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1201 *4 *5 *6 *3)) (-4 *4 (-555)) (-4 *5 (-789)) + (-4 *6 (-846)) (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1208)) (-5 *1 (-598 *3)))) ((*1 *1 *2 *1) @@ -11142,9 +10978,9 @@ (-4 *6 (-363)) (-5 *2 (-584 *6)) (-5 *1 (-583 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -3646 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2840 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-363)) (-4 *6 (-363)) - (-5 *2 (-2 (|:| -3646 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2840 *6) (|:| |coeff| *6))) (-5 *1 (-583 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -11263,7 +11099,7 @@ (-4 *8 (-1045)) (-4 *6 (-789)) (-4 *2 (-13 (-1093) - (-10 -8 (-15 -1814 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-767)))))) + (-10 -8 (-15 -1813 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-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 (-1208)) @@ -11276,8 +11112,8 @@ (-4 *2 (-945 (-948 *4) *5 *6)) (-4 *5 (-789)) (-4 *6 (-13 (-846) - (-10 -8 (-15 -2220 ((-1169) $)) - (-15 -2518 ((-3 $ "failed") (-1169)))))) + (-10 -8 (-15 -2219 ((-1169) $)) + (-15 -2517 ((-3 $ "failed") (-1169)))))) (-5 *1 (-980 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-555)) (-4 *6 (-555)) @@ -11365,24 +11201,10 @@ (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1045)) (-5 *1 (-1280 *3 *4)) (-4 *4 (-842))))) (((*1 *2 *1) - (-12 (-4 *1 (-166 *3)) (-4 *3 (-172)) (-4 *3 (-545)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-418 *3)) (-4 *3 (-545)) (-4 *3 (-555)))) - ((*1 *2 *1) (-12 (-4 *1 (-545)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *1 (-793 *3)) (-4 *3 (-172)) (-4 *3 (-545)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-829 *3)) (-4 *3 (-545)) (-4 *3 (-1093)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-839 *3)) (-4 *3 (-545)) (-4 *3 (-1093)))) - ((*1 *2 *1) - (-12 (-4 *1 (-993 *3)) (-4 *3 (-172)) (-4 *3 (-545)) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-5 *2 (-112)) (-5 *1 (-1004 *3)) (-4 *3 (-1034 (-407 (-563))))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-767)) (-4 *4 (-555)) (-5 *1 (-965 *4 *2)) - (-4 *2 (-1233 *4))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-848 *2)) (-4 *2 (-1045)) (-4 *2 (-363))))) + (-12 (-5 *2 (-1149 (-563))) (-5 *1 (-1000 *3)) (-14 *3 (-563))))) +(((*1 *2 *1) + (-12 (-4 *1 (-601 *2 *3)) (-4 *3 (-1208)) (-4 *2 (-1093)) + (-4 *2 (-846))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-1087 *3)) (-4 *3 (-945 *7 *6 *4)) (-4 *6 (-789)) (-4 *4 (-846)) (-4 *7 (-555)) @@ -11417,40 +11239,50 @@ (-12 (-5 *4 (-1085 (-407 (-948 *5)))) (-5 *3 (-407 (-948 *5))) (-4 *5 (-13 (-555) (-846) (-1034 (-563)))) (-5 *2 (-3 *3 (-316 *5))) (-5 *1 (-1162 *5))))) -(((*1 *2 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-112)) (-5 *1 (-825))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) - (-12 (-5 *3 (-563)) (-5 *5 (-684 (-225))) (-5 *4 (-225)) - (-5 *2 (-1031)) (-5 *1 (-748))))) -(((*1 *1 *2) (-12 (-5 *2 (-640 *3)) (-4 *3 (-1208)) (-4 *1 (-107 *3))))) +(((*1 *2 *2) (-12 (-5 *2 (-1113)) (-5 *1 (-330))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-114))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-1045)) (-4 *2 (-682 *4 *5 *6)) + (-5 *1 (-104 *4 *3 *2 *5 *6)) (-4 *3 (-1233 *4)) (-4 *5 (-373 *4)) + (-4 *6 (-373 *4))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1165 (-563))) (-5 *1 (-938)) (-5 *3 (-563)))) + ((*1 *2 *2) + (-12 (-4 *3 (-307)) (-4 *4 (-373 *3)) (-4 *5 (-373 *3)) + (-5 *1 (-1117 *3 *4 *5 *2)) (-4 *2 (-682 *3 *4 *5))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) + (-5 *1 (-751))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-563)) (-5 *1 (-910 *3)) (-4 *3 (-307))))) (((*1 *2 *1) (-12 (-5 *2 (-407 (-948 *3))) (-5 *1 (-453 *3 *4 *5 *6)) (-4 *3 (-555)) (-4 *3 (-172)) (-14 *4 (-917)) (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 *3)))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-846) (-555))) (-5 *2 (-112)) (-5 *1 (-276 *4 *3)) - (-4 *3 (-13 (-430 *4) (-998)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-767)) (-5 *4 (-1257 *2)) (-4 *5 (-307)) - (-4 *6 (-988 *5)) (-4 *2 (-13 (-409 *6 *7) (-1034 *6))) - (-5 *1 (-413 *5 *6 *7 *2)) (-4 *7 (-1233 *6))))) -(((*1 *2 *1) - (-12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) - (-5 *2 (-1165 *3))))) -(((*1 *2 *2 *2) - (|partial| -12 (-4 *3 (-13 (-555) (-147))) (-5 *1 (-1227 *3 *2)) - (-4 *2 (-1233 *3))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-114)) (-5 *3 (-640 *1)) (-4 *1 (-302)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-302)) (-5 *2 (-114)))) ((*1 *1 *2) (-12 (-5 *2 (-1169)) (-5 *1 (-609 *3)) (-4 *3 (-846)))) ((*1 *1 *2 *3 *4) (-12 (-5 *2 (-114)) (-5 *3 (-640 *5)) (-5 *4 (-767)) (-4 *5 (-846)) (-5 *1 (-609 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-1149 *3)) (-5 *1 (-174 *3)) (-4 *3 (-307))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-640 *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 *1) + (-12 (-4 *1 (-1201 *3 *4 *5 *6)) (-4 *3 (-555)) (-4 *4 (-789)) + (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1201 *4 *5 *6 *3)) (-4 *4 (-555)) (-4 *5 (-789)) + (-4 *6 (-846)) (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -1674)) (-5 *2 (-112)) (-5 *1 (-614)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -2484)) (-5 *2 (-112)) (-5 *1 (-614)))) + (-12 (-5 *3 (|[\|\|]| -2483)) (-5 *2 (-112)) (-5 *1 (-614)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -3563)) (-5 *2 (-112)) (-5 *1 (-614)))) + (-12 (-5 *3 (|[\|\|]| -3566)) (-5 *2 (-112)) (-5 *1 (-614)))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2598)) (-5 *2 (-112)) (-5 *1 (-686 *4)) (-4 *4 (-610 (-858))))) @@ -11531,17 +11363,15 @@ (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1208)) (-5 *1 (-598 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1208)) (-5 *1 (-1149 *3))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1248 *4)) (-5 *1 (-1250 *4 *2)) - (-4 *4 (-38 (-407 (-563))))))) -(((*1 *2 *3 *4 *4 *5 *3 *3) - (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *5 (-225)) - (-5 *2 (-1031)) (-5 *1 (-748))))) -(((*1 *1 *1) - (-12 (-5 *1 (-593 *2)) (-4 *2 (-38 (-407 (-563)))) (-4 *2 (-1045))))) -(((*1 *2 *2) - (-12 (-4 *3 (-363)) (-4 *4 (-373 *3)) (-4 *5 (-373 *3)) - (-5 *1 (-521 *3 *4 *5 *2)) (-4 *2 (-682 *3 *4 *5))))) +(((*1 *2 *1) + (-12 (-5 *2 (-640 (-563))) (-5 *1 (-1000 *3)) (-14 *3 (-563))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1208)) (-4 *3 (-373 *2)) + (-4 *4 (-373 *2)))) + ((*1 *1 *1 *2) + (-12 (|has| *1 (-6 -4409)) (-4 *1 (-601 *3 *2)) (-4 *3 (-1093)) + (-4 *2 (-1208))))) +(((*1 *1) (-12 (-4 *1 (-329 *2)) (-4 *2 (-368)) (-4 *2 (-363))))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-611 *2) (-172))) (-5 *2 (-888 *4)) (-5 *1 (-170 *4 *5 *3)) (-4 *4 (-1093)) (-4 *3 (-166 *5)))) @@ -11574,9 +11404,9 @@ (-12 (-5 *2 (-948 *3)) (-4 *3 (-1045)) (-4 *1 (-1059 *3 *4 *5)) (-4 *5 (-611 (-1169))) (-4 *4 (-789)) (-4 *5 (-846)))) ((*1 *1 *2) - (-4032 + (-4034 (-12 (-5 *2 (-948 (-563))) (-4 *1 (-1059 *3 *4 *5)) - (-12 (-2176 (-4 *3 (-38 (-407 (-563))))) (-4 *3 (-38 (-563))) + (-12 (-2174 (-4 *3 (-38 (-407 (-563))))) (-4 *3 (-38 (-563))) (-4 *5 (-611 (-1169)))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846))) (-12 (-5 *2 (-948 (-563))) (-4 *1 (-1059 *3 *4 *5)) @@ -11587,12 +11417,12 @@ (-4 *3 (-38 (-407 (-563)))) (-4 *5 (-611 (-1169))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-640 *7)) (|:| -2059 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-640 *7)) (|:| -2058 *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 (-1151)) (-5 *1 (-1063 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-640 *7)) (|:| -2059 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-640 *7)) (|:| -2058 *8))) (-4 *7 (-1059 *4 *5 *6)) (-4 *8 (-1102 *4 *5 *6 *7)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-1151)) (-5 *1 (-1138 *4 *5 *6 *7 *8)))) @@ -11625,24 +11455,27 @@ (-5 *2 (-640 (-776 *4 (-860 *6)))) (-5 *1 (-1283 *4 *5 *6)) (-14 *5 (-640 (-1169)))))) (((*1 *1 *1 *2 *1) (-12 (-4 *1 (-125 *2)) (-4 *2 (-1093))))) -(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) - (-12 (-5 *3 (-917)) (-5 *4 (-225)) (-5 *5 (-563)) (-5 *6 (-870)) - (-5 *2 (-1262)) (-5 *1 (-1258))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-640 (-839 (-225)))) (-5 *4 (-225)) (-5 *2 (-640 *4)) - (-5 *1 (-267))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) - (-4 *4 (-846)) (-4 *2 (-452))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1165 *3)) (-5 *1 (-910 *3)) (-4 *3 (-307))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-767)) (|:| |poli| *7) - (|:| |polj| *7))) - (-4 *5 (-789)) (-4 *7 (-945 *4 *5 *6)) (-4 *4 (-452)) (-4 *6 (-846)) - (-5 *2 (-112)) (-5 *1 (-449 *4 *5 *6 *7))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-767)) (-4 *3 (-1045)) (-4 *1 (-682 *3 *4 *5)) + (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) + ((*1 *1 *2) + (-12 (-4 *2 (-1045)) (-4 *1 (-1116 *3 *2 *4 *5)) (-4 *4 (-238 *3 *2)) + (-4 *5 (-238 *3 *2))))) +(((*1 *2 *3 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) + (-5 *1 (-751))))) +(((*1 *2 *1) (-12 (-5 *2 (-563)) (-5 *1 (-910 *3)) (-4 *3 (-307))))) +(((*1 *2) + (-12 (-4 *4 (-172)) (-5 *2 (-1165 (-948 *4))) (-5 *1 (-416 *3 *4)) + (-4 *3 (-417 *4)))) + ((*1 *2) + (-12 (-4 *1 (-417 *3)) (-4 *3 (-172)) (-4 *3 (-363)) + (-5 *2 (-1165 (-948 *3))))) + ((*1 *2) + (-12 (-5 *2 (-1165 (-407 (-948 *3)))) (-5 *1 (-453 *3 *4 *5 *6)) + (-4 *3 (-555)) (-4 *3 (-172)) (-14 *4 (-917)) + (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 *3)))))) +(((*1 *2 *1) (-12 (-5 *2 (-1149 *3)) (-5 *1 (-174 *3)) (-4 *3 (-307))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-917)) (-4 *6 (-13 (-555) (-846))) (-5 *2 (-640 (-316 *6))) (-5 *1 (-221 *5 *6)) (-5 *3 (-316 *6)) @@ -11669,111 +11502,84 @@ ((*1 *2 *1) (-12 (-5 *2 (-1272 *3 *4)) (-5 *1 (-1281 *3 *4)) (-4 *3 (-846)) (-4 *4 (-1045))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1 (-112) *7 (-640 *7))) (-4 *1 (-1201 *4 *5 *6 *7)) + (-4 *4 (-555)) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *7 (-1059 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-123))) ((*1 *1 *1 *1) (-5 *1 (-1113)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-640 (-684 *5))) (-5 *4 (-563)) (-4 *5 (-363)) - (-4 *5 (-1045)) (-5 *2 (-112)) (-5 *1 (-1025 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-640 (-684 *4))) (-4 *4 (-363)) (-4 *4 (-1045)) - (-5 *2 (-112)) (-5 *1 (-1025 *4))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-1257 (-563))) (-5 *3 (-563)) (-5 *1 (-1103)))) - ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-1257 (-563))) (-5 *3 (-640 (-563))) (-5 *4 (-563)) - (-5 *1 (-1103))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1165 (-563))) (-5 *1 (-938)) (-5 *3 (-563)))) - ((*1 *2 *2) - (-12 (-4 *3 (-307)) (-4 *4 (-373 *3)) (-4 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(|has| *1 (-6 -4409)) (-4 *1 (-601 *3 *4)) (-4 *3 (-1093)) + (-4 *4 (-1208)) (-5 *2 (-1262))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1165 *3)) (-4 *3 (-368)) (-4 *1 (-329 *3)) + (-4 *3 (-363))))) +(((*1 *1 *2) + (-12 (-5 *2 (-640 *1)) (-4 *3 (-1045)) (-4 *1 (-682 *3 *4 *5)) + (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-640 *3)) (-4 *3 (-1045)) (-4 *1 (-682 *3 *4 *5)) + (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1257 *3)) (-4 *3 (-1045)) (-5 *1 (-684 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-640 *4)) (-4 *4 (-1045)) (-4 *1 (-1116 *3 *4 *5 *6)) + (-4 *5 (-238 *3 *4)) (-4 *6 (-238 *3 *4))))) +(((*1 *2 *3 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) + (-5 *1 (-751))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-1165 *3)) (-5 *1 (-910 *3)) (-4 *3 (-307))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1165 (-407 (-948 *3)))) (-5 *1 (-453 *3 *4 *5 *6)) + (-4 *3 (-555)) (-4 *3 (-172)) (-14 *4 (-917)) + (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 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(-174 (-407 (-563)))) (-5 *1 (-117 *3)) (-14 *3 (-563)))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *3 (-1149 *2)) (-4 *2 (-307)) (-5 *1 (-174 *2)))) - ((*1 *1 *2) (-12 (-5 *2 (-407 *3)) (-4 *3 (-307)) (-5 *1 (-174 *3)))) - ((*1 *2 *3) - (-12 (-5 *2 (-174 (-563))) (-5 *1 (-761 *3)) (-4 *3 (-404)))) - ((*1 *2 *1) - (-12 (-5 *2 (-174 (-407 (-563)))) (-5 *1 (-867 *3)) (-14 *3 (-563)))) - ((*1 *2 *1) - (-12 (-14 *3 (-563)) (-5 *2 (-174 (-407 (-563)))) - (-5 *1 (-868 *3 *4)) (-4 *4 (-865 *3))))) + (-12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) + (-5 *2 (-1165 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1116 *3 *4 *2 *5)) (-4 *4 (-1045)) (-4 *5 (-238 *3 *4)) + (-4 *2 (-238 *3 *4))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) + (-5 *1 (-751))))) +(((*1 *1 *1) (-12 (-5 *1 (-910 *2)) (-4 *2 (-307))))) +(((*1 *2 *1) + (-12 (-5 *2 (-407 (-948 *3))) (-5 *1 (-453 *3 *4 *5 *6)) + (-4 *3 (-555)) (-4 *3 (-172)) (-14 *4 (-917)) + (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 *3)))))) (((*1 *2) (-12 (-5 *2 (-829 (-563))) (-5 *1 (-534)))) ((*1 *1) (-12 (-5 *1 (-829 *2)) (-4 *2 (-1093))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-171))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1201 *3 *4 *5 *2)) (-4 *3 (-555)) (-4 *4 (-789)) + (-4 *5 (-846)) (-4 *2 (-1059 *3 *4 *5))))) (((*1 *1 *1 *1) (-4 *1 (-123))) ((*1 *1 *1 *1) (-5 *1 (-858))) ((*1 *1 *1 *1) (-4 *1 (-963)))) -(((*1 *2 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-339 *3 *4 *5)) (-14 *3 (-640 (-1169))) - (-14 *4 (-640 (-1169))) (-4 *5 (-387)))) - ((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-339 *3 *4 *5)) (-14 *3 (-640 (-1169))) - (-14 *4 (-640 (-1169))) (-4 *5 (-387))))) -(((*1 *1) (-5 *1 (-1078)))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *5 (-225)) - (-5 *2 (-1031)) (-5 *1 (-748))))) +(((*1 *1 *2 *2) + (-12 (-5 *2 (-640 (-563))) (-5 *1 (-1000 *3)) (-14 *3 (-563))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-555) (-846))) (-5 *2 (-169 *5)) + (-5 *1 (-597 *4 *5 *3)) (-4 *5 (-13 (-430 *4) (-998) (-1193))) + (-4 *3 (-13 (-430 (-169 *4)) (-998) (-1193)))))) (((*1 *1 *1) (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-640 (-1169))) (-14 *3 (-640 (-1169))) (-4 *4 (-387)))) @@ -11783,39 +11589,29 @@ ((*1 *1 *2) (-12 (-5 *2 (-407 (-563))) (-4 *1 (-1008)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1008)) (-5 *2 (-917)))) ((*1 *1 *1) (-4 *1 (-1008)))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-379)) (-5 *3 (-640 (-263))) (-5 *1 (-261)))) - ((*1 *1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-263))))) -(((*1 *2 *3) - (-12 (-4 *4 (-349)) (-5 *2 (-418 *3)) (-5 *1 (-216 *4 *3)) - (-4 *3 (-1233 *4)))) - ((*1 *2 *3) - (-12 (-5 *2 (-418 *3)) (-5 *1 (-442 *3)) (-4 *3 (-1233 (-563))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-767)) (-5 *2 (-418 *3)) (-5 *1 (-442 *3)) - (-4 *3 (-1233 (-563))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-640 (-767))) (-5 *2 (-418 *3)) (-5 *1 (-442 *3)) - (-4 *3 (-1233 (-563))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-640 (-767))) (-5 *5 (-767)) (-5 *2 (-418 *3)) - (-5 *1 (-442 *3)) (-4 *3 (-1233 (-563))))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-767)) (-5 *2 (-418 *3)) (-5 *1 (-442 *3)) - (-4 *3 (-1233 (-563))))) - ((*1 *2 *3) - (-12 (-5 *2 (-418 *3)) (-5 *1 (-1003 *3)) - (-4 *3 (-1233 (-407 (-563)))))) - ((*1 *2 *3) - (-12 (-5 *2 (-418 *3)) (-5 *1 (-1222 *3)) (-4 *3 (-1233 (-563)))))) +(((*1 *2 *1 *1) + (|partial| -12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) + (-5 *2 (-1165 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-4 *3 (-368)) + (-5 *2 (-1165 *3))))) (((*1 *2 *3) - (-12 (-5 *2 (-1149 (-563))) (-5 *1 (-1153 *4)) (-4 *4 (-1045)) - (-5 *3 (-563))))) -(((*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 *1 *2) (-12 (-5 *2 (-767)) (-5 *1 (-128))))) + (-12 (-5 *3 (-684 *2)) (-4 *4 (-1233 *2)) + (-4 *2 (-13 (-307) (-10 -8 (-15 -2802 ((-418 $) $))))) + (-5 *1 (-499 *2 *4 *5)) (-4 *5 (-409 *2 *4)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1116 *3 *2 *4 *5)) (-4 *4 (-238 *3 *2)) + (-4 *5 (-238 *3 *2)) (-4 *2 (-1045))))) +(((*1 *2 *3 *3 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) + (-5 *1 (-751))))) +(((*1 *2 *2) + (-12 (-4 *3 (-1233 (-407 (-563)))) (-5 *1 (-909 *3 *2)) + (-4 *2 (-1233 (-407 *3)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-407 (-948 *3))) (-5 *1 (-453 *3 *4 *5 *6)) + (-4 *3 (-555)) (-4 *3 (-172)) (-14 *4 (-917)) + (-14 *5 (-640 (-1169))) (-14 *6 (-1257 (-684 *3)))))) (((*1 *2) (-12 (-4 *2 (-13 (-430 *3) (-998))) (-5 *1 (-276 *3 *2)) (-4 *3 (-13 (-846) (-555))))) @@ -11823,13 +11619,16 @@ (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-640 (-1169))) (-14 *3 (-640 (-1169))) (-4 *4 (-387)))) ((*1 *1) (-5 *1 (-477))) ((*1 *1) (-4 *1 (-1193)))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-767)) (-4 *6 (-1093)) (-4 *3 (-896 *6)) - (-5 *2 (-684 *3)) (-5 *1 (-687 *6 *3 *7 *4)) (-4 *7 (-373 *3)) - (-4 *4 (-13 (-373 *6) (-10 -7 (-6 -4407))))))) +(((*1 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-172))))) (((*1 *1 *1) (-5 *1 (-858))) ((*1 *1 *1 *1) (-5 *1 (-858))) ((*1 *1 *2 *2) (-12 (-4 *1 (-1086 *2)) (-4 *2 (-1208)))) ((*1 *1 *2) (-12 (-5 *1 (-1224 *2)) (-4 *2 (-1208))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1059 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-789)) + (-4 *4 (-846)))) + ((*1 *2 *2 *1) + (-12 (-4 *1 (-1201 *3 *4 *5 *2)) (-4 *3 (-555)) (-4 *4 (-789)) + (-4 *5 (-846)) (-4 *2 (-1059 *3 *4 *5))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-767)) (-5 *2 (-1257 (-640 (-563)))) (-5 *1 (-480)))) ((*1 *1 *2 *3) @@ -11839,21 +11638,6 @@ ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1208)) (-5 *1 (-1149 *3))))) (((*1 *1 *1) (-4 *1 (-123))) ((*1 *1 *1) (-5 *1 (-858))) ((*1 *1 *1) (-4 *1 (-963))) ((*1 *1 *1) (-5 *1 (-1113)))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-640 *1)) (-5 *3 (-640 *7)) (-4 *1 (-1065 *4 *5 *6 *7)) - (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-640 *7)) (-4 *7 (-1059 *4 *5 *6)) (-4 *4 (-452)) - (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-640 *1)) - (-4 *1 (-1065 *4 *5 *6 *7)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-640 *1)) (-4 *1 (-1065 *4 *5 *6 *3)) (-4 *4 (-452)) - (-4 *5 (-789)) (-4 *6 (-846)) (-4 *3 (-1059 *4 *5 *6)))) - ((*1 *2 *3 *1) - (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-640 *1)) - (-4 *1 (-1065 *4 *5 *6 *3))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-640 (-48))) (-5 *2 (-418 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1233 (-48))))) @@ -11902,8 +11686,8 @@ (-12 (-4 *4 (-13 (-846) - (-10 -8 (-15 -2220 ((-1169) $)) - (-15 -2518 ((-3 $ "failed") (-1169)))))) + (-10 -8 (-15 -2219 ((-1169) $)) + (-15 -2517 ((-3 $ "failed") (-1169)))))) (-4 *5 (-789)) (-4 *7 (-555)) (-5 *2 (-418 *3)) (-5 *1 (-456 *4 *5 *6 *7 *3)) (-4 *6 (-555)) (-4 *3 (-945 *7 *5 *4)))) @@ -11952,13 +11736,13 @@ (-12 (-4 *4 (-789)) (-4 *5 (-13 (-846) - (-10 -8 (-15 -2220 ((-1169) $)) - (-15 -2518 ((-3 $ "failed") (-1169)))))) + (-10 -8 (-15 -2219 ((-1169) $)) + (-15 -2517 ((-3 $ "failed") (-1169)))))) (-4 *6 (-307)) (-5 *2 (-418 *3)) (-5 *1 (-726 *4 *5 *6 *3)) (-4 *3 (-945 (-948 *6) *4 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(-5 *1 (-593 *2)) (-4 *2 (-38 (-407 (-563)))) (-4 *2 (-1045))))) + (|partial| -12 (-5 *2 (-112)) (-5 *1 (-593 *3)) (-4 *3 (-1045))))) (((*1 *2 *3) (-12 (-5 *2 (-169 (-379))) (-5 *1 (-781 *3)) (-4 *3 (-611 (-379))))) ((*1 *2 *3 *4) @@ -12469,278 +12268,323 @@ (-12 (-5 *3 (-316 (-169 *5))) (-5 *4 (-917)) (-4 *5 (-555)) (-4 *5 (-846)) (-4 *5 (-611 (-379))) (-5 *2 (-169 (-379))) (-5 *1 (-781 *5))))) -(((*1 *2 *3 *1) - (|partial| -12 (-5 *3 (-1169)) (-5 *2 (-640 (-961))) (-5 *1 (-291))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1193))))) -(((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4407)) (-4 *1 (-601 *4 *3)) (-4 *4 (-1093)) - (-4 *3 (-1208)) (-4 *3 (-1093)) (-5 *2 (-112))))) -(((*1 *1 *2) - (-12 (-5 *2 (-640 *1)) (-4 *3 (-1045)) (-4 *1 (-682 *3 *4 *5)) - (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-640 *3)) (-4 *3 (-1045)) (-4 *1 (-682 *3 *4 *5)) - (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1257 *3)) (-4 *3 (-1045)) (-5 *1 (-684 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- (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1065 *4 *5 *6 *3)) (-4 *4 (-452)) (-4 *5 (-789)) - (-4 *6 (-846)) (-4 *3 (-1059 *4 *5 *6)) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-684 (-169 (-407 (-563))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1165 (-563))) (-5 *1 (-191)) (-5 *3 (-563)))) + ((*1 *2 *3 *2) (-12 (-5 *3 (-767)) (-5 *1 (-779 *2)) (-4 *2 (-172)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1165 (-563))) (-5 *1 (-938)) (-5 *3 (-563))))) +(((*1 *2 *3 *4 *5) + (-12 (-4 *6 (-1233 *9)) (-4 *7 (-789)) (-4 *8 (-846)) (-4 *9 (-307)) + (-4 *10 (-945 *9 *7 *8)) (-5 *2 - (-640 - (-2 (|:| |outval| (-169 *4)) (|:| |outmult| (-563)) - (|:| |outvect| (-640 (-684 (-169 *4))))))) - (-5 *1 (-760 *4)) (-4 *4 (-13 (-363) (-844)))))) -(((*1 *2 *1) (-12 (-5 *2 (-1128)) (-5 *1 (-525))))) -(((*1 *1 *2) - (-12 + (-2 (|:| |deter| (-640 (-1165 *10))) + (|:| |dterm| + (-640 (-640 (-2 (|:| -1646 (-767)) (|:| |pcoef| *10))))) + (|:| |nfacts| (-640 *6)) (|:| |nlead| (-640 *10)))) + (-5 *1 (-774 *6 *7 *8 *9 *10)) (-5 *3 (-1165 *10)) (-5 *4 (-640 *6)) + (-5 *5 (-640 *10))))) +(((*1 *2 *1) (-12 (-4 *1 (-509 *3 *2)) (-4 *3 (-1093)) (-4 *2 (-846))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *4 (-1169)) (-5 *6 (-112)) + (-4 *7 (-13 (-307) (-846) (-147) (-1034 (-563)) (-636 (-563)))) + (-4 *3 (-13 (-1193) (-955) (-29 *7))) (-5 *2 - (-640 - (-2 - (|:| -2387 - (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225))) - (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) - (|:| |relerr| (-225)))) - (|:| -2557 - (-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| (-1149 (-225))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2516 - (-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 (-558))))) + (-3 (|:| |f1| (-839 *3)) (|:| |f2| (-640 (-839 *3))) + (|:| |fail| "failed") (|:| |pole| "potentialPole"))) + (-5 *1 (-219 *7 *3)) (-5 *5 (-839 *3))))) (((*1 *2 *1) - (-12 (-4 *3 (-363)) (-4 *4 (-1233 *3)) (-4 *5 (-1233 (-407 *4))) - (-5 *2 (-1257 *6)) (-5 *1 (-336 *3 *4 *5 *6)) - (-4 *6 (-342 *3 *4 *5))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-640 *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 (-555))))) -(((*1 *2 *3) - (-12 (-5 *3 (-640 *7)) (-4 *7 (-945 *4 *5 *6)) (-4 *4 (-452)) - (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-1262)) - (-5 *1 (-449 *4 *5 *6 *7))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) - (|:| |fn| (-1257 (-316 (-225)))) (|:| |yinit| (-640 (-225))) - (|:| |intvals| (-640 (-225))) (|:| |g| (-316 (-225))) - (|:| |abserr| (-225)) (|:| |relerr| (-225)))) - (-5 *2 (-379)) (-5 *1 (-205))))) -(((*1 *2) - (-12 (-5 *2 (-954 (-1113))) (-5 *1 (-343 *3 *4)) (-14 *3 (-917)) - (-14 *4 (-917)))) - ((*1 *2) - (-12 (-5 *2 (-954 (-1113))) (-5 *1 (-344 *3 *4)) (-4 *3 (-349)) - (-14 *4 (-1165 *3)))) - ((*1 *2) - (-12 (-5 *2 (-954 (-1113))) (-5 *1 (-345 *3 *4)) (-4 *3 (-349)) - (-14 *4 (-917))))) + (|partial| -12 + (-4 *3 (-13 (-846) (-1034 (-563)) (-636 (-563)) (-452))) + (-5 *2 + (-2 + (|:| |%term| + (-2 (|:| |%coef| (-1242 *4 *5 *6)) + (|:| |%expon| (-319 *4 *5 *6)) + (|:| |%expTerms| + (-640 (-2 (|:| |k| (-407 (-563))) (|:| |c| *4)))))) + (|:| |%type| (-1151)))) + (-5 *1 (-1243 *3 *4 *5 *6)) (-4 *4 (-13 (-27) (-1193) (-430 *3))) + (-14 *5 (-1169)) (-14 *6 *4)))) +(((*1 *1 *1 *1) (-4 *1 (-143))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-158 *3 *2)) + (-4 *2 (-430 *3)))) + ((*1 *2 *2 *2) (-12 (-5 *1 (-159 *2)) (-4 *2 (-545)))) + ((*1 *1 *1 *1) (-5 *1 (-858))) + ((*1 *2 *3 *4) + (-12 (-5 *4 |RationalNumber|) (-5 *2 (-1 (-563))) (-5 *1 (-1043)) + (-5 *3 (-563))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1257 (-767))) (-5 *1 (-670 *3)) (-4 *3 (-1093))))) +(((*1 *2 *1 *2) + (-12 (-4 *1 (-364 *3 *2)) (-4 *3 (-1093)) (-4 *2 (-1093))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -13858,63 +13867,54 @@ ((*1 *2 *2) (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3))))) -(((*1 *2 *2 *2) (-12 (-5 *1 (-159 *2)) (-4 *2 (-545))))) -(((*1 *2) (-12 (-5 *2 (-917)) (-5 *1 (-157))))) -(((*1 *2 *1) - (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1208)) (-4 *4 (-373 *3)) - (-4 *5 (-373 *3)) (-5 *2 (-563)))) - ((*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 (-563))))) -(((*1 *2 *3 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- (|partial| -12 (-5 *2 (-563)) (-5 *1 (-1190 *3)) (-4 *3 (-1045))))) + (-12 (-5 *2 (-1165 (-563))) (-5 *1 (-938)) (-5 *3 (-563))))) +(((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-563)) (-5 *1 (-136 *3 *4 *5)) (-14 *3 *2) + (-14 *4 (-767)) (-4 *5 (-172)))) + ((*1 *1 *1 *2 *1 *2) + (-12 (-5 *2 (-563)) (-5 *1 (-136 *3 *4 *5)) (-14 *3 *2) + (-14 *4 (-767)) (-4 *5 (-172)))) + ((*1 *2 *2 *3) + (-12 + (-5 *2 + (-504 (-407 (-563)) (-240 *5 (-767)) (-860 *4) + (-247 *4 (-407 (-563))))) + (-5 *3 (-640 (-860 *4))) (-14 *4 (-640 (-1169))) (-14 *5 (-767)) + (-5 *1 (-505 *4 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-407 (-563))) (-5 *1 (-217))))) (((*1 *2 *1) (-12 (-5 *2 (-640 (-183))) (-5 *1 (-140))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-640 *5)) (-4 *5 (-1233 *3)) (-4 *3 (-307)) - (-5 *2 (-112)) (-5 *1 (-455 *3 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-640 (-948 *4))) (-5 *3 (-640 (-1169))) (-4 *4 (-452)) - (-5 *1 (-914 *4))))) -(((*1 *1 *2 *1) (-12 (-5 *2 (-1168)) (-5 *1 (-330))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1240 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-1217 *3)) + (-5 *2 (-407 (-563)))))) (((*1 *2 *3) - (-12 (-4 *1 (-342 *4 *3 *5)) (-4 *4 (-1212)) (-4 *3 (-1233 *4)) - (-4 *5 (-1233 (-407 *3))) (-5 *2 (-112)))) + (-12 (-5 *3 (-1095 *4)) (-4 *4 (-1093)) (-5 *2 (-1 *4)) + (-5 *1 (-1013 *4)))) + ((*1 *2 *3 *3) + (-12 (-5 *2 (-1 (-379))) (-5 *1 (-1036)) (-5 *3 (-379)))) ((*1 *2 *3) - (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1212)) (-4 *4 (-1233 *3)) - (-4 *5 (-1233 (-407 *4))) (-5 *2 (-112))))) + (-12 (-5 *3 (-1087 (-563))) (-5 *2 (-1 (-563))) (-5 *1 (-1043))))) +(((*1 *2 *1) (-12 (-4 *1 (-669 *3)) (-4 *3 (-1208)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1165 *4)) (-4 *4 (-349)) + (-4 *2 + (-13 (-402) + (-10 -7 (-15 -1692 (*2 *4)) (-15 -3990 ((-917) *2)) + (-15 -4013 ((-1257 *2) (-917))) (-15 -3715 (*2 *2))))) + (-5 *1 (-356 *2 *4))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -13931,83 +13931,70 @@ ((*1 *2 *2) (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3))))) -(((*1 *1) (-5 *1 (-1258)))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-563)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1208)) (-4 *4 (-373 *2)) (-4 *5 (-373 *2)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "right") (|has| *1 (-6 -4408)) (-4 *1 (-119 *3)) + (-12 (-5 *2 "right") (|has| *1 (-6 -4409)) (-4 *1 (-119 *3)) (-4 *3 (-1208)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "left") (|has| *1 (-6 -4408)) (-4 *1 (-119 *3)) + (-12 (-5 *2 "left") (|has| *1 (-6 -4409)) (-4 *1 (-119 *3)) (-4 *3 (-1208)))) ((*1 *2 *1 *3 *2) - (-12 (|has| *1 (-6 -4408)) (-4 *1 (-288 *3 *2)) (-4 *3 (-1093)) + (-12 (|has| *1 (-6 -4409)) (-4 *1 (-288 *3 *2)) (-4 *3 (-1093)) (-4 *2 (-1208)))) ((*1 *2 *1 *3 *2) (-12 (-5 *2 (-52)) (-5 *3 (-1169)) (-5 *1 (-629)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 (-1224 (-563))) (|has| *1 (-6 -4408)) (-4 *1 (-646 *2)) + (-12 (-5 *3 (-1224 (-563))) (|has| *1 (-6 -4409)) (-4 *1 (-646 *2)) (-4 *2 (-1208)))) ((*1 *1 *1 *2 *2 *1) (-12 (-5 *2 (-640 (-563))) (-4 *1 (-682 *3 *4 *5)) (-4 *3 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(-1065 *3 *4 *5 *6)) (-4 *3 (-452)) - (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) - (-5 *1 (-1100 *3 *4 *5 *6 *7))))) -(((*1 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-391))))) + (-12 (-5 *2 (-1165 (-563))) (-5 *1 (-938)) (-5 *3 (-563))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-640 *6)) (-5 *4 (-640 (-1169))) (-4 *6 (-363)) - (-5 *2 (-640 (-294 (-948 *6)))) (-5 *1 (-538 *5 *6 *7)) - (-4 *5 (-452)) (-4 *7 (-13 (-363) (-844)))))) -(((*1 *2 *2 *3 *4 *4) - (-12 (-5 *4 (-563)) (-4 *3 (-172)) (-4 *5 (-373 *3)) - (-4 *6 (-373 *3)) (-5 *1 (-683 *3 *5 *6 *2)) - (-4 *2 (-682 *3 *5 *6))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-640 *2)) (-4 *2 (-945 *4 *5 *6)) (-4 *4 (-307)) - (-4 *5 (-789)) (-4 *6 (-846)) (-5 *1 (-447 *4 *5 *6 *2))))) -(((*1 *2 *2) (-12 (-5 *2 (-684 (-316 (-563)))) (-5 *1 (-1027))))) + (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) + (-4 *3 (-1059 *5 *6 *7)) + (-5 *2 (-640 (-2 (|:| |val| (-112)) (|:| -2058 *4)))) + (-5 *1 (-772 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3))))) +(((*1 *2 *3) + (-12 (-14 *4 (-640 (-1169))) (-14 *5 (-767)) + (-5 *2 + (-640 + (-504 (-407 (-563)) (-240 *5 (-767)) (-860 *4) + (-247 *4 (-407 (-563)))))) + (-5 *1 (-505 *4 *5)) + (-5 *3 + (-504 (-407 (-563)) (-240 *5 (-767)) (-860 *4) + (-247 *4 (-407 (-563)))))))) +(((*1 *2 *3) + (-12 (-4 *4 (-349)) (-5 *2 (-112)) (-5 *1 (-216 *4 *3)) + (-4 *3 (-1233 *4))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1240 *3 *2)) (-4 *3 (-1045)) (-4 *2 (-1217 *3))))) +(((*1 *1) (-12 (-4 *1 (-1041 *2)) (-4 *2 (-23))))) +(((*1 *2 *1) (-12 (-4 *1 (-669 *3)) (-4 *3 (-1208)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-4 *4 (-349)) (-5 *2 (-954 (-1165 *4))) (-5 *1 (-357 *4)) + (-5 *3 (-1165 *4))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -14024,14 +14011,17 @@ ((*1 *2 *2) (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1262)) (-5 *1 (-818))))) -(((*1 *1 *1) (-12 (-5 *1 (-418 *2)) (-4 *2 (-555))))) +(((*1 *1 *1) (-4 *1 (-1137)))) +(((*1 *2 *3 *3 *4 *5) + (-12 (-5 *3 (-1151)) (-4 *6 (-452)) (-4 *7 (-789)) (-4 *8 (-846)) + (-4 *4 (-1059 *6 *7 *8)) (-5 *2 (-1262)) + (-5 *1 (-772 *6 *7 *8 *4 *5)) (-4 *5 (-1065 *6 *7 *8 *4))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1045)) (-4 *3 (-788)) (-4 *2 (-363)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-563)) (-5 *1 (-225)))) ((*1 *1 *1 *1) - (-4032 (-12 (-5 *1 (-294 *2)) (-4 *2 (-363)) (-4 *2 (-1208))) + (-4034 (-12 (-5 *1 (-294 *2)) (-4 *2 (-363)) (-4 *2 (-1208))) (-12 (-5 *1 (-294 *2)) (-4 *2 (-473)) (-4 *2 (-1208))))) ((*1 *1 *1 *1) (-4 *1 (-363))) ((*1 *1 *1 *2) (-12 (-5 *2 (-563)) (-5 *1 (-379)))) @@ -14079,39 +14069,26 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1280 *2 *3)) (-4 *2 (-363)) (-4 *2 (-1045)) (-4 *3 (-842))))) -(((*1 *2 *1) - (-12 (-4 *1 (-326 *2 *3)) (-4 *3 (-788)) (-4 *2 (-1045)) - (-4 *2 (-452)))) +(((*1 *2 *3) (-12 (-5 *2 (-407 (-563))) (-5 *1 (-560)) (-5 *3 (-563)))) ((*1 *2 *3) - (-12 (-5 *3 (-640 *4)) (-4 *4 (-1233 (-563))) (-5 *2 (-640 (-563))) - (-5 *1 (-486 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-848 *2)) (-4 *2 (-1045)) (-4 *2 (-452)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-945 *3 *4 *2)) (-4 *3 (-1045)) (-4 *4 (-789)) - (-4 *2 (-846)) (-4 *3 (-452))))) + (-12 (-5 *2 (-1165 (-407 (-563)))) (-5 *1 (-938)) (-5 *3 (-563))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-504 (-407 (-563)) (-240 *5 (-767)) (-860 *4) + (-247 *4 (-407 (-563))))) + (-14 *4 (-640 (-1169))) (-14 *5 (-767)) (-5 *2 (-112)) + (-5 *1 (-505 *4 *5))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-767)) (-4 *4 (-349)) (-5 *1 (-216 *4 *2)) + (-4 *2 (-1233 *4))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| |preimage| (-640 *3)) (|:| |image| (-640 *3)))) - (-5 *1 (-901 *3)) (-4 *3 (-1093))))) -(((*1 *2 *3 *4 *5 *6) - (-12 (-5 *4 (-112)) (-5 *5 (-1095 (-767))) (-5 *6 (-767)) - (-5 *2 - (-2 (|:| |contp| (-563)) - (|:| -2760 (-640 (-2 (|:| |irr| *3) (|:| -1650 (-563))))))) - (-5 *1 (-442 *3)) (-4 *3 (-1233 (-563)))))) -(((*1 *2 *2 *1 *3 *4) - (-12 (-5 *2 (-640 *8)) (-5 *3 (-1 *8 *8 *8)) - (-5 *4 (-1 (-112) *8 *8)) (-4 *1 (-1201 *5 *6 *7 *8)) (-4 *5 (-555)) - (-4 *6 (-789)) (-4 *7 (-846)) (-4 *8 (-1059 *5 *6 *7))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-431 *3 *2)) - (-4 *2 (-430 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-379)) (-5 *1 (-97)))) - ((*1 *2 *3 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-379)) (-5 *1 (-97))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-643 *3)) (-4 *3 (-1045)) - (-5 *1 (-710 *3 *4)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1045)) (-5 *1 (-832 *3))))) + (|partial| -12 (-4 *1 (-1240 *3 *2)) (-4 *3 (-1045)) + (-4 *2 (-1217 *3))))) +(((*1 *1) (-5 *1 (-157))) + ((*1 *2 *1) (-12 (-4 *1 (-1040 *2)) (-4 *2 (-23))))) +(((*1 *2 *1) (-12 (-4 *1 (-669 *3)) (-4 *3 (-1208)) (-5 *2 (-112))))) +(((*1 *2 *2) (-12 (-5 *2 (-1165 *3)) (-4 *3 (-349)) (-5 *1 (-357 *3))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -14128,17 +14105,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3))))) -(((*1 *2) (-12 (-5 *2 (-917)) (-5 *1 (-1260)))) - ((*1 *2 *2) (-12 (-5 *2 (-917)) (-5 *1 (-1260))))) -(((*1 *2 *1) (-12 (-5 *2 (-640 (-1078))) (-5 *1 (-291))))) +(((*1 *1) (-5 *1 (-141))) ((*1 *1 *1) (-5 *1 (-144))) + ((*1 *1 *1) (-4 *1 (-1137)))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-555) (-846) (-1034 (-563)) (-636 (-563)))) + (-5 *1 (-277 *3 *2)) (-4 *2 (-13 (-27) (-1193) (-430 *3))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1169)) + (-4 *4 (-13 (-555) (-846) (-1034 (-563)) (-636 (-563)))) + (-5 *1 (-277 *4 *2)) (-4 *2 (-13 (-27) (-1193) (-430 *4))))) + ((*1 *1 *1) (-5 *1 (-379))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) + (-4 *3 (-1059 *5 *6 *7)) + (-5 *2 (-640 (-2 (|:| |val| *3) (|:| -2058 *4)))) + (-5 *1 (-772 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3))))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1 *1) (|partial| -5 *1 (-134))) ((*1 *1 *1 *1) (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-846) - (-10 -8 (-15 -2309 ((-1151) $ (-1169))) (-15 -1463 ((-1262) $)) - (-15 -2807 ((-1262) $))))))) + (-10 -8 (-15 -2308 ((-1151) $ (-1169))) (-15 -1463 ((-1262) $)) + (-15 -1651 ((-1262) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-294 *2)) (-4 *2 (-21)) (-4 *2 (-1208)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-294 *2)) (-4 *2 (-21)) (-4 *2 (-1208)))) ((*1 *1 *1 *1) @@ -14158,27 +14147,37 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-939 (-225))) (-5 *1 (-1204)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1255 *2)) (-4 *2 (-1208)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1255 *2)) (-4 *2 (-1208)) (-4 *2 (-21))))) +(((*1 *2 *3 *4 *2 *5) + (-12 (-5 *3 (-640 *8)) (-5 *4 (-640 (-888 *6))) + (-5 *5 (-1 (-885 *6 *8) *8 (-888 *6) (-885 *6 *8))) (-4 *6 (-1093)) + (-4 *8 (-13 (-1045) (-611 (-888 *6)) (-1034 *7))) + (-5 *2 (-885 *6 *8)) (-4 *7 (-13 (-1045) (-846))) + (-5 *1 (-937 *6 *7 *8))))) (((*1 *2 *3) - (-12 (-5 *3 (-640 (-563))) (-5 *2 (-563)) (-5 *1 (-486 *4)) - (-4 *4 (-1233 *2))))) -(((*1 *2 *3) (-12 (-5 *3 (-1257 *1)) (-4 *1 (-367 *2)) (-4 *2 (-172)))) - ((*1 *2) (-12 (-4 *2 (-172)) (-5 *1 (-416 *3 *2)) (-4 *3 (-417 *2)))) - ((*1 *2) (-12 (-4 *1 (-417 *2)) (-4 *2 (-172))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1257 *1)) (-4 *1 (-367 *4)) (-4 *4 (-172)) - (-5 *2 (-684 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-417 *3)) (-4 *3 (-172)) (-5 *2 (-684 *3))))) -(((*1 *1) (-5 *1 (-1057)))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-640 (-640 (-640 *5)))) (-5 *3 (-1 (-112) *5 *5)) - (-5 *4 (-640 *5)) (-4 *5 (-846)) (-5 *1 (-1179 *5))))) -(((*1 *1 *2) (-12 (-5 *2 (-640 (-330))) (-5 *1 (-330))))) -(((*1 *2 *1) (-12 (-5 *2 (-1262)) (-5 *1 (-818))))) + (-12 + (-5 *3 + (-504 (-407 (-563)) (-240 *5 (-767)) (-860 *4) + (-247 *4 (-407 (-563))))) + (-14 *4 (-640 (-1169))) (-14 *5 (-767)) (-5 *2 (-112)) + (-5 *1 (-505 *4 *5))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-767)) (-4 *4 (-349)) (-5 *1 (-216 *4 *2)) + (-4 *2 (-1233 *4))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-767)) (-4 *1 (-1233 *3)) (-4 *3 (-1045)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-917)) (-4 *1 (-1235 *3 *4)) (-4 *3 (-1045)) + (-4 *4 (-788)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-407 (-563))) (-4 *1 (-1238 *3)) (-4 *3 (-1045))))) +(((*1 *1) (-5 *1 (-157))) + ((*1 *2 *1) (-12 (-4 *1 (-1040 *2)) (-4 *2 (-23))))) +(((*1 *1 *1) (-12 (-4 *1 (-669 *2)) (-4 *2 (-1208))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225))) - (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -4166 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-2 @@ -14196,7 +14195,7 @@ (-3 (|:| |str| (-1149 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2516 + (|:| -4166 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -14204,6 +14203,8 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-558))))) +(((*1 *2 *2) + (|partial| -12 (-5 *2 (-1165 *3)) (-4 *3 (-349)) (-5 *1 (-357 *3))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -14220,19 +14221,18 @@ ((*1 *2 *2) (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-1169)) (-5 *3 (-379)) (-5 *1 (-1057))))) +(((*1 *1 *1) (-4 *1 (-1137)))) (((*1 *2 *2 *3) - (-12 (-5 *3 (-609 *2)) (-4 *2 (-13 (-27) (-1193) (-430 *4))) - (-4 *4 (-13 (-555) (-846) (-1034 (-563)) (-636 (-563)))) - (-5 *1 (-277 *4 *2))))) + (-12 (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) + (-4 *2 (-1059 *4 *5 *6)) (-5 *1 (-772 *4 *5 *6 *2 *3)) + (-4 *3 (-1065 *4 *5 *6 *2))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-157))) ((*1 *1 *1 *1) (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-846) - (-10 -8 (-15 -2309 ((-1151) $ (-1169))) (-15 -1463 ((-1262) $)) - (-15 -2807 ((-1262) $))))))) + (-10 -8 (-15 -2308 ((-1151) $ (-1169))) (-15 -1463 ((-1262) $)) + (-15 -1651 ((-1262) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-294 *2)) (-4 *2 (-25)) (-4 *2 (-1208)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-294 *2)) (-4 *2 (-25)) (-4 *2 (-1208)))) ((*1 *1 *2 *1) @@ -14255,106 +14255,76 @@ (-12 (-5 *2 (-1149 *3)) (-4 *3 (-1045)) (-5 *1 (-1153 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-939 (-225))) (-5 *1 (-1204)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1255 *2)) (-4 *2 (-1208)) (-4 *2 (-25))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-555)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3548 *3))) - (-5 *1 (-965 *4 *3)) (-4 *3 (-1233 *4))))) -(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1208)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-846)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-126 *2)) (-4 *2 (-846)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-563)) (-4 *1 (-282 *3)) (-4 *3 (-1208)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-563)) (-4 *1 (-282 *2)) (-4 *2 (-1208)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -2387 - (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225))) - (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) - (|:| |relerr| (-225)))) - (|:| -2557 - (-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| (-1149 (-225))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2516 - (-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 (-558)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-767)) (-4 *1 (-690 *2)) (-4 *2 (-1093)))) - ((*1 *1 *2) +(((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-885 *5 *3)) (-5 *4 (-888 *5)) (-4 *5 (-1093)) + (-4 *3 (-166 *6)) (-4 (-948 *6) (-882 *5)) + (-4 *6 (-13 (-882 *5) (-172))) (-5 *1 (-178 *5 *6 *3)))) + ((*1 *2 *1 *3 *2) + (-12 (-5 *2 (-885 *4 *1)) (-5 *3 (-888 *4)) (-4 *1 (-882 *4)) + (-4 *4 (-1093)))) + ((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-885 *5 *6)) (-5 *4 (-888 *5)) (-4 *5 (-1093)) + (-4 *6 (-13 (-1093) (-1034 *3))) (-4 *3 (-882 *5)) + (-5 *1 (-927 *5 *3 *6)))) + ((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-885 *5 *3)) (-4 *5 (-1093)) + (-4 *3 (-13 (-430 *6) (-611 *4) (-882 *5) (-1034 (-609 $)))) + (-5 *4 (-888 *5)) (-4 *6 (-13 (-555) (-846) (-882 *5))) + (-5 *1 (-928 *5 *6 *3)))) + ((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-885 (-563) *3)) (-5 *4 (-888 (-563))) (-4 *3 (-545)) + (-5 *1 (-929 *3)))) + ((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-885 *5 *6)) (-5 *3 (-609 *6)) (-4 *5 (-1093)) + (-4 *6 (-13 (-846) (-1034 (-609 $)) (-611 *4) (-882 *5))) + (-5 *4 (-888 *5)) (-5 *1 (-930 *5 *6)))) + ((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-881 *5 *6 *3)) (-5 *4 (-888 *5)) (-4 *5 (-1093)) + (-4 *6 (-882 *5)) (-4 *3 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|xend| (-225)) + (|:| |fn| (-1257 (-316 (-225)))) (|:| |yinit| (-640 (-225))) + (|:| |intvals| (-640 (-225))) (|:| |g| (-316 (-225))) + (|:| |abserr| (-225)) (|:| |relerr| (-225)))) + (-5 *2 (-379)) (-5 *1 (-205))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1165 *3)) (-4 *3 (-1045)) (-4 *1 (-1233 *3))))) +(((*1 *2 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-379)) (-5 *1 (-97)))) + ((*1 *2 *3 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-379)) (-5 *1 (-97))))) +(((*1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-1036))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-640 *8)) (-5 *4 (-640 *7)) (-4 *7 (-846)) + (-4 *8 (-945 *5 *6 *7)) (-4 *5 (-555)) (-4 *6 (-789)) (-5 *2 - (-640 - (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-767)) (|:| |poli| *6) - (|:| |polj| *6)))) - (-4 *3 (-789)) (-4 *6 (-945 *4 *3 *5)) (-4 *4 (-452)) (-4 *5 (-846)) - (-5 *1 (-449 *4 *3 *5 *6))))) -(((*1 *2 *3 *4 *4 *4 *3 *4 *3) - (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) - (-5 *1 (-747))))) + (-2 (|:| |particular| (-3 (-1257 (-407 *8)) "failed")) + (|:| -4013 (-640 (-1257 (-407 *8)))))) + (-5 *1 (-664 *5 *6 *7 *8))))) (((*1 *2 *3) - (-12 (-5 *3 (-767)) (-4 *4 (-363)) (-4 *5 (-1233 *4)) (-5 *2 (-1262)) - (-5 *1 (-40 *4 *5 *6 *7)) (-4 *6 (-1233 (-407 *5))) (-14 *7 *6)))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-1045)) (-5 *1 (-1229 *3 *2)) (-4 *2 (-1233 *3))))) + (-12 (-5 *3 (-917)) (-5 *2 (-1165 *4)) (-5 *1 (-357 *4)) + (-4 *4 (-349))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -15073,23 +14930,23 @@ (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3))))) (((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4407)) (-4 *1 (-489 *3)) (-4 *3 (-1208)) + (-12 (|has| *1 (-6 -4408)) (-4 *1 (-489 *3)) (-4 *3 (-1208)) (-4 *3 (-1093)) (-5 *2 (-767)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4407)) (-4 *1 (-489 *4)) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4408)) (-4 *1 (-489 *4)) (-4 *4 (-1208)) (-5 *2 (-767))))) (((*1 *2 *1 *3 *4) (-12 (-5 *3 (-917)) (-5 *4 (-1151)) (-5 *2 (-1262)) (-5 *1 (-1258))))) (((*1 *1 *2) (-12 (-5 *2 (-640 *3)) (-4 *3 (-1208)) (-4 *1 (-151 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-640 (-2 (|:| -1654 (-767)) (|:| -3408 *4) (|:| |num| *4)))) + (-5 *2 (-640 (-2 (|:| -3311 (-767)) (|:| -3412 *4) (|:| |num| *4)))) (-4 *4 (-1233 *3)) (-4 *3 (-13 (-363) (-147))) (-5 *1 (-399 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -3784 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -3785 "void"))) (-5 *3 (-640 (-948 (-563)))) (-5 *4 (-112)) (-5 *1 (-437)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -3784 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -3785 "void"))) (-5 *3 (-640 (-1169))) (-5 *4 (-112)) (-5 *1 (-437)))) ((*1 *2 *1) (-12 (-5 *2 (-1149 *3)) (-5 *1 (-598 *3)) (-4 *3 (-1208)))) @@ -15109,24 +14966,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-709 *2 *3 *4)) (-4 *2 (-846)) (-4 *3 (-1093)) (-14 *4 - (-1 (-112) (-2 (|:| -2555 *2) (|:| -1654 *3)) - (-2 (|:| -2555 *2) (|:| -1654 *3)))))) + (-1 (-112) (-2 (|:| -2552 *2) (|:| -3311 *3)) + (-2 (|:| -2552 *2) (|:| -3311 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-506)) (-5 *3 (-1111)) (-5 *1 (-834)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-869 *2 *3)) (-4 *2 (-1208)) (-4 *3 (-1208)))) ((*1 *1 *2) - (-12 (-5 *2 (-640 (-2 (|:| -2387 (-1169)) (|:| -2557 *4)))) + (-12 (-5 *2 (-640 (-2 (|:| -2387 (-1169)) (|:| -2556 *4)))) (-4 *4 (-1093)) (-5 *1 (-885 *3 *4)) (-4 *3 (-1093)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-640 *5)) (-4 *5 (-13 (-1093) (-34))) (-5 *2 (-640 (-1133 *3 *5))) (-5 *1 (-1133 *3 *5)) (-4 *3 (-13 (-1093) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-640 (-2 (|:| |val| *4) (|:| -2059 *5)))) + (-12 (-5 *3 (-640 (-2 (|:| |val| *4) (|:| -2058 *5)))) (-4 *4 (-13 (-1093) (-34))) (-4 *5 (-13 (-1093) (-34))) (-5 *2 (-640 (-1133 *4 *5))) (-5 *1 (-1133 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2059 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2058 *4))) (-4 *3 (-13 (-1093) (-34))) (-4 *4 (-13 (-1093) (-34))) (-5 *1 (-1133 *3 *4)))) ((*1 *1 *2 *3) @@ -15149,29 +15006,29 @@ (-4 *4 (-13 (-1093) (-34))) (-5 *1 (-1134 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1158 *2 *3)) (-4 *2 (-1093)) (-4 *3 (-1093))))) -(((*1 *2 *1) - (-12 (-4 *1 (-972 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-789)) - (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-5 *2 (-112))))) -(((*1 *2 *3 *3 *3 *4 *5 *5 *3) - (-12 (-5 *3 (-563)) (-5 *5 (-684 (-225))) (-5 *4 (-225)) - (-5 *2 (-1031)) (-5 *1 (-748))))) -(((*1 *2 *2 *3 *2) - (-12 (-5 *3 (-767)) (-4 *4 (-349)) (-5 *1 (-216 *4 *2)) - (-4 *2 (-1233 *4)))) - ((*1 *2 *2 *3 *2 *3) - (-12 (-5 *3 (-563)) (-5 *1 (-691 *2)) (-4 *2 (-1233 *3))))) +(((*1 *2 *3 *1 *4) + (-12 (-5 *3 (-1133 *5 *6)) (-5 *4 (-1 (-112) *6 *6)) + (-4 *5 (-13 (-1093) (-34))) (-4 *6 (-13 (-1093) (-34))) + (-5 *2 (-112)) (-5 *1 (-1134 *5 *6))))) +(((*1 *2) (-12 (-5 *2 (-563)) (-5 *1 (-922))))) +(((*1 *2 *1) (-12 (-5 *2 (-640 (-948 (-563)))) (-5 *1 (-437)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1169)) (-5 *4 (-684 (-225))) (-5 *2 (-1097)) + (-5 *1 (-755)))) + ((*1 *2 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((*1 *1 *1) (-12 (-5 *1 (-672 *2)) (-4 *2 (-846)))) @@ -15180,23 +15037,30 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-844) (-363))) (-5 *1 (-1055 *2 *3)) (-4 *3 (-1233 *2))))) -(((*1 *2 *3 *4 *3 *4 *4 *4) - (-12 (-5 *3 (-684 (-225))) (-5 *4 (-563)) (-5 *2 (-1031)) - (-5 *1 (-752))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1180 (-640 *4))) (-4 *4 (-846)) - (-5 *2 (-640 (-640 *4))) (-5 *1 (-1179 *4))))) -(((*1 *2 *2 *3 *4 *4) - (-12 (-5 *4 (-563)) (-4 *3 (-172)) (-4 *5 (-373 *3)) - (-4 *6 (-373 *3)) (-5 *1 (-683 *3 *5 *6 *2)) - (-4 *2 (-682 *3 *5 *6))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-555)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2742 *4))) - (-5 *1 (-965 *4 *3)) (-4 *3 (-1233 *4))))) -(((*1 *2) - (-12 (-4 *3 (-555)) (-5 *2 (-640 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-417 *3))))) +(((*1 *1 *1 *2) + (|partial| -12 (-5 *2 (-767)) (-4 *1 (-1233 *3)) (-4 *3 (-1045))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-945 *3 *4 *2)) (-4 *3 (-1045)) (-4 *4 (-789)) + (-4 *2 (-846)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-789)) (-4 *5 (-1045)) (-4 *6 (-945 *5 *4 *2)) + (-4 *2 (-846)) (-5 *1 (-946 *4 *2 *5 *6 *3)) + (-4 *3 + (-13 (-363) + (-10 -8 (-15 -1692 ($ *6)) (-15 -2143 (*6 $)) + (-15 -2153 (*6 $))))))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-407 (-948 *4))) (-4 *4 (-555)) + (-5 *2 (-1169)) (-5 *1 (-1039 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-684 *5)) (-5 *4 (-1257 *5)) (-4 *5 (-363)) + (-5 *2 (-112)) (-5 *1 (-662 *5)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-363)) (-4 *6 (-13 (-373 *5) (-10 -7 (-6 -4409)))) + (-4 *4 (-13 (-373 *5) (-10 -7 (-6 -4409)))) (-5 *2 (-112)) + (-5 *1 (-663 *5 *6 *4 *3)) (-4 *3 (-682 *5 *6 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-917)) (-5 *1 (-357 *3)) (-4 *3 (-349))))) +(((*1 *2 *3 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-379)) (-5 *1 (-97))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-225))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -15225,63 +15089,63 @@ ((*1 *1 *2) (-12 (-5 *2 (-1118 (-563) (-609 (-48)))) (-5 *1 (-48)))) 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(-1169)) (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3784 "void"))) + (-14 *3 (-1169)) (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3785 "void"))) (-14 *5 (-640 (-1169))) (-14 *6 (-1173)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-5 *1 (-398 *3 *4 *5 *6)) (-14 *3 (-1169)) - (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3784 "void"))) + (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3785 "void"))) (-14 *5 (-640 (-1169))) (-14 *6 (-1173)))) ((*1 *1 *2) (-12 (-5 *2 (-331 *4)) (-4 *4 (-13 (-846) (-21))) @@ -15437,14 +15301,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-434)) (-5 *1 (-437)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1173)) (|:| -2412 (-640 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1173)) (|:| -2409 (-640 (-330))))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-640 (-330))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-1257 (-694))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1173)) (|:| -2412 (-640 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1173)) (|:| -2409 (-640 (-330))))) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-640 (-330))) (-4 *1 (-441)))) @@ -15513,7 +15377,7 @@ (-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 (-640 (-2 (|:| -2311 *3) (|:| -4222 *4)))) + (-12 (-5 *2 (-640 (-2 (|:| -2310 *3) (|:| -4223 *4)))) (-4 *3 (-1045)) (-4 *4 (-722)) (-5 *1 (-731 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-563)) (-4 *1 (-759)))) ((*1 *1 *2) @@ -15522,25 +15386,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225))) - (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -4166 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-316 (-225))) - (|:| -2516 (-640 (-1087 (-839 (-225))))) + (|:| -4166 (-640 (-1087 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-316 (-225))) - (|:| -2516 (-640 (-1087 (-839 (-225))))) (|:| |abserr| (-225)) + (|:| -4166 (-640 (-1087 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225))) - (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -4166 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *2 *3) (-12 (-5 *2 (-770)) (-5 *1 (-769 *3)) (-4 *3 (-1208)))) @@ -15558,23 +15422,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -2523 (-640 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -2522 (-640 (-225))) (|:| |lb| (-640 (-839 (-225)))) (|:| |cf| (-640 (-316 (-225)))) (|:| |ub| (-640 (-839 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-640 (-316 (-225)))) - (|:| -2523 (-640 (-225))))))) + (|:| -2522 (-640 (-225))))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-640 (-316 (-225)))) (|:| -2523 (-640 (-225))))) + (-2 (|:| |lfn| (-640 (-316 (-225)))) (|:| -2522 (-640 (-225))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-316 (-225))) (|:| -2523 (-640 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -2522 (-640 (-225))) (|:| |lb| (-640 (-839 (-225)))) (|:| |cf| (-640 (-316 (-225)))) (|:| |ub| (-640 (-839 (-225)))))) (-5 *1 (-837)))) @@ -15677,10 +15541,25 @@ ((*1 *1 *2) (-12 (-5 *2 (-659 *3 *4)) (-4 *3 (-846)) (-4 *4 (-172)) (-5 *1 (-1277 *3 *4))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-363) (-147) (-1034 (-563)))) (-4 *5 (-1233 *4)) - (-5 *2 (-2 (|:| |ans| (-407 *5)) (|:| |nosol| (-112)))) - (-5 *1 (-1011 *4 *5)) (-5 *3 (-407 *5))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4408)) (-4 *1 (-235 *3)) + (-4 *3 (-1093)))) + ((*1 *1 *2 *1) + (-12 (|has| *1 (-6 -4408)) (-4 *1 (-235 *2)) (-4 *2 (-1093)))) + ((*1 *1 *2 *1) + (-12 (-4 *1 (-282 *2)) (-4 *2 (-1208)) (-4 *2 (-1093)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-282 *3)) (-4 *3 (-1208)))) + ((*1 *2 *3 *1) + (|partial| -12 (-4 *1 (-607 *3 *2)) (-4 *3 (-1093)) (-4 *2 (-1093)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *2 (-1 (-112) *4)) (-5 *3 (-563)) (-4 *4 (-1093)) + (-5 *1 (-733 *4)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-563)) (-5 *1 (-733 *2)) (-4 *2 (-1093)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1133 *3 *4)) (-4 *3 (-13 (-1093) (-34))) + (-4 *4 (-13 (-1093) (-34))) (-5 *1 (-1134 *3 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-917)) (-5 *2 (-1165 *4)) (-5 *1 (-357 *4)) (-4 *4 (-349)))) @@ -15698,12 +15577,21 @@ (-12 (-5 *3 (-563)) (-5 *2 (-901 *4)) (-5 *1 (-900 *4)) (-4 *4 (-1093)))) ((*1 *1) (-12 (-4 *1 (-988 *2)) (-4 *2 (-545)) (-4 *2 (-555))))) -(((*1 *2 *3 *2 *4 *5) - (-12 (-5 *2 (-640 *3)) (-5 *5 (-917)) (-4 *3 (-1233 *4)) - (-4 *4 (-307)) (-5 *1 (-460 *4 *3))))) -(((*1 *1) (-5 *1 (-1078)))) -(((*1 *1) (-5 *1 (-437)))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-114))))) +(((*1 *2 *2) (-12 (-5 *2 (-563)) (-5 *1 (-922))))) +(((*1 *2 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-755))))) +(((*1 *2 *1) + (-12 (-4 *3 (-363)) (-4 *4 (-789)) (-4 *5 (-846)) (-5 *2 (-112)) + (-5 *1 (-504 *3 *4 *5 *6)) (-4 *6 (-945 *3 *4 *5))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) + (|:| |fn| (-1257 (-316 (-225)))) (|:| |yinit| (-640 (-225))) + (|:| |intvals| (-640 (-225))) (|:| |g| (-316 (-225))) + (|:| |abserr| (-225)) (|:| |relerr| (-225)))) + (-5 *2 + (-2 (|:| |stiffnessFactor| (-379)) (|:| |stabilityFactor| (-379)))) + (-5 *1 (-205))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1208)))) ((*1 *1 *1) (-12 (-5 *1 (-667 *2)) (-4 *2 (-846)))) ((*1 *1 *1) (-12 (-5 *1 (-672 *2)) (-4 *2 (-846)))) @@ -15712,31 +15600,21 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-844) (-363))) (-5 *1 (-1055 *2 *3)) (-4 *3 (-1233 *2))))) -(((*1 *2 *3 *4 *4 *3 *5) - (-12 (-5 *4 (-609 *3)) (-5 *5 (-1165 *3)) - (-4 *3 (-13 (-430 *6) (-27) (-1193))) - (-4 *6 (-13 (-452) (-1034 (-563)) (-846) (-147) (-636 (-563)))) - (-5 *2 (-584 *3)) (-5 *1 (-559 *6 *3 *7)) (-4 *7 (-1093)))) - ((*1 *2 *3 *4 *4 *4 *3 *5) - (-12 (-5 *4 (-609 *3)) (-5 *5 (-407 (-1165 *3))) - (-4 *3 (-13 (-430 *6) (-27) (-1193))) - (-4 *6 (-13 (-452) (-1034 (-563)) (-846) (-147) (-636 (-563)))) - (-5 *2 (-584 *3)) (-5 *1 (-559 *6 *3 *7)) (-4 *7 (-1093))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-4 *3 (-1059 *5 *6 *7)) - (-5 *2 (-640 (-2 (|:| |val| *3) (|:| -2059 *4)))) - (-5 *1 (-1066 *5 *6 *7 *3 *4)) (-4 *4 (-1065 *5 *6 *7 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1262)) (-5 *1 (-818))))) -(((*1 *2 *3 *4 *2 *5) - (-12 (-5 *3 (-640 *8)) (-5 *4 (-640 (-888 *6))) - (-5 *5 (-1 (-885 *6 *8) *8 (-888 *6) (-885 *6 *8))) (-4 *6 (-1093)) - (-4 *8 (-13 (-1045) (-611 (-888 *6)) (-1034 *7))) - (-5 *2 (-885 *6 *8)) (-4 *7 (-13 (-1045) (-846))) - (-5 *1 (-937 *6 *7 *8))))) -(((*1 *2) - (-12 (-4 *3 (-555)) (-5 *2 (-640 (-684 *3))) (-5 *1 (-43 *3 *4)) - (-4 *4 (-417 *3))))) +(((*1 *2 *1 *1 *3) + (-12 (-4 *4 (-1045)) (-4 *5 (-789)) (-4 *3 (-846)) + (-5 *2 (-2 (|:| -1765 *1) (|:| -3443 *1))) (-4 *1 (-945 *4 *5 *3)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-1045)) (-5 *2 (-2 (|:| -1765 *1) (|:| -3443 *1))) + (-4 *1 (-1233 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-640 (-948 *6))) (-5 *4 (-640 (-1169))) + (-4 *6 (-13 (-555) (-1034 *5))) (-4 *5 (-555)) + (-5 *2 (-640 (-640 (-294 (-407 (-948 *6)))))) (-5 *1 (-1035 *5 *6))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *2 (-640 (-1165 *4))) (-5 *3 (-1165 *4)) + (-4 *4 (-905)) (-5 *1 (-658 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-917)) (-5 *1 (-357 *3)) (-4 *3 (-349))))) +(((*1 *2) (-12 (-5 *2 (-1262)) (-5 *1 (-97))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -15756,84 +15634,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-555)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2742 *4))) - (-5 *1 (-965 *4 *3)) (-4 *3 (-1233 *4))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-640 (-948 *4))) (-5 *3 (-640 (-1169))) (-4 *4 (-452)) - (-5 *1 (-914 *4))))) +(((*1 *1 *1 *1 *2 *3) + (-12 (-5 *2 (-640 (-1133 *4 *5))) (-5 *3 (-1 (-112) *5 *5)) + (-4 *4 (-13 (-1093) (-34))) (-4 *5 (-13 (-1093) (-34))) + (-5 *1 (-1134 *4 *5)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-640 (-1133 *3 *4))) (-4 *3 (-13 (-1093) (-34))) + (-4 *4 (-13 (-1093) (-34))) (-5 *1 (-1134 *3 *4))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112)))) ((*1 *1 *1 *1) (-5 *1 (-858)))) -(((*1 *2 *3 *3 *3 *3 *3 *4 *3 *4 *3 *5 *5 *3) - (-12 (-5 *3 (-563)) (-5 *4 (-112)) (-5 *5 (-684 (-225))) - (-5 *2 (-1031)) (-5 *1 (-751))))) -(((*1 *2) - (-12 (-4 *4 (-172)) (-5 *2 (-767)) (-5 *1 (-165 *3 *4)) - (-4 *3 (-166 *4)))) - ((*1 *2) - (-12 (-14 *4 *2) (-4 *5 (-1208)) (-5 *2 (-767)) - (-5 *1 (-237 *3 *4 *5)) (-4 *3 (-238 *4 *5)))) - ((*1 *2) - (-12 (-4 *4 (-846)) (-5 *2 (-767)) (-5 *1 (-429 *3 *4)) - (-4 *3 (-430 *4)))) - ((*1 *2) (-12 (-5 *2 (-767)) (-5 *1 (-544 *3)) (-4 *3 (-545)))) - ((*1 *2) (-12 (-4 *1 (-759)) (-5 *2 (-767)))) - ((*1 *2) - (-12 (-4 *4 (-172)) (-5 *2 (-767)) (-5 *1 (-792 *3 *4)) - (-4 *3 (-793 *4)))) - ((*1 *2) - (-12 (-4 *4 (-555)) (-5 *2 (-767)) (-5 *1 (-987 *3 *4)) - (-4 *3 (-988 *4)))) - ((*1 *2) - (-12 (-4 *4 (-172)) (-5 *2 (-767)) (-5 *1 (-992 *3 *4)) - (-4 *3 (-993 *4)))) - ((*1 *2) (-12 (-5 *2 (-767)) (-5 *1 (-1007 *3)) (-4 *3 (-1008)))) - ((*1 *2) (-12 (-4 *1 (-1045)) (-5 *2 (-767)))) - ((*1 *2) (-12 (-5 *2 (-767)) (-5 *1 (-1053 *3)) (-4 *3 (-1054))))) +(((*1 *2) (-12 (-5 *2 (-563)) (-5 *1 (-922))))) +(((*1 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-755))))) (((*1 *1) (-5 *1 (-112))) ((*1 *1) (-5 *1 (-614)))) -(((*1 *1 *2 *3 *1) - (-12 (-5 *2 (-1169)) (-5 *3 (-640 (-961))) (-5 *1 (-291))))) -(((*1 *2 *3 *4 *2 *5 *6) - (-12 - (-5 *5 - (-2 (|:| |done| (-640 *11)) - (|:| |todo| (-640 (-2 (|:| |val| *3) (|:| -2059 *11)))))) - (-5 *6 (-767)) - (-5 *2 (-640 (-2 (|:| |val| (-640 *10)) (|:| -2059 *11)))) - (-5 *3 (-640 *10)) (-5 *4 (-640 *11)) (-4 *10 (-1059 *7 *8 *9)) - (-4 *11 (-1065 *7 *8 *9 *10)) (-4 *7 (-452)) (-4 *8 (-789)) - (-4 *9 (-846)) (-5 *1 (-1063 *7 *8 *9 *10 *11)))) - ((*1 *2 *3 *4 *2 *5 *6) - (-12 - (-5 *5 - (-2 (|:| |done| (-640 *11)) - (|:| |todo| (-640 (-2 (|:| |val| *3) (|:| -2059 *11)))))) - (-5 *6 (-767)) - (-5 *2 (-640 (-2 (|:| |val| (-640 *10)) (|:| -2059 *11)))) - (-5 *3 (-640 *10)) (-5 *4 (-640 *11)) (-4 *10 (-1059 *7 *8 *9)) - (-4 *11 (-1102 *7 *8 *9 *10)) (-4 *7 (-452)) (-4 *8 (-789)) - (-4 *9 (-846)) (-5 *1 (-1138 *7 *8 *9 *10 *11))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-640 *6)) (-4 *6 (-846)) (-4 *4 (-363)) (-4 *5 (-789)) + (-5 *1 (-504 *4 *5 *6 *2)) (-4 *2 (-945 *4 *5 *6)))) + ((*1 *1 *1 *2) + (-12 (-4 *3 (-363)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *1 (-504 *3 *4 *5 *2)) (-4 *2 (-945 *3 *4 *5))))) (((*1 *2 *3) - (-12 (-5 *3 (-640 (-563))) (-5 *2 (-1171 (-407 (-563)))) - (-5 *1 (-190))))) -(((*1 *2 *3 *4) - (-12 - (-5 *3 - (-640 - (-2 (|:| |eqzro| (-640 *8)) (|:| |neqzro| (-640 *8)) - (|:| |wcond| (-640 (-948 *5))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1257 (-407 (-948 *5)))) - (|:| -4315 (-640 (-1257 (-407 (-948 *5)))))))))) - (-5 *4 (-1151)) (-4 *5 (-13 (-307) (-147))) (-4 *8 (-945 *5 *7 *6)) - (-4 *6 (-13 (-846) (-611 (-1169)))) (-4 *7 (-789)) (-5 *2 (-563)) - (-5 *1 (-920 *5 *6 *7 *8))))) -(((*1 *1 *1) - (-12 (-5 *1 (-593 *2)) (-4 *2 (-38 (-407 (-563)))) (-4 *2 (-1045))))) -(((*1 *1 *1 *2 *2) - (|partial| -12 (-5 *2 (-917)) (-5 *1 (-1094 *3 *4)) (-14 *3 *2) - (-14 *4 *2)))) + (-12 (-5 *3 (-684 (-316 (-225)))) + (-5 *2 + (-2 (|:| |stiffnessFactor| (-379)) (|:| |stabilityFactor| (-379)))) + (-5 *1 (-205))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-767)) (-4 *4 (-1045)) + (-5 *2 (-2 (|:| -1765 *1) (|:| -3443 *1))) (-4 *1 (-1233 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-379)) (-5 *1 (-97))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1031))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-651 *2)) (-4 *2 (-1045)) (-4 *2 (-363)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-363)) (-5 *1 (-654 *4 *2)) + (-4 *2 (-651 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-917)) (-5 *1 (-357 *3)) (-4 *3 (-349))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) @@ -15853,55 +15686,36 @@ ((*1 *2 *2) (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1169)) (-5 *3 (-640 (-961))) (-5 *1 (-109))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-563)) (-4 *2 (-430 *3)) (-5 *1 (-32 *3 *2)) - (-4 *3 (-1034 *4)) (-4 *3 (-13 (-846) (-555)))))) -(((*1 *1 *2 *3) - (-12 (-5 *1 (-427 *3 *2)) (-4 *3 (-13 (-172) (-38 (-407 (-563))))) - (-4 *2 (-13 (-846) (-21)))))) -(((*1 *2 *1) (-12 (-4 *1 (-425 *3)) (-4 *3 (-1093)) (-5 *2 (-767))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1093)) (-4 *6 (-882 *5)) (-5 *2 (-881 *5 *6 (-640 *6))) - (-5 *1 (-883 *5 *6 *4)) (-5 *3 (-640 *6)) (-4 *4 (-611 (-888 *5))))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1093)) (-5 *2 (-640 (-294 *3))) (-5 *1 (-883 *5 *3 *4)) - (-4 *3 (-1034 (-1169))) (-4 *3 (-882 *5)) (-4 *4 (-611 (-888 *5))))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1093)) (-5 *2 (-640 (-294 (-948 *3)))) - (-5 *1 (-883 *5 *3 *4)) (-4 *3 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|radicand| (-640 *5)))) - (-5 *1 (-320 *5)) (-5 *4 (-767)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-998)) (-5 *2 (-563))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-114)) (-5 *3 (-640 (-1 *4 (-640 *4)))) (-4 *4 (-1093)) - (-5 *1 (-113 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-114)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1093)) - (-5 *1 (-113 *4)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-114)) (-5 *2 (-640 (-1 *4 (-640 *4)))) - (-5 *1 (-113 *4)) (-4 *4 (-1093))))) + (-1257 (-640 (-2 (|:| -2618 (-906 *3)) (|:| -2552 (-1113)))))) + (-5 *1 (-351 *3 *4)) (-14 *3 (-917)) (-14 *4 (-917)))) + ((*1 *2) + (-12 (-5 *2 (-1257 (-640 (-2 (|:| -2618 *3) (|:| -2552 (-1113)))))) + (-5 *1 (-352 *3 *4)) (-4 *3 (-349)) (-14 *4 (-3 (-1165 *3) *2)))) + ((*1 *2) + (-12 (-5 *2 (-1257 (-640 (-2 (|:| -2618 *3) (|:| -2552 (-1113)))))) + (-5 *1 (-353 *3 *4)) (-4 *3 (-349)) (-14 *4 (-917))))) +(((*1 *1 *2) (-12 (-5 *2 (-640 *3)) (-4 *3 (-1093)) (-5 *1 (-91 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -15988,6 +15801,9 @@ (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3)))) ((*1 *1 *1) (-4 *1 (-1196)))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-1133 *3 *2)) (-4 *3 (-13 (-1093) (-34))) + (-4 *2 (-13 (-1093) (-34)))))) (((*1 *1 *1) (-12 (-4 *1 (-373 *2)) (-4 *2 (-1208)) (-4 *2 (-846)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-373 *3)) (-4 *3 (-1208)))) @@ -15996,55 +15812,51 @@ ((*1 *2 *1 *3) (-12 (-4 *4 (-1045)) (-4 *5 (-789)) (-4 *3 (-846)) (-4 *6 (-1059 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -1583 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3954 *1) (|:| |upper| *1))) (-4 *1 (-972 *4 *5 *3 *6))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-640 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-452)) - (-4 *3 (-555)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *1 (-973 *3 *4 *5 *6))))) -(((*1 *1 *1 *1 *2 *3) - (-12 (-5 *2 (-640 (-1133 *4 *5))) (-5 *3 (-1 (-112) *5 *5)) - (-4 *4 (-13 (-1093) (-34))) (-4 *5 (-13 (-1093) (-34))) - (-5 *1 (-1134 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(-563)) (-5 *1 (-204))))) +(((*1 *2 *3) + (-12 (-5 *3 (-767)) (-4 *4 (-363)) (-4 *5 (-1233 *4)) (-5 *2 (-1262)) + (-5 *1 (-40 *4 *5 *6 *7)) (-4 *6 (-1233 (-407 *5))) (-14 *7 *6)))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1233 *2)) (-4 *2 (-1045))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-363)) (-4 *5 (-555)) + (-5 *2 + (-2 (|:| |minor| (-640 (-917))) (|:| -1420 *3) + (|:| |minors| (-640 (-640 (-917)))) (|:| |ops| (-640 *3)))) + (-5 *1 (-90 *5 *3)) (-5 *4 (-917)) (-4 *3 (-651 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-640 (-1257 *5))) (-5 *4 (-563)) (-5 *2 (-1257 *5)) + (-5 *1 (-1025 *5)) (-4 *5 (-363)) (-4 *5 (-368)) (-4 *5 (-1045))))) +(((*1 *2 *3) + (-12 (-4 *4 (-27)) + (-4 *4 (-13 (-363) (-147) (-1034 (-563)) (-1034 (-407 (-563))))) + (-4 *5 (-1233 *4)) (-5 *2 (-640 (-648 (-407 *5)))) + (-5 *1 (-652 *4 *5)) (-5 *3 (-648 (-407 *5)))))) +(((*1 *2) + (-12 (-5 *2 (-684 (-906 *3))) (-5 *1 (-351 *3 *4)) (-14 *3 (-917)) + (-14 *4 (-917)))) + ((*1 *2) + (-12 (-5 *2 (-684 *3)) (-5 *1 (-352 *3 *4)) (-4 *3 (-349)) + (-14 *4 + (-3 (-1165 *3) + (-1257 (-640 (-2 (|:| -2618 *3) (|:| -2552 (-1113))))))))) + ((*1 *2) + (-12 (-5 *2 (-684 *3)) (-5 *1 (-353 *3 *4)) (-4 *3 (-349)) + (-14 *4 (-917))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -16061,38 +15873,75 @@ (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3)))) ((*1 *1 *1) (-4 *1 (-1196)))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1091 *2)) (-4 *2 (-1093)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1091 *2)) (-4 *2 (-1093))))) -(((*1 *1 *2) (-12 (-5 *2 (-1151)) (-5 *1 (-578))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-976 *2)) (-4 *2 (-1045)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-939 (-225))) (-5 *1 (-1204)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1255 *2)) (-4 *2 (-1208)) (-4 *2 (-1045))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-972 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-789)) - (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-555)) - (-5 *2 (-112))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-1262)) 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(-640 (-917)))))) + (-5 *1 (-90 *5 *3)) (-5 *4 (-917)) (-4 *3 (-651 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-640 (-684 *5))) (-5 *4 (-563)) (-4 *5 (-363)) + (-4 *5 (-1045)) (-5 *2 (-112)) (-5 *1 (-1025 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-640 (-684 *4))) (-4 *4 (-363)) (-4 *4 (-1045)) + (-5 *2 (-112)) (-5 *1 (-1025 *4))))) +(((*1 *2 *1) + (-12 (-5 *2 (-640 (-2 (|:| |gen| *3) (|:| -3372 *4)))) + (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-1093)) (-4 *4 (-23)) (-14 *5 *4)))) +(((*1 *2) + (-12 (-4 *1 (-349)) + (-5 *2 (-640 (-2 (|:| -2173 (-563)) (|:| -3311 (-563)))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -16158,65 +16024,55 @@ (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3)))) ((*1 *1 *1) (-4 *1 (-1196)))) -(((*1 *2 *1) - (-12 (-4 *1 (-1255 *2)) (-4 *2 (-1208)) (-4 *2 (-998)) - (-4 *2 (-1045))))) +(((*1 *2 *1 *1 *3 *4) + (-12 (-5 *3 (-1 (-112) *5 *5)) (-5 *4 (-1 (-112) *6 *6)) + (-4 *5 (-13 (-1093) (-34))) (-4 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*1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) @@ -16237,142 +16093,131 @@ (-12 (-5 *2 (-1149 *3)) (-4 *3 (-38 (-407 (-563)))) (-5 *1 (-1155 *3)))) ((*1 *1 *1) (-4 *1 (-1196)))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-452))) (-5 *1 (-1199 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1193)))))) -(((*1 *2 *1) (-12 (-5 *2 (-640 (-834))) (-5 *1 (-140))))) -(((*1 *2 *2) - (-12 (-5 *2 (-640 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-452)) - (-4 *3 (-555)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *1 (-973 *3 *4 *5 *6)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-640 *7)) (-5 *3 (-112)) (-4 *7 (-1059 *4 *5 *6)) - (-4 *4 (-452)) (-4 *4 (-555)) (-4 *5 (-789)) (-4 *6 (-846)) - (-5 *1 (-973 *4 *5 *6 *7))))) -(((*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 *3) (-12 (-5 *2 (-563)) (-5 *3 (-767)) (-5 *1 (-560))))) -(((*1 *2 *3) - (-12 (-4 *4 (-555)) (-4 *5 (-789)) (-4 *6 (-846)) - (-4 *7 (-1059 *4 *5 *6)) - (-5 *2 (-2 (|:| |goodPols| (-640 *7)) (|:| |badPols| (-640 *7)))) - (-5 *1 (-973 *4 *5 *6 *7)) (-5 *3 (-640 *7))))) +(((*1 *2 *1 *1 *3) + (-12 (-5 *3 (-1 (-112) *5 *5)) (-4 *5 (-13 (-1093) (-34))) + (-5 *2 (-112)) (-5 *1 (-1133 *4 *5)) (-4 *4 (-13 (-1093) (-34)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-563)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-923))))) +(((*1 *2 *2 *2) + (-12 + (-5 *2 + (-2 (|:| -4013 (-684 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-684 *3)))) + (-4 *3 (-13 (-307) (-10 -8 (-15 -2802 ((-418 $) $))))) + (-4 *4 (-1233 *3)) (-5 *1 (-499 *3 *4 *5)) (-4 *5 (-409 *3 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-563)) (-5 *2 (-640 (-640 (-225)))) (-5 *1 (-1204))))) -(((*1 *1 *2 *2 *2 *2) (-12 (-4 *1 (-993 *2)) (-4 *2 (-172))))) -(((*1 *2 *3 *3 *4 *3) - (-12 (-5 *3 (-563)) (-5 *4 (-684 (-225))) (-5 *2 (-1031)) - (-5 *1 (-743))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1022 (-839 (-563)))) - (-5 *3 (-1149 (-2 (|:| |k| (-563)) (|:| |c| *4)))) (-4 *4 (-1045)) - (-5 *1 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|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"))) + (-5 *1 (-192))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1233 *2)) (-4 *2 (-1045)) (-4 *2 (-555))))) (((*1 *2 *3 *1) (|partial| -12 (-4 *1 (-607 *3 *2)) (-4 *3 (-1093)) (-4 *2 (-1093))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-555)) (-5 *2 (-640 (-767))) (-5 *1 (-965 *4 *3)) - (-4 *3 (-1233 *4))))) -(((*1 *2 *2) (-12 (-5 *2 (-563)) (-5 *1 (-922))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1257 *4)) (-4 *4 (-349)) (-5 *2 (-1165 *4)) - (-5 *1 (-528 *4))))) -(((*1 *2 *2) - (-12 (-5 *2 (-640 *3)) (-4 *3 (-1233 (-563))) (-5 *1 (-486 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-640 (-684 *5))) (-4 *5 (-307)) (-4 *5 (-1045)) + (-5 *2 (-1257 (-1257 *5))) (-5 *1 (-1025 *5)) (-5 *4 (-1257 *5))))) +(((*1 *1 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1208)))) + ((*1 *1 *1) + (-12 (|has| *1 (-6 -4409)) (-4 *1 (-373 *2)) (-4 *2 (-1208)))) + ((*1 *1 *1) + (-12 (-5 *1 (-644 *2 *3 *4)) (-4 *2 (-1093)) (-4 *3 (-23)) + (-14 *4 *3)))) +(((*1 *2) + (-12 (-4 *1 (-349)) + (-5 *2 (-3 "prime" "polynomial" "normal" "cyclic"))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-563)) (-4 *1 (-57 *4 *5 *3)) (-4 *4 (-1208)) + (-4 *5 (-373 *4)) (-4 *3 (-373 *4))))) (((*1 *2 *1) (-12 (-5 *2 (-770)) (-5 *1 (-52))))) -(((*1 *1) (-4 *1 (-349))) - ((*1 *2 *3) - (-12 (-5 *3 (-640 *5)) (-4 *5 (-430 *4)) - (-4 *4 (-13 (-555) (-846) (-147))) - (-5 *2 - (-2 (|:| |primelt| *5) (|:| |poly| (-640 (-1165 *5))) - (|:| |prim| (-1165 *5)))) - (-5 *1 (-432 *4 *5)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-555) (-846) (-147))) - (-5 *2 - (-2 (|:| |primelt| *3) (|:| |pol1| (-1165 *3)) - (|:| |pol2| (-1165 *3)) (|:| |prim| (-1165 *3)))) - (-5 *1 (-432 *4 *3)) (-4 *3 (-27)) (-4 *3 (-430 *4)))) - ((*1 *2 *3 *4 *3 *4) - (-12 (-5 *3 (-948 *5)) (-5 *4 (-1169)) (-4 *5 (-13 (-363) (-147))) - (-5 *2 - (-2 (|:| |coef1| (-563)) (|:| |coef2| (-563)) - (|:| |prim| (-1165 *5)))) - (-5 *1 (-956 *5)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-640 (-948 *5))) (-5 *4 (-640 (-1169))) - (-4 *5 (-13 (-363) (-147))) - (-5 *2 - (-2 (|:| -2311 (-640 (-563))) (|:| |poly| (-640 (-1165 *5))) - (|:| |prim| (-1165 *5)))) - (-5 *1 (-956 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-640 (-948 *6))) (-5 *4 (-640 (-1169))) (-5 *5 (-1169)) - (-4 *6 (-13 (-363) (-147))) - (-5 *2 - (-2 (|:| -2311 (-640 (-563))) (|:| |poly| (-640 (-1165 *6))) - (|:| |prim| (-1165 *6)))) - (-5 *1 (-956 *6))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-545)) (-5 *2 (-112))))) +(((*1 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) + ((*1 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-431 *3 *2)) + (-4 *2 (-430 *3)))) + ((*1 *1 *1) (-4 *1 (-1132)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-563)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2 *2) (-12 (-5 *2 (-563)) (-5 *1 (-923))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-684 *3)) + (-4 *3 (-13 (-307) (-10 -8 (-15 -2802 ((-418 $) $))))) + (-4 *4 (-1233 *3)) (-5 *1 (-499 *3 *4 *5)) (-4 *5 (-409 *3 *4)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-684 *3)) + (-4 *3 (-13 (-307) (-10 -8 (-15 -2802 ((-418 $) $))))) + (-4 *4 (-1233 *3)) (-5 *1 (-499 *3 *4 *5)) (-4 *5 (-409 *3 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-247 *4 *5)) (-14 *4 (-640 (-1169))) (-4 *5 (-1045)) - (-5 *2 (-481 *4 *5)) (-5 *1 (-940 *4 *5))))) -(((*1 *2 *3 *3 *4 *5 *5 *5 *5 *3) - (-12 (-5 *3 (-563)) (-5 *4 (-1151)) (-5 *5 (-684 (-225))) - (-5 *2 (-1031)) (-5 *1 (-743))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-59 *6)) (-4 *6 (-1208)) - (-4 *5 (-1208)) (-5 *2 (-59 *5)) (-5 *1 (-58 *6 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) - (-4 *7 (-1208)) (-4 *5 (-1208)) (-5 *2 (-240 *6 *5)) - (-5 *1 (-239 *6 *7 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *6 *5)) (-4 *6 (-1208)) (-4 *5 (-1208)) - (-4 *2 (-373 *5)) (-5 *1 (-371 *6 *4 *5 *2)) (-4 *4 (-373 *6)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *6 *5)) (-4 *6 (-1093)) (-4 *5 (-1093)) - (-4 *2 (-425 *5)) (-5 *1 (-423 *6 *4 *5 *2)) (-4 *4 (-425 *6)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-640 *6)) (-4 *6 (-1208)) - (-4 *5 (-1208)) (-5 *2 (-640 *5)) (-5 *1 (-638 *6 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-954 *6)) (-4 *6 (-1208)) - (-4 *5 (-1208)) (-5 *2 (-954 *5)) (-5 *1 (-953 *6 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1 *3 *6 *3)) (-5 *5 (-1149 *6)) (-4 *6 (-1208)) - (-4 *3 (-1208)) (-5 *2 (-1149 *3)) (-5 *1 (-1147 *6 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-1257 *6)) (-4 *6 (-1208)) - (-4 *5 (-1208)) (-5 *2 (-1257 *5)) (-5 *1 (-1256 *6 *5))))) + (-12 + (-5 *3 + (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225))) + (|:| -4166 (-1087 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (-5 *2 + (-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 (-192))))) (((*1 *1 *2 *2 *3) (-12 (-5 *2 (-767)) (-4 *3 (-1208)) (-4 *1 (-57 *3 *4 *5)) (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) @@ -16390,34 +16235,47 @@ ((*1 *1) (-12 (-5 *1 (-1157 *2 *3)) (-14 *2 (-917)) (-4 *3 (-1045)))) ((*1 *1 *1) (-5 *1 (-1169))) ((*1 *1) (-5 *1 (-1169))) ((*1 *1) (-5 *1 (-1188)))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-962 *3)) (-4 *3 (-963))))) -(((*1 *1 *2) - (-12 (-5 *2 (-640 (-563))) (-5 *1 (-1000 *3)) (-14 *3 (-563))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-225)) (-5 *4 (-563)) - (-5 *5 (-3 (|:| |fn| (-388)) (|:| |fp| (-64 -3191)))) - (-5 *2 (-1031)) (-5 *1 (-744))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-640 (-888 *3))) (-5 *1 (-888 *3)) - (-4 *3 (-1093))))) -(((*1 *1 *1) (-4 *1 (-626))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-627 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998) (-1193)))))) -(((*1 *1 *1) - (-12 (-5 *1 (-593 *2)) (-4 *2 (-38 (-407 (-563)))) (-4 *2 (-1045))))) -(((*1 *2 *1) (-12 (-5 *2 (-1262)) (-5 *1 (-818))))) -(((*1 *2 *1) (-12 (-5 *2 (-858)) (-5 *1 (-52))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-555)) + (-5 *2 (-2 (|:| -2310 *4) (|:| -1765 *3) (|:| -3443 *3))) + (-5 *1 (-965 *4 *3)) (-4 *3 (-1233 *4)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *2 (-2 (|:| -1765 *1) (|:| -3443 *1))) (-4 *1 (-1059 *3 *4 *5)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-555)) (-4 *3 (-1045)) + (-5 *2 (-2 (|:| -2310 *3) (|:| -1765 *1) (|:| -3443 *1))) + (-4 *1 (-1233 *3))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-640 (-684 *4))) (-5 *2 (-684 *4)) (-4 *4 (-1045)) + (-5 *1 (-1025 *4))))) +(((*1 *1) + (-12 (-5 *1 (-644 *2 *3 *4)) (-4 *2 (-1093)) (-4 *3 (-23)) + (-14 *4 *3)))) (((*1 *2 *3) - (-12 (-5 *3 (-336 *5 *6 *7 *8)) (-4 *5 (-430 *4)) (-4 *6 (-1233 *5)) - (-4 *7 (-1233 (-407 *6))) (-4 *8 (-342 *5 *6 *7)) - (-4 *4 (-13 (-846) (-555) (-1034 (-563)))) (-5 *2 (-112)) - (-5 *1 (-907 *4 *5 *6 *7 *8)))) - ((*1 *2 *3) - (-12 (-5 *3 (-336 (-407 (-563)) *4 *5 *6)) - (-4 *4 (-1233 (-407 (-563)))) (-4 *5 (-1233 (-407 *4))) - (-4 *6 (-342 (-407 (-563)) *4 *5)) (-5 *2 (-112)) - (-5 *1 (-908 *4 *5 *6))))) + (-12 (-5 *3 (-917)) + (-5 *2 + (-3 (-1165 *4) + (-1257 (-640 (-2 (|:| -2618 *4) (|:| -2552 (-1113))))))) + (-5 *1 (-346 *4)) (-4 *4 (-349))))) +(((*1 *1) (-5 *1 (-55)))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-1165 *1)) (-5 *3 (-1169)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-1165 *1)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-948 *1)) (-4 *1 (-27)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1169)) (-4 *1 (-29 *3)) (-4 *3 (-13 (-846) (-555))))) + ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-13 (-846) (-555)))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-431 *3 *2)) + (-4 *2 (-430 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1132)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-563)) (-5 *2 (-1031)) (-5 *1 (-754))))) +(((*1 *2) (-12 (-5 *2 (-563)) (-5 *1 (-467)))) + ((*1 *2 *2) (-12 (-5 *2 (-563)) (-5 *1 (-467)))) + ((*1 *2) (-12 (-5 *2 (-563)) (-5 *1 (-923))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-1169)) (-5 *3 (-640 (-536))) (-5 *1 (-536))))) (((*1 *1) (-5 *1 (-577))) @@ -16428,79 +16286,51 @@ ((*1 *2 *3 *1) (-12 (-5 *3 (-563)) (-5 *2 (-1262)) (-5 *1 (-1149 *4)) (-4 *4 (-1093)) (-4 *4 (-1208))))) -(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-225)) (-5 *4 (-563)) - (-5 *5 (-3 (|:| |fn| (-388)) (|:| |fp| (-64 G)))) (-5 *2 (-1031)) - (-5 *1 (-744))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-640 (-1069 *4 *5 *2))) (-4 *4 (-1093)) - (-4 *5 (-13 (-1045) (-882 *4) (-846) (-611 (-888 *4)))) - (-4 *2 (-13 (-430 *5) (-882 *4) (-611 (-888 *4)))) - (-5 *1 (-54 *4 *5 *2)))) - ((*1 *2 *3 *2 *4) - (-12 (-5 *3 (-640 (-1069 *5 *6 *2))) (-5 *4 (-917)) (-4 *5 (-1093)) - (-4 *6 (-13 (-1045) (-882 *5) (-846) (-611 (-888 *5)))) - (-4 *2 (-13 (-430 *6) (-882 *5) (-611 (-888 *5)))) - (-5 *1 (-54 *5 *6 *2))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-767)) + (-4 *3 (-13 (-307) (-10 -8 (-15 -2802 ((-418 $) $))))) + (-4 *4 (-1233 *3)) (-5 *1 (-499 *3 *4 *5)) (-4 *5 (-409 *3 *4))))) +(((*1 *2 *3) + (-12 (-5 *2 (-418 (-1165 (-563)))) (-5 *1 (-191)) (-5 *3 (-563))))) (((*1 *1 *2) - (-12 (-5 *2 (-640 (-2 (|:| -2387 *3) (|:| -2557 *4)))) + (-12 (-5 *2 (-640 (-2 (|:| -2387 *3) (|:| -2556 *4)))) (-4 *3 (-1093)) (-4 *4 (-1093)) (-4 *1 (-1184 *3 *4)))) ((*1 *1) (-12 (-4 *1 (-1184 *2 *3)) (-4 *2 (-1093)) (-4 *3 (-1093))))) -(((*1 *2 *3) (-12 (-5 *3 (-767)) (-5 *2 (-1262)) (-5 *1 (-379)))) - ((*1 *2) (-12 (-5 *2 (-1262)) (-5 *1 (-379))))) -(((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-667 *3)) (-4 *3 (-846)))) - ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-672 *3)) (-4 *3 (-846)))) - ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-815 *3)) (-4 *3 (-846))))) -(((*1 *2 *3 *2) - (|partial| -12 (-5 *3 (-917)) (-5 *1 (-442 *2)) - (-4 *2 (-1233 (-563))))) - ((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *3 (-917)) (-5 *4 (-767)) (-5 *1 (-442 *2)) - (-4 *2 (-1233 (-563))))) - ((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *3 (-917)) (-5 *4 (-640 (-767))) (-5 *1 (-442 *2)) - (-4 *2 (-1233 (-563))))) - ((*1 *2 *3 *2 *4 *5) - (|partial| -12 (-5 *3 (-917)) (-5 *4 (-640 (-767))) (-5 *5 (-767)) - (-5 *1 (-442 *2)) (-4 *2 (-1233 (-563))))) - ((*1 *2 *3 *2 *4 *5 *6) - (|partial| -12 (-5 *3 (-917)) (-5 *4 (-640 (-767))) (-5 *5 (-767)) - (-5 *6 (-112)) (-5 *1 (-442 *2)) (-4 *2 (-1233 (-563))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-917)) (-5 *4 (-418 *2)) (-4 *2 (-1233 *5)) - (-5 *1 (-444 *5 *2)) (-4 *5 (-1045))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-640 *6) "failed") (-563) *6 *6)) (-4 *6 (-363)) - (-4 *7 (-1233 *6)) - (-5 *2 (-2 (|:| |answer| (-584 (-407 *7))) (|:| |a0| *6))) - (-5 *1 (-573 *6 *7)) (-5 *3 (-407 *7))))) (((*1 *2 *3) - (-12 (-5 *2 (-1 (-939 *3) (-939 *3))) (-5 *1 (-176 *3)) - (-4 *3 (-13 (-363) (-1193) (-998)))))) -(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-123)))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-452))) (-5 *1 (-1199 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1193)))))) -(((*1 *1 *1 *1) (-4 *1 (-545)))) -(((*1 *2 *1 *2) - (-12 (|has| *1 (-6 -4408)) (-4 *1 (-1245 *2)) (-4 *2 (-1208))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-452))) (-5 *1 (-1199 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1193)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-555) (-846) (-1034 (-563)))) (-5 *1 (-188 *3 *2)) - (-4 *2 (-13 (-27) (-1193) (-430 (-169 *3)))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1169)) (-4 *4 (-13 (-555) (-846) (-1034 (-563)))) - (-5 *1 (-188 *4 *2)) (-4 *2 (-13 (-27) (-1193) (-430 (-169 *4)))))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-452) (-846) (-1034 (-563)) (-636 (-563)))) - (-5 *1 (-1197 *3 *2)) (-4 *2 (-13 (-27) (-1193) (-430 *3))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1169)) - (-4 *4 (-13 (-452) (-846) (-1034 (-563)) (-636 (-563)))) - (-5 *1 (-1197 *4 *2)) (-4 *2 (-13 (-27) (-1193) (-430 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